Mathematical modeling of acid-base physiology
Occhipinti, Rossana; Boron, Walter F.
2015-01-01
pH is one of the most important parameters in life, influencing virtually every biological process at the cellular, tissue, and whole-body level. Thus, for cells, it is critical to regulate intracellular pH (pHi) and, for multicellular organisms, to regulate extracellular pH (pHo). pHi regulation depends on the opposing actions of plasma-membrane transporters that tend to increase pHi, and others that tend to decrease pHi. In addition, passive fluxes of uncharged species (e.g., CO2, NH3) and charged species (e.g., HCO3− , NH4+) perturb pHi. These movements not only influence one another, but also perturb the equilibria of a multitude of intracellular and extracellular buffers. Thus, even at the level of a single cell, perturbations in acid-base reactions, diffusion, and transport are so complex that it is impossible to understand them without a quantitative model. Here we summarize some mathematical models developed to shed light onto the complex interconnected events triggered by acids-base movements. We then describe a mathematical model of a spherical cell–which to our knowledge is the first one capable of handling a multitude of buffer reaction–that our team has recently developed to simulate changes in pHi and pHo caused by movements of acid-base equivalents across the plasma membrane of a Xenopus oocyte. Finally, we extend our work to a consideration of the effects of simultaneous CO2 and HCO3− influx into a cell, and envision how future models might extend to other cell types (e.g., erythrocytes) or tissues (e.g., renal proximal-tubule epithelium) important for whole-body pH homeostasis. PMID:25617697
Mathematical modeling of acid-base physiology.
Occhipinti, Rossana; Boron, Walter F
2015-01-01
pH is one of the most important parameters in life, influencing virtually every biological process at the cellular, tissue, and whole-body level. Thus, for cells, it is critical to regulate intracellular pH (pHi) and, for multicellular organisms, to regulate extracellular pH (pHo). pHi regulation depends on the opposing actions of plasma-membrane transporters that tend to increase pHi, and others that tend to decrease pHi. In addition, passive fluxes of uncharged species (e.g., CO2, NH3) and charged species (e.g., HCO3(-), [Formula: see text] ) perturb pHi. These movements not only influence one another, but also perturb the equilibria of a multitude of intracellular and extracellular buffers. Thus, even at the level of a single cell, perturbations in acid-base reactions, diffusion, and transport are so complex that it is impossible to understand them without a quantitative model. Here we summarize some mathematical models developed to shed light onto the complex interconnected events triggered by acids-base movements. We then describe a mathematical model of a spherical cells-which to our knowledge is the first one capable of handling a multitude of buffer reactions-that our team has recently developed to simulate changes in pHi and pHo caused by movements of acid-base equivalents across the plasma membrane of a Xenopus oocyte. Finally, we extend our work to a consideration of the effects of simultaneous CO2 and HCO3(-) influx into a cell, and envision how future models might extend to other cell types (e.g., erythrocytes) or tissues (e.g., renal proximal-tubule epithelium) important for whole-body pH homeostasis.
An agent-based mathematical model about carp aggregation
NASA Astrophysics Data System (ADS)
Liang, Yu; Wu, Chao
2005-05-01
This work presents an agent-based mathematical model to simulate the aggregation of carp, a harmful fish in North America. The referred mathematical model is derived from the following assumptions: (1) instead of the consensus among every carps involved in the aggregation, the aggregation of carp is completely a random and spontaneous physical behavior of numerous of independent carp; (2) carp aggregation is a collective effect of inter-carp and carp-environment interaction; (3) the inter-carp interaction can be derived from the statistical analytics about large-scale observed data. The proposed mathematical model is mainly based on empirical inter-carp force field, whose effect is featured with repulsion, parallel orientation, attraction, out-of-perception zone, and blind. Based on above mathematical model, the aggregation behavior of carp is formulated and preliminary simulation results about the aggregation of small number of carps within simple environment are provided. Further experiment-based validation about the mathematical model will be made in our future work.
Validation and upgrading of physically based mathematical models
NASA Technical Reports Server (NTRS)
Duval, Ronald
1992-01-01
The validation of the results of physically-based mathematical models against experimental results was discussed. Systematic techniques are used for: (1) isolating subsets of the simulator mathematical model and comparing the response of each subset to its experimental response for the same input conditions; (2) evaluating the response error to determine whether it is the result of incorrect parameter values, incorrect structure of the model subset, or unmodeled external effects of cross coupling; and (3) modifying and upgrading the model and its parameter values to determine the most physically appropriate combination of changes.
Mathematical Modeling and Pure Mathematics
ERIC Educational Resources Information Center
Usiskin, Zalman
2015-01-01
Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…
A Proposal for Improving Students' Mathematical Attitude Based on Mathematical Modelling
ERIC Educational Resources Information Center
Falsetti, Marcela C.; Rodriguez, Mabel A.
2005-01-01
On the occasion of having to design an introductory course of mathematics for the University (UNGS, Buenos Aires, Argentina) we took into account the perspective of mathematical modelling. In this article we present the theoretical framework that we elaborated on to design our course. This framework allowed us to adapt the generic perspectives of…
Mathematical modelling of microtumour infiltration based on in vitro experiments.
Luján, Emmanuel; Guerra, Liliana N; Soba, Alejandro; Visacovsky, Nicolás; Gandía, Daniel; Calvo, Juan C; Suárez, Cecilia
2016-08-01
The present mathematical models of microtumours consider, in general, volumetric growth and spherical tumour invasion shapes. Nevertheless in many cases, such as in gliomas, a need for more accurate delineation of tumour infiltration areas in a patient-specific manner has arisen. The objective of this study was to build a mathematical model able to describe in a case-specific way as well as to predict in a probabilistic way the growth and the real invasion pattern of multicellular tumour spheroids (in vitro model of an avascular microtumour) immersed in a collagen matrix. The two-dimensional theoretical model was represented by a reaction-convection-diffusion equation that considers logistic proliferation, volumetric growth, a rim with proliferative cells at the tumour surface and invasion with diffusive and convective components. Population parameter values of the model were extracted from the experimental dataset and a shape function that describes the invasion area was derived from each experimental case by image processing. New possible and aleatory shape functions were generated by data mining and Monte Carlo tools by means of a satellite EGARCH model, which were fed with all the shape functions of the dataset. Then the main model is used in two different ways: to reproduce the growth and invasion of a given experimental tumour in a case-specific manner when fed with the corresponding shape function (descriptive simulations) or to generate new possible tumour cases that respond to the general population pattern when fed with an aleatory-generated shape function (predictive simulations). Both types of simulations are in good agreement with empirical data, as it was revealed by area quantification and Bland-Altman analysis. This kind of experimental-numerical interaction has wide application potential in designing new strategies able to predict as much as possible the invasive behaviour of a tumour based on its particular characteristics and microenvironment
Mathematical modelling of microtumour infiltration based on in vitro experiments.
Luján, Emmanuel; Guerra, Liliana N; Soba, Alejandro; Visacovsky, Nicolás; Gandía, Daniel; Calvo, Juan C; Suárez, Cecilia
2016-08-01
The present mathematical models of microtumours consider, in general, volumetric growth and spherical tumour invasion shapes. Nevertheless in many cases, such as in gliomas, a need for more accurate delineation of tumour infiltration areas in a patient-specific manner has arisen. The objective of this study was to build a mathematical model able to describe in a case-specific way as well as to predict in a probabilistic way the growth and the real invasion pattern of multicellular tumour spheroids (in vitro model of an avascular microtumour) immersed in a collagen matrix. The two-dimensional theoretical model was represented by a reaction-convection-diffusion equation that considers logistic proliferation, volumetric growth, a rim with proliferative cells at the tumour surface and invasion with diffusive and convective components. Population parameter values of the model were extracted from the experimental dataset and a shape function that describes the invasion area was derived from each experimental case by image processing. New possible and aleatory shape functions were generated by data mining and Monte Carlo tools by means of a satellite EGARCH model, which were fed with all the shape functions of the dataset. Then the main model is used in two different ways: to reproduce the growth and invasion of a given experimental tumour in a case-specific manner when fed with the corresponding shape function (descriptive simulations) or to generate new possible tumour cases that respond to the general population pattern when fed with an aleatory-generated shape function (predictive simulations). Both types of simulations are in good agreement with empirical data, as it was revealed by area quantification and Bland-Altman analysis. This kind of experimental-numerical interaction has wide application potential in designing new strategies able to predict as much as possible the invasive behaviour of a tumour based on its particular characteristics and microenvironment.
PREFACE: Physics-Based Mathematical Models for Nanotechnology
NASA Astrophysics Data System (ADS)
Voon, Lok C. Lew Yan; Melnik, Roderick; Willatzen, Morten
2008-03-01
stain-resistant clothing, but with thousands more anticipated. The focus of this interdisciplinary workshop was on determining what kind of new theoretical and computational tools will be needed to advance the science and engineering of nanomaterials and nanostructures. Thanks to the stimulating environment of the BIRS, participants of the workshop had plenty of opportunity to exchange new ideas on one of the main topics of this workshop—physics-based mathematical models for the description of low-dimensional semiconductor nanostructures (LDSNs) that are becoming increasingly important in technological innovations. The main objective of the workshop was to bring together some of the world leading experts in the field from each of the key research communities working on different aspects of LDSNs in order to (a) summarize the state-of-the-art models and computational techniques for modeling LDSNs, (b) identify critical problems of major importance that require solution and prioritize them, (c) analyze feasibility of existing mathematical and computational methodologies for the solution of some such problems, and (d) use some of the workshop working sessions to explore promising approaches in addressing identified challenges. With the possibility of growing practically any shape and size of heterostructures, it becomes essential to understand the mathematical properties of quantum-confined structures including properties of bulk states, interface states, and surface states as a function of shape, size, and internal strain. This workshop put strong emphasis on discussions of the new mathematics needed in nanotechnology especially in relation to geometry and material-combination optimization of device properties such as electronic, optical, and magnetic properties. The problems that were addressed at this meeting are of immense importance in determining such quantum-mechanical properties and the group of invited participants covered very well all the relevant disciplines
Mathematical modeling of laser based potato cutting and peeling.
Ferraz, A Carlos O; Mittal, Gauri S; Bilanski, Walter K; Abdullah, Hussein A
2007-01-01
A mathematical model is developed and validated to predict the depth of cut in potato tuber slabs as a function of laser power and travel speed. The model considers laser processing parameters such as input power, spot size and exposure time as well as the properties of the material being cut such as specific heat, thermal conductivity, surface reflectance, etc. The model also considers the phase change of water in potato and the ignition temperature of the solid portion. The composition of the potato tuber is assumed to be of water and solid. The model also assumes that the ablation process is accomplished through ejection of liquid water, debris and water vapour, and combustion of solid. A CO(2) laser operating in c.w. mode was chosen for the experimental work because water absorbs laser energy highly at 10.6 microm, and CO(2) laser units with relatively high output power are available. Slabs of potato tuber were chosen to be laser processed since potato contains high moisture and large amounts of relatively homogeneous tissue. The results of the preliminary calculations and experiments concluded that the model is able to predict the depth of cut in potato tuber parenchyma when subjected to a CO(2) laser beam.
ERIC Educational Resources Information Center
Tan, Liang Soon; Ang, Keng Cheng
2016-01-01
A school-based professional development programme (SBPD) aimed at developing secondary school mathematics teachers' competencies to teach mathematical modelling in Singapore is presented and evaluated in this article. The SBPD is characterized by two key features--content elements to develop teachers' knowledge and skills, and transformative…
Applying Mathematical Optimization Methods to an ACT-R Instance-Based Learning Model
Said, Nadia; Engelhart, Michael; Kirches, Christian; Körkel, Stefan; Holt, Daniel V.
2016-01-01
Computational models of cognition provide an interface to connect advanced mathematical tools and methods to empirically supported theories of behavior in psychology, cognitive science, and neuroscience. In this article, we consider a computational model of instance-based learning, implemented in the ACT-R cognitive architecture. We propose an approach for obtaining mathematical reformulations of such cognitive models that improve their computational tractability. For the well-established Sugar Factory dynamic decision making task, we conduct a simulation study to analyze central model parameters. We show how mathematical optimization techniques can be applied to efficiently identify optimal parameter values with respect to different optimization goals. Beyond these methodological contributions, our analysis reveals the sensitivity of this particular task with respect to initial settings and yields new insights into how average human performance deviates from potential optimal performance. We conclude by discussing possible extensions of our approach as well as future steps towards applying more powerful derivative-based optimization methods. PMID:27387139
Applying Mathematical Optimization Methods to an ACT-R Instance-Based Learning Model.
Said, Nadia; Engelhart, Michael; Kirches, Christian; Körkel, Stefan; Holt, Daniel V
2016-01-01
Computational models of cognition provide an interface to connect advanced mathematical tools and methods to empirically supported theories of behavior in psychology, cognitive science, and neuroscience. In this article, we consider a computational model of instance-based learning, implemented in the ACT-R cognitive architecture. We propose an approach for obtaining mathematical reformulations of such cognitive models that improve their computational tractability. For the well-established Sugar Factory dynamic decision making task, we conduct a simulation study to analyze central model parameters. We show how mathematical optimization techniques can be applied to efficiently identify optimal parameter values with respect to different optimization goals. Beyond these methodological contributions, our analysis reveals the sensitivity of this particular task with respect to initial settings and yields new insights into how average human performance deviates from potential optimal performance. We conclude by discussing possible extensions of our approach as well as future steps towards applying more powerful derivative-based optimization methods. PMID:27387139
Mathematical Modelling Approach in Mathematics Education
ERIC Educational Resources Information Center
Arseven, Ayla
2015-01-01
The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…
Teaching Mathematical Modeling in Mathematics Education
ERIC Educational Resources Information Center
Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant
2016-01-01
Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…
NASA Technical Reports Server (NTRS)
Petersen, Richard H.
1997-01-01
The objectives of the Institute were: (a) increase participants' content knowledge about aeronautics, science, mathematics, and technology, (b) model and promote the use of scientific inquiry through problem-based learning, (c) investigate the use of instructional technologies and their applications to curricula, and (d) encourage the dissemination of TEI experiences to colleagues, students, and parents.
Approaching mathematical model of the immune network based DNA Strand Displacement system.
Mardian, Rizki; Sekiyama, Kosuke; Fukuda, Toshio
2013-12-01
One biggest obstacle in molecular programming is that there is still no direct method to compile any existed mathematical model into biochemical reaction in order to solve a computational problem. In this paper, the implementation of DNA Strand Displacement system based on nature-inspired computation is observed. By using the Immune Network Theory and Chemical Reaction Network, the compilation of DNA-based operation is defined and the formulation of its mathematical model is derived. Furthermore, the implementation on this system is compared with the conventional implementation by using silicon-based programming. From the obtained results, we can see a positive correlation between both. One possible application from this DNA-based model is for a decision making scheme of intelligent computer or molecular robot.
NASA Astrophysics Data System (ADS)
Wright, Vince
2014-03-01
Pirie and Kieren (1989 For the learning of mathematics, 9(3)7-11, 1992 Journal of Mathematical Behavior, 11, 243-257, 1994a Educational Studies in Mathematics, 26, 61-86, 1994b For the Learning of Mathematics, 14(1)39-43) created a model (P-K) that describes a dynamic and recursive process by which learners develop their mathematical understanding. The model was adapted to create the teaching model used in the New Zealand Numeracy Development Projects (Ministry of Education, 2007). A case study of a 3-week sequence of instruction with a group of eight 12- and 13-year-old students provided the data. The teacher/researcher used folding back to materials and images and progressing from materials to imaging to number properties to assist students to develop their understanding of frequencies as proportions. The data show that successful implementation of the model is dependent on the teacher noticing and responding to the layers of understanding demonstrated by the students and the careful selection of materials, problems and situations. It supports the use of the model as a useful part of teachers' instructional strategies and the importance of pedagogical content knowledge to the quality of the way the model is used.
ERIC Educational Resources Information Center
Yilmaz, Suha; Tekin-Dede, Ayse
2016-01-01
Mathematization competency is considered in the field as the focus of modelling process. Considering the various definitions, the components of the mathematization competency are determined as identifying assumptions, identifying variables based on the assumptions and constructing mathematical model/s based on the relations among identified…
Chen, Liang-Hsuan; Hsueh, Chan-Ching
2007-06-01
Fuzzy regression models are useful to investigate the relationship between explanatory and response variables with fuzzy observations. Different from previous studies, this correspondence proposes a mathematical programming method to construct a fuzzy regression model based on a distance criterion. The objective of the mathematical programming is to minimize the sum of distances between the estimated and observed responses on the X axis, such that the fuzzy regression model constructed has the minimal total estimation error in distance. Only several alpha-cuts of fuzzy observations are needed as inputs to the mathematical programming model; therefore, the applications are not restricted to triangular fuzzy numbers. Three examples, adopted in the previous studies, and a larger example, modified from the crisp case, are used to illustrate the performance of the proposed approach. The results indicate that the proposed model has better performance than those in the previous studies based on either distance criterion or Kim and Bishu's criterion. In addition, the efficiency and effectiveness for solving the larger example by the proposed model are also satisfactory.
Modelers' Perception of Mathematical Modeling in Epidemiology: A Web-Based Survey
Hejblum, Gilles; Setbon, Michel; Temime, Laura; Lesieur, Sophie; Valleron, Alain-Jacques
2011-01-01
Background Mathematical modeling in epidemiology (MME) is being used increasingly. However, there are many uncertainties in terms of definitions, uses and quality features of MME. Methodology/Principal Findings To delineate the current status of these models, a 10-item questionnaire on MME was devised. Proposed via an anonymous internet-based survey, the questionnaire was completed by 189 scientists who had published in the domain of MME. A small minority (18%) of respondents claimed to have in mind a concise definition of MME. Some techniques were identified by the researchers as characterizing MME (e.g. Markov models), while others–at the same level of sophistication in terms of mathematics–were not (e.g. Cox regression). The researchers' opinions were also contrasted about the potential applications of MME, perceived as higly relevant for providing insight into complex mechanisms and less relevant for identifying causal factors. The quality criteria were those of good science and were not related to the size and the nature of the public health problems addressed. Conclusions/Significance This study shows that perceptions on the nature, uses and quality criteria of MME are contrasted, even among the very community of published authors in this domain. Nevertheless, MME is an emerging discipline in epidemiology and this study underlines that it is associated with specific areas of application and methods. The development of this discipline is likely to deserve a framework providing recommendations and guidance at various steps of the studies, from design to report. PMID:21304976
Mathematical model of a galvanometer-based scanner: simulations and experiments
NASA Astrophysics Data System (ADS)
Mnerie, Corina; Preitl, Stefan; Duma, Virgil-Florin
2013-05-01
The paper presents an insight into our current researches on galvanometer-based scanners (GSs). A brief overview is first performed on the state-of-the-art, as well as on some of our contributions to optimize the scanning and the command functions of this most used scanning device. Considerations on the use of GSs in high-end biomedical imaging applications such as Optical Coherence Tomography (OCT) are made, with a focus towards obtaining the best possible duty cycles and artifact-free OCT images when using GSs for lateral scanning, as studied in our previous works. The scope of our present study is to obtain the mathematical model of a GS system (motor and controller included) in order to optimize the command functions of the device and to support the development of some more advanced control structures. The study is centered on the mathematical and experimental modeling of GSs. Thus, the results of an experimental identification made on a classical multi-parameter mathematical model proposed for such a system are presented. The experiments are carried out in different operating regimes, and the specific characteristic parameters of the GS are determined. Using these parameters obtained experimentally, we carry out simulations in Mathlab Simulink to validate the theoretical model. With the indentified model, an extended control solution is proposed. We point out the match between the theory and the results of the simulations and of the testing for different types of input signals, such as triangular, sinusoidal, and sawtooth with different duty cycles.
[Suggestions for chikungunya control based on a sensitivity analysis of a mathematical model].
Requena, David; Segovia-Juárez, José L
2016-03-01
Chikungunya fever seriously affects peoples' health and causes chronic joint pain and even disability. Chikungunya is transmitted by the bite of Aedes aegypti and Aedes albopictus. Outbreaks have been reported in throughout the world, including Latin America. Mathematical modeling studies of these outbreaks have calculated the values of various epidemiological parameters. Based on them, a mathematical model was prepared to simulate a chikungunya outbreak in a local population, which was transmitted from an neighboring infected population. A sensitivity and uncertainty analysis revealed that the mosquito-to-human and human-to-mosquito transmission rates are the variables with the highest correlation with the number infected people, which were greatest at 60 days after the first case in the neighboring population. Therefore, it is recommended to take this into consideration when planning policies to control such variables as isolation of infected people, distribution of mosquito netting and repellents, fumigation, among others. PMID:27384636
Mathematical model accurately predicts protein release from an affinity-based delivery system.
Vulic, Katarina; Pakulska, Malgosia M; Sonthalia, Rohit; Ramachandran, Arun; Shoichet, Molly S
2015-01-10
Affinity-based controlled release modulates the delivery of protein or small molecule therapeutics through transient dissociation/association. To understand which parameters can be used to tune release, we used a mathematical model based on simple binding kinetics. A comprehensive asymptotic analysis revealed three characteristic regimes for therapeutic release from affinity-based systems. These regimes can be controlled by diffusion or unbinding kinetics, and can exhibit release over either a single stage or two stages. This analysis fundamentally changes the way we think of controlling release from affinity-based systems and thereby explains some of the discrepancies in the literature on which parameters influence affinity-based release. The rate of protein release from affinity-based systems is determined by the balance of diffusion of the therapeutic agent through the hydrogel and the dissociation kinetics of the affinity pair. Equations for tuning protein release rate by altering the strength (KD) of the affinity interaction, the concentration of binding ligand in the system, the rate of dissociation (koff) of the complex, and the hydrogel size and geometry, are provided. We validated our model by collapsing the model simulations and the experimental data from a recently described affinity release system, to a single master curve. Importantly, this mathematical analysis can be applied to any single species affinity-based system to determine the parameters required for a desired release profile. PMID:25449806
A biologically based mathematical model for the induction of liver tumors in mice by dichloroacetic acid (DCA) has been developed from histopathologic analysis of the livers of exposed mice. This analysis suggests that following chronic exposure to DCA, carcinomas can arise dire...
ERIC Educational Resources Information Center
Wright, Vince
2014-01-01
Pirie and Kieren (1989 "For the learning of mathematics", 9(3)7-11, 1992 "Journal of Mathematical Behavior", 11, 243-257, 1994a "Educational Studies in Mathematics", 26, 61-86, 1994b "For the Learning of Mathematics":, 14(1)39-43) created a model (P-K) that describes a dynamic and recursive process by which…
Mathematical Modelling: A New Approach to Teaching Applied Mathematics.
ERIC Educational Resources Information Center
Burghes, D. N.; Borrie, M. S.
1979-01-01
Describes the advantages of mathematical modeling approach in teaching applied mathematics and gives many suggestions for suitable material which illustrates the links between real problems and mathematics. (GA)
Facial plastic surgery area acquisition method based on point cloud mathematical model solution.
Li, Xuwu; Liu, Fei
2013-09-01
It is one of the hot research problems nowadays to find a quick and accurate method of acquiring the facial plastic surgery area to provide sufficient but irredundant autologous or in vitro skin source for covering extensive wound, trauma, and burnt area. At present, the acquisition of facial plastic surgery area mainly includes model laser scanning, point cloud data acquisition, pretreatment of point cloud data, three-dimensional model reconstruction, and computation of area. By using this method, the area can be computed accurately, but it is hard to control the random error, and it requires a comparatively longer computation period. In this article, a facial plastic surgery area acquisition method based on point cloud mathematical model solution is proposed. This method applies symmetric treatment to the point cloud based on the pretreatment of point cloud data, through which the comparison diagram color difference map of point cloud error before and after symmetry is obtained. The slicing mathematical model of facial plastic area is got through color difference map diagram. By solving the point cloud data in this area directly, the facial plastic area is acquired. The point cloud data are directly operated in this method, which can accurately and efficiently complete the surgery area computation. The result of the comparative analysis shows the method is effective in facial plastic surgery area.
NASA Astrophysics Data System (ADS)
Charafi, My. M.; Sadok, A.; Kamal, A.; Menai, A.
A quasi-three-dimensional mathematical model has been developed to study the morphological processes based on equilibrium sediment transport method. The flow velocities are computed by a two-dimensional horizontal depth-averaged flow model (H2D) in combination with logarithmic velocity profiles. The transport of sediment particles by a flow water has been considered in the form of bed load and suspended load. The bed load transport rate is defined as the transport of particles by rolling and saltating along the bed surface and is given by the Van Rijn relationship (1987). The equilibrium suspended load transport is described in terms of an equilibrium sediment concentration profile (ce) and a logarithmic velocity (u). Based on the equilibrium transport, the bed change rate is given by integration of the sediment mass-balance equation. The model results have been compared with a Van Rijn results (equilibrium approach) and good agreement has been found.
NASA Astrophysics Data System (ADS)
Parshin, D. V.; Ufimtseva, I. V.; Cherevko, A. A.; Khe, A. K.; Orlov, K. Yu; Krivoshapkin, A. L.; Chupakhin, A. P.
2016-06-01
The present paper discusses the method of identification (diseased/healthy) human cerebral vessels by using of mathematical model. Human cerebral circulation as a single tuned circuit, which consists of blood flow, elastic vessels and elastic brain gel tissue is under consideration. Non linear Van der Pol-Duffing equation is assumed as mathematical model of cerebrovascular circulation. Hypothesis of vascular pathology existence in some position of blood vessel, based on mathematical model properties for this position is formulated. Good reliability of hypothesis is proved statistically for 7 patients with arterial aneurysms.
Mathematical Modeling: A Structured Process
ERIC Educational Resources Information Center
Anhalt, Cynthia Oropesa; Cortez, Ricardo
2015-01-01
Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…
Mathematical models of hysteresis
1998-08-01
The ongoing research has largely been focused on the development of mathematical models of hysteretic nonlinearities with nonlocal memories. The distinct feature of these nonlinearities is that their current states depend on past histories of input variations. It turns out that memories of hysteretic nonlinearities are quite selective. Indeed, experiments show that only some past input extrema (not the entire input variations) leave their marks upon future states of hysteretic nonlinearities. Thus special mathematical tools are needed in order to describe nonlocal selective memories of hysteretic nonlinearities. The origin of such tools can be traced back to the landmark paper of Preisach. Their research has been primarily concerned with Preisach-type models of hysteresis. All these models have a common generic feature; they are constructed as superpositions of simplest hysteretic nonlinearities-rectangular loops. During the past four years, the study has been by and large centered around the following topics: (1) further development of Scalar and vector Preisach-type models of hysteresis; (2) experimental testing of Preisach-type models of hysteresis; (3) development of new models for viscosity (aftereffect) in hysteretic systems; (4) development of mathematical models for superconducting hysteresis in the case of gradual resistive transitions; (5) software implementation of Preisach-type models of hysteresis; and (6) development of new ideas which have emerged in the course of the research work. The author briefly describes the main scientific results obtained in the areas outlined above.
Mathematical modeling of high-rate Anammox UASB reactor based on granular packing patterns.
Tang, Chong-Jian; He, Rui; Zheng, Ping; Chai, Li-Yuan; Min, Xiao-Bo
2013-04-15
A novel mathematical model was developed to estimate the volumetric nitrogen conversion rates of a high-rate Anammox UASB reactor based on the packing patterns of granular sludge. A series of relationships among granular packing density, sludge concentration, hydraulic retention time and volumetric conversion rate were constructed to correlate Anammox reactor performance with granular packing patterns. It was suggested that the Anammox granules packed as the equivalent simple cubic pattern in high-rate UASB reactor with packing density of 50-55%, which not only accommodated a high concentration of sludge inside the reactor, but also provided large pore volume, thus prolonging the actual substrate conversion time. Results also indicated that it was necessary to improve Anammox reactor performance by enhancing substrate loading when sludge concentration was higher than 37.8 gVSS/L. The established model was carefully calibrated and verified, and it well simulated the performance of granule-based high-rate Anammox UASB reactor.
Mathematical model for adaptive evolution of populations based on a complex domain
Ibrahim, Rabha W.; Ahmad, M.Z.; Al-Janaby, Hiba F.
2015-01-01
A mutation is ultimately essential for adaptive evolution in all populations. It arises all the time, but is mostly fixed by enzymes. Further, most do consider that the evolution mechanism is by a natural assortment of variations in organisms in line for random variations in their DNA, and the suggestions for this are overwhelming. The altering of the construction of a gene, causing a different form that may be communicated to succeeding generations, produced by the modification of single base units in DNA, or the deletion, insertion, or rearrangement of larger units of chromosomes or genes. This altering is called a mutation. In this paper, a mathematical model is introduced to this reality. The model describes the time and space for the evolution. The tool is based on a complex domain for the space. We show that the evolution is distributed with the hypergeometric function. The Boundedness of the evolution is imposed by utilizing the Koebe function. PMID:26858564
A biophysically based mathematical model for the catalytic mechanism of glutathione reductase.
Pannala, Venkat R; Bazil, Jason N; Camara, Amadou K S; Dash, Ranjan K
2013-12-01
Glutathione reductase (GR) catalyzes the reduction of oxidized glutathione (GSSG) to reduced glutathione (GSH) using NADPH as the reducing cofactor, and thereby maintains a constant GSH level in the system. GSH scavenges superoxide (O2(*-)) and hydroxyl radicals (OH) nonenzymatically or by serving as an electron donor to several enzymes involved in reactive oxygen species (ROS) detoxification. In either case, GSH oxidizes to GSSG and is subsequently regenerated by the catalytic action of GR. Although the GR kinetic mechanism has been extensively studied under various experimental conditions with variable substrates and products, the catalytic mechanism has not been studied in terms of a mechanistic model that accounts for the effects of the substrates and products on the reaction kinetics. The aim of this study is therefore to develop a comprehensive mathematical model for the catalytic mechanism of GR. We use available experimental data on GR kinetics from various species/sources to develop the mathematical model and estimate the associated model parameters. The model simulations are consistent with the experimental observation that GR operates via both ping-pong and sequential branching mechanisms based on relevant concentrations of its reaction substrate GSSG. Furthermore, we show the observed pH-dependent substrate inhibition of GR activity by GSSG and bimodal behavior of GR activity with pH. The model presents a unique opportunity to understand the effects of products on the kinetics of GR. The model simulations show that under physiological conditions, where both substrates and products are present, the flux distribution depends on the concentrations of both GSSG and NADP(+), with ping-pong flux operating at low levels and sequential flux dominating at higher levels. The kinetic model of GR may serve as a key module for the development of integrated models for ROS-scavenging systems to understand protection of cells under normal and oxidative stress
Salloum, Maher N.; Gharagozloo, Patricia E.
2013-10-01
Metal particle beds have recently become a major technique for hydrogen storage. In order to extract hydrogen from such beds, it is crucial to understand the decomposition kinetics of the metal hydride. We are interested in obtaining a a better understanding of the uranium hydride (UH3) decomposition kinetics. We first developed an empirical model by fitting data compiled from different experimental studies in the literature and quantified the uncertainty resulting from the scattered data. We found that the decomposition time range predicted by the obtained kinetics was in a good agreement with published experimental results. Secondly, we developed a physics based mathematical model to simulate the rate of hydrogen diffusion in a hydride particle during the decomposition. We used this model to simulate the decomposition of the particles for temperatures ranging from 300K to 1000K while propagating parametric uncertainty and evaluated the kinetics from the results. We compared the kinetics parameters derived from the empirical and physics based models and found that the uncertainty in the kinetics predicted by the physics based model covers the scattered experimental data. Finally, we used the physics-based kinetics parameters to simulate the effects of boundary resistances and powder morphological changes during decomposition in a continuum level model. We found that the species change within the bed occurring during the decomposition accelerates the hydrogen flow by increasing the bed permeability, while the pressure buildup and the thermal barrier forming at the wall significantly impede the hydrogen extraction.
A process-based mathematical model on methane production with emission indices for control.
Chakraborty, A; Bhattacharaya, D K
2006-08-01
In this paper, a process-based mathematical model is developed for the production of methane through biodegradation. It is a three-dimensional model given by ordinary differential equations. The results of the analysis of the model are interpreted through three emission indices, which are introduced for the first time. The estimation of either one or all of them can interpret the feasibility of the equilibrium and the long-term emission tendency of methane. The vulnerability of the methane production process with respect to soil temperature effects in methanogenic phase has been discussed and a feasible condition within a specified temperature range has defined for the nonvulnerability of the methane production process and also it has shown that under the same condition, zero-emission process of methane will be nonvulnerable with respect to the soil temperature effects in methanogenic phase. Lastly, condition for zero emission of methane is also obtained and it is interpreted through the emission indices.
Mathematical model of sarcoidosis
Hao, Wenrui; Crouser, Elliott D.; Friedman, Avner
2014-01-01
Sarcoidosis is a disease involving abnormal collection of inflammatory cells forming nodules, called granulomas. Such granulomas occur in the lung and the mediastinal lymph nodes, in the heart, and in other vital and nonvital organs. The origin of the disease is unknown, and there are only limited clinical data on lung tissue of patients. No current model of sarcoidosis exists. In this paper we develop a mathematical model on the dynamics of the disease in the lung and use patients’ lung tissue data to validate the model. The model is used to explore potential treatments. PMID:25349384
NASA Astrophysics Data System (ADS)
Carrejo, David John
construction of the learners' models included several robust conceptions of average velocity and considerations of what constitutes a "good enough" model to use when describing and predicting motion. The emergence of these themes has implications for teaching and learning mathematics through an inquiry-based approach to kinematics.
Authenticity of Mathematical Modeling
ERIC Educational Resources Information Center
Tran, Dung; Dougherty, Barbara J.
2014-01-01
Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…
NASA Astrophysics Data System (ADS)
Seaman, Aden; Dao, Thanh-Son; McPhee, John
2014-06-01
In this paper, we survey two kinds of mathematics-based battery models intended for use in hybrid and electric vehicle simulation. The first is circuit-based, which is founded upon the electrical behaviour of the battery, and abstracts away the electrochemistry into equivalent electrical components. The second is chemistry-based, which is founded upon the electrochemical equations of the battery chemistry.
Analysis of laser remote fusion cutting based on a mathematical model
Matti, R. S.; Ilar, T.; Kaplan, A. F. H.
2013-12-21
Laser remote fusion cutting is analyzed by the aid of a semi-analytical mathematical model of the processing front. By local calculation of the energy balance between the absorbed laser beam and the heat losses, the three-dimensional vaporization front can be calculated. Based on an empirical model for the melt flow field, from a mass balance, the melt film and the melting front can be derived, however only in a simplified manner and for quasi-steady state conditions. Front waviness and multiple reflections are not modelled. The model enables to compare the similarities, differences, and limits between laser remote fusion cutting, laser remote ablation cutting, and even laser keyhole welding. In contrast to the upper part of the vaporization front, the major part only slightly varies with respect to heat flux, laser power density, absorptivity, and angle of front inclination. Statistical analysis shows that for high cutting speed, the domains of high laser power density contribute much more to the formation of the front than for low speed. The semi-analytical modelling approach offers flexibility to simplify part of the process physics while, for example, sophisticated modelling of the complex focused fibre-guided laser beam is taken into account to enable deeper analysis of the beam interaction. Mechanisms like recast layer generation, absorptivity at a wavy processing front, and melt film formation are studied too.
NASA Astrophysics Data System (ADS)
Canelas, Ricardo; Heleno, Sandra; Pestana, Rita; Ferreira, Rui M. L.
2014-05-01
The objective of the present work is to devise a methodology to validate 2DH shallow-water models suitable to simulate flow hydrodynamics and channel morphology. For this purpose, a 2DH mathematical model, assembled at CEHIDRO, IST, is employed to model Tagus river floods over a 70 km reach and Synthetic Aperture Radar (SAR) images are collected to retrieve planar inundation extents. The model is suited for highly unsteady discontinuous flows over complex, time-evolving geometries, employing a finite-volume discretization scheme, based on a flux-splitting technique incorporating a reviewed version of the Roe Riemann solver. Novel closure terms for the non-equilibrium sediment transport model are included. New boundary conditions are employed, based on the Riemann variables associated the outgoing characteristic fields, coping with the provided hydrographs in a mathematically coherent manner. A high resolution Digital Elevation Model (DEM) is used and levee structures are considered as fully erodible elements. Spatially heterogeneous roughness characteristics are derived from land-use databases such as CORINE LandCover 2006. SAR satellite imagery of the floods is available and is used to validate the simulation results, with particular emphasis on the 2000/2001 flood. The delimited areas from the satellite and simulations are superimposed. The quality of the adjustment depends on the calibration of roughness coefficients and the spatial discretization of with small structures, with lengths at the order of the spatial discretization. Flow depths and registered discharges are recovered from the simulation and compared with data from a measuring station in the domain, with the comparison revealing remarkably high accuracy, both in terms of amplitudes and phase. Further inclusion of topographical detail should improve the comparison of flood extents regarding satellite data. The validated model was then employed to simulate 100-year floods in the same reach. The
A Primer for Mathematical Modeling
ERIC Educational Resources Information Center
Sole, Marla
2013-01-01
With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school…
Mathematical Modelling in European Education
ERIC Educational Resources Information Center
Ferri, Rita Borromeo
2013-01-01
Teaching and learning of mathematical modelling has become a key competence within school curricula and educational standards in many countries of the world. The term mathematical modelling, its meaning, and how it can be implemented in mathematics lessons have been intensively discussed during several Conferences of the European Society for…
Mathematical Modeling: Convoying Merchant Ships
ERIC Educational Resources Information Center
Mathews, Susann M.
2004-01-01
This article describes a mathematical model that connects mathematics with social studies. Students use mathematics to model independent versus convoyed ship deployments and sinkings to determine if the British should have convoyed their merchant ships during World War I. During the war, the British admiralty opposed sending merchant ships grouped…
NASA Astrophysics Data System (ADS)
Ataei, Sh; Mahmud, Z.; Khalid, M. N.
2014-04-01
The students learning outcomes clarify what students should know and be able to demonstrate after completing their course. So, one of the issues on the process of teaching and learning is how to assess students' learning. This paper describes an application of the dichotomous Rasch measurement model in measuring the cognitive process of engineering students' learning of mathematics. This study provides insights into the perspective of 54 engineering students' cognitive ability in learning Calculus III based on Bloom's Taxonomy on 31 items. The results denote that some of the examination questions are either too difficult or too easy for the majority of the students. This analysis yields FIT statistics which are able to identify if there is data departure from the Rasch theoretical model. The study has identified some potential misfit items based on the measurement of ZSTD where the removal misfit item was accomplished based on the MNSQ outfit of above 1.3 or less than 0.7 logit. Therefore, it is recommended that these items be reviewed or revised to better match the range of students' ability in the respective course.
Chronology of DIC technique based on the fundamental mathematical modeling and dehydration impact.
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. PMID:25477631
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.
Teaching Conceptual Model-Based Word Problem Story Grammar to Enhance Mathematics Problem Solving
ERIC Educational Resources Information Center
Xin, Yan Ping; Wiles, Ben; Lin, Yu-Ying
2008-01-01
Borrowing the concept of story grammar from reading comprehension literature, the purpose of this study was to examine the effect of teaching "word problem (WP) story grammar" on arithmetic WP solving that emphasizes the algebraic expression of mathematical relations in conceptual models. Participants were five students in Grades 4 and 5 with or…
Physical and mathematical cochlear models
NASA Astrophysics Data System (ADS)
Lim, Kian-Meng
2000-10-01
The cochlea is an intricate organ in the inner ear responsible for our hearing. Besides acting as a transducer to convert mechanical sound vibrations to electrical neural signals, the cochlea also amplifies and separates the sound signal into its spectral components for further processing in the brain. It operates over a broad-band of frequency and a huge dynamic range of input while maintaining a low power consumption. The present research takes the approach of building cochlear models to study and understand the underlying mechanics involved in the functioning of the cochlea. Both physical and mathematical models of the cochlea are constructed. The physical model is a first attempt to build a life- sized replica of the human cochlea using advanced micro- machining techniques. The model takes a modular design, with a removable silicon-wafer based partition membrane encapsulated in a plastic fluid chamber. Preliminary measurements in the model are obtained and they compare roughly with simulation results. Parametric studies on the design parameters of the model leads to an improved design of the model. The studies also revealed that the width and orthotropy of the basilar membrane in the cochlea have significant effects on the sharply tuned responses observed in the biological cochlea. The mathematical model is a physiologically based model that includes three-dimensional viscous fluid flow and a tapered partition with variable properties along its length. A hybrid asymptotic and numerical method provides a uniformly valid and efficient solution to the short and long wave regions in the model. Both linear and non- linear activity are included in the model to simulate the active cochlea. The mathematical model has successfully reproduced many features of the response in the biological cochlea, as observed in experiment measurements performed on animals. These features include sharply tuned frequency responses, significant amplification with inclusion of activity
Modeling Zombie Outbreaks: A Problem-Based Approach to Improving Mathematics One Brain at a Time
ERIC Educational Resources Information Center
Lewis, Matthew; Powell, James A.
2016-01-01
A great deal of educational literature has focused on problem-based learning (PBL) in mathematics at the primary and secondary level, but arguably there is an even greater need for PBL in college math courses. We present a project centered around the Humans versus Zombies moderated tag game played on the Utah State University campus. We discuss…
Modelling and Optimizing Mathematics Learning in Children
ERIC Educational Resources Information Center
Käser, Tanja; Busetto, Alberto Giovanni; Solenthaler, Barbara; Baschera, Gian-Marco; Kohn, Juliane; Kucian, Karin; von Aster, Michael; Gross, Markus
2013-01-01
This study introduces a student model and control algorithm, optimizing mathematics learning in children. The adaptive system is integrated into a computer-based training system for enhancing numerical cognition aimed at children with developmental dyscalculia or difficulties in learning mathematics. The student model consists of a dynamic…
NASA Astrophysics Data System (ADS)
Sapunov, Valentin; Dikinis, Alexandr; Voronov, Nikolai
2014-05-01
Russian Federation having giant area has low concentration of land meteorological check points. Net of monitoring is not enough for effective forecast and prediction of weather dynamics and extremely situations. Under increase of extremely situations and incidents - hurricanes et al (two times from begin of XXI century) reconstruction and "perestroika" of monitoring net is needful and necessary. The basis of such a progress is distant monitoring using planes and satellites adding land contact monitoring base on efforts of existed points and stations. Interaction of contact and distant views may make hydro meteorological data and prediction more fine and significant. Tradition physical methods must be added by new biological methods of modern study. According to gotten researches animal are able to predict extremely hazards of natural and anthropogenic nature basing of interaction between biological matter and probable physical field that is under primary study. For example it was animals which forecasted dropping of Chelyabinsk meteorite of 2013. Adding of biological indication with complex of meteorological data may increase significance of hazard prediction. The uniting of all data and approaches may become basis of proposed mathematical hydro meteorological weather models. Introduction to practice reported complex methods may decrease of loss from hydro meteorological risks and hazards and increase stability of country economics.
ERIC Educational Resources Information Center
Ruthven, Kenneth; Hennessy, Sara
2002-01-01
Analyzes the pedagogical ideas underpinning teachers' accounts of the successful use of computer-based tools and resources to support the teaching and learning of mathematics. Organizes central themes to form a pedagogical model capable of informing the use of such technologies in classroom teaching and generating theoretical conjectures for…
Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches
ERIC Educational Resources Information Center
Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem
2014-01-01
Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…
Mathematical model of orbital and ground-based cross-dispersion spectrographs
NASA Astrophysics Data System (ADS)
Yushkin, M. V.; Fatkhullin, T. A.; Panchuk, V. E.
2016-07-01
We present the technique and algorithm of numerical modeling of high-resolution spectroscopic equipment. The software is implemented in C++ using nVidia CUDA technology. We report the results of currently developedmodeling of new-generation echelle spectrographs. To validate the algorithms used to construct the mathematical model, we present the results of modeling of NES spectrograph of the 6-m telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences. A comparison of simulated and real images of the spectra acquired with NES spectrograph demonstrates good agreement between the model constructed and experimental data.
Mathematical modeling and analysis of EDM process parameters based on Taguchi design of experiments
NASA Astrophysics Data System (ADS)
Laxman, J.; Raj, K. Guru
2015-12-01
Electro Discharge Machining is a process used for machining very hard metals, deep and complex shapes by metal erosion in all types of electro conductive materials. The metal is removed through the action of an electric discharge of short duration and high current density between the tool and the work piece. The eroded metal on the surface of both work piece and the tool is flushed away by the dielectric fluid. The objective of this work is to develop a mathematical model for an Electro Discharge Machining process which provides the necessary equations to predict the metal removal rate, electrode wear rate and surface roughness. Regression analysis is used to investigate the relationship between various process parameters. The input parameters are taken as peak current, pulse on time, pulse off time, tool lift time. and the Metal removal rate, electrode wear rate and surface roughness are as responses. Experiments are conducted on Titanium super alloy based on the Taguchi design of experiments i.e. L27 orthogonal experiments.
Mathematical modeling of kidney transport.
Layton, Anita T
2013-01-01
In addition to metabolic waste and toxin excretion, the kidney also plays an indispensable role in regulating the balance of water, electrolytes, nitrogen, and acid-base. In this review, we describe representative mathematical models that have been developed to better understand kidney physiology and pathophysiology, including the regulation of glomerular filtration, the regulation of renal blood flow by means of the tubuloglomerular feedback mechanisms and of the myogenic mechanism, the urine concentrating mechanism, epithelial transport, and regulation of renal oxygen transport. We discuss the extent to which these modeling efforts have expanded our understanding of renal function in both health and disease.
What Is Measured in Mathematics Tests? Construct Validity of Curriculum-Based Mathematics Measures.
ERIC Educational Resources Information Center
Thurber, Robin Schul; Shinn, Mark R.; Smolkowski, Keith
2002-01-01
Mathematics curriculum-based measurement (M-CBM) is one tool that has been developed for formative evaluation in mathematics. This study examines what constructs M-CBM actually measures in the context of a range of other mathematics measures. Results indicated that a two-factor model of mathematics where Computation and Applications were distinct…
Explorations in Elementary Mathematical Modeling
ERIC Educational Resources Information Center
Shahin, Mazen
2010-01-01
In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematical tools in this course are the difference equations and matrix algebra. We also integrate computer technology and…
Mathematical Models for Elastic Structures
NASA Astrophysics Data System (ADS)
Villaggio, Piero
1997-10-01
During the seventeenth century, several useful theories of elastic structures emerged, with applications to civil and mechanical engineering problems. Recent and improved mathematical tools have extended applications into new areas such as mathematical physics, geomechanics, and biomechanics. This book offers a critically filtered collection of the most significant theories dealing with elastic slender bodies. It includes mathematical models involving elastic structures that are used to solve practical problems with particular emphasis on nonlinear problems.
Are Clade Specific HIV Vaccines a Necessity? An Analysis Based on Mathematical Models.
Dimitrov, Dobromir; Kublin, James G; Ramsey, Scott; Corey, Lawrence
2015-12-01
As HIV-1 envelope immune responses are critical to vaccine related protection, most candidate HIV vaccines entering efficacy trials are based upon a clade specific design. This need for clade specific vaccine prototypes markedly reduces the implementation of potentially effective HIV vaccines. We utilized a mathematical model to determine the effectiveness of immediate roll-out of a non-clade matched vaccine with reduced efficacy compared to constructing clade specific vaccines, which would take considerable time to manufacture and test in safety and efficacy trials. We simulated the HIV epidemic in San Francisco (SF) and South Africa (SA) and projected effectiveness of three vaccination strategies: i) immediate intervention with a 20-40% vaccine efficacy (VE) non-matched vaccine, ii) delayed intervention by developing a 50% VE clade-specific vaccine, and iii) immediate intervention with a non-matched vaccine replaced by a clade-specific vaccine when developed. Immediate vaccination with a non-clade matched vaccine, even with reduced efficacy, would prevent thousands of new infections in SF and millions in SA over 30 years. Vaccination with 50% VE delayed for five years needs six and 12 years in SA to break-even with immediate 20 and 30% VE vaccination, respectively, while not able to surpass the impact of immediate 40% VE vaccination over 30 years. Replacing a 30% VE with a 50% VE vaccine after 5 years reduces the HIV acquisition by 5% compared to delayed vaccination. The immediate use of an HIV vaccine with reduced VE in high risk communities appears desirable over a short time line but higher VE should be the pursued to achieve strong long-term impact. Our analysis illustrates the importance of developing surrogate markers (correlates of protection) to allow bridging types of immunogenicity studies to support more rapid assessment of clade specific vaccines. PMID:26844286
ERIC Educational Resources Information Center
Roduta Roberts, Mary; Alves, Cecilia B.; Chu, Man-Wai; Thompson, Margaret; Bahry, Louise M.; Gotzmann, Andrea
2014-01-01
The purpose of this study was to evaluate the adequacy of three cognitive models, one developed by content experts and two generated from student verbal reports for explaining examinee performance on a grade 3 diagnostic mathematics test. For this study, the items were developed to directly measure the attributes in the cognitive model. The…
Water network cost optimization in a paper mill based on a new library of mathematical models.
Lizarralde, I; Claeys, F; Ordóñez, R; de Gracia, M; Sancho, L; Grau, P
2012-01-01
The increasing costs associated with water supply and the disposal of wastewater has stimulated industries to seek more efficient water management systems. Mathematical modelling and simulation can be a very valuable tool for the study of the multiple alternatives available whilst assessing optimum solutions for water management in industry. This study introduces a new steady state model library able to reproduce industrial water circuits. It has been implemented in a novel software framework for the representation, simulation and optimization of industrial water networks. A water circuit representing a paper mill has been modelled and simulated showing the capability to reproduce real case studies. Alternative scenarios for the water network have also been tested to assess the capability of the models to optimize water circuits minimizing total cost. PMID:22592461
Mathematical modeling of glycerol biotransformation
NASA Astrophysics Data System (ADS)
Popova-Krumova, Petya; Yankova, Sofia; Ilieva, Biliana
2013-12-01
A method for mathematical modeling of glycerol biotransformation by Klebsiella oxytoca is presented. Glycerol is a renewable resource for it is formed as a by-product during biodiesel production. Because of its large volume production, it seems to be a good idea to develop a technology that converts this waste into products of high value (1, 3-Propanediol; 2, 3-Butanediol). The kinetic model of this process consists of many equations and parameters. The minimization of the least square function will be used for model parameters identification. In cases of parameters identification in multiparameter models the minimization of the least square function is very difficult because it is multiextremal. This is the main problem in the multiextremal function minimization which will be solved on the base a hierarchical approach, using a polynomial approximation of the experimental data.
Mathematical model for gyroscope effects
NASA Astrophysics Data System (ADS)
Usubamatov, Ryspek
2015-05-01
Gyroscope effects are used in many engineering calculations of rotating parts, and a gyroscope is the basic unit of numerous devices and instruments used in aviation, space, marine and other industries. The primary attribute of a gyroscope is a spinning rotor that persists in maintaining its plane of rotation, creating gyroscope effects. Numerous publications represent the gyroscope theory using mathematical models based on the law of kinetic energy conservation and the rate of change in angular momentum of a spinning rotor. Gyroscope theory still attracts many researchers who continue to discover new properties of gyroscopic devices. In reality, gyroscope effects are more complex and known mathematical models do not accurately reflect the actual motions. Analysis of forces acting on a gyroscope shows that four dynamic components act simultaneously: the centrifugal, inertial and Coriolis forces and the rate of change in angular momentum of the spinning rotor. The spinning rotor generates a rotating plane of centrifugal and Coriols forces that resist the twisting of the spinning rotor with external torque applied. The forced inclination of the spinning rotor generates inertial forces, resulting in precession torque of a gyroscope. The rate of change of the angular momentum creates resisting and precession torques which are not primary one in gyroscope effects. The new mathematical model for the gyroscope motions under the action of the external torque applied can be as base for new gyroscope theory. At the request of the author of the paper, this corrigendum was issued on 24 May 2016 to correct an incomplete Table 1 and errors in Eq. (47) and Eq. (48).
ERIC Educational Resources Information Center
Juska, Alfonsas; Gedminiene, Genovaite; Ivanec, Ruta
2006-01-01
This paper has arisen as a result of teaching Models in Biology to undergraduates of Bioengineering at the Gediminas Technical University of Vilnius. The aim is to teach the students to use a fresh approach to the problems they are familiar with, to come up with an articulate verbal model after a mental effort, to express it in rigorous…
Mathematical Modeling of Diverse Phenomena
NASA Technical Reports Server (NTRS)
Howard, J. C.
1979-01-01
Tensor calculus is applied to the formulation of mathematical models of diverse phenomena. Aeronautics, fluid dynamics, and cosmology are among the areas of application. The feasibility of combining tensor methods and computer capability to formulate problems is demonstrated. The techniques described are an attempt to simplify the formulation of mathematical models by reducing the modeling process to a series of routine operations, which can be performed either manually or by computer.
Mathematical models of behavior of individual animals.
Tsibulsky, Vladimir L; Norman, Andrew B
2007-01-01
This review is focused on mathematical modeling of behaviors of a whole organism with special emphasis on models with a clearly scientific approach to the problem that helps to understand the mechanisms underlying behavior. The aim is to provide an overview of old and contemporary mathematical models without complex mathematical details. Only deterministic and stochastic, but not statistical models are reviewed. All mathematical models of behavior can be divided into two main classes. First, models that are based on the principle of teleological determinism assume that subjects choose the behavior that will lead them to a better payoff in the future. Examples are game theories and operant behavior models both of which are based on the matching law. The second class of models are based on the principle of causal determinism, which assume that subjects do not choose from a set of possibilities but rather are compelled to perform a predetermined behavior in response to specific stimuli. Examples are perception and discrimination models, drug effects models and individual-based population models. A brief overview of the utility of each mathematical model is provided for each section.
Mathematical modelling of cucumber (cucumis sativus) drying
NASA Astrophysics Data System (ADS)
Shahari, N.; Hussein, S. M.; Nursabrina, M.; Hibberd, S.
2014-07-01
This paper investigates the applicability of using an experiment based mathematical model (empirical model) and a single phase mathematical model with shrinkage to describe the drying curve of cucumis sativus (cucumber). Drying experiments were conducted using conventional air drying and data obtained from these experiments were fitted to seven empirical models using non-linear least square regression based on the Levenberg Marquardt algorithm. The empirical models were compared according to their root mean square error (RMSE), sum of square error (SSE) and coefficient of determination (R2). A logarithmic model was found to be the best empirical model to describe the drying curve of cucumber. The numerical result of a single phase mathematical model with shrinkage was also compared with experiment data for cucumber drying. A good agreement was obtained between the model predictions and the experimental data.
Mathematical Models of Waiting Time.
ERIC Educational Resources Information Center
Gordon, Sheldon P.; Gordon, Florence S.
1990-01-01
Considered are several mathematical models that can be used to study different waiting situations. Problems involving waiting at a red light, bank, restaurant, and supermarket are discussed. A computer program which may be used with these problems is provided. (CW)
Mathematical Models for Doppler Measurements
NASA Technical Reports Server (NTRS)
Lear, William M.
1987-01-01
Error analysis increases precision of navigation. Report presents improved mathematical models of analysis of Doppler measurements and measurement errors of spacecraft navigation. To take advantage of potential navigational accuracy of Doppler measurements, precise equations relate measured cycle count to position and velocity. Drifts and random variations in transmitter and receiver oscillator frequencies taken into account. Mathematical models also adapted to aircraft navigation, radar, sonar, lidar, and interferometry.
Mathematical Models of Elementary Mathematics Learning and Performance. Final Report.
ERIC Educational Resources Information Center
Suppes, Patrick
This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the…
Social and Motivational Bases for Mathematical Understanding.
ERIC Educational Resources Information Center
Hatano, Giyoo
1988-01-01
Describes a model of cognitive and motivational processes in mathematics learning and relates the model to Brazilian street mathematics and abacus operation. Proposes instructional strategies for motivating conceptual understanding in school mathematics learning. (RJC)
Automatic mathematical modeling for space application
NASA Technical Reports Server (NTRS)
Wang, Caroline K.
1987-01-01
A methodology for automatic mathematical modeling is described. The major objective is to create a very friendly environment for engineers to design, maintain and verify their model and also automatically convert the mathematical model into FORTRAN code for conventional computation. A demonstration program was designed for modeling the Space Shuttle Main Engine simulation mathematical model called Propulsion System Automatic Modeling (PSAM). PSAM provides a very friendly and well organized environment for engineers to build a knowledge base for base equations and general information. PSAM contains an initial set of component process elements for the Space Shuttle Main Engine simulation and a questionnaire that allows the engineer to answer a set of questions to specify a particular model. PSAM is then able to automatically generate the model and the FORTRAN code. A future goal is to download the FORTRAN code to the VAX/VMS system for conventional computation.
Image-based quantification and mathematical modeling of spatial heterogeneity in ESC colonies.
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. PMID:25605123
Annual Perspectives in Mathematics Education 2016: Mathematical Modeling and Modeling Mathematics
ERIC Educational Resources Information Center
Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.
2016-01-01
Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…
Shankar Subramaniam
2009-04-01
This final project report summarizes progress made towards the objectives described in the proposal entitled “Developing New Mathematical Models for Multiphase Flows Based on a Fundamental Probability Density Function Approach”. Substantial progress has been made in theory, modeling and numerical simulation of turbulent multiphase flows. The consistent mathematical framework based on probability density functions is described. New models are proposed for turbulent particle-laden flows and sprays.
Suarez, Cecilia; Maglietti, Felipe; Colonna, Mario; Breitburd, Karina; Marshall, Guillermo
2012-01-01
Gliomas are the most common primary brain tumors and yet almost incurable due mainly to their great invasion capability. This represents a challenge to present clinical oncology. Here, we introduce a mathematical model aiming to improve tumor spreading capability definition. The model consists in a time dependent reaction-diffusion equation in a three-dimensional spatial domain that distinguishes between different brain topological structures. The model uses a series of digitized images from brain slices covering the whole human brain. The Talairach atlas included in the model describes brain structures at different levels. Also, the inclusion of the Brodmann areas allows prediction of the brain functions affected during tumor evolution and the estimation of correlated symptoms. The model is solved numerically using patient-specific parametrization and finite differences. Simulations consider an initial state with cellular proliferation alone (benign tumor), and an advanced state when infiltration starts (malign tumor). Survival time is estimated on the basis of tumor size and location. The model is used to predict tumor evolution in two clinical cases. In the first case, predictions show that real infiltrative areas are underestimated by current diagnostic imaging. In the second case, tumor spreading predictions were shown to be more accurate than those derived from previous models in the literature. Our results suggest that the inclusion of differential migration in glioma growth models constitutes another step towards a better prediction of tumor infiltration at the moment of surgical or radiosurgical target definition. Also, the addition of physiological/psychological considerations to classical anatomical models will provide a better and integral understanding of the patient disease at the moment of deciding therapeutic options, taking into account not only survival but also life quality. PMID:22761843
Suarez, Cecilia; Maglietti, Felipe; Colonna, Mario; Breitburd, Karina; Marshall, Guillermo
2012-01-01
Gliomas are the most common primary brain tumors and yet almost incurable due mainly to their great invasion capability. This represents a challenge to present clinical oncology. Here, we introduce a mathematical model aiming to improve tumor spreading capability definition. The model consists in a time dependent reaction-diffusion equation in a three-dimensional spatial domain that distinguishes between different brain topological structures. The model uses a series of digitized images from brain slices covering the whole human brain. The Talairach atlas included in the model describes brain structures at different levels. Also, the inclusion of the Brodmann areas allows prediction of the brain functions affected during tumor evolution and the estimation of correlated symptoms. The model is solved numerically using patient-specific parametrization and finite differences. Simulations consider an initial state with cellular proliferation alone (benign tumor), and an advanced state when infiltration starts (malign tumor). Survival time is estimated on the basis of tumor size and location. The model is used to predict tumor evolution in two clinical cases. In the first case, predictions show that real infiltrative areas are underestimated by current diagnostic imaging. In the second case, tumor spreading predictions were shown to be more accurate than those derived from previous models in the literature. Our results suggest that the inclusion of differential migration in glioma growth models constitutes another step towards a better prediction of tumor infiltration at the moment of surgical or radiosurgical target definition. Also, the addition of physiological/psychological considerations to classical anatomical models will provide a better and integral understanding of the patient disease at the moment of deciding therapeutic options, taking into account not only survival but also life quality.
ERIC Educational Resources Information Center
Yuliani, Kiki; Saragih, Sahat
2015-01-01
The purpose of this research was to: 1) development of learning devices based guided discovery model in improving of understanding concept and critical thinking mathematically ability of students at Islamic Junior High School; 2) describe improvement understanding concept and critical thinking mathematically ability of students at MTs by using…
Alba-Martínez, Jose; Trujillo, Macarena; Blasco-Gimenez, Ramon; Berjano, Enrique
2012-01-01
Radiofrequency cardiac ablation (RFCA) has been used to treat certain types of cardiac arrhythmias by producing a thermal lesion. Even though a tissue temperature higher than 50ºC is required to destroy the target, thermal mapping is not currently used during RFCA. Our aim was thus to develop mathematical models capable of estimating tissue temperature from tissue characteristics acquired or estimated at the beginning of the procedure (electrical conductivity, thermal conductivity, specific heat and density) and the applied voltage at any time. Biological tissue was considered as a system with an input (applied voltage) and output (tissue temperature), and so the mathematical models were based on transfer functions relating these variables. We used theoretical models based on finite element method to verify the mathematical models. Firstly, we solved finite element models to identify the transfer functions between the temperature at a depth of 4 mm and a constant applied voltage using a 7Fr and 4 mm electrode. The results showed that the relationships can be expressed as first-order transfer functions. Changes in electrical conductivity only affected the static gain of the system, while specific heat variations produced a change in the dynamic system response. In contrast, variations in thermal conductivity modified both the static gain and the dynamic system response. Finally, to assess the performance of the transfer functions obtained, we conducted a new set of computer simulations using a controlled temperature protocol and considering the temperature dependence of the thermal and electrical conductivities, i.e. conditions closer to those found in clinical use. The results showed that the difference between the values estimated from transfer functions and the temperatures obtained from finite element models was less than 4ºC, which suggests that the proposed method could be used to estimate tissue temperature in real time. PMID:22715345
Mathematics Teachers' Ideas about Mathematical Models: A Diverse Landscape
ERIC Educational Resources Information Center
Bautista, Alfredo; Wilkerson-Jerde, Michelle H.; Tobin, Roger G.; Brizuela, Bárbara M.
2014-01-01
This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers' ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers' written responses to three open-ended…
ERIC Educational Resources Information Center
Street, Garrett M.; Laubach, Timothy A.
2013-01-01
We provide a 5E structured-inquiry lesson so that students can learn more of the mathematics behind the logistic model of population biology. By using models and mathematics, students understand how population dynamics can be influenced by relatively simple changes in the environment.
Mathematical modeling in soil science
NASA Astrophysics Data System (ADS)
Tarquis, Ana M.; Gasco, Gabriel; Saa-Requejo, Antonio; Méndez, Ana; Andina, Diego; Sánchez, M. Elena; Moratiel, Rubén; Antón, Jose Manuel
2015-04-01
Teaching in context can be defined as teaching a mathematical idea or process by using a problem, situation, or data to enhance the teaching and learning process. The same problem or situation may be used many times, at different mathematical levels to teach different objectives. A common misconception exists that assigning/teaching applications is teaching in context. While both use problems, the difference is in timing, in purpose, and in student outcome. In this work, one problem situation is explored thoroughly at different levels of understanding and other ideas are suggested for classroom explorations. Some teachers, aware of the difficulties some students have with mathematical concepts, try to teach quantitative sciences without using mathematical tools. Such attempts are not usually successful. The answer is not in discarding the mathematics, but in finding ways to teach mathematically-based concepts to students who need them but who find them difficult. The computer is an ideal tool for this purpose. To this end, teachers of the Soil Science and Mathematics Departments of the UPM designed a common practice to teach to the students the role of soil on the carbon sequestration. The objective of this work is to explain the followed steps to the design of the practice. Acknowledgement Universidad Politécnica de Madrid (UPM) for the Projects in Education Innovation IE12_13-02009 and IE12_13-02012 is gratefully acknowledge.
NASA Astrophysics Data System (ADS)
Solovyova, N. V.; Lobkovsky, L. I.
2015-09-01
This paper proposes a method of mathematical modelling of ecological risk based on a synthesis of dynamic and probabilistic risk assessment techniques. The probability of assessment of an acceptable probability of an anthropogenic impact to minimize economic costs is proposed. The dependence of an acceptable probability of an anthropogenic impact on the ecological risk is demonstrated with an example calculation. The results of the modelling of the state of a shelf ecosystem based on the dynamic model are used for the calculation as source information. Based on this synthesis, the calculation results bring about the opportunity to balance ecological-economic goals of achieving safe development of the shelf and to satisfy the involuntary necessity to reduce the costs on environmental protection measures, while maintaining the priority of environmental requirements.
Mathematical Models of Gene Regulation
NASA Astrophysics Data System (ADS)
Mackey, Michael C.
2004-03-01
This talk will focus on examples of mathematical models for the regulation of repressible operons (e.g. the tryptophan operon), inducible operons (e.g. the lactose operon), and the lysis/lysogeny switch in phage λ. These ``simple" gene regulatory elements can display characteristics experimentally of rapid response to perturbations and bistability, and biologically accurate mathematical models capture these aspects of the dynamics. The models, if realistic, are always nonlinear and contain significant time delays due to transcriptional and translational delays that pose substantial problems for the analysis of the possible ranges of dynamics.
Dambacher, Jeffrey M; Rothlisberg, Peter C; Loneragan, Neil R
2015-01-01
A major decline in the catch of the banana prawn [shrimp], Penaeus (Fenneropenaeus) merguiensis, occurred over a six-year period in the Weipa region of the northeastern Gulf of Carpentaria, Australia. Three main hypotheses have been developed to explain this decline: (1) prawn recruitment collapsed due to overfishing; (2) recruitment collapsed due to a change in the prawn's environment; and (3) adult banana prawns were still present, but fishers could no longer effectively find or catch them. Qualitative mathematical models were used to link population biology, environmental factors, and fishery dynamics to evaluate the alternative hypotheses. This modeling approach provides the means to rapidly integrate knowledge across disciplines and consider alternative hypotheses about how the structure and function of an ecosystem affects its dynamics. Alternative models were constructed to address the different hypotheses and also to encompass a diversity of opinion about the underlying dynamics of the system. Key findings from these analyses are that: instability in the system can arise when discarded fishery bycatch supports relatively high predation pressure; system stability can be enhanced by management of fishing effort or stock catchability; catch per unit effort is not necessarily a reliable indicator of stock abundance; a change in early-season rainfall should affect all stages in the banana prawn's life cycle; and a reduced catch in the Weipa region can create and reinforce a shift in fishing effort away from Weipa. Results from the models informed an approach to test the hypotheses (i.e., an experimental fishing program), and promoted understanding of the system among researchers, management agencies, and industry. The analytical tools developed in this work to address stages of a prawn life cycle and fishery dynamics are generally applicable to any exploited natural. resource. PMID:26255373
Dambacher, Jeffrey M; Rothlisberg, Peter C; Loneragan, Neil R
2015-01-01
A major decline in the catch of the banana prawn [shrimp], Penaeus (Fenneropenaeus) merguiensis, occurred over a six-year period in the Weipa region of the northeastern Gulf of Carpentaria, Australia. Three main hypotheses have been developed to explain this decline: (1) prawn recruitment collapsed due to overfishing; (2) recruitment collapsed due to a change in the prawn's environment; and (3) adult banana prawns were still present, but fishers could no longer effectively find or catch them. Qualitative mathematical models were used to link population biology, environmental factors, and fishery dynamics to evaluate the alternative hypotheses. This modeling approach provides the means to rapidly integrate knowledge across disciplines and consider alternative hypotheses about how the structure and function of an ecosystem affects its dynamics. Alternative models were constructed to address the different hypotheses and also to encompass a diversity of opinion about the underlying dynamics of the system. Key findings from these analyses are that: instability in the system can arise when discarded fishery bycatch supports relatively high predation pressure; system stability can be enhanced by management of fishing effort or stock catchability; catch per unit effort is not necessarily a reliable indicator of stock abundance; a change in early-season rainfall should affect all stages in the banana prawn's life cycle; and a reduced catch in the Weipa region can create and reinforce a shift in fishing effort away from Weipa. Results from the models informed an approach to test the hypotheses (i.e., an experimental fishing program), and promoted understanding of the system among researchers, management agencies, and industry. The analytical tools developed in this work to address stages of a prawn life cycle and fishery dynamics are generally applicable to any exploited natural. resource.
Using Covariation Reasoning to Support Mathematical Modeling
ERIC Educational Resources Information Center
Jacobson, Erik
2014-01-01
For many students, making connections between mathematical ideas and the real world is one of the most intriguing and rewarding aspects of the study of mathematics. In the Common Core State Standards for Mathematics (CCSSI 2010), mathematical modeling is highlighted as a mathematical practice standard for all grades. To engage in mathematical…
Mathematical model for bone mineralization
Komarova, Svetlana V.; Safranek, Lee; Gopalakrishnan, Jay; Ou, Miao-jung Yvonne; McKee, Marc D.; Murshed, Monzur; Rauch, Frank; Zuhr, Erica
2015-01-01
Defective bone mineralization has serious clinical manifestations, including deformities and fractures, but the regulation of this extracellular process is not fully understood. We have developed a mathematical model consisting of ordinary differential equations that describe collagen maturation, production and degradation of inhibitors, and mineral nucleation and growth. We examined the roles of individual processes in generating normal and abnormal mineralization patterns characterized using two outcome measures: mineralization lag time and degree of mineralization. Model parameters describing the formation of hydroxyapatite mineral on the nucleating centers most potently affected the degree of mineralization, while the parameters describing inhibitor homeostasis most effectively changed the mineralization lag time. Of interest, a parameter describing the rate of matrix maturation emerged as being capable of counter-intuitively increasing both the mineralization lag time and the degree of mineralization. We validated the accuracy of model predictions using known diseases of bone mineralization such as osteogenesis imperfecta and X-linked hypophosphatemia. The model successfully describes the highly nonlinear mineralization dynamics, which includes an initial lag phase when osteoid is present but no mineralization is evident, then fast primary mineralization, followed by secondary mineralization characterized by a continuous slow increase in bone mineral content. The developed model can potentially predict the function for a mutated protein based on the histology of pathologic bone samples from mineralization disorders of unknown etiology. PMID:26347868
Ping, Qingyun; Abu-Reesh, Ibrahim M; He, Zhen
2016-11-01
Boron removal is an arising issue in desalination plants due to boron's toxicity. As an emerging treatment concept, bioelectrochemical systems (BES) can achieve potentially cost-effective boron removal by taking advantage of cathodic-produced alkali. Prior studies have demonstrated successful removal of boron in microbial desalination cells (MDCs) and microbial fuel cells (MFCs), both of which are representative BES. Herein, mathematical models were developed to further evaluate boron removal by different BES and understand the key operating factors. The models delivered very good prediction of the boron concentration in the MDC integrated with Donnan Dialysis (DD) system with the lowest relative root-mean-square error (RMSE) of 0.00%; the predication of the MFC performance generated the highest RMSE of 18.55%. The model results of salt concentration, solution pH, and current generation were well fitted with experimental data for RMSE values mostly below 10%. The long term simulation of the MDC-DD system suggests that the accumulation of salt in the catholyte/stripping solution could have a positive impact on the removal of boron due to osmosis-driven convection. The current generation in the MDC may have little influence on the boron removal, while in the MFC the current-driven electromigration can contribute up to 40% of boron removal. Osmosis-induced convection transport of boron could be the major driving force for boron removal to a low level <2mgL(-1). The ratio between the anolyte and the catholyte flow rates should be kept >22.2 in order to avoid boron accumulation in the anolyte effluent.
Ping, Qingyun; Abu-Reesh, Ibrahim M; He, Zhen
2016-11-01
Boron removal is an arising issue in desalination plants due to boron's toxicity. As an emerging treatment concept, bioelectrochemical systems (BES) can achieve potentially cost-effective boron removal by taking advantage of cathodic-produced alkali. Prior studies have demonstrated successful removal of boron in microbial desalination cells (MDCs) and microbial fuel cells (MFCs), both of which are representative BES. Herein, mathematical models were developed to further evaluate boron removal by different BES and understand the key operating factors. The models delivered very good prediction of the boron concentration in the MDC integrated with Donnan Dialysis (DD) system with the lowest relative root-mean-square error (RMSE) of 0.00%; the predication of the MFC performance generated the highest RMSE of 18.55%. The model results of salt concentration, solution pH, and current generation were well fitted with experimental data for RMSE values mostly below 10%. The long term simulation of the MDC-DD system suggests that the accumulation of salt in the catholyte/stripping solution could have a positive impact on the removal of boron due to osmosis-driven convection. The current generation in the MDC may have little influence on the boron removal, while in the MFC the current-driven electromigration can contribute up to 40% of boron removal. Osmosis-induced convection transport of boron could be the major driving force for boron removal to a low level <2mgL(-1). The ratio between the anolyte and the catholyte flow rates should be kept >22.2 in order to avoid boron accumulation in the anolyte effluent. PMID:27387806
Mathematical models for exotic wakes
NASA Astrophysics Data System (ADS)
Basu, Saikat; Stremler, Mark
2014-11-01
Vortex wakes are a common occurrence in the environment around us; the most famous example being the von Kármán vortex street with two vortices being shed by the bluff body in each cycle. However, frequently there can be many other more exotic wake configurations with different vortex arrangements, based on the flow parameters and the bluff body dimensions and/or its oscillation characteristics. Some examples include wakes with periodic shedding of three vortices (`P+S' mode) and four vortices (symmetric `2P' mode, staggered `2P' mode, `2C' mode). We present mathematical models for such wakes assuming two-dimensional potential flows with embedded point vortices. The spatial alignment of the vortices is inspired by the experimentally observed wakes. The idealized system follows a Hamiltonian formalism. Model-based analysis reveals a rich dynamics pertaining to the relative vortex motion in the mid-wake region. Downstream evolution of the vortices, as predicted from the model results, also show good correspondence with wake-shedding experiments performed on flowing soap films.
The 24-Hour Mathematical Modeling Challenge
ERIC Educational Resources Information Center
Galluzzo, Benjamin J.; Wendt, Theodore J.
2015-01-01
Across the mathematics curriculum there is a renewed emphasis on applications of mathematics and on mathematical modeling. Providing students with modeling experiences beyond the ordinary classroom setting remains a challenge, however. In this article, we describe the 24-hour Mathematical Modeling Challenge, an extracurricular event that exposes…
Mathematical Modeling: A Bridge to STEM Education
ERIC Educational Resources Information Center
Kertil, Mahmut; Gurel, Cem
2016-01-01
The purpose of this study is making a theoretical discussion on the relationship between mathematical modeling and integrated STEM education. First of all, STEM education perspective and the construct of mathematical modeling in mathematics education is introduced. A review of literature is provided on how mathematical modeling literature may…
Mathematical circulatory system model
NASA Technical Reports Server (NTRS)
Lakin, William D. (Inventor); Stevens, Scott A. (Inventor)
2010-01-01
A system and method of modeling a circulatory system including a regulatory mechanism parameter. In one embodiment, a regulatory mechanism parameter in a lumped parameter model is represented as a logistic function. In another embodiment, the circulatory system model includes a compliant vessel, the model having a parameter representing a change in pressure due to contraction of smooth muscles of a wall of the vessel.
Comprehensive Mathematical Model Of Real Fluids
NASA Technical Reports Server (NTRS)
Anderson, Peter G.
1996-01-01
Mathematical model of thermodynamic properties of water, steam, and liquid and gaseous hydrogen and oxygen developed for use in computational simulations of flows of mass and heat in main engine of space shuttle. Similar models developed for other fluids and applications. Based on HBMS equation of state.
NASA Astrophysics Data System (ADS)
Lee, Taek-Soo; Frey, Eric C.; Tsui, Benjamin M. W.
2015-04-01
This paper presents two 4D mathematical observer models for the detection of motion defects in 4D gated medical images. Their performance was compared with results from human observers in detecting a regional motion abnormality in simulated 4D gated myocardial perfusion (MP) SPECT images. The first 4D mathematical observer model extends the conventional channelized Hotelling observer (CHO) based on a set of 2D spatial channels and the second is a proposed model that uses a set of 4D space-time channels. Simulated projection data were generated using the 4D NURBS-based cardiac-torso (NCAT) phantom with 16 gates/cardiac cycle. The activity distribution modelled uptake of 99mTc MIBI with normal perfusion and a regional wall motion defect. An analytical projector was used in the simulation and the filtered backprojection (FBP) algorithm was used in image reconstruction followed by spatial and temporal low-pass filtering with various cut-off frequencies. Then, we extracted 2D image slices from each time frame and reorganized them into a set of cine images. For the first model, we applied 2D spatial channels to the cine images and generated a set of feature vectors that were stacked for the images from different slices of the heart. The process was repeated for each of the 1,024 noise realizations, and CHO and receiver operating characteristics (ROC) analysis methodologies were applied to the ensemble of the feature vectors to compute areas under the ROC curves (AUCs). For the second model, a set of 4D space-time channels was developed and applied to the sets of cine images to produce space-time feature vectors to which the CHO methodology was applied. The AUC values of the second model showed better agreement (Spearman’s rank correlation (SRC) coefficient = 0.8) to human observer results than those from the first model (SRC coefficient = 0.4). The agreement with human observers indicates the proposed 4D mathematical observer model provides a good predictor of the
Lee, Taek-Soo; Frey, Eric C; Tsui, Benjamin M W
2015-04-01
This paper presents two 4D mathematical observer models for the detection of motion defects in 4D gated medical images. Their performance was compared with results from human observers in detecting a regional motion abnormality in simulated 4D gated myocardial perfusion (MP) SPECT images. The first 4D mathematical observer model extends the conventional channelized Hotelling observer (CHO) based on a set of 2D spatial channels and the second is a proposed model that uses a set of 4D space-time channels. Simulated projection data were generated using the 4D NURBS-based cardiac-torso (NCAT) phantom with 16 gates/cardiac cycle. The activity distribution modelled uptake of (99m)Tc MIBI with normal perfusion and a regional wall motion defect. An analytical projector was used in the simulation and the filtered backprojection (FBP) algorithm was used in image reconstruction followed by spatial and temporal low-pass filtering with various cut-off frequencies. Then, we extracted 2D image slices from each time frame and reorganized them into a set of cine images. For the first model, we applied 2D spatial channels to the cine images and generated a set of feature vectors that were stacked for the images from different slices of the heart. The process was repeated for each of the 1,024 noise realizations, and CHO and receiver operating characteristics (ROC) analysis methodologies were applied to the ensemble of the feature vectors to compute areas under the ROC curves (AUCs). For the second model, a set of 4D space-time channels was developed and applied to the sets of cine images to produce space-time feature vectors to which the CHO methodology was applied. The AUC values of the second model showed better agreement (Spearman's rank correlation (SRC) coefficient = 0.8) to human observer results than those from the first model (SRC coefficient = 0.4). The agreement with human observers indicates the proposed 4D mathematical observer model provides a good predictor of the
Zhu, Xu; Straubinger, Robert M.; Jusko, William J.
2015-01-01
Combination chemotherapy is standard treatment for pancreatic cancer. However, current drugs lack efficacy for most patients and selection and evaluation of new combination regimens is empirical and time-consuming. The efficacy of gemcitabine, a standard-of-care agent, combined with birinapant, a pro-apoptotic antagonist of Inhibitor of Apoptosis Proteins (IAPs), was investigated in pancreatic cancer cells. PANC-1 cells were treated with vehicle, gemcitabine (6, 10, 20 nM), birinapant (50, 200, 500 nM), and combinations of the two drugs. Temporal changes in cell numbers, cell cycle distribution, and apoptosis were measured. A basic pharmacodynamic (PD) model based on cell numbers, and a mechanism-based PD model integrating all measurements, were developed. The basic PD model indicated that synergistic effects occurred in both cell proliferation and death processes. The mechanism-based model captured key features of drug action: temporary cell cycle arrest in S phase induced by gemcitabine alone, apoptosis induced by birinapant alone, and prolonged cell cycle arrest and enhanced apoptosis induced by the combination. A drug interaction term ψ was employed in the models to signify interactions of the combination when data were limited. When more experimental information was utilized, ψ values approaching 1 indicated that specific mechanisms of interactions were captured better. PD modeling identified the potential benefit of combining gemcitabine and birinapant, and characterized the key interaction pathways. An optimal treatment schedule of pretreatment with gemcitabine for 24-48 h was suggested based on model prediction and was verified experimentally. This approach provides a generalizable modeling platform for exploring combinations of cytostatic and cytotoxic agents in cancer cell cultures. PMID:26252969
Teachers' Conceptions of Mathematical Modeling
ERIC Educational Resources Information Center
Gould, Heather
2013-01-01
The release of the "Common Core State Standards for Mathematics" in 2010 resulted in a new focus on mathematical modeling in United States curricula. Mathematical modeling represents a way of doing and understanding mathematics new to most teachers. The purpose of this study was to determine the conceptions and misconceptions held by…
Mathematical Modeling in the Undergraduate Curriculum
ERIC Educational Resources Information Center
Toews, Carl
2012-01-01
Mathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advanced mathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…
Chen, W; Desai, D; Good, D; Crison, J; Timmins, P; Paruchuri, S; Wang, J; Ha, K
2016-08-01
A computational fluid dynamic (CFD) model was developed to predict metformin release from a hydroxypropylmethylcellulose (HPMC) matrix-based extended-release formulation that took into consideration the physical and chemical properties of the drug substance, composition, as well as size and shape of the tablet. New high dose strength (1000 mg) tablet geometry was selected based on the surface area/volume (SA/V) approach advocated by Lapidus/Lordi/Reynold to obtain the desired equivalent metformin release kinetics. Maintaining a similar SA/V ratio across all extended-release metformin hydrochloride (Met XR) tablet strengths that had different geometries provided similar simulations of dissolution behavior. Experimental dissolution profiles of three lots of high-strength tablets agreed with the simulated release kinetics. Additionally, a pharmacokinetic absorption model was developed using GastroPlus™ software and known physicochemical, pharmacokinetic, and in vitro dissolution properties of metformin to predict the clinical exposure of the new high strength (1000 mg) tablet prior to conducting a human clinical bioequivalence study. In vitro metformin release kinetics were utilized in the absorption model to predict exposures in humans for new 1000-mg Met XR tablets, and the absorption model correctly projected equivalent in vivo exposure across all dose strengths. A clinical bioequivalence study was pursued based on the combined modeling results and demonstrated equivalent exposure as predicted by the simulations. PMID:26729531
Mathematical Modeling of Cellular Metabolism.
Berndt, Nikolaus; Holzhütter, Hermann-Georg
2016-01-01
Cellular metabolism basically consists of the conversion of chemical compounds taken up from the extracellular environment into energy (conserved in energy-rich bonds of organic phosphates) and a wide array of organic molecules serving as catalysts (enzymes), information carriers (nucleic acids), and building blocks for cellular structures such as membranes or ribosomes. Metabolic modeling aims at the construction of mathematical representations of the cellular metabolism that can be used to calculate the concentration of cellular molecules and the rates of their mutual chemical interconversion in response to varying external conditions as, for example, hormonal stimuli or supply of essential nutrients. Based on such calculations, it is possible to quantify complex cellular functions as cellular growth, detoxification of drugs and xenobiotic compounds or synthesis of exported molecules. Depending on the specific questions to metabolism addressed, the methodological expertise of the researcher, and available experimental information, different conceptual frameworks have been established, allowing the usage of computational methods to condense experimental information from various layers of organization into (self-) consistent models. Here, we briefly outline the main conceptual frameworks that are currently exploited in metabolism research. PMID:27557541
Mathematical Modeling of Cellular Metabolism.
Berndt, Nikolaus; Holzhütter, Hermann-Georg
2016-01-01
Cellular metabolism basically consists of the conversion of chemical compounds taken up from the extracellular environment into energy (conserved in energy-rich bonds of organic phosphates) and a wide array of organic molecules serving as catalysts (enzymes), information carriers (nucleic acids), and building blocks for cellular structures such as membranes or ribosomes. Metabolic modeling aims at the construction of mathematical representations of the cellular metabolism that can be used to calculate the concentration of cellular molecules and the rates of their mutual chemical interconversion in response to varying external conditions as, for example, hormonal stimuli or supply of essential nutrients. Based on such calculations, it is possible to quantify complex cellular functions as cellular growth, detoxification of drugs and xenobiotic compounds or synthesis of exported molecules. Depending on the specific questions to metabolism addressed, the methodological expertise of the researcher, and available experimental information, different conceptual frameworks have been established, allowing the usage of computational methods to condense experimental information from various layers of organization into (self-) consistent models. Here, we briefly outline the main conceptual frameworks that are currently exploited in metabolism research.
Mathematical Models for Somite Formation
Baker, Ruth E.; Schnell, Santiago; Maini, Philip K.
2009-01-01
Somitogenesis is the process of division of the anterior–posterior vertebrate embryonic axis into similar morphological units known as somites. These segments generate the prepattern which guides formation of the vertebrae, ribs and other associated features of the body trunk. In this work, we review and discuss a series of mathematical models which account for different stages of somite formation. We begin by presenting current experimental information and mechanisms explaining somite formation, highlighting features which will be included in the models. For each model we outline the mathematical basis, show results of numerical simulations, discuss their successes and shortcomings and avenues for future exploration. We conclude with a brief discussion of the state of modeling in the field and current challenges which need to be overcome in order to further our understanding in this area. PMID:18023728
NASA Astrophysics Data System (ADS)
Faria, Ana; Bateira, Carlos; Laura, Soares; Fernandes, Joana; Gonçalves, José; Marques, Fernando
2016-04-01
The work focuses the evaluation of landslide susceptibility in Douro Region agricultural terraces, supported by dry stone walls and earth embankments, using two physically based models. The applied models, SHALSTAB (Montgomery et al.,1994; Dietrich et al., 1995) and SINMAP (PACK et al., 2005), combine an infinite slope stability model with a steady state hydrological model, and both use the following geophysical parameters: cohesion, friction angle, specific weight and soil thickness. The definition of the contributing areas is different in both models. The D∞ methodology used by SINMAP model suggests a great influence of the terraces morphology, providing a much more diffuse flow on the internal flow modelling. The MD8 used in SHALSTAB promotes an important degree of flow concentration, representing an internal flow based on preferential paths of the runoff as the areas more susceptible to saturation processes. The model validation is made through the contingency matrix method (Fawcett, 2006; Raia et al., 2014) and implies the confrontation with the inventory of past landslides. The True Positive Rate shows that SHALSTAB classifies 77% of the landslides on the high susceptibility areas, while SINMAP reaches 90%. The SINMAP has a False Positive Rate (represents the percentage of the slipped area that is classified as unstable but without landslides) of 83% and the SHALSTAB has 67%. The reliability (analyzes the areas that were correctly classified on the total area) of SHALSTAB is better (33% against 18% of SINMAP). Relative to Precision (refers to the ratio of the slipped area correctly classified over the whole area classified as unstable) SHALSTAB has better results (0.00298 against 0.00283 of SINMAP). It was elaborate the index TPR/FPR and better results obtained by SHALSTAB (1.14 against 1.09 of SINMAP). SHALSTAB shows a better performance in the definition of susceptibility most prone areas to instability processes. One of the reasons for the difference of
Mathematical modeling of molecular diffusion through mucus
Cu, Yen; Saltzman, W. Mark
2008-01-01
The rate of molecular transport through the mucus gel can be an important determinant of efficacy for therapeutic agents delivered by oral, intranasal, intravaginal/rectal, and intraocular routes. Transport through mucus can be described by mathematical models based on principles of physical chemistry and known characteristics of the mucus gel, its constituents, and of the drug itself. In this paper, we review mathematical models of molecular diffusion in mucus, as well as the techniques commonly used to measure diffusion of solutes in the mucus gel, mucus gel mimics, and mucosal epithelia. PMID:19135488
NASA Astrophysics Data System (ADS)
Real, Joaquin; Morales, Marco; Garcia, Alicia; Garofano, Virginia; Martinez-Capel, Francisco; Frances, Felix
2010-05-01
Initially riparian vegetation modeling was focused on the study of ecological patches without taking into account the interactive effects of structures and processes in between them (Tabacchi et al., 1998). One of the greatest challenges, when carrying out a riparian ecosystem restoration, is to understand the physical and ecological processes of a system and the interaction and feedback within these processes. Jorde (2002) pointed out the importance of addressing complex linkages between processes and biotic interactions in research and in the development of restoration projects over larger spatial and temporal scales in the future. According to Tabacchi et al. (2000), the water cycle in riparian zones depends on three important relations: the water absorption by the plants, water storage and atmospherical return by evaporation. During recent years a variety of ecological models have taken into account the changes in the plant species as consequence of changes in the environmental variables and hydrological alterations (Baptist, 2005; Braatne et al., 2002; Glenz, 2005; Hooke et al., 2005; Murphy et al., 2006). Most of these models are based on functional relationships between river hydrology and vegetation species or communities. In semiarid regions we make the hypothesis transpiration will be one of the key factors determining the riparian vegetation presence and therefore, we will not consider in our model other factors as recruitment, flood damages, etc. The objectives of this work are: firstly to develop a model capable of simulating several riparian vegetation types which can be applied in a wide range of conditions across Mediterranean environments; and secondly to calibrate and to validate the model in several Mediterranean river stretches of the Iberian Peninsula, both in undisturbed and disturbed flow regimes. To achieve these objectives the following methodology has been applied. The model has been conceptualized as a static tank flow model based on the
Mathematical modeling of CSF pulsatile hydrodynamics based on fluid-solid interaction.
Masoumi, Nafiseh; Bastani, Dariush; Najarian, Siamak; Ganji, Fariba; Farmanzad, Farhad; Seddighi, Amir Saeed
2010-06-01
Intracranial pressure (ICP) is derived from cerebral blood pressure and cerebrospinal fluid (CSF) circulatory dynamics and can be affected in the course of many diseases. Computer analysis of the ICP time pattern plays a crucial role in the diagnosis and treatment of those diseases. This study proposes the application of Linninger et al.'s [IEEE Trans. Biomed. Eng., vol. 52, no. 4, pp. 557-565, Apr. 2005] fluid-solid interaction model of CSF hydrodynamic in ventricular system based on our clinical data from a group of patients with brain parenchyma tumor. The clinical experiments include the arterial blood pressure (ABP), venous blood pressure, and ICP in the subarachnoid space (SAS). These data were used as inputs to the model that predicts the intracranial dynamic phenomena. In addition, the model has been modified by considering CSF pulsatile production rate as the major factor of CSF motion. The approximations of ventricle enlargement, CSF pressure distribution in the ventricular system and CSF velocity magnitude in the aqueduct and foramina were obtained in this study. The observation of reversal flow in the CSF flow pattern due to brain tissue compression is another finding in our investigation. Based on the experimental results, no existence of large transmural pressure differences were found in the brain system. The measured pressure drop in the ventricular system was less than 5 Pa. Moreover, the CSF flow pattern, ICP distribution, and velocity magnitude were in good agreement with the published models and CINE (phase-contrast magnetic resonance imaging) experiments, respectively.
Strategies to Support Students' Mathematical Modeling
ERIC Educational Resources Information Center
Jung, Hyunyi
2015-01-01
An important question for mathematics teachers is this: "How can we help students learn mathematics to solve everyday problems, rather than teaching them only to memorize rules and practice mathematical procedures?" Teaching students using modeling activities can help them learn mathematics in real-world problem-solving situations that…
Opinions of Secondary School Mathematics Teachers on Mathematical Modelling
ERIC Educational Resources Information Center
Tutak, Tayfun; Güder, Yunus
2013-01-01
The aim of this study is to identify the opinions of secondary school mathematics teachers about mathematical modelling. Qualitative research was used. The participants of the study were 40 secondary school teachers working in the Bingöl Province in Turkey during 2012-2013 education year. Semi-structured interview form prepared by the researcher…
Mathematical models of diabetes progression.
De Gaetano, Andrea; Hardy, Thomas; Beck, Benoit; Abu-Raddad, Eyas; Palumbo, Pasquale; Bue-Valleskey, Juliana; Pørksen, Niels
2008-12-01
Few attempts have been made to model mathematically the progression of type 2 diabetes. A realistic representation of the long-term physiological adaptation to developing insulin resistance is necessary for effectively designing clinical trials and evaluating diabetes prevention or disease modification therapies. Writing a good model for diabetes progression is difficult because the long time span of the disease makes experimental verification of modeling hypotheses extremely awkward. In this context, it is of primary importance that the assumptions underlying the model equations properly reflect established physiology and that the mathematical formulation of the model give rise only to physically plausible behavior of the solutions. In the present work, a model of the pancreatic islet compensation is formulated, its physiological assumptions are presented, some fundamental qualitative characteristics of its solutions are established, the numerical values assigned to its parameters are extensively discussed (also with reference to available cross-sectional epidemiologic data), and its performance over the span of a lifetime is simulated under various conditions, including worsening insulin resistance and primary replication defects. The differences with respect to two previously proposed models of diabetes progression are highlighted, and therefore, the model is proposed as a realistic, robust description of the evolution of the compensation of the glucose-insulin system in healthy and diabetic individuals. Model simulations can be run from the authors' web page.
The Nature of Mathematical Modeling
NASA Astrophysics Data System (ADS)
Gershenfeld, Neil
2011-06-01
Preface; 1. Introduction; Part I. Analytical Models: 2. Ordinary differential and difference equations; 3. Partial differential equations; 4. Variational principles; 5. Random systems; Part II. Numerical Models: 6. Finite differences: ordinary difference equations; 7. Finite differences: partial differential equations; 8. Finite elements; 9. Cellular automata and lattice gases; Part III. Observational Models: 10. Function fitting; 11. Transforms; 12. Architectures; 13. Optimization and search; 14. Clustering and density estimation; 15. Filtering and state estimation; 16. Linear and nonlinear time series; Appendix 1. Graphical and mathematical software; Appendix 2. Network programming; Appendix 3. Benchmarking; Appendix 4. Problem solutions; Bibliography.
NASA Astrophysics Data System (ADS)
Mi, Ye
1998-12-01
The major objective of this thesis is focused on theoretical and experimental investigations of identifying and characterizing vertical and horizontal flow regimes in two-phase flows. A methodology of flow regime identification with impedance-based neural network systems and a comprehensive model of vertical slug flow have been developed. Vertical slug flow has been extensively investigated and characterized with geometric, kinematic and hydrodynamic parameters. A multi-sensor impedance void-meter and a multi-sensor magnetic flowmeter were developed. The impedance void-meter was cross-calibrated with other reliable techniques for void fraction measurements. The performance of the impedance void-meter to measure the void propagation velocity was evaluated by the drift flux model. It was proved that the magnetic flowmeter was applicable to vertical slug flow measurements. Separable signals from these instruments allow us to unearth most characteristics of vertical slug flow. A methodology of vertical flow regime identification was developed. Supervised neural network and self-organizing neural network systems were employed. First, they were trained with results from an idealized simulation of impedance in a two-phase mixture. The simulation was mainly based on Mishima and Ishii's flow regime map, the drift flux model, and the newly developed model of slug flow. Then, these trained systems were tested with impedance signals. The results showed that the neural network systems were appropriate classifiers of vertical flow regimes. The theoretical models and experimental databases used in the simulation were reliable. Furthermore, this approach was applied successfully to horizontal flow identification. A comprehensive model was developed to predict important characteristics of vertical slug flow. It was realized that the void fraction of the liquid slug is determined by the relative liquid motion between the Taylor bubble tail and the Taylor bubble wake. Relying on this
Summer Camp of Mathematical Modeling in China
ERIC Educational Resources Information Center
Tian, Xiaoxi; Xie, Jinxing
2013-01-01
The Summer Camp of Mathematical Modeling in China is a recently created experience designed to further Chinese students' academic pursuits in mathematical modeling. Students are given more than three months to research on a mathematical modeling project. Researchers and teams with outstanding projects are invited to the Summer Camp to present…
Zhang, Zili; Gao, Chao; Liu, Yuxin; Qian, Tao
2014-09-01
Ant colony optimization (ACO) algorithms often fall into the local optimal solution and have lower search efficiency for solving the travelling salesman problem (TSP). According to these shortcomings, this paper proposes a universal optimization strategy for updating the pheromone matrix in the ACO algorithms. The new optimization strategy takes advantages of the unique feature of critical paths reserved in the process of evolving adaptive networks of the Physarum-inspired mathematical model (PMM). The optimized algorithms, denoted as PMACO algorithms, can enhance the amount of pheromone in the critical paths and promote the exploitation of the optimal solution. Experimental results in synthetic and real networks show that the PMACO algorithms are more efficient and robust than the traditional ACO algorithms, which are adaptable to solve the TSP with single or multiple objectives. Meanwhile, we further analyse the influence of parameters on the performance of the PMACO algorithms. Based on these analyses, the best values of these parameters are worked out for the TSP.
An, Guohua; Widness, John A; Mock, Donald M; Veng-Pedersen, Peter
2016-09-01
Direct measurement of red blood cell (RBC) survival in humans has improved from the original accurate but limited differential agglutination technique to the current reliable, safe, and accurate biotin method. Despite this, all of these methods are time consuming and require blood sampling over several months to determine the RBC lifespan. For situations in which RBC survival information must be obtained quickly, these methods are not suitable. With the exception of adults and infants, RBC survival has not been extensively investigated in other age groups. To address this need, we developed a novel, physiology-based mathematical model that quickly estimates RBC lifespan in healthy individuals at any age. The model is based on the assumption that the total number of RBC recirculations during the lifespan of each RBC (denoted by N max) is relatively constant for all age groups. The model was initially validated using the data from our prior infant and adult biotin-labeled red blood cell studies and then extended to the other age groups. The model generated the following estimated RBC lifespans in 2-year-old, 5-year-old, 8-year-old, and 10-year-old children: 62, 74, 82, and 86 days, respectively. We speculate that this model has useful clinical applications. For example, HbA1c testing is not reliable in identifying children with diabetes because HbA1c is directly affected by RBC lifespan. Because our model can estimate RBC lifespan in children at any age, corrections to HbA1c values based on the model-generated RBC lifespan could improve diabetes diagnosis as well as therapy in children.
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. PMID:26309390
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. PMID:26309390
NASA Technical Reports Server (NTRS)
Gassaway, J. D.; Mahmood, Q.; Trotter, J. D.
1978-01-01
A system was developed for depositing aluminum and aluminum alloys by the D.C. sputtering technique. This system which was designed for a high level of cleanliness and ion monitoring the deposition parameters during film preparation is ready for studying the deposition and annealing parameters upon double level metal preparation. The finite element method was studied for use in the computer modeling of two dimensional MOS transistor structures. An algorithm was developed for implementing a computer study which is based upon the finite difference method. The program was modified and used to calculate redistribution data for boron and phosphorous which had been predeposited by ion implantation with range and straggle conditions typical of those used at MSFC. Data were generated for 111 oriented SOS films with redistribution in N2, dry O2 and steam ambients. Data are given showing both two dimensional effects and the evolution of the junction depth, sheet resistance and integrated dose with redistribution time.
A mathematical model to optimize the drain phase in gravity-based peritoneal dialysis systems.
Akonur, Alp; Lo, Ying-Cheng; Cizman, Borut
2010-01-01
Use of patient-specific drain-phase parameters has previously been suggested to improve peritoneal dialysis (PD) adequacy. Improving management of the drain period may also help to minimize intraperitoneal volume (IPV). A typical gravity-based drain profile consists of a relatively constant initial fast-flow period, followed by a transition period and a decaying slow-flow period. That profile was modeled using the equation VD(t) = (V(D0) - Q(MAX) x t) xphi + (V(D0) x e(-alphat)) x (1 - phi), where V(D)(t) is the time-dependent dialysate volume; V(D0), the dialysate volume at the start of the drain; Q(MAX), the maximum drain flow rate; alpha, the exponential drain constant; and phi, the unit step function with respect to the flow transition. We simulated the effects of the assumed patient-specific maximum drain flow (Q(MAX)) and transition volume (psi), and the peritoneal volume percentage when transition occurs,for fixed device-specific drain parameters. Average patient transport parameters were assumed during 5-exchange therapy with 10 L of PD solution. Changes in therapy performance strongly depended on the drain parameters. Comparing 400 mL/85% with 200 mL/65% (Q(MAX/psi), drain time (7.5 min vs. 13.5 min) and IPV (2769 mL vs. 2355 mL) increased when the initial drain flow was low and the transition quick. Ultrafiltration and solute clearances remained relatively similar. Such differences were augmented up to a drain time of 22 minutes and an IPV of more than 3 L when Q(MAX) was 100 mL/min. The ability to model individual drain conditions together with water and solute transport may help to prevent patient discomfort with gravity-based PD. However, it is essential to note that practical difficulties such as displaced catheters and obstructed flow paths cause variability in drain characteristics even for the same patient, limiting the clinical applicability of this model.
Mathematical Modeling of Loop Heat Pipes
NASA Technical Reports Server (NTRS)
Kaya, Tarik; Ku, Jentung; Hoang, Triem T.; Cheung, Mark L.
1998-01-01
The primary focus of this study is to model steady-state performance of a Loop Heat Pipe (LHP). The mathematical model is based on the steady-state energy balance equations at each component of the LHP. The heat exchange between each LHP component and the surrounding is taken into account. Both convection and radiation environments are modeled. The loop operating temperature is calculated as a function of the applied power at a given loop condition. Experimental validation of the model is attempted by using two different LHP designs. The mathematical model is tested at different sink temperatures and at different elevations of the loop. Tbc comparison of the calculations and experimental results showed very good agreement (within 3%). This method proved to be a useful tool in studying steady-state LHP performance characteristics.
Mathematical models of bipolar disorder
NASA Astrophysics Data System (ADS)
Daugherty, Darryl; Roque-Urrea, Tairi; Urrea-Roque, John; Troyer, Jessica; Wirkus, Stephen; Porter, Mason A.
2009-07-01
We use limit cycle oscillators to model bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about 1% of the United States adult population. We consider two non-linear oscillator models of a single bipolar patient. In both frameworks, we begin with an untreated individual and examine the mathematical effects and resulting biological consequences of treatment. We also briefly consider the dynamics of interacting bipolar II individuals using weakly-coupled, weakly-damped harmonic oscillators. We discuss how the proposed models can be used as a framework for refined models that incorporate additional biological data. We conclude with a discussion of possible generalizations of our work, as there are several biologically-motivated extensions that can be readily incorporated into the series of models presented here.
Mathematical Model for Mapping Students' Cognitive Capability
ERIC Educational Resources Information Center
Tambunan, Hardi
2016-01-01
The quality mapping of educational unit program is important issue in education in Indonesia today in an effort to improve the quality of education. The objective of this study is to make a mathematical model to find out the map of students' capability in mathematics. It has been made a mathematical model to be used in the mapping of students'…
Identification of the noise using mathematical modelling
NASA Astrophysics Data System (ADS)
Dobeš, Josef; Kozubková, Milada; Mahdal, Miroslav
2016-03-01
In engineering applications the noisiness of a component or the whole device is a common problem. Currently, a lot of effort is put to eliminate noise of the already produced devices, to prevent generation of acoustic waves during the design of new components, or to specify the operating problems based on noisiness change. The experimental method and the mathematical modelling method belong to these identification methods. With the power of today's computers the ability to identify the sources of the noise on the mathematical modelling level is a very appreciated tool for engineers. For example, the noise itself may be generated by the vibration of the solid object, combustion, shock, fluid flow around an object or cavitation at the fluid flow in an object. For the given task generating the noise using fluid flow on the selected geometry and propagation of the acoustic waves and their subsequent identification are solved and evaluated. In this paper the principle of measurement of variables describing the fluid flow field and acoustic field are described. For the solution of fluid flow a mathematical model implemented into the CFD code is used. The mathematical modelling evaluation of the flow field is compared to the experimental data.
Mathematical model for citric acid fermentation.
Hu, J; Wu, P
1993-01-01
The kinetics for biomass proliferation, medium consumption and citric acid production in the course of citric acid fermentation were studied, and the mathematical models describing the course of citric acid fermentation were obtained in this paper. Based on the statistical data of experiment, the model was verified, and the model parameters were estimated with the results of the experiment. The results showed that the curves obtained by model calculation fitted with the ones determined by the experiments well, and the models described correctly the course of the citric acid fermentation. This is important for computer application to control the course of fermentation and realize the optimum of fermentation process.
Inquiry-Based Mathematics Curriculum Design for Young Children-Teaching Experiment and Reflection
ERIC Educational Resources Information Center
Wu, Su-Chiao; Lin, Fou-Lai
2016-01-01
A group of teacher educators and practitioners in mathematics education and early childhood education generalized a set of inquiry-based mathematics models for Taiwanese young children of ages 3-6 and designed a series of inquiry-based mathematics curriculum tasks in cultivate the children's diverse mathematical concepts and mathematical power. In…
Mathematical models of malaria - a review
2011-01-01
Mathematical models have been used to provide an explicit framework for understanding malaria transmission dynamics in human population for over 100 years. With the disease still thriving and threatening to be a major source of death and disability due to changed environmental and socio-economic conditions, it is necessary to make a critical assessment of the existing models, and study their evolution and efficacy in describing the host-parasite biology. In this article, starting from the basic Ross model, the key mathematical models and their underlying features, based on their specific contributions in the understanding of spread and transmission of malaria have been discussed. The first aim of this article is to develop, starting from the basic models, a hierarchical structure of a range of deterministic models of different levels of complexity. The second objective is to elaborate, using some of the representative mathematical models, the evolution of modelling strategies to describe malaria incidence by including the critical features of host-vector-parasite interactions. Emphasis is more on the evolution of the deterministic differential equation based epidemiological compartment models with a brief discussion on data based statistical models. In this comprehensive survey, the approach has been to summarize the modelling activity in this area so that it helps reach a wider range of researchers working on epidemiology, transmission, and other aspects of malaria. This may facilitate the mathematicians to further develop suitable models in this direction relevant to the present scenario, and help the biologists and public health personnel to adopt better understanding of the modelling strategies to control the disease PMID:21777413
Mathematical modeling of cold cap
Pokorny, Richard; Hrma, Pavel R.
2012-10-13
The ultimate goal of studies of cold cap behavior in glass melters is to increase the rate of glass processing in an energy-efficient manner. Regrettably, mathematical models, which are ideal tools for assessing the responses of melters to process parameters, have not paid adequate attention to the cold cap. In this study, we consider a cold cap resting on a pool of molten glass from which it receives a steady heat flux while temperature, velocity, and extent of conversion are functions of the position along the vertical coordinate. A one-dimensional (1D) mathematical model simulates this process by solving the differential equations for mass and energy balances with appropriate boundary conditions and constitutive relationships for material properties. The sensitivity analyses on the effects of incoming heat fluxes to the cold cap through its lower and upper boundaries show that the cold cap thickness increases as the heat flux from above increases, and decreases as the total heat flux increases. We also discuss the effects of foam, originating from batch reactions and from redox reactions in molten glass and argue that models must represent the foam layer to achieve a reliable prediction of the melting rate as a function of feed properties and melter conditions.
ERIC Educational Resources Information Center
Partnership for Assessment of Readiness for College and Careers (NJ1), 2011
2011-01-01
The PARCC Model Content Frameworks for Mathematics and ELA/Literacy have been developed through a state-led process in collaboration with members of the Common Core State Standards (CCSS) writing teams. The frameworks were reviewed by the public between August 3-31, 2011. Nearly 1,000 responses were collected, and respondents included K-12…
ERIC Educational Resources Information Center
Paterson, Judy; Sneddon, Jamie
2011-01-01
This article reports on the learning conversations between a mathematician and a mathematics educator as they worked together to change the delivery model of a third year discrete mathematics course from a traditional lecture mode to team-based learning (TBL). This change prompted the mathematician to create team tasks which increasingly focused…
A mathematical model of a computational problem solving system
NASA Astrophysics Data System (ADS)
Aris, Teh Noranis Mohd; Nazeer, Shahrin Azuan
2015-05-01
This paper presents a mathematical model based on fuzzy logic for a computational problem solving system. The fuzzy logic uses truth degrees as a mathematical model to represent vague algorithm. The fuzzy logic mathematical model consists of fuzzy solution and fuzzy optimization modules. The algorithm is evaluated based on a software metrics calculation that produces the fuzzy set membership. The fuzzy solution mathematical model is integrated in the fuzzy inference engine that predicts various solutions to computational problems. The solution is extracted from a fuzzy rule base. Then, the solutions are evaluated based on a software metrics calculation that produces the level of fuzzy set membership. The fuzzy optimization mathematical model is integrated in the recommendation generation engine that generate the optimize solution.
Lensless ghost imaging based on mathematical simulation and experimental simulation
NASA Astrophysics Data System (ADS)
Liu, Yanyan; Wang, Biyi; Zhao, Yingchao; Dong, Junzhang
2014-02-01
The differences of conventional imaging and correlated imaging are discussed in this paper. The mathematical model of lensless ghost imaging system is set up and the image of double slits is computed by mathematical simulation. The results are also testified by the experimental verification. Both the theory simulation and experimental verifications results shows that the mathematical model based on statistical optical principle are keeping consistent with real experimental results.
A Generative Model of Mathematics Learning
ERIC Educational Resources Information Center
Wittrock, M. C.
1974-01-01
The learning of mathematics is presented as a cognitive process rather than as a behavioristic one. A generative model of mathematics learning is described. Learning with understanding can occur with discovery or reception treatments. Relevant empirical research is discussed and implications for teaching mathematics as a generative process are…
On Fences, Forms and Mathematical Modeling
ERIC Educational Resources Information Center
Lege, Jerry
2009-01-01
The white picket fence is an integral component of the iconic American townscape. But, for mathematics students, it can be a mathematical challenge. Picket fences in a variety of styles serve as excellent sources to model constant, step, absolute value, and sinusoidal functions. "Principles and Standards for School Mathematics" (NCTM 2000)…
Mathematical Modeling in the Secondary School Curriculum.
ERIC Educational Resources Information Center
Swetz, Frank, Ed.; Hartzler, J. S., Ed.
Over the past 10 years, national conferences and committees investigating the state of American mathematics education have advocated an increased emphasis on problem solving and mathematical modeling situations in the secondary school curriculum. However, little effort has been made to prepare secondary school teachers to use mathematical modeling…
Mathematical model for classification of EEG signals
NASA Astrophysics Data System (ADS)
Ortiz, Victor H.; Tapia, Juan J.
2015-09-01
A mathematical model to filter and classify brain signals from a brain machine interface is developed. The mathematical model classifies the signals from the different lobes of the brain to differentiate the signals: alpha, beta, gamma and theta, besides the signals from vision, speech, and orientation. The model to develop further eliminates noise signals that occur in the process of signal acquisition. This mathematical model can be used on different platforms interfaces for rehabilitation of physically handicapped persons.
ERIC Educational Resources Information Center
Rodgers, Lindsay D.
2011-01-01
The following paper examined the effects of a new method of teaching for remedial mathematics, named the hybrid model of instruction. Due to increasing importance of high stakes testing, the study sought to determine if this method of instruction, that blends traditional teaching and problem-based learning, had different learning effects on…
Naderinezhad, Samira; Etesami, Nasrin; Poormalek Najafabady, Arefe; Ghasemi Falavarjani, Majid
2016-01-01
The effect of air temperature, air velocity, and sample shapes (circle and square with the same cross-sectional area) on kinetic drying of potato slices in a tunnel dryer was investigated experimentally and a suitable drying model was developed. The experiments of drying of potato slices were conducted at an air temperature of 45-70°C with an air velocity 1.60 and 1.81 m sec(-1). Results showed that drying temperature was the most effective parameter in the drying rate. The influence of air velocity was more profound in low temperature. The time for drying square slices was lower compared to the circle ones. Furthermore, drying data were fitted to different empirical models. Among the models, Midilli-Kucuk was the best to explain the single layer drying of potato slices. The parameters of this model were determined as functions of air velocity and temperature by multiple regression analysis for circle and square slices. Various statistical parameters were examined for evaluating the model.
Mathematical Modeling of Electronic Devices and Circuits
NASA Astrophysics Data System (ADS)
Singh, B. P.; Singh, Meena; Roy, Sanjay Kumar
2010-11-01
The necessity of modeling lies in the nature of technology and its advancement. The modeling minimizes time and cost of the process involved. The mathematical model provides an insight into the behavior of the physical system that reduces the problem to its essential characteristics. The floating admittance matrix (FAM) approach is an elegant method of mathematical modeling of electronic devices and circuits.
Students' Approaches to Learning a New Mathematical Model
ERIC Educational Resources Information Center
Flegg, Jennifer A.; Mallet, Daniel G.; Lupton, Mandy
2013-01-01
In this article, we report on the findings of an exploratory study into the experience of undergraduate students as they learn new mathematical models. Qualitative and quantitative data based around the students' approaches to learning new mathematical models were collected. The data revealed that students actively adopt three approaches to…
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. PMID:26877072
Mathematical modelling of leprosy and its control.
Blok, David J; de Vlas, Sake J; Fischer, Egil A J; Richardus, Jan Hendrik
2015-03-01
Leprosy or Hansen's disease is an infectious disease caused by the bacterium Mycobacterium leprae. The annual number of new leprosy cases registered worldwide has remained stable over the past years at over 200,000. Early case finding and multidrug therapy have not been able interrupt transmission completely. Elimination requires innovation in control and sustained commitment. Mathematical models can be used to predict the course of leprosy incidence and the effect of intervention strategies. Two compartmental models and one individual-based model have been described in the literature. Both compartmental models investigate the course of leprosy in populations and the long-term impact of control strategies. The individual-based model focusses on transmission within households and the impact of case finding among contacts of new leprosy patients. Major improvement of these models should result from a better understanding of individual differences in exposure to infection and developing leprosy after exposure. Most relevant are contact heterogeneity, heterogeneity in susceptibility and spatial heterogeneity. Furthermore, the existing models have only been applied to a limited number of countries. Parameterization of the models for other areas, in particular those with high incidence, is essential to support current initiatives for the global elimination of leprosy. Many challenges remain in understanding and dealing with leprosy. The support of mathematical models for understanding leprosy epidemiology and supporting policy decision making remains vital. PMID:25765193
Anderson, Debra F.; Cheung, Cecilia Y.
2014-01-01
Experimentation in late-gestation fetal sheep has suggested that regulation of amniotic fluid (AF) volume occurs primarily by modulating the rate of intramembranous transport of water and solutes across the amnion into underlying fetal blood vessels. In order to gain insight into intramembranous transport mechanisms, we developed a computer model that allows simulation of experimentally measured changes in AF volume and composition over time. The model included fetal urine excretion and lung liquid secretion as inflows into the amniotic compartment plus fetal swallowing and intramembranous absorption as outflows. By using experimental flows and solute concentrations for urine, lung liquid, and swallowed fluid in combination with the passive and active transport mechanisms of the intramembranous pathway, we simulated AF responses to basal conditions, intra-amniotic fluid infusions, fetal intravascular infusions, urine replacement, and tracheoesophageal occlusion. The experimental data are consistent with four intramembranous transport mechanisms acting in concert: 1) an active unidirectional bulk transport of AF with all dissolved solutes out of AF into fetal blood presumably by vesicles; 2) passive bidirectional diffusion of solutes, such as sodium and chloride, between fetal blood and AF; 3) passive bidirectional water movement between AF and fetal blood; and 4) unidirectional transport of lactate into the AF. Further, only unidirectional bulk transport is dynamically regulated. The simulations also identified areas for future study: 1) identifying intramembranous stimulators and inhibitors, 2) determining the semipermeability characteristics of the intramembranous pathway, and 3) characterizing the vesicles that are the primary mediators of intramembranous transport. PMID:25186112
Brace, Robert A; Anderson, Debra F; Cheung, Cecilia Y
2014-11-15
Experimentation in late-gestation fetal sheep has suggested that regulation of amniotic fluid (AF) volume occurs primarily by modulating the rate of intramembranous transport of water and solutes across the amnion into underlying fetal blood vessels. In order to gain insight into intramembranous transport mechanisms, we developed a computer model that allows simulation of experimentally measured changes in AF volume and composition over time. The model included fetal urine excretion and lung liquid secretion as inflows into the amniotic compartment plus fetal swallowing and intramembranous absorption as outflows. By using experimental flows and solute concentrations for urine, lung liquid, and swallowed fluid in combination with the passive and active transport mechanisms of the intramembranous pathway, we simulated AF responses to basal conditions, intra-amniotic fluid infusions, fetal intravascular infusions, urine replacement, and tracheoesophageal occlusion. The experimental data are consistent with four intramembranous transport mechanisms acting in concert: 1) an active unidirectional bulk transport of AF with all dissolved solutes out of AF into fetal blood presumably by vesicles; 2) passive bidirectional diffusion of solutes, such as sodium and chloride, between fetal blood and AF; 3) passive bidirectional water movement between AF and fetal blood; and 4) unidirectional transport of lactate into the AF. Further, only unidirectional bulk transport is dynamically regulated. The simulations also identified areas for future study: 1) identifying intramembranous stimulators and inhibitors, 2) determining the semipermeability characteristics of the intramembranous pathway, and 3) characterizing the vesicles that are the primary mediators of intramembranous transport.
A Model for Teaching College Remedial Mathematics.
ERIC Educational Resources Information Center
Friedman, Mordechai
1986-01-01
A model for teaching college remedial mathematics is presented, with information on the background, the development of the model, and the model itself, as well as a discussion of how the model is used. (MNS)
Basic Perforator Flap Hemodynamic Mathematical Model
Tao, Youlun; Ding, Maochao; Wang, Aiguo; Zhuang, Yuehong; Chang, Shi-Min; Mei, Jin; Hallock, Geoffrey G.
2016-01-01
Background: A mathematical model to help explain the hemodynamic characteristics of perforator flaps based on blood flow resistance systems within the flap will serve as a theoretical guide for the future study and clinical applications of these flaps. Methods: There are 3 major blood flow resistance network systems of a perforator flap. These were defined as the blood flow resistance of an anastomosis between artery and artery of adjacent perforasomes, between artery and vein within a perforasome, and then between vein and vein corresponding to the outflow of that perforasome. From this, a calculation could be made of the number of such blood flow resistance network systems that must be crossed for all perforasomes within a perforator flap to predict whether that arrangement would be viable. Results: The summation of blood flow resistance networks from each perforasome in a given perforator flap could predict which portions would likely survive. This mathematical model shows how this is directly dependent on the location of the vascular pedicle to the flap and whether supercharging or superdrainage maneuvers have been added. These configurations will give an estimate of the hemodynamic characteristics for the given flap design. Conclusions: This basic mathematical model can (1) conveniently determine the degree of difficulty for each perforasome within a perforator flap to survive; (2) semiquantitatively allow the calculation of basic hemodynamic parameters; and (3) allow the assessment of the pros and cons expected for each pattern of perforasomes encountered clinically based on predictable hemodynamic observations. PMID:27579238
How parrots talk: insights based on CT scans, image processing, and mathematical models
NASA Astrophysics Data System (ADS)
Patterson, Dianne K.; Pepperberg, Irene M.; Story, Brad H.; Hoffman, Eric A.
1997-05-01
Little is known about mechanisms of speech production in parrots. Recently, however, techniques for correlating vocal tract shape with vowel production in humans have become more sophisticated and we have adapted these techniques for use with parrots. We scanned two grey parrot heads with intact vocal tracts. One specimen, 'Oldbird' was fixed with its beak propped open; the second 'Youngbird' was fixed with its beak closed. Using VIDA software, we (1) established that differences in tongue and larynx positioning resulted from opening or closing the beak; and (2) obtained lengths and area functions for the trachea, glottis, pharynx, mouth, and choana for both specimens and esophageal length and area functions for the first specimen. We entered lengths and area functions into a 1D wave propagation model to determine the natural formant frequencies associated with an open versus closed beak. We also determined how manipulating lengths and area functions could affect formant frequency and relative intensity. Finally, by comparing observed grey parrot vowel formant, we predict how the parrot uses its vocal tract to produce speech.
The Activity System of School-Teaching Mathematics and Mathematical Modelling.
ERIC Educational Resources Information Center
Julie, Cyril
2002-01-01
Focuses on the activity system of school-teaching mathematics and the impact of mathematical modeling. Describes the Applications of and Modeling in School Mathematics Project (AMSMAP) which investigates teachers' mathematical modeling and its relationship to a hypothesized school mathematical modeling activity system. Discusses the notion of an…
Rybakova, Katja N; Tomaszewska, Aleksandra; van Mourik, Simon; Blom, Joke; Westerhoff, Hans V; Carlberg, Carsten; Bruggeman, Frank J
2015-01-01
Changes in transcription factor levels, epigenetic status, splicing kinetics and mRNA degradation can each contribute to changes in the mRNA dynamics of a gene. We present a novel method to identify which of these processes is changed in cells in response to external signals or as a result of a diseased state. The method employs a mathematical model, for which the kinetics of gene regulation, splicing, elongation and mRNA degradation were estimated from experimental data of transcriptional dynamics. The time-dependent dynamics of several species of adipose differentiation-related protein (ADRP) mRNA were measured in response to ligand activation of the transcription factor peroxisome proliferator-activated receptor δ (PPARδ). We validated the method by monitoring the mRNA dynamics upon gene activation in the presence of a splicing inhibitor. Our mathematical model correctly identifies splicing as the inhibitor target, despite the noise in the data.
Mathematical modeling of deformation during hot rolling
Jin, D.; Stachowiak, R.G.; Samarasekera, I.V.; Brimacombe, J.K.
1994-12-31
The deformation that occurs in the roll bite during the hot rolling of steel, particularly the strain-rate and strain distribution, has been mathematically modeled using finite-element analysis. In this paper three different finite-element models are compared with one another and with industrial measurements. The first model is an Eulerian analysis based on the flow formulation method, while the second utilizes an Updated Lagrangian approach. The third model is based on a commercially available program DEFORM which also utilizes a Lagrangian reference frame. Model predictions of strain and strain-rate distribution, particularly near the surface of the slab, are strongly influenced by the treatment of friction at the boundary and the magnitude of the friction coefficient or shear factor. Roll forces predicted by the model have been compared with industrial rolling loads from a seven-stand hot-strip mill.
Aircraft engine mathematical model - linear system approach
NASA Astrophysics Data System (ADS)
Rotaru, Constantin; Roateşi, Simona; Cîrciu, Ionicǎ
2016-06-01
This paper examines a simplified mathematical model of the aircraft engine, based on the theory of linear and nonlinear systems. The dynamics of the engine was represented by a linear, time variant model, near a nominal operating point within a finite time interval. The linearized equations were expressed in a matrix form, suitable for the incorporation in the MAPLE program solver. The behavior of the engine was included in terms of variation of the rotational speed following a deflection of the throttle. The engine inlet parameters can cover a wide range of altitude and Mach numbers.
Mathematical and computational models of plasma flows
NASA Astrophysics Data System (ADS)
Brushlinsky, K. V.
Investigations of plasma flows are of interest, firstly, due to numerous applications, and secondly, because of their general principles, which form a special branch of physics: the plasma dynamics. Numerical simulation and computation, together with theoretic and experimental methods, play an important part in these investigations. Speaking on flows, a relatively dense plasma is mentioned, so its mathematical models appertain to the fluid mechanics, i.e., they are based on the magnetohydrodynamic description of plasma. Time dependent two dimensional models of plasma flows of two wide-spread types are considered: the flows across the magnetic field and those in the magnetic field plane.
NASA Astrophysics Data System (ADS)
Paterson, Judy; Sneddon, Jamie
2011-10-01
This article reports on the learning conversations between a mathematician and a mathematics educator as they worked together to change the delivery model of a third year discrete mathematics course from a traditional lecture mode to team-based learning (TBL). This change prompted the mathematician to create team tasks which increasingly focused on what he calls the 'unspoken curriculum': mathematical thinking. We consider the ways in which the TBL model promoted and enabled this in the light of literature on mathematical thinking, sense-making and behaviours, and strongly suggest that this approach warrants more attention from the mathematics teaching community. We also discuss shifts in the mathematician's thinking about task construction as he refined the tasks to encourage students to think and behave like mathematicians.
Dermol, Janja; Miklavčič, Damijan
2014-12-01
High voltage electric pulses cause electroporation of the cell membrane. Consequently, flow of the molecules across the membrane increases. In our study we investigated possibility to predict the percentage of the electroporated cells in an inhomogeneous electric field on the basis of the experimental results obtained when cells were exposed to a homogeneous electric field. We compared and evaluated different mathematical models previously suggested by other authors for interpolation of the results (symmetric sigmoid, asymmetric sigmoid, hyperbolic tangent and Gompertz curve). We investigated the density of the cells and observed that it has the most significant effect on the electroporation of the cells while all four of the mathematical models yielded similar results. We were able to predict electroporation of cells exposed to an inhomogeneous electric field based on mathematical modeling and using mathematical formulations of electroporation probability obtained experimentally using exposure to the homogeneous field of the same density of cells. Models describing cell electroporation probability can be useful for development and presentation of treatment planning for electrochemotherapy and non-thermal irreversible electroporation.
Constructing a Model of Mathematical Literacy.
ERIC Educational Resources Information Center
Pugalee, David K.
1999-01-01
Discusses briefly the call for mathematical literacy and the need for a model that articulates the fluid and dynamic nature of this form of literacy. Presents such a model which uses two concentric circles, one depicting the four processes of mathematical literacy (representing, manipulating, reasoning, and problem solving) and enablers that…
Mathematical Modelling as a Professional Task
ERIC Educational Resources Information Center
Frejd, Peter; Bergsten, Christer
2016-01-01
Educational research literature on mathematical modelling is extensive. However, not much attention has been paid to empirical investigations of its scholarly knowledge from the perspective of didactic transposition processes. This paper reports from an interview study of mathematical modelling activities involving nine professional model…
Scaffolding Mathematical Modelling with a Solution Plan
ERIC Educational Resources Information Center
Schukajlow, Stanislaw; Kolter, Jana; Blum, Werner
2015-01-01
In the study presented in this paper, we examined the possibility to scaffold mathematical modelling with strategies. The strategies were prompted using an instrument called "solution plan" as a scaffold. The effects of this step by step instrument on mathematical modelling competency and on self-reported strategies were tested using…
NASA Astrophysics Data System (ADS)
Belyavskii, V. V.; Nikolayev, Yu. I.
2011-01-01
We propose a system for the analysis of magnetotelluric (MT) data, which makes use of the invariant characteristics of the impedance tensor such as the maximum and minimum induction curves and the phase tensor. We examine the coefficients of the appearance and normalization of principal values of the impedance tensor. By the case study for Koryakiya, it is shown that the three-dimensional (3D) mathematical modeling and the Wiese-Parkinson vectors allow one to correct the results of one-dimensional (1D) and two-dimensional (2D) inversion of MT curves. Comparison between model and observed data based on the 1D inversion of MTS curves provides a pictorial view of the distortions of MT curves and their sensitivity to the parameters of a geological cross section.
Mathematics in the Biology Classroom: A Model of Interdisciplinary Education
ERIC Educational Resources Information Center
Hodgson, Ted; Keck, Robert; Patterson, Richard; Maki, Dan
2005-01-01
This article describes an interdisciplinary course that develops essential mathematical modeling skills within an introductory biology setting. The course embodies recent recommendations regarding the need for interdisciplinary, inquiry-based mathematical preparation of undergraduates in the biological sciences. Evaluation indicates that the…
Rival approaches to mathematical modelling in immunology
NASA Astrophysics Data System (ADS)
Andrew, Sarah M.; Baker, Christopher T. H.; Bocharov, Gennady A.
2007-08-01
In order to formulate quantitatively correct mathematical models of the immune system, one requires an understanding of immune processes and familiarity with a range of mathematical techniques. Selection of an appropriate model requires a number of decisions to be made, including a choice of the modelling objectives, strategies and techniques and the types of model considered as candidate models. The authors adopt a multidisciplinary perspective.
ERIC Educational Resources Information Center
Horton, Robert M.; Leonard, William H.
2005-01-01
In science, inquiry is used as students explore important and interesting questions concerning the world around them. In mathematics, one contemporary inquiry approach is to create models that describe real phenomena. Creating mathematical models using spreadsheets can help students learn at deep levels in both science and mathematics, and give…
A Seminar in Mathematical Model-Building.
ERIC Educational Resources Information Center
Smith, David A.
1979-01-01
A course in mathematical model-building is described. Suggested modeling projects include: urban problems, biology and ecology, economics, psychology, games and gaming, cosmology, medicine, history, computer science, energy, and music. (MK)
The Effect of Teacher Beliefs on Student Competence in Mathematical Modeling--An Intervention Study
ERIC Educational Resources Information Center
Mischo, Christoph; Maaß, Katja
2013-01-01
This paper presents an intervention study whose aim was to promote teacher beliefs about mathematics and learning mathematics and student competences in mathematical modeling. In the intervention, teachers received written curriculum materials about mathematical modeling. The concept underlying the materials was based on constructivist ideas and…
Mathematical modeling of radio systems and devices
NASA Astrophysics Data System (ADS)
Borisov, Iu. P.; Tsvetnov, V. V.
Methods for developing mathematical models of radio systems and devices are presented with emphasis on the functional approach to the modeling of radio systems. In particular, attention is given to the formal description of radio systems, computer-aided modeling of radio systems, a classification of methods of radio system modeling, and methods of mathematical description of signals and noise. Specific methods discussed include the carrier method, the complex envelope method, the method of statistical equivalents, and the information parameter method.
NASA Astrophysics Data System (ADS)
Nauta, Margaret Mary
1997-09-01
This study investigated a model of predictors of career aspirations among two groups of women: students in mathematics, physical science, and engineering majors and students in biological science majors. Based on theories of women's career development and social-cognitive theories, it was hypothesized that ability, self-efficacy, positivity of role model influence, and role conflict would influence the career aspirations of these women. It was further hypothesized that the students' year in school would contribute to this model as a predictor variable. Five hundred forty-six students (representing a 71% response rate) from Iowa State University were surveyed by mail to evaluate the fit of this model. The structural equation modeling procedure revealed that the career aspirations of the two groups of women were directly predicted by self-efficacy and role conflict and indirectly predicted by year in school, academic ability, and positivity of role model influence. The model for this combined group of students represented a good overall fit, explaining 94% of the covariation among the measured variables. When the two groups of students were compared, identical models for women in the two groups revealed different relationships among the variables. In contrast to the women in math, physical science, and engineering majors, the relationships between ability and self-efficacy and between positivity of role model influence and self-efficacy were significantly lower in magnitude for women in the biological sciences group. In addition to providing a parsimonious model for conceptualizing the experiences of women in traditionally male fields, this study's findings have implications for increasing the number of women who aspire to advanced careers in these occupations. Primarily, this study suggests that interventions designed to increase the degree to which students are influenced positively by role models may increase their self-efficacy expectations and may decrease the
A mathematical model of leptin resistance.
Jacquier, Marine; Soula, Hédi A; Crauste, Fabien
2015-09-01
Obesity is often associated with leptin resistance, which leads to a physiological system with high leptin concentration but unable to respond to leptin signals and to regulate food intake. We propose a mathematical model of the leptin-leptin receptors system, based on the assumption that leptin is a regulator of its own receptor activity, and investigate its qualitative behavior. Based on current knowledge and previous models developed for body weight dynamics in rodents, the model includes the dynamics of leptin, leptin receptors and the regulation of food intake and body weight. It displays two stable equilibria, one representing a healthy state and the other one an obese and leptin resistant state. We show that a constant leptin injection can lead to leptin resistance and that a temporal variation in some parameter values influencing food intake can induce a change of equilibrium and a pathway to leptin resistance and obesity.
The mathematics of cancer: integrating quantitative models.
Altrock, Philipp M; Liu, Lin L; Michor, Franziska
2015-12-01
Mathematical modelling approaches have become increasingly abundant in cancer research. The complexity of cancer is well suited to quantitative approaches as it provides challenges and opportunities for new developments. In turn, mathematical modelling contributes to cancer research by helping to elucidate mechanisms and by providing quantitative predictions that can be validated. The recent expansion of quantitative models addresses many questions regarding tumour initiation, progression and metastases as well as intra-tumour heterogeneity, treatment responses and resistance. Mathematical models can complement experimental and clinical studies, but also challenge current paradigms, redefine our understanding of mechanisms driving tumorigenesis and shape future research in cancer biology.
Computer-Game-Based Tutoring of Mathematics
ERIC Educational Resources Information Center
Ke, Fengfeng
2013-01-01
This in-situ, descriptive case study examined the potential of implementing computer mathematics games as an anchor for tutoring of mathematics. Data were collected from middle school students at a rural pueblo school and an urban Hispanic-serving school, through in-field observation, content analysis of game-based tutoring-learning interactions,…
Mathematical Models for Library Systems Analysis.
ERIC Educational Resources Information Center
Leimkuhler, F. F.
1967-01-01
The paper reviews the research on design and operation of research libraries sponsored by the Purdue University Libraries and the Purdue School of Industrial Engineering. The use of mathematical models in library operations research is discussed. Among the mathematical methods discussed are marginal analysis or cost minimization, computer…
Mathematical Programming Models in Educational Planning.
ERIC Educational Resources Information Center
McNamara, James F.
This document begins by defining and discussing educational planning. A brief overview of mathematical programing with an explanation of the general linear programing model is then provided. Some recent applications of mathematical programing techniques to educational planning problems are reviewed, and their implications for educational research…
Mathematical Modelling in the Early School Years
ERIC Educational Resources Information Center
English, Lyn D.; Watters, James J.
2005-01-01
In this article we explore young children's development of mathematical knowledge and reasoning processes as they worked two modelling problems (the "Butter Beans Problem" and the "Airplane Problem"). The problems involve authentic situations that need to be interpreted and described in mathematical ways. Both problems include tables of data,…
Modelling Mathematical Argumentation: The Importance of Qualification
ERIC Educational Resources Information Center
Inglis, Matthew; Mejia-Ramos, Juan; Simpson, Adrian
2007-01-01
In recent years several mathematics education researchers have attempted to analyse students' arguments using a restricted form of Toulmina's ["The Uses of Argument," Cambridge University Press, UK, 1958] argumentation scheme. In this paper we report data from task-based interviews conducted with highly talented postgraduate mathematics students,…
a Discrete Mathematical Model to Simulate Malware Spreading
NASA Astrophysics Data System (ADS)
Del Rey, A. Martin; Sánchez, G. Rodriguez
2012-10-01
With the advent and worldwide development of Internet, the study and control of malware spreading has become very important. In this sense, some mathematical models to simulate malware propagation have been proposed in the scientific literature, and usually they are based on differential equations exploiting the similarities with mathematical epidemiology. The great majority of these models study the behavior of a particular type of malware called computer worms; indeed, to the best of our knowledge, no model has been proposed to simulate the spreading of a computer virus (the traditional type of malware which differs from computer worms in several aspects). In this sense, the purpose of this work is to introduce a new mathematical model not based on continuous mathematics tools but on discrete ones, to analyze and study the epidemic behavior of computer virus. Specifically, cellular automata are used in order to design such model.
Corey, Katelyn C; Noymer, Andrew
2016-01-01
Using a mathematical model with realistic demography, we analyze a large outbreak of measles in Muyinga sector in rural Burundi in 1988-1989. We generate simulated epidemic curves and age × time epidemic surfaces, which we qualitatively and quantitatively compare with the data. Our findings suggest that supplementary immunization activities (SIAs) should be used in places where routine vaccination cannot keep up with the increasing numbers of susceptible individuals resulting from population growth or from logistical problems such as cold chain maintenance. We use the model to characterize the relationship between SIA frequency and SIA age range necessary to suppress measles outbreaks. If SIAs are less frequent, they must expand their target age range.
Corey, Katelyn C; Noymer, Andrew
2016-01-01
Using a mathematical model with realistic demography, we analyze a large outbreak of measles in Muyinga sector in rural Burundi in 1988-1989. We generate simulated epidemic curves and age × time epidemic surfaces, which we qualitatively and quantitatively compare with the data. Our findings suggest that supplementary immunization activities (SIAs) should be used in places where routine vaccination cannot keep up with the increasing numbers of susceptible individuals resulting from population growth or from logistical problems such as cold chain maintenance. We use the model to characterize the relationship between SIA frequency and SIA age range necessary to suppress measles outbreaks. If SIAs are less frequent, they must expand their target age range. PMID:27672515
Corey, Katelyn C.
2016-01-01
Using a mathematical model with realistic demography, we analyze a large outbreak of measles in Muyinga sector in rural Burundi in 1988–1989. We generate simulated epidemic curves and age × time epidemic surfaces, which we qualitatively and quantitatively compare with the data. Our findings suggest that supplementary immunization activities (SIAs) should be used in places where routine vaccination cannot keep up with the increasing numbers of susceptible individuals resulting from population growth or from logistical problems such as cold chain maintenance. We use the model to characterize the relationship between SIA frequency and SIA age range necessary to suppress measles outbreaks. If SIAs are less frequent, they must expand their target age range. PMID:27672515
Corey, Katelyn C.
2016-01-01
Using a mathematical model with realistic demography, we analyze a large outbreak of measles in Muyinga sector in rural Burundi in 1988–1989. We generate simulated epidemic curves and age × time epidemic surfaces, which we qualitatively and quantitatively compare with the data. Our findings suggest that supplementary immunization activities (SIAs) should be used in places where routine vaccination cannot keep up with the increasing numbers of susceptible individuals resulting from population growth or from logistical problems such as cold chain maintenance. We use the model to characterize the relationship between SIA frequency and SIA age range necessary to suppress measles outbreaks. If SIAs are less frequent, they must expand their target age range.
Mathematical Modeling of Chemical Stoichiometry
ERIC Educational Resources Information Center
Croteau, Joshua; Fox, William P.; Varazo, Kristofoland
2007-01-01
In beginning chemistry classes, students are taught a variety of techniques for balancing chemical equations. The most common method is inspection. This paper addresses using a system of linear mathematical equations to solve for the stoichiometric coefficients. Many linear algebra books carry the standard balancing of chemical equations as an…
A Mathematical Model of Idiopathic Pulmonary Fibrosis
Hao, Wenrui; Marsh, Clay; Friedman, Avner
2015-01-01
Idiopathic pulmonary fibrosis (IPF) is a disease of unknown etiology, and life expectancy of 3-5 years after diagnosis. The incidence rate in the United States is estimated as high as 15 per 100,000 persons per year. The disease is characterized by repeated injury to the alveolar epithelium, resulting in inflammation and deregulated repair, leading to scarring of the lung tissue, resulting in progressive dyspnea and hypoxemia. The disease has no cure, although new drugs are in clinical trials and two agents have been approved for use by the FDA. In the present paper we develop a mathematical model based on the interactions among cells and proteins that are involved in the progression of the disease. The model simulations are shown to be in agreement with available lung tissue data of human patients. The model can be used to explore the efficacy of potential drugs. PMID:26348490
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.
Mathematical Model Development and Simulation Support
NASA Technical Reports Server (NTRS)
Francis, Ronald C.; Tobbe, Patrick A.
2000-01-01
This report summarizes the work performed in support of the Contact Dynamics 6DOF Facility and the Flight Robotics Lab at NASA/ MSFC in the areas of Mathematical Model Development and Simulation Support.
Cooking Potatoes: Experimentation and Mathematical Modeling.
ERIC Educational Resources Information Center
Chen, Xiao Dong
2002-01-01
Describes a laboratory activity involving a mathematical model of cooking potatoes that can be solved analytically. Highlights the microstructure aspects of the experiment. Provides the key aspects of the results, detailed background readings, laboratory procedures and data analyses. (MM)
Genetic demographic networks: Mathematical model and applications.
Kimmel, Marek; Wojdyła, Tomasz
2016-10-01
Recent improvement in the quality of genetic data obtained from extinct human populations and their ancestors encourages searching for answers to basic questions regarding human population history. The most common and successful are model-based approaches, in which genetic data are compared to the data obtained from the assumed demography model. Using such approach, it is possible to either validate or adjust assumed demography. Model fit to data can be obtained based on reverse-time coalescent simulations or forward-time simulations. In this paper we introduce a computational method based on mathematical equation that allows obtaining joint distributions of pairs of individuals under a specified demography model, each of them characterized by a genetic variant at a chosen locus. The two individuals are randomly sampled from either the same or two different populations. The model assumes three types of demographic events (split, merge and migration). Populations evolve according to the time-continuous Moran model with drift and Markov-process mutation. This latter process is described by the Lyapunov-type equation introduced by O'Brien and generalized in our previous works. Application of this equation constitutes an original contribution. In the result section of the paper we present sample applications of our model to both simulated and literature-based demographies. Among other we include a study of the Slavs-Balts-Finns genetic relationship, in which we model split and migrations between the Balts and Slavs. We also include another example that involves the migration rates between farmers and hunters-gatherers, based on modern and ancient DNA samples. This latter process was previously studied using coalescent simulations. Our results are in general agreement with the previous method, which provides validation of our approach. Although our model is not an alternative to simulation methods in the practical sense, it provides an algorithm to compute pairwise
Mathematical modeling of a rotary hearth calciner
Meisingset, H.C.; Balchen, J.G.; Fernandez, R.
1996-10-01
Calcination of petroleum coke is a thermal process where green petroleum coke is heat-treated to a pre-determined temperature. During heat treatment the associated moisture is removed and the volatile combustible matter (VCM) is released. The VCM is burned in the gas phase giving the energy to sustain the process. In addition, structural changes take place. The combination of the final calcination temperature and the residence time determine the final real density of the calcined coke. Depending on its further use, different real density requirements may arise. It is important to control the dynamics of the calcination process so that the specified final quality is achieved. A dynamic mathematical model of a Rotary Hearth Calciner is presented. The model is based on physicochemical laws involving the most important phenomena taking place and the relevant calcination parameters. The temperature profile in the coke bed is predicted which in terms is related to the real density of the coke.
Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics
Davies, Robin; Hodge, Terrell; Enyedi, Alexander
2010-01-01
We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network. PMID:20810955
Mathematical biology modules based on modern molecular biology and modern discrete mathematics.
Robeva, Raina; Davies, Robin; Hodge, Terrell; Enyedi, Alexander
2010-01-01
We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network.
Mathematical model of tumor-immune surveillance.
Mahasa, Khaphetsi Joseph; Ouifki, Rachid; Eladdadi, Amina; Pillis, Lisette de
2016-09-01
We present a novel mathematical model involving various immune cell populations and tumor cell populations. The model describes how tumor cells evolve and survive the brief encounter with the immune system mediated by natural killer (NK) cells and the activated CD8(+) cytotoxic T lymphocytes (CTLs). The model is composed of ordinary differential equations describing the interactions between these important immune lymphocytes and various tumor cell populations. Based on up-to-date knowledge of immune evasion and rational considerations, the model is designed to illustrate how tumors evade both arms of host immunity (i.e. innate and adaptive immunity). The model predicts that (a) an influx of an external source of NK cells might play a crucial role in enhancing NK-cell immune surveillance; (b) the host immune system alone is not fully effective against progression of tumor cells; (c) the development of immunoresistance by tumor cells is inevitable in tumor immune surveillance. Our model also supports the importance of infiltrating NK cells in tumor immune surveillance, which can be enhanced by NK cell-based immunotherapeutic approaches.
ERIC Educational Resources Information Center
Kartal, Ozgul; Dunya, Beyza Aksu; Diefes-Dux, Heidi A.; Zawojewski, Judith S.
2016-01-01
Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…
ERIC Educational Resources Information Center
Czocher, Jennifer A.
2016-01-01
This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…
Mathematical biodynamic feedthrough model applied to rotorcraft.
Venrooij, Joost; Mulder, Mark; Abbink, David A; van Paassen, Marinus M; Mulder, Max; van der Helm, Frans C T; Bulthoff, Heinrich H
2014-07-01
Biodynamic feedthrough (BDFT) occurs when vehicle accelerations feed through the human body and cause involuntary control inputs. This paper proposes a model to quantitatively predict this effect in rotorcraft. This mathematical BDFT model aims to fill the gap between the currently existing black box BDFT models and physical BDFT models. The model structure was systematically constructed using asymptote modeling, a procedure described in detail in this paper. The resulting model can easily be implemented in many typical rotorcraft BDFT studies, using the provided model parameters. The model's performance was validated in both the frequency and time domain. Furthermore, it was compared with several recent BDFT models. The results show that the proposed mathematical model performs better than typical black box models and is easier to parameterize and implement than a recent physical model.
ERIC Educational Resources Information Center
Pieters, Stefanie; Roeyers, Herbert; Rosseel, Yves; Van Waelvelde, Hilde; Desoete, Annemie
2015-01-01
A relationship between motor and mathematical skills has been shown by previous research. However, the question of whether subtypes can be differentiated within developmental coordination disorder (DCD) and/or mathematical learning disability (MLD) remains unresolved. In a sample of children with and without DCD and/or MLD, a data-driven…
ERIC Educational Resources Information Center
Rattanatumma, Tawachai; Puncreobutr, Vichian
2016-01-01
The objective of this study was to compare the effectiveness of teaching methods in improving Mathematics Learning Achievement and Problem solving ability of students at an international college. This is a Quasi-Experimental Research which was done the study with the first year students who have registered to study Mathematics subject at St.…
Tutorial: Mathematical Modeling of Library Systems.
ERIC Educational Resources Information Center
Rouse, William B.
1979-01-01
Discusses the purpose of mathematical models and reviews the phases of the modeling process--defining performance, representing the problem, predicting performance, estimating parameters, defining optimization criterion, determining solution, and implementing results. Reviews of book-use, resource allocation, and library network models are…
Mathematical Modelling with 9-Year-Olds
ERIC Educational Resources Information Center
English, Lyn D.; Watters, James J.
2005-01-01
This paper reports on the mathematical modelling of four classes of 4th-grade children as they worked on a modelling problem involving the selection of an Australian swimming team for the 2004 Olympics. The problem was implemented during the second year of the children's participation in a 3-year longitudinal program of modelling experiences…
Mathematical model for contemplative amoeboid locomotion.
Ueda, Kei-Ichi; Takagi, Seiji; Nishiura, Yasumasa; Nakagaki, Toshiyuki
2011-02-01
It has recently been reported that even single-celled organisms appear to be "indecisive" or "contemplative" when confronted with an obstacle. When the amoeboid organism Physarum plasmodium encounters the chemical repellent quinine during migration along a narrow agar lane, it stops for a period of time (typically several hours) and then suddenly begins to move again. When movement resumes, three distinct types of behavior are observed: The plasmodium continues forward, turns back, or migrates in both directions simultaneously. Here, we develop a continuum mathematical model of the cell dynamics of contemplative amoeboid movement. Our model incorporates the dynamics of the mass flow of the protoplasmic sol, in relation to the generation of pressure based on the autocatalytic kinetics of pseudopod formation and retraction (mainly, sol-gel conversion accompanying actin-myosin dynamics). The biological justification of the model is tested by comparing with experimentally measured spatiotemporal profiles of the cell thickness. The experimentally observed types of behavior are reproduced in simulations based on our model, and the core logic of the modeled behavior is clarified by means of nonlinear dynamics. An on-off transition between the refractory and activated states of the chemical reactivity that takes place at the leading edge of the plasmodium plays a key role in the emergence of contemplative behavior.
Mathematical model for contemplative amoeboid locomotion
NASA Astrophysics Data System (ADS)
Ueda, Kei-Ichi; Takagi, Seiji; Nishiura, Yasumasa; Nakagaki, Toshiyuki
2011-02-01
It has recently been reported that even single-celled organisms appear to be “indecisive” or “contemplative” when confronted with an obstacle. When the amoeboid organism Physarum plasmodium encounters the chemical repellent quinine during migration along a narrow agar lane, it stops for a period of time (typically several hours) and then suddenly begins to move again. When movement resumes, three distinct types of behavior are observed: The plasmodium continues forward, turns back, or migrates in both directions simultaneously. Here, we develop a continuum mathematical model of the cell dynamics of contemplative amoeboid movement. Our model incorporates the dynamics of the mass flow of the protoplasmic sol, in relation to the generation of pressure based on the autocatalytic kinetics of pseudopod formation and retraction (mainly, sol-gel conversion accompanying actin-myosin dynamics). The biological justification of the model is tested by comparing with experimentally measured spatiotemporal profiles of the cell thickness. The experimentally observed types of behavior are reproduced in simulations based on our model, and the core logic of the modeled behavior is clarified by means of nonlinear dynamics. An on-off transition between the refractory and activated states of the chemical reactivity that takes place at the leading edge of the plasmodium plays a key role in the emergence of contemplative behavior.
Incorporating neurophysiological concepts in mathematical thermoregulation models
NASA Astrophysics Data System (ADS)
Kingma, Boris R. M.; Vosselman, M. J.; Frijns, A. J. H.; van Steenhoven, A. A.; van Marken Lichtenbelt, W. D.
2014-01-01
Skin blood flow (SBF) is a key player in human thermoregulation during mild thermal challenges. Various numerical models of SBF regulation exist. However, none explicitly incorporates the neurophysiology of thermal reception. This study tested a new SBF model that is in line with experimental data on thermal reception and the neurophysiological pathways involved in thermoregulatory SBF control. Additionally, a numerical thermoregulation model was used as a platform to test the function of the neurophysiological SBF model for skin temperature simulation. The prediction-error of the SBF-model was quantified by root-mean-squared-residual (RMSR) between simulations and experimental measurement data. Measurement data consisted of SBF (abdomen, forearm, hand), core and skin temperature recordings of young males during three transient thermal challenges (1 development and 2 validation). Additionally, ThermoSEM, a thermoregulation model, was used to simulate body temperatures using the new neurophysiological SBF-model. The RMSR between simulated and measured mean skin temperature was used to validate the model. The neurophysiological model predicted SBF with an accuracy of RMSR < 0.27. Tskin simulation results were within 0.37 °C of the measured mean skin temperature. This study shows that (1) thermal reception and neurophysiological pathways involved in thermoregulatory SBF control can be captured in a mathematical model, and (2) human thermoregulation models can be equipped with SBF control functions that are based on neurophysiology without loss of performance. The neurophysiological approach in modelling thermoregulation is favourable over engineering approaches because it is more in line with the underlying physiology.
Incorporating neurophysiological concepts in mathematical thermoregulation models.
Kingma, Boris R M; Vosselman, M J; Frijns, A J H; van Steenhoven, A A; van Marken Lichtenbelt, W D
2014-01-01
Skin blood flow (SBF) is a key player in human thermoregulation during mild thermal challenges. Various numerical models of SBF regulation exist. However, none explicitly incorporates the neurophysiology of thermal reception. This study tested a new SBF model that is in line with experimental data on thermal reception and the neurophysiological pathways involved in thermoregulatory SBF control. Additionally, a numerical thermoregulation model was used as a platform to test the function of the neurophysiological SBF model for skin temperature simulation. The prediction-error of the SBF-model was quantified by root-mean-squared-residual (RMSR) between simulations and experimental measurement data. Measurement data consisted of SBF (abdomen, forearm, hand), core and skin temperature recordings of young males during three transient thermal challenges (1 development and 2 validation). Additionally, ThermoSEM, a thermoregulation model, was used to simulate body temperatures using the new neurophysiological SBF-model. The RMSR between simulated and measured mean skin temperature was used to validate the model. The neurophysiological model predicted SBF with an accuracy of RMSR < 0.27. Tskin simulation results were within 0.37 °C of the measured mean skin temperature. This study shows that (1) thermal reception and neurophysiological pathways involved in thermoregulatory SBF control can be captured in a mathematical model, and (2) human thermoregulation models can be equipped with SBF control functions that are based on neurophysiology without loss of performance. The neurophysiological approach in modelling thermoregulation is favourable over engineering approaches because it is more in line with the underlying physiology.
Mathematical Model of Evolution of Brain Parcellation.
Ferrante, Daniel D; Wei, Yi; Koulakov, Alexei A
2016-01-01
We study the distribution of brain and cortical area sizes [parcellation units (PUs)] obtained for three species: mouse, macaque, and human. We find that the distribution of PU sizes is close to lognormal. We propose the mathematical model of evolution of brain parcellation based on iterative fragmentation and specialization. In this model, each existing PU has a probability to be split that depends on PU size only. This model suggests that the same evolutionary process may have led to brain parcellation in these three species. Within our model, region-to-region (macro) connectivity is given by the outer product form. We show that most experimental data on non-zero macaque cortex macroscopic-level connections can be explained by the outer product power-law form suggested by our model (62% for area V1). We propose a multiplicative Hebbian learning rule for the macroconnectome that could yield the correct scaling of connection strengths between areas. We thus propose an evolutionary model that may have contributed to both brain parcellation and mesoscopic level connectivity in mammals. PMID:27378859
Mathematical Model of Evolution of Brain Parcellation
Ferrante, Daniel D.; Wei, Yi; Koulakov, Alexei A.
2016-01-01
We study the distribution of brain and cortical area sizes [parcellation units (PUs)] obtained for three species: mouse, macaque, and human. We find that the distribution of PU sizes is close to lognormal. We propose the mathematical model of evolution of brain parcellation based on iterative fragmentation and specialization. In this model, each existing PU has a probability to be split that depends on PU size only. This model suggests that the same evolutionary process may have led to brain parcellation in these three species. Within our model, region-to-region (macro) connectivity is given by the outer product form. We show that most experimental data on non-zero macaque cortex macroscopic-level connections can be explained by the outer product power-law form suggested by our model (62% for area V1). We propose a multiplicative Hebbian learning rule for the macroconnectome that could yield the correct scaling of connection strengths between areas. We thus propose an evolutionary model that may have contributed to both brain parcellation and mesoscopic level connectivity in mammals. PMID:27378859
Mathematical Models of Tuberculosis Reactivation and Relapse
Wallis, Robert S.
2016-01-01
The natural history of human infection with Mycobacterium tuberculosis (Mtb) is highly variable, as is the response to treatment of active tuberculosis. There is presently no direct means to identify individuals in whom Mtb infection has been eradicated, whether by a bactericidal immune response or sterilizing antimicrobial chemotherapy. Mathematical models can assist in such circumstances by measuring or predicting events that cannot be directly observed. The 3 models discussed in this review illustrate instances in which mathematical models were used to identify individuals with innate resistance to Mtb infection, determine the etiologic mechanism of tuberculosis in patients treated with tumor necrosis factor blockers, and predict the risk of relapse in persons undergoing tuberculosis treatment. These examples illustrate the power of various types of mathematic models to increase knowledge and thereby inform interventions in the present global tuberculosis epidemic. PMID:27242697
ERIC Educational Resources Information Center
Ciltas, Alper; Isik, Ahmet
2013-01-01
The aim of this study was to examine the modelling skills of prospective elementary mathematics teachers who were studying the mathematical modelling method. The research study group was composed of 35 prospective teachers. The exploratory case analysis method was used in the study. The data were obtained via semi-structured interviews and a…
Dependability breakeven point mathematical model for production - quality strategy support
NASA Astrophysics Data System (ADS)
Vilcu, Adrian; Verzea, Ion; Chaib, Rachid
2016-08-01
This paper connects the field of dependability system with the production-quality strategies through a new mathematical model based on breakeven points. The novelties consist in the identification of the parameters of dependability system which, in safety control, represents the degree to which an item is capable of performing its required function at any randomly chosen time during its specified operating period disregarding non-operation related influences, as well as the analysis of the production-quality strategies, defining a mathematical model based on a new concept - dependability breakeven points, model validation on datasets and shows the practical applicability of this new approach.
Mathematical modelling of autothermal thermophilic aerobic digesters.
Gomez, J; de Gracia, M; Ayesa, E; Garcia-Heras, J L
2007-03-01
This paper presents a new mathematical model for Autothermal Thermophilic Aerobic Digesters. The reactor has been modelled as two completely mixed volumes to separately predict the behaviour of the liquid and gaseous phases as well as the interrelation between them. The model includes biochemical transformations based on the standard Activated Sludge Models of IWA, as well as physico-chemical transformations associated with the chemical equilibria and the mass transfer between the liquid and the gaseous phases similar to those proposed in the ADM1 of IWA. An energy balance has also been included in the model in order to predict the temperature of the system. This thermal balance takes into account all those biochemical and physico-chemical transformations that entail the most relevant heat interchanges. Reactor performance has been explored by simulation in two different scenarios: in the first where it acts as the initial stage in a Dual system, and in the second where it acts as a single-stage treatment. Each scenario enabled the identification of the relevance of the different parameters. PMID:17258787
Mathematical model for predicting human vertebral fracture
NASA Technical Reports Server (NTRS)
Benedict, J. V.
1973-01-01
Mathematical model has been constructed to predict dynamic response of tapered, curved beam columns in as much as human spine closely resembles this form. Model takes into consideration effects of impact force, mass distribution, and material properties. Solutions were verified by dynamic tests on curved, tapered, elastic polyethylene beam.
Mathematical modeling relevant to closed artificial ecosystems
DeAngelis, D.L.
2003-01-01
The mathematical modeling of ecosystems has contributed much to the understanding of the dynamics of such systems. Ecosystems can include not only the natural variety, but also artificial systems designed and controlled by humans. These can range from agricultural systems and activated sludge plants, down to mesocosms, microcosms, and aquaria, which may have practical or research applications. Some purposes may require the design of systems that are completely closed, as far as material cycling is concerned. In all cases, mathematical modeling can help not only to understand the dynamics of the system, but also to design methods of control to keep the system operating in desired ranges. This paper reviews mathematical modeling relevant to the simulation and control of closed or semi-closed artificial ecosystems designed for biological production and recycling in applications in space. Published by Elsevier Science Ltd on behalf of COSPAR.
A Taxonomy-Based Approach to Shed Light on the Babel of Mathematical Models for Rice Simulation
NASA Technical Reports Server (NTRS)
Confalonieri, Roberto; Bregaglio, Simone; Adam, Myriam; Ruget, Francoise; Li, Tao; Hasegawa, Toshihiro; Yin, Xinyou; Zhu, Yan; Boote, Kenneth; Buis, Samuel; Ruane, Alex C.
2016-01-01
For most biophysical domains, differences in model structures are seldom quantified. Here, we used a taxonomy-based approach to characterise thirteen rice models. Classification keys and binary attributes for each key were identified, and models were categorised into five clusters using a binary similarity measure and the unweighted pair-group method with arithmetic mean. Principal component analysis was performed on model outputs at four sites. Results indicated that (i) differences in structure often resulted in similar predictions and (ii) similar structures can lead to large differences in model outputs. User subjectivity during calibration may have hidden expected relationships between model structure and behaviour. This explanation, if confirmed, highlights the need for shared protocols to reduce the degrees of freedom during calibration, and to limit, in turn, the risk that user subjectivity influences model performance.
Mathematical Modeling of Electrochemical Flow Capacitors
Hoyt, NC; Wainright, JS; Savinell, RF
2015-01-13
Electrochemical flow capacitors (EFCs) for grid-scale energy storage are a new technology that is beginning to receive interest. Prediction of the expected performance of such systems is important as modeling can be a useful avenue in the search for design improvements. Models based off of circuit analogues exist to predict EFC performance, but these suffer from deficiencies (e.g. a multitude of fitting constants that are required and the ability to analyze only one spatial direction at a time). In this paper mathematical models based off of three-dimensional macroscopic balances (similar to models for porous electrodes) are reported. Unlike existing three-dimensional porous electrode-based approaches for modeling slurry electrodes, advection (i.e., transport associated with bulk fluid motion) of the overpotential is included in order to account for the surface charge at the interface between flowing particles and the electrolyte. Doing so leads to the presence of overpotential boundary layers that control the performance of EFCs. These models were used to predict the charging behavior of an EFC under both flowing and non-flowing conditions. Agreement with experimental data was good, including proper prediction of the steady-state current that is achieved during charging of a flowing EFC. (C) The Author(s) 2015. Published by ECS. This is an open access article distributed under the terms of the Creative Commons Attribution Non-Commercial No Derivatives 4.0 License (CC BY-NC-ND, http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial reuse, distribution, and reproduction in any medium, provided the original work is not changed in any way and is properly cited. For permission for commercial reuse, please email: oa@electrochem.org. All rights reserved.
Voters' Fickleness:. a Mathematical Model
NASA Astrophysics Data System (ADS)
Boccara, Nino
This paper presents a spatial agent-based model in order to study the evolution of voters' choice during the campaign of a two-candidate election. Each agent, represented by a point inside a two-dimensional square, is under the influence of its neighboring agents, located at a Euclidean distance less than or equal to d, and under the equal influence of both candidates seeking to win its support. Moreover, each agent located at time t at a given point moves at the next timestep to a randomly selected neighboring location distributed normally around its position at time t. Besides their location in space, agents are characterized by their level of awareness, a real a ∈ [0, 1], and their opinion ω ∈ {-1, 0, +1}, where -1 and +1 represent the respective intentions to cast a ballot in favor of one of the two candidates while 0 indicates either disinterest or refusal to vote. The essential purpose of the paper is qualitative; its aim is to show that voters' fickleness is strongly correlated to the level of voters' awareness and the efficiency of candidates' propaganda.
Cocaine addiction and personality: a mathematical model.
Caselles, Antonio; Micó, Joan C; Amigó, Salvador
2010-05-01
The existence of a close relation between personality and drug consumption is recognized, but the corresponding causal connection is not well known. Neither is it well known whether personality exercises an influence predominantly at the beginning and development of addiction, nor whether drug consumption produces changes in personality. This paper presents a dynamic mathematical model of personality and addiction based on the unique personality trait theory (UPTT) and the general modelling methodology. This model attempts to integrate personality, the acute effect of drugs, and addiction. The UPTT states the existence of a unique trait of personality called extraversion, understood as a dimension that ranges from impulsive behaviour and sensation-seeking (extravert pole) to fearful and anxious behaviour (introvert pole). As a consequence of drug consumption, the model provides the main patterns of extraversion dynamics through a system of five coupled differential equations. It combines genetic extraversion, as a steady state, and dynamic extraversion in a unique variable measured on the hedonic scale. The dynamics of this variable describes the effects of stimulant drugs on a short-term time scale (typical of the acute effect); while its mean time value describes the effects of stimulant drugs on a long-term time scale (typical of the addiction effect). This understanding may help to develop programmes of prevention and intervention in drug misuse. PMID:20030966
Mathematical modelling of animate and intentional motion.
Rittscher, Jens; Blake, Andrew; Hoogs, Anthony; Stein, Gees
2003-01-01
Our aim is to enable a machine to observe and interpret the behaviour of others. Mathematical models are employed to describe certain biological motions. The main challenge is to design models that are both tractable and meaningful. In the first part we will describe how computer vision techniques, in particular visual tracking, can be applied to recognize a small vocabulary of human actions in a constrained scenario. Mainly the problems of viewpoint and scale invariance need to be overcome to formalize a general framework. Hence the second part of the article is devoted to the question whether a particular human action should be captured in a single complex model or whether it is more promising to make extensive use of semantic knowledge and a collection of low-level models that encode certain motion primitives. Scene context plays a crucial role if we intend to give a higher-level interpretation rather than a low-level physical description of the observed motion. A semantic knowledge base is used to establish the scene context. This approach consists of three main components: visual analysis, the mapping from vision to language and the search of the semantic database. A small number of robust visual detectors is used to generate a higher-level description of the scene. The approach together with a number of results is presented in the third part of this article. PMID:12689374
Genetic demographic networks: Mathematical model and applications.
Kimmel, Marek; Wojdyła, Tomasz
2016-10-01
Recent improvement in the quality of genetic data obtained from extinct human populations and their ancestors encourages searching for answers to basic questions regarding human population history. The most common and successful are model-based approaches, in which genetic data are compared to the data obtained from the assumed demography model. Using such approach, it is possible to either validate or adjust assumed demography. Model fit to data can be obtained based on reverse-time coalescent simulations or forward-time simulations. In this paper we introduce a computational method based on mathematical equation that allows obtaining joint distributions of pairs of individuals under a specified demography model, each of them characterized by a genetic variant at a chosen locus. The two individuals are randomly sampled from either the same or two different populations. The model assumes three types of demographic events (split, merge and migration). Populations evolve according to the time-continuous Moran model with drift and Markov-process mutation. This latter process is described by the Lyapunov-type equation introduced by O'Brien and generalized in our previous works. Application of this equation constitutes an original contribution. In the result section of the paper we present sample applications of our model to both simulated and literature-based demographies. Among other we include a study of the Slavs-Balts-Finns genetic relationship, in which we model split and migrations between the Balts and Slavs. We also include another example that involves the migration rates between farmers and hunters-gatherers, based on modern and ancient DNA samples. This latter process was previously studied using coalescent simulations. Our results are in general agreement with the previous method, which provides validation of our approach. Although our model is not an alternative to simulation methods in the practical sense, it provides an algorithm to compute pairwise
Primary School Pre-Service Mathematics Teachers' Views on Mathematical Modeling
ERIC Educational Resources Information Center
Karali, Diren; Durmus, Soner
2015-01-01
The current study aimed to identify the views of pre-service teachers, who attended a primary school mathematics teaching department but did not take mathematical modeling courses. The mathematical modeling activity used by the pre-service teachers was developed with regards to the modeling activities utilized by Lesh and Doerr (2003) in their…
Mathematical modeling plasma transport in tokamaks
Quiang, Ji
1995-12-31
In this work, the author applied a systematic calibration, validation and application procedure based on the methodology of mathematical modeling to international thermonuclear experimental reactor (ITER) ignition studies. The multi-mode plasma transport model used here includes a linear combination of drift wave branch and ballooning branch instabilities with two a priori uncertain constants to account for anomalous plasma transport in tokamaks. A Bayesian parameter estimation method is used including experimental calibration error/model offsets and error bar rescaling factors to determine the two uncertain constants in the transport model with quantitative confidence level estimates for the calibrated parameters, which gives two saturation levels of instabilities. This method is first tested using a gyroBohm multi-mode transport model with a pair of DIII-D discharge experimental data, and then applied to calibrating a nominal multi-mode transport model against a broad database using twelve discharges from seven different tokamaks. The calibrated transport model is then validated on five discharges from JT-60 with no adjustable constants. The results are in a good agreement with experimental data. Finally, the resulting class of multi-mode tokamak plasma transport models is applied to the transport analysis of the ignition probability in a next generation machine, ITER. A reference simulation of basic ITER engineering design activity (EDA) parameters shows that a self-sustained thermonuclear burn with 1.5 GW output power can be achieved provided that impurity control makes radiative losses sufficiently small at an average plasma density of 1.2 X 10{sup 20}/m{sup 3} with 50 MW auxiliary heating. The ignition probability of ITER for the EDA parameters, can be formally as high as 99.9% in the present context. The same probability for concept design activity (CDA) parameters of ITER, which has smaller size and lower current, is only 62.6%.
NASA Astrophysics Data System (ADS)
Wardono; Waluya, S. B.; Mariani, Scolastika; Candra D, S.
2016-02-01
This study aims to find out that there are differences in mathematical literacy ability in content Change and Relationship class VII Junior High School 19, Semarang by Problem Based Learning (PBL) model with an Indonesian Realistic Mathematics Education (called Pendidikan Matematika Realistik Indonesia or PMRI in Indonesia) approach assisted Elearning Edmodo, PBL with a PMRI approach, and expository; to know whether the group of students with learning PBL models with PMRI approach and assisted E-learning Edmodo can improve mathematics literacy; to know that the quality of learning PBL models with a PMRI approach assisted E-learning Edmodo has a good category; to describe the difficulties of students in working the problems of mathematical literacy ability oriented PISA. This research is a mixed methods study. The population was seventh grade students of Junior High School 19, Semarang Indonesia. Sample selection is done by random sampling so that the selected experimental class 1, class 2 and the control experiment. Data collected by the methods of documentation, tests and interviews. From the results of this study showed average mathematics literacy ability of students in the group PBL models with a PMRI approach assisted E-learning Edmodo better than average mathematics literacy ability of students in the group PBL models with a PMRI approach and better than average mathematics literacy ability of students in the expository models; Mathematics literacy ability in the class using the PBL model with a PMRI approach assisted E-learning Edmodo have increased and the improvement of mathematics literacy ability is higher than the improvement of mathematics literacy ability of class that uses the model of PBL learning with PMRI approach and is higher than the improvement of mathematics literacy ability of class that uses the expository models; The quality of learning using PBL models with a PMRI approach assisted E-learning Edmodo have very good category.
ERIC Educational Resources Information Center
Carrejo, David J.; Marshall, Jill
2007-01-01
This paper focuses on the construction, development, and use of mathematical models by prospective science and mathematics teachers enrolled in a university physics course. By studying their involvement in an inquiry-based, experimental approach to learning kinematics, we address a fundamental question about the meaning and role of abstraction in…
The (Mathematical) Modeling Process in Biosciences
Torres, Nestor V.; Santos, Guido
2015-01-01
In this communication, we introduce a general framework and discussion on the role of models and the modeling process in the field of biosciences. The objective is to sum up the common procedures during the formalization and analysis of a biological problem from the perspective of Systems Biology, which approaches the study of biological systems as a whole. We begin by presenting the definitions of (biological) system and model. Particular attention is given to the meaning of mathematical model within the context of biology. Then, we present the process of modeling and analysis of biological systems. Three stages are described in detail: conceptualization of the biological system into a model, mathematical formalization of the previous conceptual model and optimization and system management derived from the analysis of the mathematical model. All along this work the main features and shortcomings of the process are analyzed and a set of rules that could help in the task of modeling any biological system are presented. Special regard is given to the formative requirements and the interdisciplinary nature of this approach. We conclude with some general considerations on the challenges that modeling is posing to current biology. PMID:26734063
Turbulent motion of mass flows. Mathematical modeling
NASA Astrophysics Data System (ADS)
Eglit, Margarita; Yakubenko, Alexander; Yakubenko, Tatiana
2016-04-01
New mathematical models for unsteady turbulent mass flows, e.g., dense snow avalanches and landslides, are presented. Such models are important since most of large scale flows are turbulent. In addition to turbulence, the two other important points are taken into account: the entrainment of the underlying material by the flow and the nonlinear rheology of moving material. The majority of existing models are based on the depth-averaged equations and the turbulent character of the flow is accounted by inclusion of drag proportional to the velocity squared. In this paper full (not depth-averaged) equations are used. It is assumed that basal entrainment takes place if the bed friction equals the shear strength of the underlying layer (Issler D, M. Pastor Peréz. 2011). The turbulent characteristics of the flow are calculated using a three-parameter differential model (Lushchik et al., 1978). The rheological properties of moving material are modeled by one of the three types of equations: 1) Newtonian fluid with high viscosity, 2) power-law fluid and 3) Bingham fluid. Unsteady turbulent flows down long homogeneous slope are considered. The flow dynamical parameters and entrainment rate behavior in time as well as their dependence on properties of moving and underlying materials are studied numerically. REFERENCES M.E. Eglit and A.E. Yakubenko, 2014. Numerical modeling of slope flows entraining bottom material. Cold Reg. Sci. Technol., 108, 139-148 Margarita E. Eglit and Alexander E. Yakubenko, 2016. The effect of bed material entrainment and non-Newtonian rheology on dynamics of turbulent slope flows. Fluid Dynamics, 51(3) Issler D, M. Pastor Peréz. 2011. Interplay of entrainment and rheology in snow avalanches; a numerical study. Annals of Glaciology, 52(58), 143-147 Lushchik, V.G., Paveliev, A.A. , and Yakubenko, A.E., 1978. Three-parameter model of shear turbulence. Fluid Dynamics, 13, (3), 350-362
Biologically based dose-response (BBDR) models comprise one way to incorporate mechanistic information into a dose-response assessment to be used for risk assessments. The chemotherapeutic drug 5-fluorouracil (5-FU) has been used as a prototypic compound for the construction of ...
On Mathematical Modeling Of Quantum Systems
Achuthan, P.; Narayanankutty, Karuppath
2009-07-02
The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantum mechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantum mechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM, though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well.
Mathematical Models of Cardiac Pacemaking Function
NASA Astrophysics Data System (ADS)
Li, Pan; Lines, Glenn T.; Maleckar, Mary M.; Tveito, Aslak
2013-10-01
Over the past half century, there has been intense and fruitful interaction between experimental and computational investigations of cardiac function. This interaction has, for example, led to deep understanding of cardiac excitation-contraction coupling; how it works, as well as how it fails. However, many lines of inquiry remain unresolved, among them the initiation of each heartbeat. The sinoatrial node, a cluster of specialized pacemaking cells in the right atrium of the heart, spontaneously generates an electro-chemical wave that spreads through the atria and through the cardiac conduction system to the ventricles, initiating the contraction of cardiac muscle essential for pumping blood to the body. Despite the fundamental importance of this primary pacemaker, this process is still not fully understood, and ionic mechanisms underlying cardiac pacemaking function are currently under heated debate. Several mathematical models of sinoatrial node cell membrane electrophysiology have been constructed as based on different experimental data sets and hypotheses. As could be expected, these differing models offer diverse predictions about cardiac pacemaking activities. This paper aims to present the current state of debate over the origins of the pacemaking function of the sinoatrial node. Here, we will specifically review the state-of-the-art of cardiac pacemaker modeling, with a special emphasis on current discrepancies, limitations, and future challenges.
On Mathematical Modeling Of Quantum Systems
NASA Astrophysics Data System (ADS)
Achuthan, P.; Narayanankutty, Karuppath
2009-07-01
The world of physical systems at the most fundamental levels is replete with efficient, interesting models possessing sufficient ability to represent the reality to a considerable extent. So far, quantum mechanics (QM) forming the basis of almost all natural phenomena, has found beyond doubt its intrinsic ingenuity, capacity and robustness to stand the rigorous tests of validity from and through appropriate calculations and experiments. No serious failures of quantum mechanical predictions have been reported, yet. However, Albert Einstein, the greatest theoretical physicist of the twentieth century and some other eminent men of science have stated firmly and categorically that QM, though successful by and large, is incomplete. There are classical and quantum reality models including those based on consciousness. Relativistic quantum theoretical approaches to clearly understand the ultimate nature of matter as well as radiation have still much to accomplish in order to qualify for a final theory of everything (TOE). Mathematical models of better, suitable character as also strength are needed to achieve satisfactory explanation of natural processes and phenomena. We, in this paper, discuss some of these matters with certain apt illustrations as well.
Two Mathematical Models of Nonlinear Vibrations
NASA Technical Reports Server (NTRS)
Brugarolas, Paul; Bayard, David; Spanos, John; Breckenridge, William
2007-01-01
Two innovative mathematical models of nonlinear vibrations, and methods of applying them, have been conceived as byproducts of an effort to develop a Kalman filter for highly precise estimation of bending motions of a large truss structure deployed in outer space from a space-shuttle payload bay. These models are also applicable to modeling and analysis of vibrations in other engineering disciplines, on Earth as well as in outer space.
A mathematical model of the CH-53 helicopter
NASA Technical Reports Server (NTRS)
Sturgeon, W. R.; Phillips, J. D.
1980-01-01
A mathematical model suitable for real time simulation of the CH-53 helicopter is presented. This model, which is based on modified nonlinear classical rotor theory and nonlinear fuselage aerodynamics, will be used to support terminal-area guidance and navigation studies on a fixed-base simulator. Validation is achieved by comparing the model response with that of a similar aircraft and by a qualitative comparison of the handling characteristics made by experienced pilots.
Introduction to mathematical models and methods
Siddiqi, A. H.; Manchanda, P.
2012-07-17
Some well known mathematical models in the form of partial differential equations representing real world systems are introduced along with fundamental concepts of Image Processing. Notions such as seismic texture, seismic attributes, core data, well logging, seismic tomography and reservoirs simulation are discussed.
Wheels, Cranks, and Cams: An Animated Spreadsheet-Based Mathematical Model of a Four-Stroke Engine.
ERIC Educational Resources Information Center
Callender, J. T.; Jackson, R.
1998-01-01
Analyzes the mathematics of rotational and translational motion and how one can influence the other in the context of cams and cranks. Describes how the individual components can be brought together to simulate a four-stroke engine and how the engine animates again using the same simple macro. (Author/ASK)
Some mathematical tools for a modeller's workbench
NASA Technical Reports Server (NTRS)
Cohen, E.
1984-01-01
The development of a mathematical software tools in workbench environment to model related objects more straightforward is outlined. A computer model from informal drawings and a plastic model of a helicopter is discussed. Lofting was the predominant, characteristic modelling technique. Ships and airplane designs use lofting as a technique because they have defined surfaces, (hulls and fuselages) from vertical station cuts perpendicular to the vertical center plane defining the major axis of reflective symmetry. A turbine blade from a jet engine was modelled in this way. The aerodynamic portion and the root comes from different paradigms. The union of these two parts into a coherent model is shown.
Mathematical model of the SH-3G helicopter
NASA Technical Reports Server (NTRS)
Phillips, J. D.
1982-01-01
A mathematical model of the Sikorsky SH-3G helicopter based on classical nonlinear, quasi-steady rotor theory was developed. The model was validated statically and dynamically by comparison with Navy flight-test data. The model incorporates ad hoc revisions which address the ideal assumptions of classical rotor theory and improve the static trim characteristics to provide a more realistic simulation, while retaining the simplicity of the classical model.
ERIC Educational Resources Information Center
Bukova-Guzel, Esra
2011-01-01
This study examines the approaches displayed by pre-service mathematics teachers in their experiences of constructing mathematical modelling problems and the extent to which they perform the modelling process when solving the problems they construct. This case study was carried out with 35 pre-service teachers taking the Mathematical Modelling…
Mathematical challenges in glacier modeling (Invited)
NASA Astrophysics Data System (ADS)
jouvet, G.
2013-12-01
Many of Earth's glaciers are currently shrinking and it is expected that this trend will continue as global warming progresses. To virtually reproduce the evolution of glaciers and finally to predict their future, one needs to couple models of different disciplines and scales. Indeed, the slow motion of ice is described by fluid mechanics equations while the daily snow precipitations and melting are described by hydrological and climatic models. Less visible, applied mathematics are essential to run such a coupling at two different levels: by solving numerically the underlying equations and by seeking parameters using optimisation methods. This talk aims to make visible the role of mathematics in this area. I will first present a short educational film I have made for the "Mathematics of Planet Earth 2013", which is an introduction to the topic. To go further, solving the mechanical model of ice poses several mathematical challenges due to the complexity of the equations and geometries of glaciers. Then, I will describe some strategies to deal with such difficulties and design robust simulation tools. Finally, I will present some simulations of the largest glacier of the European Alps, the Aletsch glacier. As a less unexpected application, I will show how these results allowed us to make a major advance in a police investigation started in 1926.
NASA Astrophysics Data System (ADS)
Smith, Erick; Haarer, Shawn; Confrey, Jere
Although reform efforts in mathematics education have called for more diverse views of mathematics, there have been few studies of how mathematics is used and takes form in practices outside of mathematics itself. Thus legitimate diverse models have largely been missing in education. This study attempts to broaden our understanding of mathematics by investigating how applied mathematicians and biologists, working together to construct dynamic population models, understand these models within the framework of their perspective practices, that is how these models take on a role as ''boundary objects'' between the two practices. By coming to understand how these models function within the practice of biology, the paper suggests that mathematics educators have the opportunity both to reevaluate their own assumptions about modeling and to build an understanding of the dialectic process necessary for these models to develop an epistemological basis that is shared across practices. Investigating this dialectic process is both important and missing in most mathematical classrooms.1
ERIC Educational Resources Information Center
Bukova-Guzel, Esra; Canturk-Gunhan, Berna
2011-01-01
The purpose of the study is to determine prospective mathematics teachers' views about using computer-based instructional materials in constructing mathematical concepts and to reveal how the sample computer-based instructional materials for different mathematical concepts altered their views. This is a qualitative study involving twelve…
A Mathematical Model for Suppression Subtractive Hybridization
Gadgil, Chetan; Rink, Anette; Beattie, Craig
2002-01-01
Suppression subtractive hybridization (SSH) is frequently used to unearth differentially expressed genes on a whole-genome scale. Its versatility is based on combining cDNA library subtraction and normalization, which allows the isolation of sequences of varying degrees of abundance and differential expression. SSH is a complex process with many adjustable parameters that affect the outcome of gene isolation.We present a mathematical model of SSH based on DNA hybridization kinetics for assessing the effect of various parameters to facilitate its optimization. We derive an equation for the probability that a particular differentially expressed species is successfully isolated and use this to quantify the effect of the following parameters related to the cDNA sample: (a) mRNA abundance; (b) partial sequence complementarity to other species; and (3) degree of differential expression. We also evaluate the effect of parameters related to the process, including: (a) reaction times; and (b) extent of driver excess used in the two hybridization reactions. The optimum set of process parameters for successful isolation of differentially expressed species depends on transcript abundance. We show that the reaction conditions have a significant effect on the occurrence of false-positives and formulate strategies to isolate specific subsets of differentially expressed genes. We also quantify the effect of non-specific hybridization on the false-positive results and present strategies for spiking cDNA sequences to address this problem. PMID:18629052
Zhang, Pei; Li, Yi
2016-03-01
Existing prediction models of soil organic matter content (SOC) are restricted by some factors, such as sampling scale, soil type and spectral parameters of samples. Therefore, it is necessary to make a comparative analysis on larger scales to build a quantitative model with better feasibility and greater accuracy. A total of 225 soil samples were collected in an extensive region of the upper reaches of Heihe river basin. SOC and spectral reflectance were being measured. All the samples were divided into 2 subsets--a modeling subset (180 samples) and a validation subset (45 samples). Six indices were obtained through transformation of soil spectral reflectance (R), continuum-removal (CR), reciprocal (REC), logarithm of reciprocal (LR), first-order differential (FDR) and Kubelka-Munck transformation coefficient (K-M). To build the mathematical model of SOC with 12 spectral indices, two methods, i. e., stepwise linear regression and partial least-square regression were used based on the modeling subset, respectively; the validation subset is used for model evaluation. The results indicated that, (1) Regardless of different modeling methods, model between SOC and LR index was always the best among the 6 reflectance-related indices. LR was the best index for predicting SOC; (2) For the model based on the LR index, the accuracy of model using partial least-square regression method was better than that using stepwise linear regression method; (3) 225 samples were compared to verify the former available published SOC model. Both the predicted and measured values passed the mean value t-test, and the Pearson correlation coefficient reached 0.826. It shows that local prediction model can be applied to the research of predicting SOC in the larger scale.
Asymmetrical passive intermodulation distortions of memristors with mathematical behavior models
NASA Astrophysics Data System (ADS)
Wu, Yongle; Jin, Qiuyan; Wang, Weimin; Liu, Yuanan
2016-10-01
A rigorous mathematical explanation and accurate numerical prediction for asymmetrical passive intermodulation (PIM) distortions of memristors are investigated in this article. This theoretical explanation is based on behavior models of memristors representing the interrelation between terminated voltages and currents. The simulated single-tone and two-tone signal spectrums for extremely low-frequency (Hz) and microwave (GHz) applications verify our proposed mathematical approach and the new discovery of asymmetrical PIM distortions. This presented method provides an innovative choice to model and simulate the external performance of circuits and systems with asymmetrical PIM distortions in the future.
Mathematical Modelling of Turbidity Currents
NASA Astrophysics Data System (ADS)
Fay, G. L.; Fowler, A.; Howell, P.
2011-12-01
A turbidity current is a submarine sediment flow which propagates downslope through the ocean into the deep sea. Turbidity currents can occur randomly and without much warning and consequently are hard to observe and measure. The driving force in a turbidity current is the presence of sediment in the current - gravity acts on the sediment in suspension, causing it to move downstream through the ocean water. A phenomenon known as ignition or autosuspension has been observed in turbidity currents in submarine canyons, and it occurs when a current travelling downslope gathers speed as it erodes sediment from the sea floor in a self-reinforcing cycle. Using the turbidity current model of Parker et al. (Journal of Fluid Mechanics, 1986) we investigate the evolution of a 1-D turbidity current as it moves downstream. To seek a better understanding of the dynamics of flow as the current evolves in space and time, we present analytical results alongside computed numerical solutions, incorporating entrainment of water and erosion and deposition of sediment. We consider varying slope functions and inlet conditions and attempt to predict when the current will become extinct. We examine currents which are in both supercritical and subcritical flow regimes and consider the dynamics of the flow as the current switches regime.
The stability of colorectal cancer mathematical models
NASA Astrophysics Data System (ADS)
Khairudin, Nur Izzati; Abdullah, Farah Aini
2013-04-01
Colorectal cancer is one of the most common types of cancer. To better understand about the kinetics of cancer growth, mathematical models are used to provide insight into the progression of this natural process which enables physicians and oncologists to determine optimal radiation and chemotherapy schedules and develop a prognosis, both of which are indispensable for treating cancer. This thesis investigates the stability of colorectal cancer mathematical models. We found that continuous saturating feedback is the best available model of colorectal cancer growth. We also performed stability analysis. The result shows that cancer progress in sequence of genetic mutations or epigenetic which lead to a very large number of cells population until become unbounded. The cell population growth initiate and its saturating feedback is overcome when mutation changes causing the net per-capita growth rate of stem or transit cells exceed critical threshold.
Mathematical modeling of biomass fuels formation process.
Gaska, Krzysztof; Wandrasz, Andrzej J
2008-01-01
The increasing demand for thermal and electric energy in many branches of industry and municipal management accounts for a drastic diminishing of natural resources (fossil fuels). Meanwhile, in numerous technical processes, a huge mass of wastes is produced. A segregated and converted combustible fraction of the wastes, with relatively high calorific value, may be used as a component of formed fuels. The utilization of the formed fuel components from segregated groups of waste in associated processes of co-combustion with conventional fuels causes significant savings resulting from partial replacement of fossil fuels, and reduction of environmental pollution resulting directly from the limitation of waste migration to the environment (soil, atmospheric air, surface and underground water). The realization of technological processes with the utilization of formed fuel in associated thermal systems should be qualified by technical criteria, which means that elementary processes as well as factors of sustainable development, from a global viewpoint, must not be disturbed. The utilization of post-process waste should be preceded by detailed technical, ecological and economic analyses. In order to optimize the mixing process of fuel components, a mathematical model of the forming process was created. The model is defined as a group of data structures which uniquely identify a real process and conversion of this data in algorithms based on a problem of linear programming. The paper also presents the optimization of parameters in the process of forming fuels using a modified simplex algorithm with a polynomial worktime. This model is a datum-point in the numerical modeling of real processes, allowing a precise determination of the optimal elementary composition of formed fuels components, with assumed constraints and decision variables of the task.
Mathematical modeling of the aerodynamic characteristics in flight dynamics
NASA Technical Reports Server (NTRS)
Tobak, M.; Chapman, G. T.; Schiff, L. B.
1984-01-01
Basic concepts involved in the mathematical modeling of the aerodynamic response of an aircraft to arbitrary maneuvers are reviewed. The original formulation of an aerodynamic response in terms of nonlinear functionals is shown to be compatible with a derivation based on the use of nonlinear functional expansions. Extensions of the analysis through its natural connection with ideas from bifurcation theory are indicated.
Mathematical models of regulatory mechanisms of sleep-wake rhythms.
Nakao, M; Karashima, A; Katayama, N
2007-05-01
Studies of regulatory mechanisms of sleep-wake rhythms have benefited greatly from mathematical modeling. There are two major frameworks of modeling: one integrates homeostatic and circadian regulations and the other consists of multiple interacting oscillators. In this article, model constructions based on these respective frameworks and their characteristics are reviewed. The two-process model and the multioscillator model are explained in detail. An appropriate mathematical abstraction is also shown to provide a viewpoint unifying the model structures, which might seem to be distinct. Recently acquired knowledge of neural regulatory mechanisms of sleep-wake rhythm has prompted modeling at the neural network level. Such a detailed model is also reviewed, and could be used to explore a possible neural mechanism underlying a pathological state of sleep-wake rhythm. PMID:17364138
Antioxidant Capacity: Experimental Determination by EPR Spectroscopy and Mathematical Modeling.
Polak, Justyna; Bartoszek, Mariola; Chorążewski, Mirosław
2015-07-22
A new method of determining antioxidant capacity based on a mathematical model is presented in this paper. The model was fitted to 1000 data points of electron paramagnetic resonance (EPR) spectroscopy measurements of various food product samples such as tea, wine, juice, and herbs with Trolox equivalent antioxidant capacity (TEAC) values from 20 to 2000 μmol TE/100 mL. The proposed mathematical equation allows for a determination of TEAC of food products based on a single EPR spectroscopy measurement. The model was tested on the basis of 80 EPR spectroscopy measurements of herbs, tea, coffee, and juice samples. The proposed model works for both strong and weak antioxidants (TEAC values from 21 to 2347 μmol TE/100 mL). The determination coefficient between TEAC values obtained experimentally and TEAC values calculated with proposed mathematical equation was found to be R(2) = 0.98. Therefore, the proposed new method of TEAC determination based on a mathematical model is a good alternative to the standard EPR method due to its being fast, accurate, inexpensive, and simple to perform. PMID:26120897
Implementing the Standards: Incorporating Mathematical Modeling into the Curriculum.
ERIC Educational Resources Information Center
Swetz, Frank
1991-01-01
Following a brief historical review of the mechanism of mathematical modeling, examples are included that associate a mathematical model with given data (changes in sea level) and that model a real-life situation (process of parallel parking). Also provided is the rationale for the curricular implementation of mathematical modeling. (JJK)
Mathematical Modeling for Preservice Teachers: A Problem from Anesthesiology.
ERIC Educational Resources Information Center
Lingefjard, Thomas
2002-01-01
Addresses the observed actions of prospective Swedish mathematics teachers as they worked with a modeling situation. Explores prospective teachers' preparation to teach in grades 4-12 during a course of mathematical modeling. Focuses on preservice teachers' understanding of modeling and how they relate mathematical models to the real world.…
An Experimental Approach to Mathematical Modeling in Biology
ERIC Educational Resources Information Center
Ledder, Glenn
2008-01-01
The simplest age-structured population models update a population vector via multiplication by a matrix. These linear models offer an opportunity to introduce mathematical modeling to students of limited mathematical sophistication and background. We begin with a detailed discussion of mathematical modeling, particularly in a biological context.…
Computing Linear Mathematical Models Of Aircraft
NASA Technical Reports Server (NTRS)
Duke, Eugene L.; Antoniewicz, Robert F.; Krambeer, Keith D.
1991-01-01
Derivation and Definition of Linear Aircraft Model (LINEAR) computer program provides user with powerful, and flexible, standard, documented, and verified software tool for linearization of mathematical models of aerodynamics of aircraft. Intended for use in software tool to drive linear analysis of stability and design of control laws for aircraft. Capable of both extracting such linearized engine effects as net thrust, torque, and gyroscopic effects, and including these effects in linear model of system. Designed to provide easy selection of state, control, and observation variables used in particular model. Also provides flexibility of allowing alternate formulations of both state and observation equations. Written in FORTRAN.
Gifted Learners and Mathematical Achievement: An Analysis of Gifted Instructional Models
ERIC Educational Resources Information Center
Anderson, Lezley Barker
2013-01-01
The purpose of this causal-comparative study was to examine whether differences exist in the mathematics achievement of fifth grade gifted students based on the instructional delivery model used for mathematics instruction, cluster or collaborative, as defined by the Georgia Department of Education. The content area of mathematics, an area…
Mathematical models of ABE fermentation: review and analysis.
Mayank, Rahul; Ranjan, Amrita; Moholkar, Vijayanand S
2013-12-01
Among different liquid biofuels that have emerged in the recent past, biobutanol produced via fermentation processes is of special interest due to very similar properties to that of gasoline. For an effective design, scale-up, and optimization of the acetone-butanol-ethanol (ABE) fermentation process, it is necessary to have insight into the micro- and macro-mechanisms of the process. The mathematical models for ABE fermentation are efficient tools for this purpose, which have evolved from simple stoichiometric fermentation equations in the 1980s to the recent sophisticated and elaborate kinetic models based on metabolic pathways. In this article, we have reviewed the literature published in the area of mathematical modeling of the ABE fermentation. We have tried to present an analysis of these models in terms of their potency in describing the overall physiology of the process, design features, mode of operation along with comparison and validation with experimental results. In addition, we have also highlighted important facets of these models such as metabolic pathways, basic kinetics of different metabolites, biomass growth, inhibition modeling and other additional features such as cell retention and immobilized cultures. Our review also covers the mathematical modeling of the downstream processing of ABE fermentation, i.e. recovery and purification of solvents through flash distillation, liquid-liquid extraction, and pervaporation. We believe that this review will be a useful source of information and analysis on mathematical models for ABE fermentation for both the appropriate scientific and engineering communities. PMID:23072615
Mathematical models of ABE fermentation: review and analysis.
Mayank, Rahul; Ranjan, Amrita; Moholkar, Vijayanand S
2013-12-01
Among different liquid biofuels that have emerged in the recent past, biobutanol produced via fermentation processes is of special interest due to very similar properties to that of gasoline. For an effective design, scale-up, and optimization of the acetone-butanol-ethanol (ABE) fermentation process, it is necessary to have insight into the micro- and macro-mechanisms of the process. The mathematical models for ABE fermentation are efficient tools for this purpose, which have evolved from simple stoichiometric fermentation equations in the 1980s to the recent sophisticated and elaborate kinetic models based on metabolic pathways. In this article, we have reviewed the literature published in the area of mathematical modeling of the ABE fermentation. We have tried to present an analysis of these models in terms of their potency in describing the overall physiology of the process, design features, mode of operation along with comparison and validation with experimental results. In addition, we have also highlighted important facets of these models such as metabolic pathways, basic kinetics of different metabolites, biomass growth, inhibition modeling and other additional features such as cell retention and immobilized cultures. Our review also covers the mathematical modeling of the downstream processing of ABE fermentation, i.e. recovery and purification of solvents through flash distillation, liquid-liquid extraction, and pervaporation. We believe that this review will be a useful source of information and analysis on mathematical models for ABE fermentation for both the appropriate scientific and engineering communities.
Mathematical modeling and simulation of seated stability.
Tanaka, Martin L; Ross, Shane D; Nussbaum, Maury A
2010-03-22
Various methods have been used to quantify the kinematic variability or stability of the human spine. However, each of these methods evaluates dynamic behavior within the stable region of state space. In contrast, our goal was to determine the extent of the stable region. A 2D mathematical model was developed for a human sitting on an unstable seat apparatus (i.e., the "wobble chair"). Forward dynamic simulations were used to compute trajectories based on the initial state. From these trajectories, a scalar field of trajectory divergence was calculated, specifically a finite time Lyapunov exponent (FTLE) field. Theoretically, ridges of local maxima within this field are expected to partition the state space into regions of qualitatively different behavior. We found that ridges formed at the boundary between regions of stability and failure (i.e., falling). The location of the basin of stability found using the FTLE field matched well with the basin of stability determined by an alternative method. In addition, an equilibrium manifold was found, which describes a set of equilibrium configurations that act as a low dimensional attractor in the controlled system. These simulations are a first step in developing a method to locate state space boundaries for torso stability. Identifying these boundaries may provide a framework for assessing factors that contribute to health risks associated with spinal injury and poor balance recovery (e.g., age, fatigue, load/weight, and distribution). Furthermore, an approach is presented that can be adapted to find state space boundaries in other biomechanical applications.
Editorial: Mathematical modelling of infectious diseases.
Fenton, Andy
2016-06-01
The field of disease ecology - the study of the spread and impact of parasites and pathogens within their host populations and communities - has a long history of using mathematical models. Dating back over 100 years, researchers have used mathematics to describe the spread of disease-causing agents, understand the relationship between host density and transmission and plan control strategies. The use of mathematical modelling in disease ecology exploded in the late 1970s and early 1980s through the work of Anderson and May (Anderson and May, 1978, 1981, 1992; May and Anderson, 1978), who developed the fundamental frameworks for studying microparasite (e.g. viruses, bacteria and protozoa) and macroparasite (e.g. helminth) dynamics, emphasizing the importance of understanding features such as the parasite's basic reproduction number (R 0) and critical community size that form the basis of disease ecology research to this day. Since the initial models of disease population dynamics, which primarily focused on human diseases, theoretical disease research has expanded hugely to encompass livestock and wildlife disease systems, and also to explore evolutionary questions such as the evolution of parasite virulence or drug resistance. More recently there have been efforts to broaden the field still further, to move beyond the standard 'one-host-one-parasite' paradigm of the original models, to incorporate many aspects of complexity of natural systems, including multiple potential host species and interactions among multiple parasite species. PMID:27027318
Building Mathematical Models of Simple Harmonic and Damped Motion.
ERIC Educational Resources Information Center
Edwards, Thomas
1995-01-01
By developing a sequence of mathematical models of harmonic motion, shows that mathematical models are not right or wrong, but instead are better or poorer representations of the problem situation. (MKR)
Zhang, Zili; Gao, Chao; Lu, Yuxiao; Liu, Yuxin; Liang, Mingxin
2016-01-01
Bi-objective Traveling Salesman Problem (bTSP) is an important field in the operations research, its solutions can be widely applied in the real world. Many researches of Multi-objective Ant Colony Optimization (MOACOs) have been proposed to solve bTSPs. However, most of MOACOs suffer premature convergence. This paper proposes an optimization strategy for MOACOs by optimizing the initialization of pheromone matrix with the prior knowledge of Physarum-inspired Mathematical Model (PMM). PMM can find the shortest route between two nodes based on the positive feedback mechanism. The optimized algorithms, named as iPM-MOACOs, can enhance the pheromone in the short paths and promote the search ability of ants. A series of experiments are conducted and experimental results show that the proposed strategy can achieve a better compromise solution than the original MOACOs for solving bTSPs. PMID:26751562
Zhang, Zili; Gao, Chao; Lu, Yuxiao; Liu, Yuxin; Liang, Mingxin
2016-01-01
Bi-objective Traveling Salesman Problem (bTSP) is an important field in the operations research, its solutions can be widely applied in the real world. Many researches of Multi-objective Ant Colony Optimization (MOACOs) have been proposed to solve bTSPs. However, most of MOACOs suffer premature convergence. This paper proposes an optimization strategy for MOACOs by optimizing the initialization of pheromone matrix with the prior knowledge of Physarum-inspired Mathematical Model (PMM). PMM can find the shortest route between two nodes based on the positive feedback mechanism. The optimized algorithms, named as iPM-MOACOs, can enhance the pheromone in the short paths and promote the search ability of ants. A series of experiments are conducted and experimental results show that the proposed strategy can achieve a better compromise solution than the original MOACOs for solving bTSPs. PMID:26751562
ERIC Educational Resources Information Center
Lim, L. L.; Tso, T. -Y.; Lin, F. L.
2009-01-01
This article reports the attitudes of students towards mathematics after they had participated in an applied mathematical modelling project that was part of an Applied Mathematics course. The students were majoring in Earth Science at the National Taiwan Normal University. Twenty-six students took part in the project. It was the first time a…
ERIC Educational Resources Information Center
Martins, Ana Margarida; Vera-Licona, Paola; Laubenbacher, Reinhard
2008-01-01
This article describes a mathematical biology workshop given to secondary school teachers of the Danville area in Virginia, USA. The goal of the workshop was to enable teams of teachers with biology and mathematics expertise to incorporate lesson plans in mathematical modelling into the curriculum. The biological focus of the activities is the…
ERIC Educational Resources Information Center
Jurow, A. Susan
2004-01-01
Generalizing or making claims that extend beyond particular situations is a central mathematical practice and a focus of classroom mathematics instruction. This study examines how aspects of generality are produced through the situated activities of a group of middle school mathematics students working on an 8-week population-modeling project. The…
Mathematical Model For Deposition Of Soot
NASA Technical Reports Server (NTRS)
Makel, Darby B.
1991-01-01
Semiempirical mathematical model predicts deposition of soot in tubular gas generator in which hydrocarbon fuel burned in very-fuel-rich mixture with pure oxygen. Developed in response to concern over deposition of soot in gas generators and turbomachinery of rocket engines. Also of interest in terrestrial applications involving fuel-rich combustion or analogous process; e.g., purposeful deposition of soot to manufacture carbon black pigments.
On correct mathematical models of ecological LSS of high closure
NASA Astrophysics Data System (ADS)
Bartsev, S. I.
Usually mathematical models of natural ecological systems are implicitly based on the assumption of stoichiometrically rigid metabolism In most cases such assumption is applicable but in the case of ecological systems of high closure it can cause errors of forecast For completely closed ecological system the assumption of rigid metabolism results in completely incorrect forecast Since CELSS for long-duration missions have to be of high closure then using adequate mathematical description is of great importance for successfulness of a space mission Possible variants of non-rigid metabolism applicable to different type of biological components of CELSS are considered in the paper It is shown non-rigid models of metabolism not only eliminate incorrectness of mathematical description but as well allow to obtain more adequate estimation of stability of closed ecological systems
Modeling eBook acceptance: A study on mathematics teachers
NASA Astrophysics Data System (ADS)
Jalal, Azlin Abd; Ayub, Ahmad Fauzi Mohd; Tarmizi, Rohani Ahmad
2014-12-01
The integration and effectiveness of eBook utilization in Mathematics teaching and learning greatly relied upon the teachers, hence the need to understand their perceptions and beliefs. The eBook, an individual laptop completed with digitized textbook sofwares, were provided for each students in line with the concept of 1 student:1 laptop. This study focuses on predicting a model on the acceptance of the eBook among Mathematics teachers. Data was collected from 304 mathematics teachers in selected schools using a survey questionnaire. The selection were based on the proportionate stratified sampling. Structural Equation Modeling (SEM) were employed where the model was tested and evaluated and was found to have a good fit. The variance explained for the teachers' attitude towards eBook is approximately 69.1% where perceived usefulness appeared to be a stronger determinant compared to perceived ease of use. This study concluded that the attitude of mathematics teachers towards eBook depends largely on the perception of how useful the eBook is on improving their teaching performance, implying that teachers should be kept updated with the latest mathematical application and sofwares to use with the eBook to ensure positive attitude towards using it in class.
Automatic mathematical modeling for real time simulation system
NASA Technical Reports Server (NTRS)
Wang, Caroline; Purinton, Steve
1988-01-01
A methodology for automatic mathematical modeling and generating simulation models is described. The models will be verified by running in a test environment using standard profiles with the results compared against known results. The major objective is to create a user friendly environment for engineers to design, maintain, and verify their model and also automatically convert the mathematical model into conventional code for conventional computation. A demonstration program was designed for modeling the Space Shuttle Main Engine Simulation. It is written in LISP and MACSYMA and runs on a Symbolic 3670 Lisp Machine. The program provides a very friendly and well organized environment for engineers to build a knowledge base for base equations and general information. It contains an initial set of component process elements for the Space Shuttle Main Engine Simulation and a questionnaire that allows the engineer to answer a set of questions to specify a particular model. The system is then able to automatically generate the model and FORTRAN code. The future goal which is under construction is to download the FORTRAN code to VAX/VMS system for conventional computation. The SSME mathematical model will be verified in a test environment and the solution compared with the real data profile. The use of artificial intelligence techniques has shown that the process of the simulation modeling can be simplified.
Mathematical Models and the Experimental Analysis of Behavior
ERIC Educational Resources Information Center
Mazur, James E.
2006-01-01
The use of mathematical models in the experimental analysis of behavior has increased over the years, and they offer several advantages. Mathematical models require theorists to be precise and unambiguous, often allowing comparisons of competing theories that sound similar when stated in words. Sometimes different mathematical models may make…
Mathematical models of breast and ovarian cancers.
Botesteanu, Dana-Adriana; Lipkowitz, Stanley; Lee, Jung-Min; Levy, Doron
2016-07-01
Women constitute the majority of the aging United States (US) population, and this has substantial implications on cancer population patterns and management practices. Breast cancer is the most common women's malignancy, while ovarian cancer is the most fatal gynecological malignancy in the US. In this review, we focus on these subsets of women's cancers, seen more commonly in postmenopausal and elderly women. In order to systematically investigate the complexity of cancer progression and response to treatment in breast and ovarian malignancies, we assert that integrated mathematical modeling frameworks viewed from a systems biology perspective are needed. Such integrated frameworks could offer innovative contributions to the clinical women's cancers community, as answers to clinical questions cannot always be reached with contemporary clinical and experimental tools. Here, we recapitulate clinically known data regarding the progression and treatment of the breast and ovarian cancers. We compare and contrast the two malignancies whenever possible in order to emphasize areas where substantial contributions could be made by clinically inspired and validated mathematical modeling. We show how current paradigms in the mathematical oncology community focusing on the two malignancies do not make comprehensive use of, nor substantially reflect existing clinical data, and we highlight the modeling areas in most critical need of clinical data integration. We emphasize that the primary goal of any mathematical study of women's cancers should be to address clinically relevant questions. WIREs Syst Biol Med 2016, 8:337-362. doi: 10.1002/wsbm.1343 For further resources related to this article, please visit the WIREs website. PMID:27259061
Mathematical analysis of a muscle architecture model.
Navallas, Javier; Malanda, Armando; Gila, Luis; Rodríguez, Javier; Rodríguez, Ignacio
2009-01-01
Modeling of muscle architecture, which aims to recreate mathematically the physiological structure of the muscle fibers and motor units, is a powerful tool for understanding and modeling the mechanical and electrical behavior of the muscle. Most of the published models are presented in the form of algorithms, without mathematical analysis of mechanisms or outcomes of the model. Through the study of the muscle architecture model proposed by Stashuk, we present the analytical tools needed to better understand these models. We provide a statistical description for the spatial relations between motor units and muscle fibers. We are particularly concerned with two physiological quantities: the motor unit fiber number, which we expect to be proportional to the motor unit territory area; and the motor unit fiber density, which we expect to be constant for all motor units. Our results indicate that the Stashuk model is in good agreement with the physiological evidence in terms of the expectations outlined above. However, the resulting variance is very high. In addition, a considerable 'edge effect' is present in the outer zone of the muscle cross-section, making the properties of the motor units dependent on their location. This effect is relevant when motor unit territories and muscle cross-section are of similar size.
NASA Astrophysics Data System (ADS)
Leon, Arturo S.
2016-09-01
After the limnic eruptions at Nyos and Monoun in the 1980s, degassing pipes were installed to reduce the continuous increase of CO2 at the bottom of these lakes. The degassing system consists of a vertical pipe from the lake bottom to the surface and a small pump located near the top of the pipe, which raises water in the pipe up to a level where it becomes saturated with gas, which in turn leads to volume expansion and eruption. This paper describes two new mathematical models for predicting eruption velocity in degassing pipes based on exsolution of a single gas and the simultaneous exsolution of multiple gases. The models were applied to the degassing system of lakes Nyos and Monoun, which contain two main gases, namely CO2 and CH4. Because the volume proportion of CH4 is significant only in Lake Monoun, the Lake Nyos test case considered the CO2 gas only, while as the Lake Monoun test case considered the simultaneous exsolution of CO2 and CH4. Good agreement between the results of the models and observed data is found for both test cases. The results for the eruption in Lake Monoun considering the two main gases measured in this lake (CO2 and CH4) were found to have a better agreement with the measurements compared to the model results obtained considering the main gas only (CO2).
A Review of Mathematical Models for Leukemia and Lymphoma
Clapp, Geoffrey; Levy, Doron
2014-01-01
Recently, there has been significant activity in the mathematical community, aimed at developing quantitative tools for studying leukemia and lymphoma. Mathematical models have been applied to evaluate existing therapies and to suggest novel therapies. This article reviews the recent contributions of mathematical modeling to leukemia and lymphoma research. These developments suggest that mathematical modeling has great potential in this field. Collaboration between mathematicians, clinicians, and experimentalists can significantly improve leukemia and lymphoma therapy. PMID:26744598
Mathematical models of human african trypanosomiasis epidemiology.
Rock, Kat S; Stone, Chris M; Hastings, Ian M; Keeling, Matt J; Torr, Steve J; Chitnis, Nakul
2015-03-01
Human African trypanosomiasis (HAT), commonly called sleeping sickness, is caused by Trypanosoma spp. and transmitted by tsetse flies (Glossina spp.). HAT is usually fatal if untreated and transmission occurs in foci across sub-Saharan Africa. Mathematical modelling of HAT began in the 1980s with extensions of the Ross-Macdonald malaria model and has since consisted, with a few exceptions, of similar deterministic compartmental models. These models have captured the main features of HAT epidemiology and provided insight on the effectiveness of the two main control interventions (treatment of humans and tsetse fly control) in eliminating transmission. However, most existing models have overestimated prevalence of infection and ignored transient dynamics. There is a need for properly validated models, evolving with improved data collection, that can provide quantitative predictions to help guide control and elimination strategies for HAT.
A mathematical model of 'Pride and Prejudice'.
Rinaldi, Sergio; Rossa, Fabio Della; Landi, Pietro
2014-04-01
A mathematical model is proposed for interpreting the love story between Elizabeth and Darcy portrayed by Jane Austen in the popular novel Pride and Prejudice. The analysis shows that the story is characterized by a sudden explosion of sentimental involvements, revealed by the existence of a saddle-node bifurcation in the model. The paper is interesting not only because it deals for the first time with catastrophic bifurcations in romantic relation-ships, but also because it enriches the list of examples in which love stories are described through ordinary differential equations.
Mathematical model on a desalination process
Al-Samawi, A.A. )
1994-05-01
Mathematical models on the desalination of brackish water using EDR process are formulated. The product desalinated water variable is hypothesized as being dependent upon the following independent variables: total dissolved solids of the feed water, total dissolved solids of the product water, the rate of feed water, the temperature of feed water, the number of stages of membranes, and the energy consumption. The final model which is selected on statistical basis is considered appropriated for both prediction purposes and for the purpose of quantifying the separate effects of each significant variable upon the rate of production of desalted water variable. Results of the analysis are reported herein. 6 refs., 4 figs., 5 tabs.
Mathematical model of induced flow on the airplane vertical tail
NASA Astrophysics Data System (ADS)
Rotaru, Constantin; Cîrciu, Ionicǎ; Edu, Raluca Ioana
2016-06-01
In this paper is presented a mathematical model of the flow around the vertical tail of an airplane, based on the general elements of the aerodynamic design, with details leading to the separate formulation of the Fourier coefficients in the series solution of the Prandtl's lifting-line equation. Numerical results are obtained in Maple soft environment, for a standard configuration of an airplane geometry. The results include the discussion of the vortex model for the sidewash gradient on the vertical stabilizer.
ERIC Educational Resources Information Center
Smith, Erick; Haarer, Shawn; Confrey, Jere
1997-01-01
Provides details of a study that attempts to broaden the understanding of mathematics by investigating how applied mathematicians and biologists collaborate in developing dynamic population models. (DDR)
A mathematical model for predicting the viability of airborne viruses.
Posada, J A; Redrow, J; Celik, I
2010-03-01
A mathematical model was developed to predict the viability of airborne viruses. The model uses water activity as the primary independent variable and an exponential decay function for the viability of the virus. This model was tested using published experimental data obtained by different investigators for influenza, Langat and polio viruses. The aerosolized media were modelled as a binary solution of water and sodium chloride. The water activity is related directly to the solute concentration in the binary solution. The minimum viability usually occurred just above the efflorescence point, which is the relative humidity at which the solution crystallizes. The relationship between water activity and relative humidity is based on the Köhler theory, whereby the Kelvin term was taken into account. Physical explanations are provided on the variation of viral viability at different relative humidity levels. The predictions obtained by the proposed mathematical model compare well with most of the published experimental data.
Declarative representation of uncertainty in mathematical models.
Miller, Andrew K; Britten, Randall D; Nielsen, Poul M F
2012-01-01
An important aspect of multi-scale modelling is the ability to represent mathematical models in forms that can be exchanged between modellers and tools. While the development of languages like CellML and SBML have provided standardised declarative exchange formats for mathematical models, independent of the algorithm to be applied to the model, to date these standards have not provided a clear mechanism for describing parameter uncertainty. Parameter uncertainty is an inherent feature of many real systems. This uncertainty can result from a number of situations, such as: when measurements include inherent error; when parameters have unknown values and so are replaced by a probability distribution by the modeller; when a model is of an individual from a population, and parameters have unknown values for the individual, but the distribution for the population is known. We present and demonstrate an approach by which uncertainty can be described declaratively in CellML models, by utilising the extension mechanisms provided in CellML. Parameter uncertainty can be described declaratively in terms of either a univariate continuous probability density function or multiple realisations of one variable or several (typically non-independent) variables. We additionally present an extension to SED-ML (the Simulation Experiment Description Markup Language) to describe sampling sensitivity analysis simulation experiments. We demonstrate the usability of the approach by encoding a sample model in the uncertainty markup language, and by developing a software implementation of the uncertainty specification (including the SED-ML extension for sampling sensitivty analyses) in an existing CellML software library, the CellML API implementation. We used the software implementation to run sampling sensitivity analyses over the model to demonstrate that it is possible to run useful simulations on models with uncertainty encoded in this form.
Declarative Representation of Uncertainty in Mathematical Models
Miller, Andrew K.; Britten, Randall D.; Nielsen, Poul M. F.
2012-01-01
An important aspect of multi-scale modelling is the ability to represent mathematical models in forms that can be exchanged between modellers and tools. While the development of languages like CellML and SBML have provided standardised declarative exchange formats for mathematical models, independent of the algorithm to be applied to the model, to date these standards have not provided a clear mechanism for describing parameter uncertainty. Parameter uncertainty is an inherent feature of many real systems. This uncertainty can result from a number of situations, such as: when measurements include inherent error; when parameters have unknown values and so are replaced by a probability distribution by the modeller; when a model is of an individual from a population, and parameters have unknown values for the individual, but the distribution for the population is known. We present and demonstrate an approach by which uncertainty can be described declaratively in CellML models, by utilising the extension mechanisms provided in CellML. Parameter uncertainty can be described declaratively in terms of either a univariate continuous probability density function or multiple realisations of one variable or several (typically non-independent) variables. We additionally present an extension to SED-ML (the Simulation Experiment Description Markup Language) to describe sampling sensitivity analysis simulation experiments. We demonstrate the usability of the approach by encoding a sample model in the uncertainty markup language, and by developing a software implementation of the uncertainty specification (including the SED-ML extension for sampling sensitivty analyses) in an existing CellML software library, the CellML API implementation. We used the software implementation to run sampling sensitivity analyses over the model to demonstrate that it is possible to run useful simulations on models with uncertainty encoded in this form. PMID:22802941
Assessment of Primary 5 Students' Mathematical Modelling Competencies
ERIC Educational Resources Information Center
Chan, Chun Ming Eric; Ng, Kit Ee Dawn; Widjaja, Wanty; Seto, Cynthia
2012-01-01
Mathematical modelling is increasingly becoming part of an instructional approach deemed to develop students with competencies to function as 21st century learners and problem solvers. As mathematical modelling is a relatively new domain in the Singapore primary school mathematics curriculum, many teachers may not be aware of the learning outcomes…
Exploring the Relationship between Mathematical Modelling and Classroom Discourse
ERIC Educational Resources Information Center
Redmond, Trevor; Sheehy, Joanne; Brown, Raymond
2010-01-01
This paper explores the notion that the discourse of the mathematics classroom impacts on the practices that students engage when modelling mathematics. Using excerpts of a Year 12 student's report on modelling Newton's law of cooling, this paper argues that when students engage with the discourse of their mathematics classroom in a manner that…
Modelling of and Conjecturing on a Soccer Ball in a Korean Eighth Grade Mathematics Classroom
ERIC Educational Resources Information Center
Lee, Kyeong-Hwa
2011-01-01
The purpose of this article was to describe the task design and implementation of cultural artefacts in a mathematics lesson based on the integration of modelling and conjecturing perspectives. The conceived process of integrating a soccer ball into mathematics lessons via modelling- and conjecturing-based instruction was first detailed. Next, the…
Mathematical Modeling and Simulation of Seated Stability
Tanaka, Martin L.; Ross, Shane D.; Nussbaum, Maury A.
2009-01-01
Various methods have been used to quantify the kinematic variability or stability of the human spine. However, each of these methods evaluates dynamic behavior within the stable region of state space. In contrast, our goal was to determine the extent of the stable region. A 2D mathematical model was developed for a human sitting on an unstable seat apparatus (i.e., the “wobble chair”). Forward dynamic simulations were used to compute trajectories based on the initial state. From these trajectories, a scalar field of trajectory divergence was calculated, specifically a finite time Lyapunov exponent (FTLE) field. Theoretically, ridges of local maxima within this field are expected to partition the state space into regions of qualitatively different behavior. We found that ridges formed at the boundary between regions of stability and failure (i.e., falling). The location of the basin of stability found using the FTLE field matched well with the basin of stability determined by an alternative method. In addition, an equilibrium manifold was found, which describes a set of equilibrium configurations that act as a low dimensional attractor in the controlled system. These simulations are a first step in developing a method to locate state space boundaries for torso stability. Identifying these boundaries may provide a framework for assessing factors that contribute to health risks associated with spinal injury and poor balance recovery (e.g., age, fatigue, load/weight and distribution). Furthermore, an approach is presented that can be adapted to find state space boundaries in other biomechanical applications. PMID:20018288
Mathematical model to predict drivers' reaction speeds.
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. PMID:22431214
Mathematical model to predict drivers' reaction speeds.
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.
Mathematical Modeling of Extinction of Inhomogeneous Populations
Karev, G.P.; Kareva, I.
2016-01-01
Mathematical models of population extinction have a variety of applications in such areas as ecology, paleontology and conservation biology. Here we propose and investigate two types of sub-exponential models of population extinction. Unlike the more traditional exponential models, the life duration of sub-exponential models is finite. In the first model, the population is assumed to be composed clones that are independent from each other. In the second model, we assume that the size of the population as a whole decreases according to the sub-exponential equation. We then investigate the “unobserved heterogeneity”, i.e. the underlying inhomogeneous population model, and calculate the distribution of frequencies of clones for both models. We show that the dynamics of frequencies in the first model is governed by the principle of minimum of Tsallis information loss. In the second model, the notion of “internal population time” is proposed; with respect to the internal time, the dynamics of frequencies is governed by the principle of minimum of Shannon information loss. The results of this analysis show that the principle of minimum of information loss is the underlying law for the evolution of a broad class of models of population extinction. Finally, we propose a possible application of this modeling framework to mechanisms underlying time perception. PMID:27090117
NASA Astrophysics Data System (ADS)
Petoshin, V. I.; Chasovnikov, E. A.
2011-05-01
Aerodynamic loads in problems of flight dynamics of passenger aircraft in stalled flow regimes are described using a mathematical model that includes an ordinary linear first-order differential equation. A procedure for determining the parameters of the mathematical model is proposed which is based on approximating experimental frequency characteristics with the frequency characteristics of the linearized mathematical model. The mathematical model was verified by tests of a modern passenger aircraft model in a wind tunnel.
Mathematical modeling of the coating process.
Toschkoff, Gregor; Khinast, Johannes G
2013-12-01
Coating of tablets is a common unit operation in the pharmaceutical industry. In most cases, the final product must meet strict quality requirements; to meet them, a detailed understanding of the coating process is required. To this end, numerous experiment studies have been performed. However, to acquire a mechanistic understanding, experimental data must be interpreted in the light of mathematical models. In recent years, a combination of analytical modeling and computational simulations enabled deeper insights into the nature of the coating process. This paper presents an overview of modeling and simulation approaches of the coating process, covering various relevant aspects from scale-up considerations to coating mass uniformity investigations and models for drop atomization. The most important analytical and computational concepts are presented and the findings are compared.
Mathematical modelling of hepatic lipid metabolism.
Pratt, Adrian C; Wattis, Jonathan A D; Salter, Andrew M
2015-04-01
The aim of this paper is to develop a mathematical model capable of simulating the metabolic response to a variety of mixed meals in fed and fasted conditions with particular emphasis placed on the hepatic triglyceride element of the model. Model validation is carried out using experimental data for the ingestion of three mixed composition meals over a 24-h period. Comparison with experimental data suggests the model predicts key plasma lipids accurately given a prescribed insulin profile. One counter-intuitive observation to arise from simulations is that liver triglyceride initially decreases when a high fat meal is ingested, a phenomenon potentially explained by the carbohydrate portion of the meal raising plasma insulin.
Mathematical Models of Continuous Flow Electrophoresis
NASA Technical Reports Server (NTRS)
Saville, D. A.; Snyder, R. S.
1985-01-01
Development of high resolution continuous flow electrophoresis devices ultimately requires comprehensive understanding of the ways various phenomena and processes facilitate or hinder separation. A comprehensive model of the actual three dimensional flow, temperature and electric fields was developed to provide guidance in the design of electrophoresis chambers for specific tasks and means of interpreting test data on a given chamber. Part of the process of model development includes experimental and theoretical studies of hydrodynamic stability. This is necessary to understand the origin of mixing flows observed with wide gap gravitational effects. To insure that the model accurately reflects the flow field and particle motion requires extensive experimental work. Another part of the investigation is concerned with the behavior of concentrated sample suspensions with regard to sample stream stability particle-particle interactions which might affect separation in an electric field, especially at high field strengths. Mathematical models will be developed and tested to establish the roles of the various interactions.
Mathematics of tsunami: modelling and identification
NASA Astrophysics Data System (ADS)
Krivorotko, Olga; Kabanikhin, Sergey
2015-04-01
Tsunami (long waves in the deep water) motion caused by underwater earthquakes is described by shallow water equations ( { ηtt = div (gH (x,y)-gradη), (x,y) ∈ Ω, t ∈ (0,T ); η|t=0 = q(x,y), ηt|t=0 = 0, (x,y) ∈ Ω. ( (1) Bottom relief H(x,y) characteristics and the initial perturbation data (a tsunami source q(x,y)) are required for the direct simulation of tsunamis. The main difficulty problem of tsunami modelling is a very big size of the computational domain (Ω = 500 × 1000 kilometres in space and about one hour computational time T for one meter of initial perturbation amplitude max|q|). The calculation of the function η(x,y,t) of three variables in Ω × (0,T) requires large computing resources. We construct a new algorithm to solve numerically the problem of determining the moving tsunami wave height S(x,y) which is based on kinematic-type approach and analytical representation of fundamental solution. Proposed algorithm of determining the function of two variables S(x,y) reduces the number of operations in 1.5 times than solving problem (1). If all functions does not depend on the variable y (one dimensional case), then the moving tsunami wave height satisfies of the well-known Airy-Green formula: S(x) = S(0)° --- 4H (0)/H (x). The problem of identification parameters of a tsunami source using additional measurements of a passing wave is called inverse tsunami problem. We investigate two different inverse problems of determining a tsunami source q(x,y) using two different additional data: Deep-ocean Assessment and Reporting of Tsunamis (DART) measurements and satellite altimeters wave-form images. These problems are severely ill-posed. The main idea consists of combination of two measured data to reconstruct the source parameters. We apply regularization techniques to control the degree of ill-posedness such as Fourier expansion, truncated singular value decomposition, numerical regularization. The algorithm of selecting the truncated number of
Mathematical modeling to predict residential solid waste generation
Ojeda Benitez, Sara; Vega, Carolina Armijo de
2008-07-01
One of the challenges faced by waste management authorities is determining the amount of waste generated by households in order to establish waste management systems, as well as trying to charge rates compatible with the principle applied worldwide, and design a fair payment system for households according to the amount of residential solid waste (RSW) they generate. The goal of this research work was to establish mathematical models that correlate the generation of RSW per capita to the following variables: education, income per household, and number of residents. This work was based on data from a study on generation, quantification and composition of residential waste in a Mexican city in three stages. In order to define prediction models, five variables were identified and included in the model. For each waste sampling stage a different mathematical model was developed, in order to find the model that showed the best linear relation to predict residential solid waste generation. Later on, models to explore the combination of included variables and select those which showed a higher R{sup 2} were established. The tests applied were normality, multicolinearity and heteroskedasticity. Another model, formulated with four variables, was generated and the Durban-Watson test was applied to it. Finally, a general mathematical model is proposed to predict residential waste generation, which accounts for 51% of the total.
Santos, Guido; Díaz, Mario; Torres, Néstor V
2016-01-01
A connection between lipid rafts and Alzheimer's disease has been studied during the last decades. Mathematical modeling approaches have recently been used to correlate the effects of lipid composition changes in the physicochemical properties of raft-like membranes. Here we propose an agent based model to assess the effect of lipid changes in lipid rafts on the evolution and progression of Alzheimer's disease using lipid profile data obtained in an established model of familial Alzheimer's disease. We have observed that lipid raft size and lipid mobility in non-raft domains are two main factors that increase during age and are accelerated in the transgenic Alzheimer's disease mouse model. The consequences of these changes are discussed in the context of neurotoxic amyloid β production. Our agent based model predicts that increasing sterols (mainly cholesterol) and long-chain polyunsaturated fatty acids (LCPUFA) (mainly DHA, docosahexaenoic acid) proportions in the membrane composition might delay the onset and progression of the disease.
Santos, Guido; Díaz, Mario; Torres, Néstor V
2016-01-01
A connection between lipid rafts and Alzheimer's disease has been studied during the last decades. Mathematical modeling approaches have recently been used to correlate the effects of lipid composition changes in the physicochemical properties of raft-like membranes. Here we propose an agent based model to assess the effect of lipid changes in lipid rafts on the evolution and progression of Alzheimer's disease using lipid profile data obtained in an established model of familial Alzheimer's disease. We have observed that lipid raft size and lipid mobility in non-raft domains are two main factors that increase during age and are accelerated in the transgenic Alzheimer's disease mouse model. The consequences of these changes are discussed in the context of neurotoxic amyloid β production. Our agent based model predicts that increasing sterols (mainly cholesterol) and long-chain polyunsaturated fatty acids (LCPUFA) (mainly DHA, docosahexaenoic acid) proportions in the membrane composition might delay the onset and progression of the disease. PMID:27014089
Santos, Guido; Díaz, Mario; Torres, Néstor V.
2016-01-01
A connection between lipid rafts and Alzheimer's disease has been studied during the last decades. Mathematical modeling approaches have recently been used to correlate the effects of lipid composition changes in the physicochemical properties of raft-like membranes. Here we propose an agent based model to assess the effect of lipid changes in lipid rafts on the evolution and progression of Alzheimer's disease using lipid profile data obtained in an established model of familial Alzheimer's disease. We have observed that lipid raft size and lipid mobility in non-raft domains are two main factors that increase during age and are accelerated in the transgenic Alzheimer's disease mouse model. The consequences of these changes are discussed in the context of neurotoxic amyloid β production. Our agent based model predicts that increasing sterols (mainly cholesterol) and long-chain polyunsaturated fatty acids (LCPUFA) (mainly DHA, docosahexaenoic acid) proportions in the membrane composition might delay the onset and progression of the disease. PMID:27014089
Mathematical modeling of infectious disease dynamics
Siettos, Constantinos I.; Russo, Lucia
2013-01-01
Over the last years, an intensive worldwide effort is speeding up the developments in the establishment of a global surveillance network for combating pandemics of emergent and re-emergent infectious diseases. Scientists from different fields extending from medicine and molecular biology to computer science and applied mathematics have teamed up for rapid assessment of potentially urgent situations. Toward this aim mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. To better understand and model the contagious dynamics the impact of numerous variables ranging from the micro host–pathogen level to host-to-host interactions, as well as prevailing ecological, social, economic, and demographic factors across the globe have to be analyzed and thoroughly studied. Here, we present and discuss the main approaches that are used for the surveillance and modeling of infectious disease dynamics. We present the basic concepts underpinning their implementation and practice and for each category we give an annotated list of representative works. PMID:23552814
Fernández Bou, Ángel S; Nascentes, Alexandre Lioi; Costa Pereira, Barbara; Da Silva, Leonardo Duarte Batista; Alberto Ferreira, João; Campos, Juacyara Carbonelli
2015-01-01
The experiments performed in this study consisted of 16 batch reactors fed different mixtures of landfill leachate combined with synthetic wastewater treated using the Powdered Activated Carbon Treatment (PACT) process. The objective was to measure the COD mass removal per liter each day for each reactor using two models: the first model combined the variables PAC concentration (0 g·L(-1), 2 g·L(-1), 4 g·L(-1), and 6 g·L(-1)) and leachate rate in the wastewater (0%, 2%, 5%, and 10%), and the second model combined the PAC concentration and the influent COD. The Response Surface Methodology with Central Composite Design was used to describe the response surface of both models considered in this study. Domestic wastewater was produced under controlled conditions in the laboratory where the experiments were performed. The results indicated that the PAC effect was null when the influent did not contain leachate; however, as the concentration of leachate applied to the mixture was increased, the addition of a higher PAC concentration resulted in a better COD mass removal in the reactors. The adjusted R(2) values of the two models were greater than 0.95, and the predicted R(2) values were greater than 0.93. The models may be useful for wastewater treatment companies to calculate PAC requirements in order to meet COD mass removal objectives in combined treatment. PMID:25723064
Fernández Bou, Ángel S; Nascentes, Alexandre Lioi; Costa Pereira, Barbara; Da Silva, Leonardo Duarte Batista; Alberto Ferreira, João; Campos, Juacyara Carbonelli
2015-01-01
The experiments performed in this study consisted of 16 batch reactors fed different mixtures of landfill leachate combined with synthetic wastewater treated using the Powdered Activated Carbon Treatment (PACT) process. The objective was to measure the COD mass removal per liter each day for each reactor using two models: the first model combined the variables PAC concentration (0 g·L(-1), 2 g·L(-1), 4 g·L(-1), and 6 g·L(-1)) and leachate rate in the wastewater (0%, 2%, 5%, and 10%), and the second model combined the PAC concentration and the influent COD. The Response Surface Methodology with Central Composite Design was used to describe the response surface of both models considered in this study. Domestic wastewater was produced under controlled conditions in the laboratory where the experiments were performed. The results indicated that the PAC effect was null when the influent did not contain leachate; however, as the concentration of leachate applied to the mixture was increased, the addition of a higher PAC concentration resulted in a better COD mass removal in the reactors. The adjusted R(2) values of the two models were greater than 0.95, and the predicted R(2) values were greater than 0.93. The models may be useful for wastewater treatment companies to calculate PAC requirements in order to meet COD mass removal objectives in combined treatment.
Technology Transfer Automated Retrieval System (TEKTRAN)
Metabolic reconstructions (MRs) are common denominators in systems biology and represent biochemical, genetic, and genomic (BiGG) knowledge-bases for target organisms by capturing currently available information in a consistent, structured manner. Salmonella enterica subspecies I serovar Typhimurium...
Adequate mathematical modelling of environmental processes
NASA Astrophysics Data System (ADS)
Chashechkin, Yu. D.
2012-04-01
In environmental observations and laboratory visualization both large scale flow components like currents, jets, vortices, waves and a fine structure are registered (different examples are given). The conventional mathematical modeling both analytical and numerical is directed mostly on description of energetically important flow components. The role of a fine structures is still remains obscured. A variety of existing models makes it difficult to choose the most adequate and to estimate mutual assessment of their degree of correspondence. The goal of the talk is to give scrutiny analysis of kinematics and dynamics of flows. A difference between the concept of "motion" as transformation of vector space into itself with a distance conservation and the concept of "flow" as displacement and rotation of deformable "fluid particles" is underlined. Basic physical quantities of the flow that are density, momentum, energy (entropy) and admixture concentration are selected as physical parameters defined by the fundamental set which includes differential D'Alembert, Navier-Stokes, Fourier's and/or Fick's equations and closing equation of state. All of them are observable and independent. Calculations of continuous Lie groups shown that only the fundamental set is characterized by the ten-parametric Galilelian groups reflecting based principles of mechanics. Presented analysis demonstrates that conventionally used approximations dramatically change the symmetries of the governing equations sets which leads to their incompatibility or even degeneration. The fundamental set is analyzed taking into account condition of compatibility. A high order of the set indicated on complex structure of complete solutions corresponding to physical structure of real flows. Analytical solutions of a number problems including flows induced by diffusion on topography, generation of the periodic internal waves a compact sources in week-dissipative media as well as numerical solutions of the same
A mathematical model of the sleep/wake cycle.
Rempe, Michael J; Best, Janet; Terman, David
2010-05-01
We present a biologically-based mathematical model that accounts for several features of the human sleep/wake cycle. These features include the timing of sleep and wakefulness under normal and sleep-deprived conditions, ultradian rhythms, more frequent switching between sleep and wakefulness due to the loss of orexin and the circadian dependence of several sleep measures. The model demonstrates how these features depend on interactions between a circadian pacemaker and a sleep homeostat and provides a biological basis for the two-process model for sleep regulation. The model is based on previous "flip-flop" conceptual models for sleep/wake and REM/NREM and we explore whether the neuronal components in these flip-flop models, with the inclusion of a sleep-homeostatic process and the circadian pacemaker, are sufficient to account for the features of the sleep/wake cycle listed above. The model is minimal in the sense that, besides the sleep homeostat and constant cortical drives, the model includes only those nuclei described in the flip-flop models. Each of the cell groups is modeled by at most two differential equations for the evolution of the total population activity, and the synaptic connections are consistent with those described in the flip-flop models. A detailed analysis of the model leads to an understanding of the mathematical mechanisms, as well as insights into the biological mechanisms, underlying sleep/wake dynamics.
Mathematical modelling of eukaryotic DNA replication.
Hyrien, Olivier; Goldar, Arach
2010-01-01
Eukaryotic DNA replication is a complex process. Replication starts at thousand origins that are activated at different times in S phase and terminates when converging replication forks meet. Potential origins are much more abundant than actually fire within a given S phase. The choice of replication origins and their time of activation is never exactly the same in any two cells. Individual origins show different efficiencies and different firing time probability distributions, conferring stochasticity to the DNA replication process. High-throughput microarray and sequencing techniques are providing increasingly huge datasets on the population-averaged spatiotemporal patterns of DNA replication in several organisms. On the other hand, single-molecule replication mapping techniques such as DNA combing provide unique information about cell-to-cell variability in DNA replication patterns. Mathematical modelling is required to fully comprehend the complexity of the chromosome replication process and to correctly interpret these data. Mathematical analysis and computer simulations have been recently used to model and interpret genome-wide replication data in the yeast Saccharomyces cerevisiae and Schizosaccharomyces pombe, in Xenopus egg extracts and in mammalian cells. These works reveal how stochasticity in origin usage confers robustness and reliability to the DNA replication process. PMID:20205354
Designing Technology-Based Mathematics Lessons: A Pedagogical Framework
ERIC Educational Resources Information Center
Chua, Boon-Liang; Wu, Yingkang
2005-01-01
To integrate technology into mathematics teaching and learning effectively, teachers could create a technology-based learning environment that provides students with opportunities to experience the process of mathematical investigation. These opportunities range from exploring using mathematical ideas to making and testing conjectures, as well as…
Place-Based Mathematics Education: A Conflated Pedagogy?
ERIC Educational Resources Information Center
Showalter, Daniel A.
2013-01-01
Place-based mathematics education (PBME) has the potential to engage students with the mathematics inherent in the local land, culture, and community. However, research has identified daunting barriers to this pedagogy, especially in abstract mathematics courses such as algebra and beyond. In this study, 15 graduates of a doctoral program in rural…
Building Mathematics Achievement Models in Four Countries Using TIMSS 2003
ERIC Educational Resources Information Center
Wang, Ze; Osterlind, Steven J.; Bergin, David A.
2012-01-01
Using the Trends in International Mathematics and Science Study 2003 data, this study built mathematics achievement models of 8th graders in four countries: the USA, Russia, Singapore and South Africa. These 4 countries represent the full spectrum of mathematics achievement. In addition, they represent 4 continents, and they include 2 countries…
Preparing Secondary Mathematics Teachers: A Focus on Modeling in Algebra
ERIC Educational Resources Information Center
Jung, Hyunyi; Mintos, Alexia; Newton, Jill
2015-01-01
This study addressed the opportunities to learn (OTL) modeling in algebra provided to secondary mathematics pre-service teachers (PSTs). To investigate these OTL, we interviewed five instructors of required mathematics and mathematics education courses that had the potential to include opportunities for PSTs to learn algebra at three universities.…
Computer-Assisted Mathematics--A Model Approach.
ERIC Educational Resources Information Center
Bitter, Gary G.
1987-01-01
Discussion of need for improved mathematics education of preservice teachers focuses on a model program, the Mathematics Fitness Project, that includes a computer-generated testing system, management system, and remediation system. Use of the system to improve mathematics skills and attitudes of college students and post high school adults is…
Dong, Fangliang; Xu, Daliang; Wang, Zhe; Dong, Miaowu
2015-12-01
This paper mainly focuses on Ebola prediction and optimal location of emergency supplies delivery in Guinea, Liberia and Sierra Leone. First, an epidemic model called SEIIRHF model which takes the susceptible, the exposed, the infected, the recovered, the ones in hospital and the buried into consideration is developed to evaluate Ebola propagation. In this model, the infected and the ones in hospital are divided into two categories, serious infected and not serious, to simulate Ebola patients who are in ICU or not. Data of total and death cases from WHO website are used to curve fit. Then the curve is tested by data acquired recently. According to the curve, we predict there are 4000 total cases and 2500 death cases in Guinea, 9509 total cases and 4166 death cases in Liberia, 12,556 total cases and 3933 death cases in Sierra Leone by end of June, 2015. Then Clustering method is adopted to divide the most serious regions in a country into several parts, each part has a location of medicine delivery. Then two circular routes in different directions are decided by using TSP (Traveling Salesman Problem) method with consideration of medicine can be delivered within several hours by a car. Thus, DUBREKA, KOUROUSSA, and MACENTA in Guinea, Grand Bassa in Liberia and Tonkolili in Sierra Leone are selected as location of delivery respectively. Besides, Guinea has 6 delivery routes, Liberia has 2 delivery routes and Sierra Leone has 2 delivery routes.
Vats, Siddharth; Maurya, Devendra Prasad; Jain, Ayushi; Mall, Varija; Negi, Sangeeta
2013-11-01
The objective of this study was to optimize the physico-enzymatic pretreatment of P. roxburghii fallen foliage (needles) to produce reducing sugars through response surface methodology (RSM) with central composite face centered design (CCD). Under this, five parameters, i.e., concentration of laccase, cellulose and xylanase, steam explosion pressure and incubation period, at three levels with twenty six runs were taken into account. Cellulase, xylanase and laccase enzymes with activity 4.563, 38.32 and 0.05 IU/mL, respectively, were produced from locally isolated microbial strains. The analysis of variance (ANOVA) was applied for the validation of the predicted model at 95% of confidence level. This model predicted 334 mg/g release of reducing sugars on treating P. roxburghii fallen foliage with 1.18 mL of cellulose, 0.31 mL of xylanase and 0.01 mL of laccase, 14.39 psi steam explosion pressure and 24 h of incubation time. The experimental results obtained were in good agreement to predicted values, making it a reliable optimized model for five factors in combination to predict reducing sugar yield for ethanol production for bio-fuel industry.
Mathematical Modeling of Microbial Community Dynamics: A Methodological Review
Song, Hyun-Seob; Cannon, William R.; Beliaev, Alex S.; Konopka, Allan
2014-10-17
Microorganisms in nature form diverse communities that dynamically change in structure and function in response to environmental variations. As a complex adaptive system, microbial communities show higher-order properties that are not present in individual microbes, but arise from their interactions. Predictive mathematical models not only help to understand the underlying principles of the dynamics and emergent properties of natural and synthetic microbial communities, but also provide key knowledge required for engineering them. In this article, we provide an overview of mathematical tools that include not only current mainstream approaches, but also less traditional approaches that, in our opinion, can be potentially useful. We discuss a broad range of methods ranging from low-resolution supra-organismal to high-resolution individual-based modeling. Particularly, we highlight the integrative approaches that synergistically combine disparate methods. In conclusion, we provide our outlook for the key aspects that should be further developed to move microbial community modeling towards greater predictive power.
Mathematical Model of the Jet Engine Fuel System
NASA Astrophysics Data System (ADS)
Klimko, Marek
2015-05-01
The paper discusses the design of a simplified mathematical model of the jet (turbo-compressor) engine fuel system. The solution will be based on the regulation law, where the control parameter is a fuel mass flow rate and the regulated parameter is the rotational speed. A differential equation of the jet engine and also differential equations of other fuel system components (fuel pump, throttle valve, pressure regulator) will be described, with respect to advanced predetermined simplifications.
Thiele, Ines; Hyduke, Daniel R.; Steeb, Benjamin; Fankam, Guy; Allen, Douglas K.; Bazzani, Susanna; Charusanti, Pep; Chen, Feng-Chi; Fleming, Ronan MT; Hsiung, Chao A.; De Keersmaecker, Sigrid CJ; Liao, Yu-Chieh; Marchal, Kathleen; Mo, Monica L.; Özdemir, Emre; Raghunathan, Anu; Reed, Jennifer L.; Shin, Sook-Il; Sigurbjörnsdóttir, Sara; Steinmann, Jonas; Sudarsan, Suresh; Swainston, Neil; Thijs, Inge M.; Zengler, Karsten; Palsson, Bernhard O.; Adkins, Joshua N.; Bumann, Dirk
2011-01-01
Metabolic reconstructions (MRs) are common denominators in systems biology and represent biochemical, genetic, and genomic (BiGG) knowledge-bases for target organisms by capturing currently available information in a consistent, structured manner. Salmonella enterica subspecies I serovar Typhimurium is a human pathogen, causes various diseases and its increasing antibiotic resistance poses a public health problem. Here, we describe a community-driven effort, in which more than 20 experts in S. Typhimurium biology and systems biology collaborated to reconcile and expand the S. Typhimurium BiGG knowledge-base. The consensus MR was obtained starting from two independently developed MRs for S. Typhimurium. Key results of this reconstruction jamboree include i) development and implementation of a community-based workflow for MR annotation and reconciliation; ii) incorporation of thermodynamic information; and iii) use of the consensus MR to identify potential multi-target drug therapy approaches. Finally, taken together, with the growing number of parallel MRs a structured, community-driven approach will be necessary to maximize quality while increasing adoption of MRs in experimental design and interpretation.
A novel mathematical model for controllable near-field electrospinning
Ru, Changhai E-mail: luojun@shu.edu.cn; Chen, Jie; Shao, Zhushuai; Pang, Ming; Luo, Jun E-mail: luojun@shu.edu.cn
2014-01-15
Near-field electrospinning (NFES) had better controllability than conventional electrospinning. However, due to the lack of guidance of theoretical model, precise deposition of micro/nano fibers could only accomplished by experience. To analyze the behavior of charged jet in NFES using mathematical model, the momentum balance equation was simplified and a new expression between jet cross-sectional radius and axial position was derived. Using this new expression and mass conservation equation, expressions for jet cross-sectional radius and velocity were derived in terms of axial position and initial jet acceleration in the form of exponential functions. Based on Slender-body theory and Giesekus model, a quadratic equation for initial jet acceleration was acquired. With the proposed model, it was able to accurately predict the diameter and velocity of polymer fibers in NFES, and mathematical analysis rather than experimental methods could be applied to study the effects of the process parameters in NFES. Moreover, the movement velocity of the collector stage can be regulated by mathematical model rather than experience. Therefore, the model proposed in this paper had important guiding significance to precise deposition of polymer fibers.
Mathematical analysis of intermittent gas injection model in oil production
NASA Astrophysics Data System (ADS)
Tasmi, Silvya, D. R.; Pudjo, S.; Leksono, M.; Edy, S.
2016-02-01
Intermittent gas injection is a method to help oil production process. Gas is injected through choke in surface and then gas into tubing. Gas forms three areas in tubing: gas column area, film area and slug area. Gas column is used to propel slug area until surface. A mathematical model of intermittent gas injection is developed in gas column area, film area and slug area. Model is expanding based on mass and momentum conservation. Using assume film thickness constant in tubing, model has been developed by Tasmi et. al. [14]. Model consists of 10 ordinary differential equations. In this paper, assumption of pressure in gas column is uniform. Model consist of 9 ordinary differential equations. Connection of several variables can be obtained from this model. Therefore, dynamics of all variables that affect to intermittent gas lift process can be seen from four equations. To study the behavior of variables can be analyzed numerically and mathematically. In this paper, simple mathematically analysis approach is used to study behavior of the variables. Variables that affect to intermittent gas injection are pressure in upstream valve and in gas column. Pressure in upstream valve will decrease when gas mass in valve greater than gas mass in choke. Dynamic of the pressure in the gas column will decrease and increase depending on pressure in upstream valve.
Missing the Promise of Mathematical Modeling
ERIC Educational Resources Information Center
Meyer, Dan
2015-01-01
The Common Core State Standards for Mathematics (CCSSM) have exerted enormous pressure on every participant in a child's education. Students are struggling to meet new standards for mathematics learning, and parents are struggling to understand how to help them. Teachers are growing in their capacity to develop new mathematical competencies, and…
Middle School Mathematics Clinic: A Theoretical Model.
ERIC Educational Resources Information Center
Gore, Ethel V.
This paper describes a middle school mathematics clinic in the District of Columbia Public Schools, which was designed to aid students in the transition from mathematics in the primary grades to high school mathematics courses. It is intended to provide the low achiever with effective diagnostic and corrective instruction by the best trained…
Mathematical model of renal interstitial fibrosis
Hao, Wenrui; Rovin, Brad H.; Friedman, Avner
2014-01-01
Lupus nephritis (LN) is an autoimmune disease that occurs when autoantibodies complex with self-antigen and form immune complexes that accumulate in the glomeruli. These immune complexes initiate an inflammatory response resulting in glomerular injury. LN often concomitantly affects the tubulointerstitial compartment of the kidney, leading first to interstitial inflammation and subsequently to interstitial fibrosis and atrophy of the renal tubules if not appropriately treated. Presently the only way to assess interstitial inflammation and fibrosis is through kidney biopsy, which is invasive and cannot be repeated frequently. Hence, monitoring of disease progression and response to therapy is suboptimal. In this paper we describe a mathematical model of the progress from tubulointerstitial inflammation to fibrosis. We demonstrate how the model can be used to monitor treatments for interstitial fibrosis in LN with drugs currently being developed or used for nonrenal fibrosis. PMID:25225370
Mathematical modeling of a thermovoltaic cell
NASA Technical Reports Server (NTRS)
White, Ralph E.; Kawanami, Makoto
1992-01-01
A new type of battery named 'Vaporvolt' cell is in the early stage of its development. A mathematical model of a CuO/Cu 'Vaporvolt' cell is presented that can be used to predict the potential and the transport behavior of the cell during discharge. A sensitivity analysis of the various transport and electrokinetic parameters indicates which parameters have the most influence on the predicted energy and power density of the 'Vaporvolt' cell. This information can be used to decide which parameters should be optimized or determined more accurately through further modeling or experimental studies. The optimal thicknesses of electrodes and separator, the concentration of the electrolyte, and the current density are determined by maximizing the power density. These parameter sensitivities and optimal design parameter values will help in the development of a better CuO/Cu 'Vaporvolt' cell.
Mathematical Modeling of the Auditory Periphery.
NASA Astrophysics Data System (ADS)
Koshigoe, Shozo
The auditory periphery is conventionally divided into three parts, namely, the outer, middle, and inner ear (or cochlea). Mathematical modeling of the auditory periphery has been used for increasing our understanding of its mechanics via the simulation of experimental results, and for estimating unknown parameters. The various techniques used in this study for modeling the auditory periphery are: (1) Green function methods for investigation of the external ear directional filter functions; (2) finite difference methods in cochlear mechanical model calculations; (3) dispersion relation tests of the consistency of model calculations; (4) dispersion relation checks of experimental cochlear response data for approximate consistency with the implications of causality, linearity, time translation invariance, and minimum phase behavior; (5) dispersion relation tests of the stability of the linear cochlear models with active elements; (6) the introduction of viscosity effects in cochlear mechanics in order to account for data on the low frequency cochlear input impedance; and (7) the incorporation of a non-linear feedback outer-hair-cell model into a cochlear model in order to account for the physiological and psychological data (such as spontaneous and induced acoustic emissions from human ears and their active non-linear interactions with external stimuli).
Lin, Z; Gehring, R; Mochel, J P; Lavé, T; Riviere, J E
2016-10-01
This review provides a tutorial for individuals interested in quantitative veterinary pharmacology and toxicology and offers a basis for establishing guidelines for physiologically based pharmacokinetic (PBPK) model development and application in veterinary medicine. This is important as the application of PBPK modeling in veterinary medicine has evolved over the past two decades. PBPK models can be used to predict drug tissue residues and withdrawal times in food-producing animals, to estimate chemical concentrations at the site of action and target organ toxicity to aid risk assessment of environmental contaminants and/or drugs in both domestic animals and wildlife, as well as to help design therapeutic regimens for veterinary drugs. This review provides a comprehensive summary of PBPK modeling principles, model development methodology, and the current applications in veterinary medicine, with a focus on predictions of drug tissue residues and withdrawal times in food-producing animals. The advantages and disadvantages of PBPK modeling compared to other pharmacokinetic modeling approaches (i.e., classical compartmental/noncompartmental modeling, nonlinear mixed-effects modeling, and interspecies allometric scaling) are further presented. The review finally discusses contemporary challenges and our perspectives on model documentation, evaluation criteria, quality improvement, and offers solutions to increase model acceptance and applications in veterinary pharmacology and toxicology.
Mechanical-mathematical modeling for landslide process
NASA Astrophysics Data System (ADS)
Svalova, V.
2009-04-01
500 m and displacement of a landslide in the plan over 1 m. Last serious activization of a landslide has taken place in 2002 with a motion on 53 cm. Catastrophic activization of the deep blockglide landslide in the area of Khoroshevo in Moscow took place in 2006-2007. A crack of 330 m long appeared in the old sliding circus, along which a new 220 m long creeping block was separated from the plateau and began sinking with a displaced surface of the plateau reaching to 12 m. Such activization of the landslide process was not observed in Moscow since mid XIX century. The sliding area of Khoroshevo was stable during long time without manifestations of activity. Revealing of the reasons of deformation and development of ways of protection from deep landslide motions is extremely actual and difficult problem which decision is necessary for preservation of valuable historical monuments and modern city constructions. The reasons of activization and protective measures are discussed. Structure of monitoring system for urban territories is elaborated. Mechanical-mathematical model of high viscous fluid was used for modeling of matter behavior on landslide slopes. Equation of continuity and an approximated equation of the Navier-Stockes for slow motions in a thin layer were used. The results of modelling give possibility to define the place of highest velocity on landslide surface, which could be the best place for monitoring post position. Model can be used for calibration of monitoring equipment and gives possibility to investigate some fundamental aspects of matter movement on landslide slope.
Generalized Mathematical Model Predicting the Mechanical Processing Topography
NASA Astrophysics Data System (ADS)
Leonov, S. L.; Markov, A. M.; Belov, A. B.; Sczygol, N.
2016-04-01
We propose a unified approach for the construction of mathematical models for the formation of surface topography and calculation of its roughness parameters for different methods of machining processes. The approach is based on a process of geometric copy tool in the material which superimposes plastico-elastic deformation, oscillatory occurrences in processing and random components of the profile. The unified approach makes it possible to reduce the time forcreation of simulated stochastic model for a specific type of processing and guarantee the accuracy of geometric parameters calculation of the surface. We make an application example of generalized model for calculation of roughness density distribution Ra in external sharpening.
Analysis of unstable modes distinguishes mathematical models of flagellar motion
Bayly, P. V.; Wilson, K. S.
2015-01-01
The mechanisms underlying the coordinated beating of cilia and flagella remain incompletely understood despite the fundamental importance of these organelles. The axoneme (the cytoskeletal structure of cilia and flagella) consists of microtubule doublets connected by passive and active elements. The motor protein dynein is known to drive active bending, but dynein activity must be regulated to generate oscillatory, propulsive waveforms. Mathematical models of flagellar motion generate quantitative predictions that can be analysed to test hypotheses concerning dynein regulation. One approach has been to seek periodic solutions to the linearized equations of motion. However, models may simultaneously exhibit both periodic and unstable modes. Here, we investigate the emergence and coexistence of unstable and periodic modes in three mathematical models of flagellar motion, each based on a different dynein regulation hypothesis: (i) sliding control; (ii) curvature control and (iii) control by interdoublet separation (the ‘geometric clutch’ (GC)). The unstable modes predicted by each model are used to critically evaluate the underlying hypothesis. In particular, models of flagella with ‘sliding-controlled’ dynein activity admit unstable modes with non-propulsive, retrograde (tip-to-base) propagation, sometimes at the same parameter values that lead to periodic, propulsive modes. In the presence of these retrograde unstable modes, stable or periodic modes have little influence. In contrast, unstable modes of the GC model exhibit switching at the base and propulsive base-to-tip propagation. PMID:25833248
NASA Astrophysics Data System (ADS)
Banasiak, J.
2016-03-01
Since the emergence of systematic science it has been recognized that a natural phenomenon can be described by different models that vary in their complexity and their ability to capture the details of the features relevant at the required level of the resolution. It has been tacitly assumed that whenever two such models are applicable at the same level, they must provide equivalent descriptions of the phenomenon. One of the earliest and most celebrated examples of this type is offered by gas flow which can be described either by the Boltzmann equation at a suitably understood molecular level or by the Euler or Navier-Stokes equations at the level of continuum. More precisely, the flow of a gas as a continuous medium, or, in other words, at the macro level, can be explained in more detail by analysing elementary collisions between pairs of molecules. Thus, the Boltzmann equation is often recognized as a more detailed equation of gas at the so-called mesoscopic, or kinetic, level from which macroscopic properties of gas, such as density, momentum or temperature, can be derived. It should be noted that one can model gas at an even more fundamental, or micro, level by tracing the motion of individual molecules by solving the system of the Newton equations that describe their interactions, [11].
ERIC Educational Resources Information Center
Akgün, Levent
2015-01-01
The aim of this study is to identify prospective secondary mathematics teachers' opinions about the mathematical modeling method and the applicability of this method in high schools. The case study design, which is among the qualitative research methods, was used in the study. The study was conducted with six prospective secondary mathematics…
Mathematics Models in Chemistry--An Innovation for Non-Mathematics and Non-Science Majors
ERIC Educational Resources Information Center
Rash, Agnes M.; Zurbach, E. Peter
2004-01-01
The intention of this article is to present a year-long interdisciplinary course, Mathematical Models in Chemistry. The course is comprised of eleven units, each of which has both a mathematical and a chemical component. A syllabus of the course is given and the format of the class is explained. The interaction of the professors and the content is…
ERIC Educational Resources Information Center
Jitendra, Asha K.; Nelson, Gena; Pulles, Sandra M.; Kiss, Allyson J.; Houseworth, James
2016-01-01
The purpose of the present review was to evaluate the quality of the research and evidence base for representation of problems as a strategy to enhance the mathematical performance of students with learning disabilities and those at risk for mathematics difficulties. The authors evaluated 25 experimental and quasiexperimental studies according to…
Mathematical Modeling of the Origins of Life
NASA Technical Reports Server (NTRS)
Pohorille, Andrew
2006-01-01
The emergence of early metabolism - a network of catalyzed chemical reactions that supported self-maintenance, growth, reproduction and evolution of the ancestors of contemporary cells (protocells) was a critical, but still very poorly understood step on the path from inanimate to animate matter. Here, it is proposed and tested through mathematical modeling of biochemically plausible systems that the emergence of metabolism and its initial evolution towards higher complexity preceded the emergence of a genome. Even though the formation of protocellular metabolism was driven by non-genomic, highly stochastic processes the outcome was largely deterministic, strongly constrained by laws of chemistry. It is shown that such concepts as speciation and fitness to the environment, developed in the context of genomic evolution, also held in the absence of a genome.
Mathematical analysis of epidemiological models with heterogeneity
Van Ark, J.W.
1992-01-01
For many diseases in human populations the disease shows dissimilar characteristics in separate subgroups of the population; for example, the probability of disease transmission for gonorrhea or AIDS is much higher from male to female than from female to male. There is reason to construct and analyze epidemiological models which allow this heterogeneity of population, and to use these models to run computer simulations of the disease to predict the incidence and prevalence of the disease. In the models considered here the heterogeneous population is separated into subpopulations whose internal and external interactions are homogeneous in the sense that each person in the population can be assumed to have all average actions for the people of that subpopulation. The first model considered is an SIRS models; i.e., the Susceptible can become Infected, and if so he eventually Recovers with temporary immunity, and after a period of time becomes Susceptible again. Special cases allow for permanent immunity or other variations. This model is analyzed and threshold conditions are given which determine whether the disease dies out or persists. A deterministic model is presented; this model is constructed using difference equations, and it has been used in computer simulations for the AIDS epidemic in the homosexual population in San Francisco. The homogeneous version and the heterogeneous version of the differential-equations and difference-equations versions of the deterministic model are analyzed mathematically. In the analysis, equilibria are identified and threshold conditions are set forth for the disease to die out if the disease is below the threshold so that the disease-free equilibrium is globally asymptotically stable. Above the threshold the disease persists so that the disease-free equilibrium is unstable and there is a unique endemic equilibrium.
Noise in restaurants: levels and mathematical model.
To, Wai Ming; Chung, Andy
2014-01-01
Noise affects the dining atmosphere and is an occupational hazard to restaurant service employees worldwide. This paper examines the levels of noise in dining areas during peak hours in different types of restaurants in Hong Kong SAR, China. A mathematical model that describes the noise level in a restaurant is presented. The 1-h equivalent continuous noise level (L(eq,1-h)) was measured using a Type-1 precision integral sound level meter while the occupancy density, the floor area of the dining area, and the ceiling height of each of the surveyed restaurants were recorded. It was found that the measured noise levels using Leq,1-h ranged from 67.6 to 79.3 dBA in Chinese restaurants, from 69.1 to 79.1 dBA in fast food restaurants, and from 66.7 to 82.6 dBA in Western restaurants. Results of the analysis of variance show that there were no significant differences between means of the measured noise levels among different types of restaurants. A stepwise multiple regression analysis was employed to determine the relationships between geometrical and operational parameters and the measured noise levels. Results of the regression analysis show that the measured noise levels depended on the levels of occupancy density only. By reconciling the measured noise levels and the mathematical model, it was found that people in restaurants increased their voice levels when the occupancy density increased. Nevertheless, the maximum measured hourly noise level indicated that the noise exposure experienced by restaurant service employees was below the regulated daily noise exposure value level of 85 dBA.
Noise in restaurants: levels and mathematical model.
To, Wai Ming; Chung, Andy
2014-01-01
Noise affects the dining atmosphere and is an occupational hazard to restaurant service employees worldwide. This paper examines the levels of noise in dining areas during peak hours in different types of restaurants in Hong Kong SAR, China. A mathematical model that describes the noise level in a restaurant is presented. The 1-h equivalent continuous noise level (L(eq,1-h)) was measured using a Type-1 precision integral sound level meter while the occupancy density, the floor area of the dining area, and the ceiling height of each of the surveyed restaurants were recorded. It was found that the measured noise levels using Leq,1-h ranged from 67.6 to 79.3 dBA in Chinese restaurants, from 69.1 to 79.1 dBA in fast food restaurants, and from 66.7 to 82.6 dBA in Western restaurants. Results of the analysis of variance show that there were no significant differences between means of the measured noise levels among different types of restaurants. A stepwise multiple regression analysis was employed to determine the relationships between geometrical and operational parameters and the measured noise levels. Results of the regression analysis show that the measured noise levels depended on the levels of occupancy density only. By reconciling the measured noise levels and the mathematical model, it was found that people in restaurants increased their voice levels when the occupancy density increased. Nevertheless, the maximum measured hourly noise level indicated that the noise exposure experienced by restaurant service employees was below the regulated daily noise exposure value level of 85 dBA. PMID:25387532
Mathematical modeling of stormwater pollution in a tidal embayment
Najjar, K.F.
1989-01-01
It has been recognized for many years that stormwater runoff provides a transport mechanism for non-point pollutants into the nation's waterways. As more watershed areas continue to urbanize, greater increases in pollutant loadings will continue to impact the water quality of the receiving water bodies. In many instances, the pollutant impact exceeds the assimilative capacity of the receiving water. To estimate the potential impacts of stormwater pollution, mathematical models are constructed. In this dissertation, mathematical models have been constructed to estimate the non-point pollutant loadings from an urbanizing area as well as to model the assimilative capacity of the receiving tidal embayment system. The models are capable of simulating the hydrologic aspects as well as the water quality cycles of the system as a function of urbanization. In determining the response of the receiving water system to stormwater loadings, the change in receiving water quality is modeled spatially as well as temporally. The overall model is composed of three subsystem models: a stormwater model, a hydrodynamic tidal model, and a receiving water quality model. Construction of the stormwater model is based on STORM (Storage, Treatment, Overflow, Runoff Model) by the US Army Corps of Engineers. A ground water component to the model has been added to adjust the model for application to the study area, Lakes Bay, New Jersey. The tidal model is developed from a pseudo two-dimensional approach. The methodology utilizes the link-node concept to simulate the embayment system. Solutions to equations of motion and continuity are solved using a finite difference method. The receiving water quality model is a two-dimensional time variable water quality model which is based in a finite segment approach.
Mathematical and computer modeling of component surface shaping
NASA Astrophysics Data System (ADS)
Lyashkov, A.
2016-04-01
The process of shaping technical surfaces is an interaction of a tool (a shape element) and a component (a formable element or a workpiece) in their relative movements. It was established that the main objects of formation are: 1) a discriminant of a surfaces family, formed by the movement of the shape element relatively the workpiece; 2) an enveloping model of the real component surface obtained after machining, including transition curves and undercut lines; 3) The model of cut-off layers obtained in the process of shaping. When modeling shaping objects there are a lot of insufficiently solved or unsolved issues that make up a single scientific problem - a problem of qualitative shaping of the surface of the tool and then the component surface produced by this tool. The improvement of known metal-cutting tools, intensive development of systems of their computer-aided design requires further improvement of the methods of shaping the mating surfaces. In this regard, an important role is played by the study of the processes of shaping of technical surfaces with the use of the positive aspects of analytical and numerical mathematical methods and techniques associated with the use of mathematical and computer modeling. The author of the paper has posed and has solved the problem of development of mathematical, geometric and algorithmic support of computer-aided design of cutting tools based on computer simulation of the shaping process of surfaces.
Review and verification of CARE 3 mathematical model and code
NASA Technical Reports Server (NTRS)
Rose, D. M.; Altschul, R. E.; Manke, J. W.; Nelson, D. L.
1983-01-01
The CARE-III mathematical model and code verification performed by Boeing Computer Services were documented. The mathematical model was verified for permanent and intermittent faults. The transient fault model was not addressed. The code verification was performed on CARE-III, Version 3. A CARE III Version 4, which corrects deficiencies identified in Version 3, is being developed.
Mathematical Model for the Mineralization of Bone
NASA Technical Reports Server (NTRS)
Martin, Bruce
1994-01-01
A mathematical model is presented for the transport and precipitation of mineral in refilling osteons. One goal of this model was to explain calcification 'halos,' in which the bone near the haversian canal is more highly mineralized than the more peripheral lamellae, which have been mineralizing longer. It was assumed that the precipitation rate of mineral is proportional to the difference between the local concentration of calcium ions and an equilibrium concentration and that the transport of ions is by either diffusion or some other concentration gradient-dependent process. Transport of ions was assumed to be slowed by the accumulation of mineral in the matrix along the transport path. ne model also mimics bone apposition, slowing of apposition during refilling, and mineralization lag time. It was found that simple diffusion cannot account for the transport of calcium ions into mineralizing bone, because the diffusion coefficient is two orders of magnitude too low. If a more rapid concentration gradient-driven means of transport exists, the model demonstrates that osteonal geometry and variable rate of refilling work together to produce calcification halos, as well as the primary and secondary calcification effect reported in the literature.
Mathematical Model for the Mineralization of Bone
NASA Technical Reports Server (NTRS)
Martin, Bruce
1994-01-01
A mathematical model is presented for the transport and precipitation of mineral in refilling osteons. One goal of this model was to explain calcification 'halos,' in which the bone near the haversian canal is more highly mineralized than the more peripheral lamellae, which have been mineralizing longer. It was assumed that the precipitation rate of mineral is proportional to the difference between the local concentration of calcium ions and an equilibrium concentration and that the transport of ions is by either diffusion or some other concentration gradient-dependent process. Transport of ions was assumed to be slowed by the accumulation of mineral in the matrix along the transport path. The model also mimics bone apposition, slowing of apposition during refilling, and mineralization lag time. It was found that simple diffusion cannot account for the transport of calcium ions into mineralizing bone, because the diffusion coefficient is two orders of magnitude too low. If a more rapid concentration gradient-driven means of transport exists, the model demonstrates that osteonal geometry and variable rate of refilling work together to produce calcification halos, as well as the primary and secondary calcification effect reported in the literature.
Analyzing electrical activities of pancreatic β cells using mathematical models.
Cha, Chae Young; Powell, Trevor; Noma, Akinori
2011-11-01
Bursts of repetitive action potentials are closely related to the regulation of glucose-induced insulin secretion in pancreatic β cells. Mathematical studies with simple β-cell models have established the central principle that the burst-interburst events are generated by the interaction between fast membrane excitation and slow cytosolic components. Recently, a number of detailed models have been developed to simulate more realistic β cell activity based on expanded findings on biophysical characteristics of cellular components. However, their complex structures hinder our intuitive understanding of the underlying mechanisms, and it is becoming more difficult to dissect the role of a specific component out of the complex network. We have recently developed a new detailed model by incorporating most of ion channels and transporters recorded experimentally (the Cha-Noma model), yet the model satisfies the charge conservation law and reversible responses to physiological stimuli. Here, we review the mechanisms underlying bursting activity by applying mathematical analysis tools to representative simple and detailed models. These analyses include time-based simulation, bifurcation analysis and lead potential analysis. In addition, we introduce a new steady-state I-V (ssI-V) curve analysis. We also discuss differences in electrical signals recorded from isolated single cells or from cells maintaining electrical connections within multi-cell preparations. Towards this end, we perform simulations with our detailed pancreatic β-cell model.
Mathematical model insights into arsenic detoxification
2011-01-01
Background Arsenic in drinking water, a major health hazard to millions of people in South and East Asia and in other parts of the world, is ingested primarily as trivalent inorganic arsenic (iAs), which then undergoes hepatic methylation to methylarsonic acid (MMAs) and a second methylation to dimethylarsinic acid (DMAs). Although MMAs and DMAs are also known to be toxic, DMAs is more easily excreted in the urine and therefore methylation has generally been considered a detoxification pathway. A collaborative modeling project between epidemiologists, biologists, and mathematicians has the purpose of explaining existing data on methylation in human studies in Bangladesh and also testing, by mathematical modeling, effects of nutritional supplements that could increase As methylation. Methods We develop a whole body mathematical model of arsenic metabolism including arsenic absorption, storage, methylation, and excretion. The parameters for arsenic methylation in the liver were taken from the biochemical literature. The transport parameters between compartments are largely unknown, so we adjust them so that the model accurately predicts the urine excretion rates of time for the iAs, MMAs, and DMAs in single dose experiments on human subjects. Results We test the model by showing that, with no changes in parameters, it predicts accurately the time courses of urinary excretion in mutiple dose experiments conducted on human subjects. Our main purpose is to use the model to study and interpret the data on the effects of folate supplementation on arsenic methylation and excretion in clinical trials in Bangladesh. Folate supplementation of folate-deficient individuals resulted in a 14% decrease in arsenicals in the blood. This is confirmed by the model and the model predicts that arsenicals in the liver will decrease by 19% and arsenicals in other body stores by 26% in these same individuals. In addition, the model predicts that arsenic methyltransferase has been
Web-Based Implementation of Discrete Mathematics
ERIC Educational Resources Information Center
Love, Tanzy; Keinert, Fritz; Shelley, Mack
2006-01-01
The Department of Mathematics at Iowa State University teaches a freshman-level Discrete Mathematics course with total enrollment of about 1,800 students per year. The traditional format includes large lectures, with about 150 students each, taught by faculty and temporary instructors in two class sessions per week and recitation sections, with…
Mathematical model of one-man air revitalization system
NASA Technical Reports Server (NTRS)
1976-01-01
A mathematical model was developed for simulating the steady state performance in electrochemical CO2 concentrators which utilize (NMe4)2 CO3 (aq.) electrolyte. This electrolyte, which accommodates a wide range of air relative humidity, is most suitable for one-man air revitalization systems. The model is based on the solution of coupled nonlinear ordinary differential equations derived from mass transport and rate equations for the processes which take place in the cell. The boundary conditions are obtained by solving the mass and energy transport equations. A shooting method is used to solve the differential equations.
A review on mathematical models for estimating indoor radon concentrations.
Park, Ji Hyun; Kang, Dae Ryong; Kim, Jinheum
2016-01-01
Radiation from natural sources is one of causes of the environmental diseases. Radon is the leading environmental cause of lung cancer next to smoking. To investigate the relationship between indoor radon concentrations and lung cancer, researchers must be able to estimate an individual's cumulative level of indoor radon exposure and to do so, one must first be able to assess indoor radon concentrations. In this article, we outline factors affecting indoor radon concentrations and review related mathematical models based on the mass balance equation and the differential equations. Furthermore, we suggest the necessities of applying time-dependent functions for indoor radon concentrations and developing stochastic models. PMID:26925235
A 6DOF mathematical model of parachute in Mars EDL
NASA Astrophysics Data System (ADS)
Shen, Ganghui; Xia, Yuanqing; Sun, Haoran
2015-04-01
The base of the dynamics characteristic research on the parachute and vehicle system is to establish a dynamics model, during the parachute descent phase, which can accurately display the relationship among the velocity, altitude and attitude angles as well as the variation of time. This paper starts with a new tracking law - ADRC in Mars entry guidance, which affects the initial states of the parachute deployment point and determines precision landing capability. Then, the influence of unsteady resistance to the parachute in Martian air is considered as the added mass, and a 6DOF nonlinear mathematical model of the parachute and vehicle system is established.
Impulsive mathematical modeling of ascorbic acid metabolism in healthy subjects.
Bachar, Mostafa; Raimann, Jochen G; Kotanko, Peter
2016-03-01
In this work, we develop an impulsive mathematical model of Vitamin C (ascorbic acid) metabolism in healthy subjects for daily intake over a long period of time. The model includes the dynamics of ascorbic acid plasma concentration, the ascorbic acid absorption in the intestines and a novel approach to quantify the glomerular excretion of ascorbic acid. We investigate qualitative and quantitative dynamics. We show the existence and uniqueness of the global asymptotic stability of the periodic solution. We also perform a numerical simulation for the entire time period based on published data reporting parameters reflecting ascorbic acid metabolism at different oral doses of ascorbic acid.
A Mathematical Model of a Simple Amplifier Using a Ferroelectric Transistor
NASA Technical Reports Server (NTRS)
Sayyah, Rana; Hunt, Mitchell; MacLeod, Todd C.; Ho, Fat D.
2009-01-01
This paper presents a mathematical model characterizing the behavior of a simple amplifier using a FeFET. The model is based on empirical data and incorporates several variables that affect the output, including frequency, load resistance, and gate-to-source voltage. Since the amplifier is the basis of many circuit configurations, a mathematical model that describes the behavior of a FeFET-based amplifier will help in the integration of FeFETs into many other circuits.
Mathematics Teacher TPACK Standards and Development Model
ERIC Educational Resources Information Center
Niess, Margaret L.; Ronau, Robert N.; Shafer, Kathryn G.; Driskell, Shannon O.; Harper, Suzanne R.; Johnston, Christopher; Browning, Christine; Ozgun-Koca, S. Asli; Kersaint, Gladis
2009-01-01
What knowledge is needed to teach mathematics with digital technologies? The overarching construct, called technology, pedagogy, and content knowledge (TPACK), has been proposed as the interconnection and intersection of technology, pedagogy, and content knowledge. Mathematics Teacher TPACK Standards offer guidelines for thinking about this…
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…
Some Models of Mathematics Teachers' Centres.
ERIC Educational Resources Information Center
Seiferth, Berniece B.
There are two types of teacher centres in Great Britain, multi-purpose centres designed for all subjects of the curriculum, and topical centres which deal specifically with one area of subject matter such as mathematics, English, etc. In this paper, the five mathematics centres in London are analyzed for purpose, materials available, and…
Fernández-Colino, A; Bermudez, J M; Arias, F J; Quinteros, D; Gonzo, E
2016-04-01
Transversality between mathematical modeling, pharmacology, and materials science is essential in order to achieve controlled-release systems with advanced properties. In this regard, the area of biomaterials provides a platform for the development of depots that are able to achieve controlled release of a drug, whereas pharmacology strives to find new therapeutic molecules and mathematical models have a connecting function, providing a rational understanding by modeling the parameters that influence the release observed. Herein we present a mechanism which, based on reasonable assumptions, explains the experimental data obtained very well. In addition, we have developed a simple and accurate “lumped” kinetics model to correctly fit the experimentally observed drug-release behavior. This lumped model allows us to have simple analytic solutions for the mass and rate of drug release as a function of time without limitations of time or mass of drug released, which represents an important step-forward in the area of in vitro drug delivery when compared to the current state of the art in mathematical modeling. As an example, we applied the mechanism and model to the release data for acetazolamide from a recombinant polymer. Both materials were selected because of a need to develop a suitable ophthalmic formulation for the treatment of glaucoma. The in vitro release model proposed herein provides a valuable predictive tool for ensuring product performance and batch-to-batch reproducibility, thus paving the way for the development of further pharmaceutical devices.
Fernández-Colino, A; Bermudez, J M; Arias, F J; Quinteros, D; Gonzo, E
2016-04-01
Transversality between mathematical modeling, pharmacology, and materials science is essential in order to achieve controlled-release systems with advanced properties. In this regard, the area of biomaterials provides a platform for the development of depots that are able to achieve controlled release of a drug, whereas pharmacology strives to find new therapeutic molecules and mathematical models have a connecting function, providing a rational understanding by modeling the parameters that influence the release observed. Herein we present a mechanism which, based on reasonable assumptions, explains the experimental data obtained very well. In addition, we have developed a simple and accurate “lumped” kinetics model to correctly fit the experimentally observed drug-release behavior. This lumped model allows us to have simple analytic solutions for the mass and rate of drug release as a function of time without limitations of time or mass of drug released, which represents an important step-forward in the area of in vitro drug delivery when compared to the current state of the art in mathematical modeling. As an example, we applied the mechanism and model to the release data for acetazolamide from a recombinant polymer. Both materials were selected because of a need to develop a suitable ophthalmic formulation for the treatment of glaucoma. The in vitro release model proposed herein provides a valuable predictive tool for ensuring product performance and batch-to-batch reproducibility, thus paving the way for the development of further pharmaceutical devices. PMID:26838852
ERIC Educational Resources Information Center
Marshall, Neil; Buteau, Chantal
2014-01-01
As part of their undergraduate mathematics curriculum, students at Brock University learn to create and use computer-based tools with dynamic, visual interfaces, called Exploratory Objects, developed for the purpose of conducting pure or applied mathematical investigations. A student's Development Process Model of creating and using an Exploratory…
ERIC Educational Resources Information Center
Huang, Tzu-Hua; Liu, Yuan-Chen; Chang, Hsiu-Chen
2012-01-01
This study developed a computer-assisted mathematical problem-solving system in the form of a network instruction website to help low-achieving second- and third-graders in mathematics with word-based addition and subtraction questions in Taiwan. According to Polya's problem-solving model, the system is designed to guide these low-achievers…
ERIC Educational Resources Information Center
Norton, Anderson; McCloskey, Andrea; Hudson, Rick A.
2011-01-01
In order to evaluate the effectiveness of an experimental elementary mathematics field experience course, we have designed a new assessment instrument. These video-based prediction assessments engage prospective teachers in a video analysis of a child solving mathematical tasks. The prospective teachers build a model of that child's mathematics…
Mathematical modeling of Chikungunya fever control
NASA Astrophysics Data System (ADS)
Hincapié-Palacio, Doracelly; Ospina, Juan
2015-05-01
Chikungunya fever is a global concern due to the occurrence of large outbreaks, the presence of persistent arthropathy and its rapid expansion throughout various continents. Globalization and climate change have contributed to the expansion of the geographical areas where mosquitoes Aedes aegypti and Aedes albopictus (Stegomyia) remain. It is necessary to improve the techniques of vector control in the presence of large outbreaks in The American Region. We derive measures of disease control, using a mathematical model of mosquito-human interaction, by means of three scenarios: a) a single vector b) two vectors, c) two vectors and human and non-human reservoirs. The basic reproductive number and critical control measures were deduced by using computer algebra with Maple (Maplesoft Inc, Ontario Canada). Control measures were simulated with parameter values obtained from published data. According to the number of households in high risk areas, the goals of effective vector control to reduce the likelihood of mosquito-human transmission would be established. Besides the two vectors, if presence of other non-human reservoirs were reported, the monthly target of effective elimination of the vector would be approximately double compared to the presence of a single vector. The model shows the need to periodically evaluate the effectiveness of vector control measures.
iSTEM: Promoting Fifth Graders' Mathematical Modeling
ERIC Educational Resources Information Center
Yanik, H. Bahadir; Karabas, Celil
2014-01-01
Modeling requires that people develop representations or procedures to address particular problem situations (Lesh et al. 2000). Mathematical modeling is used to describe essential characteristics of a phenomenon or a situation that one intends to study in the real world through building mathematical objects. This article describes how fifth-grade…
Mathematical Manipulative Models: In Defense of "Beanbag Biology"
ERIC Educational Resources Information Center
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…
Visual Modeling as a Motivation for Studying Mathematics and Art
ERIC Educational Resources Information Center
Sendova, Evgenia; Grkovska, Slavica
2005-01-01
The paper deals with the possibility of enriching the curriculum in mathematics, informatics and art by means of visual modeling of abstract paintings. The authors share their belief that in building a computer model of a construct, one gains deeper insight into the construct, and is motivated to elaborate one's knowledge in mathematics and…
The limitations of mathematical modeling in high school physics education
NASA Astrophysics Data System (ADS)
Forjan, Matej
The theme of the doctoral dissertation falls within the scope of didactics of physics. Theoretical analysis of the key constraints that occur in the transmission of mathematical modeling of dynamical systems into field of physics education in secondary schools is presented. In an effort to explore the extent to which current physics education promotes understanding of models and modeling, we analyze the curriculum and the three most commonly used textbooks for high school physics. We focus primarily on the representation of the various stages of modeling in the solved tasks in textbooks and on the presentation of certain simplifications and idealizations, which are in high school physics frequently used. We show that one of the textbooks in most cases fairly and reasonably presents the simplifications, while the other two half of the analyzed simplifications do not explain. It also turns out that the vast majority of solved tasks in all the textbooks do not explicitly represent model assumptions based on what we can conclude that in high school physics the students do not develop sufficiently a sense of simplification and idealizations, which is a key part of the conceptual phase of modeling. For the introduction of modeling of dynamical systems the knowledge of students is also important, therefore we performed an empirical study on the extent to which high school students are able to understand the time evolution of some dynamical systems in the field of physics. The research results show the students have a very weak understanding of the dynamics of systems in which the feedbacks are present. This is independent of the year or final grade in physics and mathematics. When modeling dynamical systems in high school physics we also encounter the limitations which result from the lack of mathematical knowledge of students, because they don't know how analytically solve the differential equations. We show that when dealing with one-dimensional dynamical systems
ERIC Educational Resources Information Center
Hong, Sehee; Yoo, Sung-Kyung; You, Sukkyung; Wu, Chih-Chun
2010-01-01
This study focused on comparing the longitudinal associations between two types of parental involvement (i.e., mathematics value and academic reinforcement) and high school students' mathematics achievement, using data from the Longitudinal Study of American Youth (LSAY). Results, based on multivariate autoregressive cross-lagged modeling,…
Mathematical modeling of the neuron morphology using two dimensional images.
Rajković, Katarina; Marić, Dušica L; Milošević, Nebojša T; Jeremic, Sanja; Arsenijević, Valentina Arsić; Rajković, Nemanja
2016-02-01
In this study mathematical analyses such as the analysis of area and length, fractal analysis and modified Sholl analysis were applied on two dimensional (2D) images of neurons from adult human dentate nucleus (DN). Using mathematical analyses main morphological properties were obtained including the size of neuron and soma, the length of all dendrites, the density of dendritic arborization, the position of the maximum density and the irregularity of dendrites. Response surface methodology (RSM) was used for modeling the size of neurons and the length of all dendrites. However, the RSM model based on the second-order polynomial equation was only possible to apply to correlate changes in the size of the neuron with other properties of its morphology. Modeling data provided evidence that the size of DN neurons statistically depended on the size of the soma, the density of dendritic arborization and the irregularity of dendrites. The low value of mean relative percent deviation (MRPD) between the experimental data and the predicted neuron size obtained by RSM model showed that model was suitable for modeling the size of DN neurons. Therefore, RSM can be generally used for modeling neuron size from 2D images.
Willenbring, James M.; Bartlett, Roscoe Ainsworth; Heroux, Michael Allen
2012-01-01
Software lifecycles are becoming an increasingly important issue for computational science and engineering (CSE) software. The process by which a piece of CSE software begins life as a set of research requirements and then matures into a trusted high-quality capability is both commonplace and extremely challenging. Although an implicit lifecycle is obviously being used in any effort, the challenges of this process - respecting the competing needs of research vs. production - cannot be overstated. Here we describe a proposal for a well-defined software lifecycle process based on modern Lean/Agile software engineering principles. What we propose is appropriate for many CSE software projects that are initially heavily focused on research but also are expected to eventually produce usable high-quality capabilities. The model is related to TriBITS, a build, integration and testing system, which serves as a strong foundation for this lifecycle model, and aspects of this lifecycle model are ingrained in the TriBITS system. Here, we advocate three to four phases or maturity levels that address the appropriate handling of many issues associated with the transition from research to production software. The goals of this lifecycle model are to better communicate maturity levels with customers and to help to identify and promote Software Engineering (SE) practices that will help to improve productivity and produce better software. An important collection of software in this domain is Trilinos, which is used as the motivation and the initial target for this lifecycle model. However, many other related and similar CSE (and non-CSE) software projects can also make good use of this lifecycle model, especially those that use the TriBITS system. Indeed this lifecycle process, if followed, will enable large-scale sustainable integration of many complex CSE software efforts across several institutions.
Mathematical modeling as a tool for investigating cell cycle control networks.
Sible, Jill C; Tyson, John J
2007-02-01
Although not a traditional experimental "method," mathematical modeling can provide a powerful approach for investigating complex cell signaling networks, such as those that regulate the eukaryotic cell division cycle. We describe here one modeling approach based on expressing the rates of biochemical reactions in terms of nonlinear ordinary differential equations. We discuss the steps and challenges in assigning numerical values to model parameters and the importance of experimental testing of a mathematical model. We illustrate this approach throughout with the simple and well-characterized example of mitotic cell cycles in frog egg extracts. To facilitate new modeling efforts, we describe several publicly available modeling environments, each with a collection of integrated programs for mathematical modeling. This review is intended to justify the place of mathematical modeling as a standard method for studying molecular regulatory networks and to guide the non-expert to initiate modeling projects in order to gain a systems-level perspective for complex control systems. PMID:17189866
Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century.
Ganusov, Vitaly V
2016-01-01
While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest "strong inference in mathematical modeling" as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century.
Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century.
Ganusov, Vitaly V
2016-01-01
While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest "strong inference in mathematical modeling" as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century. PMID:27499750
Mathematical modeling and the neuroscience of metaphor
NASA Astrophysics Data System (ADS)
Rising, Hawley K., III
2008-02-01
We look at a characterization of metaphor from cognitive linguistics, extracting the salient features of metaphorical processing. We examine the neurobiology of dendrites, specifically spike timing-dependent plasticity (STDP), and the modulation of backpropagating action potentials (bAPs), to generate a neuropil-centric model of cortical processing based on signal timing and reverberation between regions. We show how this model supports the basic features of metaphorical processing previously extracted. Finally, we model this system using a combination of euclidean, projective, and hyperbolic geometries, and show how the resulting model accounts for this processing, and relates to other neural network models
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.
Mathematical modeling of the human knee joint
Ricafort, Juliet
1996-05-01
A model was developed to determine the forces exerted by several flexor and extensor muscles of the human knee under static conditions. The following muscles were studied: the gastrocnemius, biceps femoris, semitendinosus, semimembranosus, and the set of quadricep muscles. The tibia and fibula were each modeled as rigid bodies; muscles were modeled by their functional lines of action in space. Assumptions based on previous data were used to resolve the indeterminacy.
Variational Data Assimilation Technique in Mathematical Modeling of Ocean Dynamics
NASA Astrophysics Data System (ADS)
Agoshkov, V. I.; Zalesny, V. B.
2012-03-01
Problems of the variational data assimilation for the primitive equation ocean model constructed at the Institute of Numerical Mathematics, Russian Academy of Sciences are considered. The model has a flexible computational structure and consists of two parts: a forward prognostic model, and its adjoint analog. The numerical algorithm for the forward and adjoint models is constructed based on the method of multicomponent splitting. The method includes splitting with respect to physical processes and space coordinates. Numerical experiments are performed with the use of the Indian Ocean and the World Ocean as examples. These numerical examples support the theoretical conclusions and demonstrate the rationality of the approach using an ocean dynamics model with an observed data assimilation procedure.
Mathematical modeling of a hydrophilic cylinder floating on water.
Mao, Zai-Sha; Yang, Chao; Chen, Jiayong
2012-07-01
In this paper, a hydrostatic model of the surface profile anchored to the upper edge of a vertical cylinder is proposed to explain why coins can float on water surface. The sharp edge of a cylinder is thus modeled as a round smooth surface on which the contact line may be anchored at a position according to the weight of the cylinder. The mathematical model of the surface profile is established based on the hydrostatics and a third order ordinary differential equation is resulted. Numerical solution of the model demonstrates under practical conditions the existence of the surface profiles that provide reasonable uplifting force at the contact line so that the force is available for floating coins on water surface. The proposed model explains the obviously enlarged apparent contact angle and the edge effect in the literature. The numerical simulation is found in very good agreement with the experimental data in the literature. PMID:22520711
Strong Inference in Mathematical Modeling: A Method for Robust Science in the Twenty-First Century
Ganusov, Vitaly V.
2016-01-01
While there are many opinions on what mathematical modeling in biology is, in essence, modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions. Only when this tool is applied appropriately, as microscope is used to look at small items, it may allow to understand importance of specific mechanisms/assumptions in biological processes. Mathematical modeling can be less useful or even misleading if used inappropriately, for example, when a microscope is used to study stars. According to some philosophers (Oreskes et al., 1994), the best use of mathematical models is not when a model is used to confirm a hypothesis but rather when a model shows inconsistency of the model (defined by a specific set of assumptions) and data. Following the principle of strong inference for experimental sciences proposed by Platt (1964), I suggest “strong inference in mathematical modeling” as an effective and robust way of using mathematical modeling to understand mechanisms driving dynamics of biological systems. The major steps of strong inference in mathematical modeling are (1) to develop multiple alternative models for the phenomenon in question; (2) to compare the models with available experimental data and to determine which of the models are not consistent with the data; (3) to determine reasons why rejected models failed to explain the data, and (4) to suggest experiments which would allow to discriminate between remaining alternative models. The use of strong inference is likely to provide better robustness of predictions of mathematical models and it should be strongly encouraged in mathematical modeling-based publications in the Twenty-First century. PMID:27499750
Helping Students Become Better Mathematical Modelers: Pseudosteady-State Approximations.
ERIC Educational Resources Information Center
Bunge, Annette L.; Miller, Ronald L.
1997-01-01
Undergraduate and graduate students are often confused about several aspects of modeling physical systems. Describes an approach to address these issues using a single physical transport problem that can be analyzed with multiple mathematical models. (DKM)
Mathematical modeling of heat transfer problems in the permafrost
NASA Astrophysics Data System (ADS)
Gornov, V. F.; Stepanov, S. P.; Vasilyeva, M. V.; Vasilyev, V. I.
2014-11-01
In this work we present results of numerical simulation of three-dimensional temperature fields in soils for various applied problems: the railway line in the conditions of permafrost for different geometries, the horizontal tunnel underground storage and greenhouses of various designs in the Far North. Mathematical model of the process is described by a nonstationary heat equation with phase transitions of pore water. The numerical realization of the problem is based on the finite element method using a library of scientific computing FEniCS. For numerical calculations we use high-performance computing systems.
Cordero, V V; Cavinder, C A; Tedeschi, L O; Sigler, D H; Vogelsang, M M; Arnold, C E
2013-05-01
Mathematical nutrition models have been developed for beef and dairy cattle to estimate dietary energy intake needed to change BCS. Similar technology has not been used to improve nutrition and feeding strategies for horses. An accurate equine nutrition model may enhance feeding management and reduce the costs of unnecessary overfeeding and promote an optimal level of fatness to achieve reproductive efficiency. The objectives of this study were to develop and evaluate a mathematical nutrition model capable of accurately predicting dietary energy changes to alter BW, rump fat (RF) thickness, and overall body fat (BF), which is needed to maximize profitability and productivity of mares. Model structure was similar to a previously developed model for cattle, and literature data for Quarter Horse mares were used to parameterize the horse model in predicting DE requirement associated with BCS changes. Evaluation of the horse model was performed using an independent dataset comprising 20 nonlactating Quarter Horse mares. Pretrial BCS was used to assign mares to 1 of 4 treatment groups and fed to alter BCS by 1 unit as follows: from 4 to 5 (Group 1), 5 to 4 (Group 2), 6 to 7 (Group 3), and 7 to 6 (Group 4). The BCS, RF thickness, and BW were measured for each mare before the commencement of the feeding trial and once per week thereafter for the duration of a 30-d feeding trial. Initial and target BCS, percent BF, and BW data were collected from each mare and inputted into the model. Mares were individually fed according to the DE suggestions proposed by the model to achieve the targeted BCS change within 30 d. The coefficient of determination of observed and model-predicted values (model precision) was 0.907 (P < 0.001) for BCS, 0.607 (P < 0.001) for percent BF, and 0.94 (P < 0.001) for BW. The BCS was highly correlated to percent BF (r = 0.808; P = 0.01). We concluded the reparameterized model was reliable to predict changes in BW and BCS, but more work is needed to
Mathematical model of the electric arc furnace. Final report
Szekely, J.
1982-07-01
Electric Arc Furnace Steelmaking is responsible for some 25% of the steel produced in the US and this proportion is likely to grow in the future. This operation consumes some 1.4 x 10/sup 10/ kWh annually at an overall process efficiency of about 60 to 75%. The purpose of this program has been to develop a mathematical model representing the energy transfer in electric arc furnaces with the objective of defining means for the optimization of the system, such that the energy consumption is reduced. Through the statement of the appropriate transport equations, subject to certain simplifying assumptions, a mathematical model has been developed to represent heat and fluid flow phenomena in the arc, the interaction of the arc with the bath, and bath circulation in electric arc furnaces. While there is a paucity of reliable information for the critical testing of the model as a description of industrial scale arc furnaces, there is enough data on plasmas, arcs and some industrial units to prove that the basic premises of the modelling effort are sound; indeed the predictions based on the model were found to be consistent with industrial scale measurements.
Typhoid transmission: a historical perspective on mathematical model development.
Bakach, Iurii; Just, Matthew R; Gambhir, Manoj; Fung, Isaac Chun-Hai
2015-11-01
Mathematical models of typhoid transmission were first developed nearly half a century ago. To facilitate a better understanding of the historical development of this field, we reviewed mathematical models of typhoid and summarized their structures and limitations. Eleven models, published in 1971 to 2014, were reviewed. While models of typhoid vaccination are well developed, we highlight the need to better incorporate water, sanitation and hygiene interventions into models of typhoid and other foodborne and waterborne diseases. Mathematical modeling is a powerful tool to test and compare different intervention strategies which is important in the world of limited resources. By working collaboratively, epidemiologists and mathematicians should build better mathematical models of typhoid transmission, including pharmaceutical and non-pharmaceutical interventions, which will be useful in epidemiological and public health practice.
Physical vs. Mathematical Models in Rock Mechanics
NASA Astrophysics Data System (ADS)
Morozov, I. B.; Deng, W.
2013-12-01
One of the less noted challenges in understanding the mechanical behavior of rocks at both in situ and lab conditions is the character of theoretical approaches being used. Currently, the emphasis is made on spatial averaging theories (homogenization and numerical models of microstructure), empirical models for temporal behavior (material memory, compliance functions and complex moduli), and mathematical transforms (Laplace and Fourier) used to infer the Q-factors and 'relaxation mechanisms'. In geophysical applications, we have to rely on such approaches for very broad spatial and temporal scales which are not available in experiments. However, the above models often make insufficient use of physics and utilize, for example, the simplified 'correspondence principle' instead of the laws of viscosity and friction. As a result, the commonly-used time- and frequency dependent (visco)elastic moduli represent apparent properties related to the measurement procedures and not necessarily to material properties. Predictions made from such models may therefore be inaccurate or incorrect when extrapolated beyond the lab scales. To overcome the above challenge, we need to utilize the methods of micro- and macroscopic mechanics and thermodynamics known in theoretical physics. This description is rigorous and accurate, uses only partial differential equations, and allows straightforward numerical implementations. One important observation from the physical approach is that the analysis should always be done for the specific geometry and parameters of the experiment. Here, we illustrate these methods on axial deformations of a cylindrical rock sample in the lab. A uniform, isotropic elastic rock with a thermoelastic effect is considered in four types of experiments: 1) axial extension with free transverse boundary, 2) pure axial extension with constrained transverse boundary, 3) pure bulk expansion, and 4) axial loading harmonically varying with time. In each of these cases, an
College Students Attitude and Mathematics Achievement Using Web Based Homework
ERIC Educational Resources Information Center
Leong, Kwan Eu; Alexander, Nathan
2014-01-01
The goal of this study was to understand how students' attitudes were connected to their mathematics learning and achievement. This investigation of students (n = 78) and their attitudes was specific to web-based homework in developmental mathematics courses in a two-year community college located in a large urban city in the United States. A…
Web-Based Mathematics: Some "Dos" and "Don'ts"
ERIC Educational Resources Information Center
Loong, Esther Yook-Kin
2011-01-01
This case study describes an "out of field" teacher's use of the Internet to teach a range of mathematical topics in a modified Year 8 mathematics class. It highlights the importance of three factors for implementing a discernible web-based teaching strategy: appropriate choice of web objects, effective "virtual" pedagogy, and technical support…
Inquiry-Based Learning and the Art of Mathematical Discourse
ERIC Educational Resources Information Center
von Renesse, Christine; Ecke, Volker
2015-01-01
Our particular flavor of inquiry-based learning (IBL) uses mathematical discourse, conversations, and discussions to empower students to deepen their mathematical thinking, building on strengths of students in the humanities. We present an organized catalog of powerful questions, discussion prompts, and talk moves that can help faculty facilitate…
The Consequences of a Problem-Based Mathematics Curriculum
ERIC Educational Resources Information Center
Clarke, David; Breed, Margarita; Fraser, Sherry
2004-01-01
Implementation of a problem-based mathematics curriculum, the "Interactive Mathematics Program" (IMP), at three high schools in California has been associated with more than just differences in student achievement. The outcomes that distinguished students who participated in the IMP program from students who followed a conventional…
An Assessment Model for Proof Comprehension in Undergraduate Mathematics
ERIC Educational Resources Information Center
Mejia-Ramos, Juan Pablo; Fuller, Evan; Weber, Keith; Rhoads, Kathryn; Samkoff, Aron
2012-01-01
Although proof comprehension is fundamental in advanced undergraduate mathematics courses, there has been limited research on what it means to understand a mathematical proof at this level and how such understanding can be assessed. In this paper, we address these issues by presenting a multidimensional model for assessing proof comprehension in…
Mathematical Modeling, Sense Making, and the Common Core State Standards
ERIC Educational Resources Information Center
Schoenfeld, Alan H.
2013-01-01
On October 14, 2013 the Mathematics Education Department at Teachers College hosted a full-day conference focused on the Common Core Standards Mathematical Modeling requirements to be implemented in September 2014 and in honor of Professor Henry Pollak's 25 years of service to the school. This article is adapted from my talk at this conference…
Bridging the Gap Between Common Sense and Mathematical Models
ERIC Educational Resources Information Center
Press, Laurence
1975-01-01
Describes a four-phase method of helping students who are mathematically unsophisticated and have difficulty relating their common sense, English-language understanding of a system to an abstract, mathematical description. The approach uses interactive simulation models. (Author/IRT)
Using Spreadsheets to Teach Aspects of Biology Involving Mathematical Models
ERIC Educational Resources Information Center
Carlton, Kevin; Nicholls, Mike; Ponsonby, David
2004-01-01
Some aspects of biology, for example the Hardy-Weinberg simulation of population genetics or modelling heat flow in lizards, have an undeniable mathematical basis. Students can find the level of mathematical skill required to deal with such concepts to be an insurmountable hurdle to understanding. If not used effectively, spreadsheet models…
Teaching Writing and Communication in a Mathematical Modeling Course
ERIC Educational Resources Information Center
Linhart, Jean Marie
2014-01-01
Writing and communication are essential skills for success in the workplace or in graduate school, yet writing and communication are often the last thing that instructors think about incorporating into a mathematics course. A mathematical modeling course provides a natural environment for writing assignments. This article is an analysis of the…
Pattern formation in stromatolites: insights from mathematical modelling
Cuerno, R.; Escudero, C.; García-Ruiz, J. M.; Herrero, M. A.
2012-01-01
To this day, computer models for stromatolite formation have made substantial use of the Kardar–Parisi–Zhang (KPZ) equation. Oddly enough, these studies yielded mutually exclusive conclusions about the biotic or abiotic origin of such structures. We show in this paper that, at our current state of knowledge, a purely biotic origin for stromatolites can neither be proved nor disproved by means of a KPZ-based model. What can be shown, however, is that whatever their (biotic or abiotic) origin might be, some morphologies found in actual stromatolite structures (e.g. overhangs) cannot be formed as a consequence of a process modelled exclusively in terms of the KPZ equation and acting over sufficiently large times. This suggests the need to search for alternative mathematical approaches to model these structures, some of which are discussed in this paper. PMID:21993008
Mathematical modeling of spinning elastic bodies for modal analysis.
NASA Technical Reports Server (NTRS)
Likins, P. W.; Barbera, F. J.; Baddeley, V.
1973-01-01
The problem of modal analysis of an elastic appendage on a rotating base is examined to establish the relative advantages of various mathematical models of elastic structures and to extract general inferences concerning the magnitude and character of the influence of spin on the natural frequencies and mode shapes of rotating structures. In realization of the first objective, it is concluded that except for a small class of very special cases the elastic continuum model is devoid of useful results, while for constant nominal spin rate the distributed-mass finite-element model is quite generally tractable, since in the latter case the governing equations are always linear, constant-coefficient, ordinary differential equations. Although with both of these alternatives the details of the formulation generally obscure the essence of the problem and permit very little engineering insight to be gained without extensive computation, this difficulty is not encountered when dealing with simple concentrated mass models.
Mathematical models of tumor heterogeneity and drug resistance
NASA Astrophysics Data System (ADS)
Greene, James
In this dissertation we develop mathematical models of tumor heterogeneity and drug resistance in cancer chemotherapy. Resistance to chemotherapy is one of the major causes of the failure of cancer treatment. Furthermore, recent experimental evidence suggests that drug resistance is a complex biological phenomena, with many influences that interact nonlinearly. Here we study the influence of such heterogeneity on treatment outcomes, both in general frameworks and under specific mechanisms. We begin by developing a mathematical framework for describing multi-drug resistance to cancer. Heterogeneity is reflected by a continuous parameter, which can either describe a single resistance mechanism (such as the expression of P-gp in the cellular membrane) or can account for the cumulative effect of several mechanisms and factors. The model is written as a system of integro-differential equations, structured by the continuous "trait," and includes density effects as well as mutations. We study the limiting behavior of the model, both analytically and numerically, and apply it to study treatment protocols. We next study a specific mechanism of tumor heterogeneity and its influence on cell growth: the cell-cycle. We derive two novel mathematical models, a stochastic agent-based model and an integro-differential equation model, each of which describes the growth of cancer cells as a dynamic transition between proliferative and quiescent states. By examining the role all parameters play in the evolution of intrinsic tumor heterogeneity, and the sensitivity of the population growth to parameter values, we show that the cell-cycle length has the most significant effect on the growth dynamics. In addition, we demonstrate that the agent-based model can be approximated well by the more computationally efficient integro-differential equations, when the number of cells is large. The model is closely tied to experimental data of cell growth, and includes a novel implementation of
Beliefs and Gender Differences: A New Model for Research in Mathematics Education
ERIC Educational Resources Information Center
Li, Qing
2004-01-01
The major focus of this study is to propose a new research model, namely the Modified CGI gender model, for the study of gender differences in mathematics. This model is developed based on Fennema, Carpenter, and Peterson's (1989) CGI model. To examine the validity of this new model, this study also examines the gender differences in teacher and…
Mathematical model and software for control of commissioning blast furnace
NASA Astrophysics Data System (ADS)
Spirin, N. A.; Onorin, O. P.; Shchipanov, K. A.; Lavrov, V. V.
2016-09-01
Blowing-in is a starting period of blast furnace operation after construction or major repair. The current approximation methods of blowing-in burden analysis are based on blowing-in practice of previously commissioned blast furnaces. This area is theoretically underexplored; there are no common scientifically based methods for selection of the burden composition and blast parameters. The purpose of this paper is development and scientific substantiation of the methods for selection of the burden composition and blast parameters in the blast furnace during the blowing-in period. Research methods are based on physical regularities of main processes running in the blast furnace, system analysis, and application of modern principles for development and construction of mathematical models, algorithms and software designed for automated control of complex production processes in metallurgy. As consequence of the research made by the authors the following results have been achieved: 1. A set of mathematical models for analysis of burden arrangement throughout the height of the blast furnace and for selection of optimal blast and gas dynamic parameters has been developed. 2. General principles for selection of the blowing-in burden composition and blast and gas dynamic parameters have been set up. 3. The software for the engineering and process staff of the blast furnace has been developed and introduced in the industry.
Evolvable mathematical models: A new artificial Intelligence paradigm
NASA Astrophysics Data System (ADS)
Grouchy, Paul
We develop a novel Artificial Intelligence paradigm to generate autonomously artificial agents as mathematical models of behaviour. Agent/environment inputs are mapped to agent outputs via equation trees which are evolved in a manner similar to Symbolic Regression in Genetic Programming. Equations are comprised of only the four basic mathematical operators, addition, subtraction, multiplication and division, as well as input and output variables and constants. From these operations, equations can be constructed that approximate any analytic function. These Evolvable Mathematical Models (EMMs) are tested and compared to their Artificial Neural Network (ANN) counterparts on two benchmarking tasks: the double-pole balancing without velocity information benchmark and the challenging discrete Double-T Maze experiments with homing. The results from these experiments show that EMMs are capable of solving tasks typically solved by ANNs, and that they have the ability to produce agents that demonstrate learning behaviours. To further explore the capabilities of EMMs, as well as to investigate the evolutionary origins of communication, we develop NoiseWorld, an Artificial Life simulation in which interagent communication emerges and evolves from initially noncommunicating EMM-based agents. Agents develop the capability to transmit their x and y position information over a one-dimensional channel via a complex, dialogue-based communication scheme. These evolved communication schemes are analyzed and their evolutionary trajectories examined, yielding significant insight into the emergence and subsequent evolution of cooperative communication. Evolved agents from NoiseWorld are successfully transferred onto physical robots, demonstrating the transferability of EMM-based AIs from simulation into physical reality.
Computer-Based Mathematics Instructions for Engineering Students
NASA Technical Reports Server (NTRS)
Khan, Mustaq A.; Wall, Curtiss E.
1996-01-01
Almost every engineering course involves mathematics in one form or another. The analytical process of developing mathematical models is very important for engineering students. However, the computational process involved in the solution of some mathematical problems may be very tedious and time consuming. There is a significant amount of mathematical software such as Mathematica, Mathcad, and Maple designed to aid in the solution of these instructional problems. The use of these packages in classroom teaching can greatly enhance understanding, and save time. Integration of computer technology in mathematics classes, without de-emphasizing the traditional analytical aspects of teaching, has proven very successful and is becoming almost essential. Sample computer laboratory modules are developed for presentation in the classroom setting. This is accomplished through the use of overhead projectors linked to graphing calculators and computers. Model problems are carefully selected from different areas.
Mathematical Modeling of Spreading Cortical Depression: Spiral and Reverberating Waves
NASA Astrophysics Data System (ADS)
Tuckwell, Henry C.
2008-07-01
Mathematical models of spreading depression are considered in the form of reaction-diffusion systems in two space dimensions. The systems are solved numerically. In the two component model with potassium and calcium ion concentrations, we demonstrate, using updated parameter values, travelling solitary waves of increased potassium and decreased calcium. These have circular wavefronts emanating from a region of application of potassium chloride. The collision of two such waves does not, as in one space dimension, result in annihilation but the formation of a unified wave with a large wavefront. For the first time we show that the mathematical model reproduces the actual properties of spreading depression waves in cortical structures. With attention to geometry, timing and location of stimuli we have succeeded in finding reverberating waves matching experiment. By simulating the technique of anodal block, spiral waves have also been demonstrated which parallel those found experimentally. The six-component model, which contains additionally sodium, chloride, glutamate and GABA, is also investigated in 2 space dimensions, including an experimentally based exchange pump for sodium and potassium. Solutions are obtained without (amplitude 29 mM external K+) and with action potentials (amplitude 44 mM external K+) with speeds of propagation, allowing for tortuosity, of 1.4 mm/minute and 2.7 mm/minute, respectively. When action potentials are included a somewhat higher pump strength is required to ensure the return to resting state.
Mathematical modeling of efficient protocols to control glioma growth.
Branco, J R; Ferreira, J A; de Oliveira, Paula
2014-09-01
In this paper we propose a mathematical model to describe the evolution of glioma cells taking into account the viscoelastic properties of brain tissue. The mathematical model is established considering that the glioma cells are of two phenotypes: migratory and proliferative. The evolution of the migratory cells is described by a diffusion-reaction equation of non Fickian type deduced considering a mass conservation law with a non Fickian migratory mass flux. The evolution of the proliferative cells is described by a reaction equation. A stability analysis that leads to the design of efficient protocols is presented. Numerical simulations that illustrate the behavior of the mathematical model are included.
Mathematical modeling of urea transport in the kidney.
Layton, Anita T
2014-01-01
Mathematical modeling techniques have been useful in providing insights into biological systems, including the kidney. This article considers some of the mathematical models that concern urea transport in the kidney. Modeling simulations have been conducted to investigate, in the context of urea cycling and urine concentration, the effects of hypothetical active urea secretion into pars recta. Simulation results suggest that active urea secretion induces a "urea-selective" improvement in urine concentrating ability. Mathematical models have also been built to study the implications of the highly structured organization of tubules and vessels in the renal medulla on urea sequestration and cycling. The goal of this article is to show how physiological problems can be formulated and studied mathematically, and how such models may provide insights into renal functions.
Nonlinear mathematical modeling and sensitivity analysis of hydraulic drive unit
NASA Astrophysics Data System (ADS)
Kong, Xiangdong; Yu, Bin; Quan, Lingxiao; Ba, Kaixian; Wu, Liujie
2015-09-01
The previous sensitivity analysis researches are not accurate enough and also have the limited reference value, because those mathematical models are relatively simple and the change of the load and the initial displacement changes of the piston are ignored, even experiment verification is not conducted. Therefore, in view of deficiencies above, a nonlinear mathematical model is established in this paper, including dynamic characteristics of servo valve, nonlinear characteristics of pressure-flow, initial displacement of servo cylinder piston and friction nonlinearity. The transfer function block diagram is built for the hydraulic drive unit closed loop position control, as well as the state equations. Through deriving the time-varying coefficient items matrix and time-varying free items matrix of sensitivity equations respectively, the expression of sensitivity equations based on the nonlinear mathematical model are obtained. According to structure parameters of hydraulic drive unit, working parameters, fluid transmission characteristics and measured friction-velocity curves, the simulation analysis of hydraulic drive unit is completed on the MATLAB/Simulink simulation platform with the displacement step 2 mm, 5 mm and 10 mm, respectively. The simulation results indicate that the developed nonlinear mathematical model is sufficient by comparing the characteristic curves of experimental step response and simulation step response under different constant load. Then, the sensitivity function time-history curves of seventeen parameters are obtained, basing on each state vector time-history curve of step response characteristic. The maximum value of displacement variation percentage and the sum of displacement variation absolute values in the sampling time are both taken as sensitivity indexes. The sensitivity indexes values above are calculated and shown visually in histograms under different working conditions, and change rules are analyzed. Then the sensitivity
A mathematical model and numerical method for thermoelectric DNA sequencing
NASA Astrophysics Data System (ADS)
Shi, Liwei; Guilbeau, Eric J.; Nestorova, Gergana; Dai, Weizhong
2014-05-01
Single nucleotide polymorphisms (SNPs) are single base pair variations within the genome that are important indicators of genetic predisposition towards specific diseases. This study explores the feasibility of SNP detection using a thermoelectric sequencing method that measures the heat released when DNA polymerase inserts a deoxyribonucleoside triphosphate into a DNA strand. We propose a three-dimensional mathematical model that governs the DNA sequencing device with a reaction zone that contains DNA template/primer complex immobilized to the surface of the lower channel wall. The model is then solved numerically. Concentrations of reactants and the temperature distribution are obtained. Results indicate that when the nucleoside is complementary to the next base in the DNA template, polymerization occurs lengthening the complementary polymer and releasing thermal energy with a measurable temperature change, implying that the thermoelectric conceptual device for sequencing DNA may be feasible for identifying specific genes in individuals.
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.
Innovative mathematical modeling in environmental remediation.
Yeh, Gour-Tsyh; Gwo, Jin-Ping; Siegel, Malcolm D; Li, Ming-Hsu; Fang, Yilin; Zhang, Fan; Luo, Wensui; Yabusaki, Steve B
2013-05-01
There are two different ways to model reactive transport: ad hoc and innovative reaction-based approaches. The former, such as the Kd simplification of adsorption, has been widely employed by practitioners, while the latter has been mainly used in scientific communities for elucidating mechanisms of biogeochemical transport processes. It is believed that innovative mechanistic-based models could serve as protocols for environmental remediation as well. This paper reviews the development of a mechanistically coupled fluid flow, thermal transport, hydrologic transport, and reactive biogeochemical model and example-applications to environmental remediation problems. Theoretical bases are sufficiently described. Four example problems previously carried out are used to demonstrate how numerical experimentation can be used to evaluate the feasibility of different remediation approaches. The first one involved the application of a 56-species uranium tailing problem to the Melton Branch Subwatershed at Oak Ridge National Laboratory (ORNL) using the parallel version of the model. Simulations were made to demonstrate the potential mobilization of uranium and other chelating agents in the proposed waste disposal site. The second problem simulated laboratory-scale system to investigate the role of natural attenuation in potential off-site migration of uranium from uranium mill tailings after restoration. It showed inadequacy of using a single Kd even for a homogeneous medium. The third example simulated laboratory experiments involving extremely high concentrations of uranium, technetium, aluminum, nitrate, and toxic metals (e.g., Ni, Cr, Co). The fourth example modeled microbially-mediated immobilization of uranium in an unconfined aquifer using acetate amendment in a field-scale experiment. The purposes of these modeling studies were to simulate various mechanisms of mobilization and immobilization of radioactive wastes and to illustrate how to apply reactive transport
[Mathematical model of value of population].
Sha, J; Wang, S
1983-09-29
The authors define the value of population as an economic concept and present mathematical formulas for calculating this value. Included in this theoretical discussion are different kinds of surplus value of population and the social significance of population value. PMID:12279805
Making Insulation Decisions through Mathematical Modeling
ERIC Educational Resources Information Center
Yanik, H. Bahadir; Memis, Yasin
2014-01-01
Engaging students in studies about conservation and sustainability can support their understanding of making environmental conscious decisions to conserve Earth. This article aims to contribute these efforts and direct students' attention to how they can use mathematics to make environmental decisions. Contributors to iSTEM: Integrating…
Modeling Students' Interest in Mathematics Homework
ERIC Educational Resources Information Center
Xu, Jianzhong; Yuan, Ruiping; Xu, Brian; Xu, Melinda
2016-01-01
The authors examine the factors influencing mathematics homework interest for Chinese students and compare the findings with a recent study involving U.S. students. The findings from multilevel analyses revealed that some predictors for homework interest functioned similarly (e.g., affective attitude toward homework, learning-oriented reasons,…
Kinetic investigation and mathematical modeling of methanogenesis of glucose
Kalyuzhnyy, S.V.; Sklyar, V.I.; Varfolomeyev, S.D.; Gachok, V.P.
1991-12-31
The kinetic regularities of anaerobic conversion of glucose, and intermediates of its decomposition (ethanol, butyrate, and acetate) by a microbial methanogenic association from anaerobic digester were investigated. Kinetic scheme for conversion of glucose is suggested, and the mathematical model based on the scheme is evolved. The model includes growth and metabolism of three kinds of microorganisms-acid producents, and acetate- and hydrogen-utilizing methane producents; of cell lysis with consequent fermentation of {open_quotes}died biomass{close_quotes} to acetate, hydrogen, and carbon dioxide; of induction and repression of the enzyme responsible for decomposition of butyrate, and for a number of regulations depending on the concentrations of intermediates in glucose metabolism. The values of parameters of the model have been calculated, sufficiently describing the experimental regularities. The numerical experiments have enabled us to reveal and describe the principal regulating factors of glucose methanogenesis.
Mathematical modelling of post combustion in Dofasco`s KOBM
Gou, H.; Irons, G.A.; Lu, W.K.
1992-12-31
In the AISI Direct Steelmaking program, trials were undertaken in Dofasco`s 300 Tonne KOBM to examine post combustion. To support this work, a two-dimensional turbulent mathematical model has been developed to describe gas flow, combustion reactions and heat transfer (radiation and convection) in converter-type steelmaking processes. Gaseous flow patterns, temperature and heat flux distributions in the furnace were calculated with this model. Key findings are: The post combustion ratio is determined from the rates of oxygen supply, oxygen used for decarburization and the remainder available for post combustion, i.e. deducible from a mass balance calculation, comparison between the heat transfer fluxes calculated based on the model and those measured industrially indicates that the conventionally defined heat transfer efficiency over-estimates the heat recovered by the bath by about 20%, and the location of the combustion zone can be controlled, to a certain extent, by adjusting the lance practice.
Mathematical modelling of post combustion in Dofasco's KOBM
Gou, H.; Irons, G.A.; Lu, W.K.
1992-01-01
In the AISI Direct Steelmaking program, trials were undertaken in Dofasco's 300 Tonne KOBM to examine post combustion. To support this work, a two-dimensional turbulent mathematical model has been developed to describe gas flow, combustion reactions and heat transfer (radiation and convection) in converter-type steelmaking processes. Gaseous flow patterns, temperature and heat flux distributions in the furnace were calculated with this model. Key findings are: The post combustion ratio is determined from the rates of oxygen supply, oxygen used for decarburization and the remainder available for post combustion, i.e. deducible from a mass balance calculation, comparison between the heat transfer fluxes calculated based on the model and those measured industrially indicates that the conventionally defined heat transfer efficiency over-estimates the heat recovered by the bath by about 20%, and the location of the combustion zone can be controlled, to a certain extent, by adjusting the lance practice.
Mathematical Model of Oxygen Transport in Tuberculosis Granulomas.
Datta, Meenal; Via, Laura E; Chen, Wei; Baish, James W; Xu, Lei; Barry, Clifton E; Jain, Rakesh K
2016-04-01
Pulmonary granulomas--the hallmark of Mycobacterium tuberculosis (MTB) infection--are dense cellular lesions that often feature regions of hypoxia and necrosis, partially due to limited transport of oxygen. Low oxygen in granulomas can impair the host immune response, while MTB are able to adapt and persist in hypoxic environments. Here, we used a physiologically based mathematical model of oxygen diffusion and consumption to calculate oxygen profiles within the granuloma, assuming Michaelis-Menten kinetics. An approximate analytical solution--using a priori and newly estimated parameters from experimental data in a rabbit model of tuberculosis--was able to predict the size of hypoxic and necrotic regions in agreement with experimental results from the animal model. Such quantitative understanding of transport limitations can inform future tuberculosis therapeutic strategies that may include adjunct host-directed therapies that facilitate oxygen and drug delivery for more effective treatment.
Mathematical model and numerical algorithm for aerodynamical flow
NASA Astrophysics Data System (ADS)
Shaydurov, V.; Shchepanovskaya, G.; Yakubovich, M.
2016-10-01
In the paper, a mathematical model and a numerical algorithm are proposed for modeling an air flow. The proposed model is based on the time-dependent Navier-Stokes equations for viscous heat-conducting gas. The energy equation and the state equations are modified to account for two kinds of `internal' energy. The first one is the usual translational and rotational energy of molecules which defines the thermodynamical temperature and the pressure. The second one is the subgrid energy of small turbulent eddies. A numerical algorithm is proposed for solving the formulated initial-boundary value problem as a combination of the semi-Lagrangian approximation for Lagrange transport derivatives and the conforming finite element method for other terms. A numerical example illustrates these approaches.
System and mathematical modeling of quadrotor dynamics
NASA Astrophysics Data System (ADS)
Goodman, Jacob M.; Kim, Jinho; Gadsden, S. Andrew; Wilkerson, Stephen A.
2015-05-01
Unmanned aerial systems (UAS) are becoming increasingly visible in our daily lives; and range in operation from search and rescue, monitoring hazardous environments, and to the delivery of goods. One of the most popular UAS are based on a quad-rotor design. These are typically small devices that rely on four propellers for lift and movement. Quad-rotors are inherently unstable, and rely on advanced control methodologies to keep them operating safely and behaving in a predictable and desirable manner. The control of these devices can be enhanced and improved by making use of an accurate dynamic model. In this paper, we examine a simple quadrotor model, and note some of the additional dynamic considerations that were left out. We then compare simulation results of the simple model with that of another comprehensive model.
A Missing Piece in an Elementary School Mathematics Teacher's Knowledge Base
ERIC Educational Resources Information Center
Anderson, Hal; Kim, Simon
2003-01-01
Elementary school mathematics teaching begins with the teacher's understanding of the mathematical content to be taught. The teacher knows how to "do" the mathematics, i. e., understands the concepts and truths concerning that mathematics. The teacher then decides how to present the mathematics. Based on the students' background in mathematics,…
ERIC Educational Resources Information Center
Akiba, Motoko; Chiu, Ya-Fang; Zhuang, Yue-Lin; Mueller, Heather E.
2008-01-01
Using the NAEP nationally-representative data collected from eighth-graders, we investigated the relative exposure of American Indian/Alaska Native (AIAN) students to mathematics teachers who are knowledgeable about standards, participate in standards-based professional development, and practice standards-based instruction; American Indian/Alaska…
Mathematical modeling of electrochemical remediation for soils under galvanostatic conditions.
Teutli León, M M; Oropeza Guzmán, M T; González, I
2001-01-01
This work proposes a mathematical model for the electrochemical remediation of clayey soils based on the total volume concept for a two-phase system. The mathematical formulation was done including contributions from theories for: groundwater, membranes, porous electrodes and environmental soil chemistry. The resulting model accounts for: free and complexed species in the soil matrix and the pore solution; chemical reactions taking place on either phase and/or between phases; a dynamic soil surface charge affected by the ion content of the pore solution; and electroneutrality of the total volume. Soil surface charge was included in a modified Ohm's law (voltage gradient) and in a modified Schlög's law (convective movement). Numerical implementation was done using orthogonal collocation on finite elements for spatial derivatives, and forward finite differences for time derivatives. Visual Fortran supported by IMSL subroutines was used for computer simulation. Model predictions were successfully compared with reported experimental data. Also, an analysis of pH profiles through the soil is provided for conditions when parameters including hydrostatic head, applied current density and initial pH are modified.
Artificial intelligence and mathematical modeling applied to wireline log interpretation
Khan, K.A.
1995-08-01
Wireline log interpretation is a powerful tool for evaluation of formation characteristics which in turn are used for identification of reservoir and estimation of recoverable hydrocarbons. The log data is stored and plotted using computer applications but manual procedures are mostly adopted for reading the logs and interpreting their signature into the subsurface formations. Keeping in view the new trend of applying artificial intelligence and neural networks to geological applications, an artificial intelligence based approach has been developed for computerized interpretation of logs. The working of this technique involves mathematical models based on curve analyzers which take into account the changing trend of each log curve and then pool out parameters to mathematical equations or directly to the artificial intelligent logic. Such logic has been developed for interpreting all major types of logs like spontaneous potential, gamma ray, sonic, density, neuron and various types of resistivity logs. Thus each log is interpreted independently, for example sand line and shale base lines are automatically marked from spontaneous potential logs and clay percentage is mapped from gamma ray logs. Finally an integrated artificial intelligent analysis takes into account all the logs, their independent interpretations and the local geological information and interprets the subsurface geological picture comprising of various formations.
Science modelling in pre-calculus: how to make mathematics problems contextually meaningful
NASA Astrophysics Data System (ADS)
Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen
2011-04-01
'Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum' (National Council of Teachers of Mathematics (NCTM), Principles and Standards for School Mathematics, NCTM, Reston, VA, 2000). Commonly used pre-calculus textbooks provide a wide range of application problems. However, these problems focus students' attention on evaluating or solving pre-arranged formulas for given values. The role of scientific content is reduced to provide a background for these problems instead of being sources of data gathering for inducing mathematical tools. Students are neither required to construct mathematical models based on the contexts nor are they asked to validate or discuss the limitations of applied formulas. Using these contexts, the instructor may think that he/she is teaching problem solving, where in reality he/she is teaching algorithms of the mathematical operations (G. Kulm (ed.), New directions for mathematics assessment, in Assessing Higher Order Thinking in Mathematics, Erlbaum, Hillsdale, NJ, 1994, pp. 221-240). Without a thorough representation of the physical phenomena and the mathematical modelling processes undertaken, problem solving unintentionally appears as simple algorithmic operations. In this article, we deconstruct the representations of mathematics problems from selected pre-calculus textbooks and explicate their limitations. We argue that the structure and content of those problems limits students' coherent understanding of mathematical modelling, and this could result in weak student problem-solving skills. Simultaneously, we explore the ways to enhance representations of those mathematical problems, which we have characterized as lacking a meaningful physical context and limiting coherent student understanding. In light of our discussion, we recommend an alternative to strengthen the process of teaching mathematical modelling - utilization
ERIC Educational Resources Information Center
Nakamura, Yasuyuki; Nishi, Shinnosuke; Muramatsu, Yuta; Yasutake, Koichi; Yamakawa, Osamu; Tagawa, Takahiro
2014-01-01
In this paper, we introduce a mathematical model for collaborative learning and the answering process for multiple-choice questions. The collaborative learning model is inspired by the Ising spin model and the model for answering multiple-choice questions is based on their difficulty level. An intensive simulation study predicts the possibility of…
Classical and Weak Solutions for Two Models in Mathematical Finance
NASA Astrophysics Data System (ADS)
Gyulov, Tihomir B.; Valkov, Radoslav L.
2011-12-01
We study two mathematical models, arising in financial mathematics. These models are one-dimensional analogues of the famous Black-Scholes equation on finite interval. The main difficulty is the degeneration at the both ends of the space interval. First, classical solutions are studied. Positivity and convexity properties of the solutions are discussed. Variational formulation in weighted Sobolev spaces is introduced and existence and uniqueness of the weak solution is proved. Maximum principle for weak solution is discussed.
NASA Astrophysics Data System (ADS)
Vasechkina, E. F.; Kazankova, I. I.
2014-11-01
A mathematical model simulating the growth and development of the mussel Mytilus galloprovincialis Lam. on artificial substrates has been constructed. The model is based on experimental data and contains mathematical descriptions of the filtration, respiration, excretion, spawning, and growth of an individual during its ontogenesis from the moment it attaches to a solid substrate to the attainment of a marketable size. The test computations have been compared to the available observation data for mussel farms.
Discrete Mathematical Approaches to Graph-Based Traffic Analysis
Joslyn, Cliff A.; Cowley, Wendy E.; Hogan, Emilie A.; Olsen, Bryan K.
2014-04-01
Modern cyber defense and anlaytics requires general, formal models of cyber systems. Multi-scale network models are prime candidates for such formalisms, using discrete mathematical methods based in hierarchically-structured directed multigraphs which also include rich sets of labels. An exemplar of an application of such an approach is traffic analysis, that is, observing and analyzing connections between clients, servers, hosts, and actors within IP networks, over time, to identify characteristic or suspicious patterns. Towards that end, NetFlow (or more generically, IPFLOW) data are available from routers and servers which summarize coherent groups of IP packets flowing through the network. In this paper, we consider traffic analysis of Netflow using both basic graph statistics and two new mathematical measures involving labeled degree distributions and time interval overlap measures. We do all of this over the VAST test data set of 96M synthetic Netflow graph edges, against which we can identify characteristic patterns of simulated ground-truth network attacks.
Some Aspects of Mathematical Model of Collaborative Learning
ERIC Educational Resources Information Center
Nakamura, Yasuyuki; Yasutake, Koichi; Yamakawa, Osamu
2012-01-01
There are some mathematical learning models of collaborative learning, with which we can learn how students obtain knowledge and we expect to design effective education. We put together those models and classify into three categories; model by differential equations, so-called Ising spin and a stochastic process equation. Some of the models do not…
Academic Libraries as a Context for Teaching Mathematical Modeling
ERIC Educational Resources Information Center
Warwick, Jon
2008-01-01
The teaching of mathematical modeling to undergraduate students requires that students are given ample opportunity to develop their own models and experience first-hand the process of model building. Finding an appropriate context within which modeling can be undertaken is not a simple task as it needs to be readily understandable and seen as…
Innovative mathematical modeling in environmental remediation
Yeh, Gour T.; Gwo, Jin Ping; Siegel, Malcolm D.; Li, Ming-Hsu; Fang, Yilin; Zhang, Fan; Luo, Wensui; Yabusaki, Steven B.
2013-05-01
There are two different ways to model reactive transport: ad hoc and innovative reaction-based approaches. The former, such as the Kd simplification of adsorption, has been widely employed by practitioners, while the latter has been mainly used in scientific communities for elucidating mechanisms of biogeochemical transport processes. It is believed that innovative mechanistic-based models could serve as protocols for environmental remediation as well. This paper reviews the development of a mechanistically coupled fluid flow, thermal transport, hydrologic transport, and reactive biogeochemical model and example-applications to environmental remediation problems. Theoretical bases are sufficiently described. Four example problems previously carried out are used to demonstrate how numerical experimentation can be used to evaluate the feasibility of different remediation approaches. The first one involved the application of a 56-species uranium tailing problem to the Melton Branch Subwatershed at Oak Ridge National Laboratory (ORNL) using the parallel version of the model. Simulations were made to demonstrate the potential mobilization of uranium and other chelating agents in the proposed waste disposal site. The second problem simulated laboratory-scale system to investigate the role of natural attenuation in potential off-site migration of uranium from uranium mill tailings after restoration. It showed inadequacy of using a single Kd even for a homogeneous medium. The third example simulated laboratory experiments involving extremely high concentrations of uranium, technetium, aluminum, nitrate, and toxic metals (e.g.,Ni, Cr, Co).The fourth example modeled microbially-mediated immobilization of uranium in an unconfined aquifer using acetate amendment in a field-scale experiment. The purposes of these modeling studies were to simulate various mechanisms of mobilization and immobilization of radioactive wastes and to illustrate how to apply reactive transport models
Design and mathematical modelling of a synthetic symbiotic ecosystem.
Kambam, P K R; Henson, M A; Sun, L
2008-01-01
Artificial microbial ecosystems have been increasingly used to understand principles of ecology. These systems offer unique capabilities to mimic a variety of ecological interactions that otherwise would be difficult to study experimentally in a reasonable period of time. However, the elucidation of the genetic bases for these interactions remains a daunting challenge. To address this issue, we have designed and analysed a synthetic symbiotic ecosystem in which the genetic nature of the microbial interactions is defined explicitly. A mathematical model of the gene regulatory network in each species and their interaction through quorum sensing mediated intercellular signalling was derived to investigate the effect of system components on cooperative behaviour. Dynamic simulation and bifurcation analysis showed that the designed system admits a stable coexistence steady state for sufficiently large initial cell concentrations of the two species. The steady-state fraction of each species could be altered by varying model parameters associated with gene transcription and signalling molecule synthesis rates. The design also admitted a stable steady state corresponding to extinction of the two species for low initial cell concentrations and stable periodic solutions over certain domains of parameter space. The mathematical analysis was shown to provide insights into natural microbial ecosystems and to allow identification of molecular targets for engineering system behaviour.
Mathematical modelling of flow distribution in the human cardiovascular system
NASA Technical Reports Server (NTRS)
Sud, V. K.; Srinivasan, R. S.; Charles, J. B.; Bungo, M. W.
1992-01-01
The paper presents a detailed model of the entire human cardiovascular system which aims to study the changes in flow distribution caused by external stimuli, changes in internal parameters, or other factors. The arterial-venous network is represented by 325 interconnected elastic segments. The mathematical description of each segment is based on equations of hydrodynamics and those of stress/strain relationships in elastic materials. Appropriate input functions provide for the pumping of blood by the heart through the system. The analysis employs the finite-element technique which can accommodate any prescribed boundary conditions. Values of model parameters are from available data on physical and rheological properties of blood and blood vessels. As a representative example, simulation results on changes in flow distribution with changes in the elastic properties of blood vessels are discussed. They indicate that the errors in the calculated overall flow rates are not significant even in the extreme case of arteries and veins behaving as rigid tubes.
A mathematical model for the iron/chromium redox battery
NASA Technical Reports Server (NTRS)
Fedkiw, P. S.; Watts, R. W.
1984-01-01
A mathematical model has been developed to describe the isothermal operation of a single anode-separator-cathode unit cell in a redox-flow battery and has been applied to the NASA iron/chromium system. The model, based on porous electrode theory, incorporates redox kinetics, mass transfer, and ohmic effects as well as the parasitic hydrogen reaction which occurs in the chromium electrode. A numerical parameter study was carried out to predict cell performance to aid in the rational design, scale-up, and operation of the flow battery. The calculations demonstrate: (1) an optimum electrode thickness and electrolyte flow rate exist; (2) the amount of hydrogen evolved and, hence, cycle faradaic efficiency, can be affected by cell geometry, flow rate, and charging procedure; (3) countercurrent flow results in enhanced cell performance over cocurrent flow; and (4) elevated temperature operation enhances cell performance.
Mathematical modelling methodologies in predictive food microbiology: a SWOT analysis.
Ferrer, Jordi; Prats, Clara; López, Daniel; Vives-Rego, Josep
2009-08-31
Predictive microbiology is the area of food microbiology that attempts to forecast the quantitative evolution of microbial populations over time. This is achieved to a great extent through models that include the mechanisms governing population dynamics. Traditionally, the models used in predictive microbiology are whole-system continuous models that describe population dynamics by means of equations applied to extensive or averaged variables of the whole system. Many existing models can be classified by specific criteria. We can distinguish between survival and growth models by seeing whether they tackle mortality or cell duplication. We can distinguish between empirical (phenomenological) models, which mathematically describe specific behaviour, and theoretical (mechanistic) models with a biological basis, which search for the underlying mechanisms driving already observed phenomena. We can also distinguish between primary, secondary and tertiary models, by examining their treatment of the effects of external factors and constraints on the microbial community. Recently, the use of spatially explicit Individual-based Models (IbMs) has spread through predictive microbiology, due to the current technological capacity of performing measurements on single individual cells and thanks to the consolidation of computational modelling. Spatially explicit IbMs are bottom-up approaches to microbial communities that build bridges between the description of micro-organisms at the cell level and macroscopic observations at the population level. They provide greater insight into the mesoscale phenomena that link unicellular and population levels. Every model is built in response to a particular question and with different aims. Even so, in this research we conducted a SWOT (Strength, Weaknesses, Opportunities and Threats) analysis of the different approaches (population continuous modelling and Individual-based Modelling), which we hope will be helpful for current and future
Mathematical modelling methodologies in predictive food microbiology: a SWOT analysis.
Ferrer, Jordi; Prats, Clara; López, Daniel; Vives-Rego, Josep
2009-08-31
Predictive microbiology is the area of food microbiology that attempts to forecast the quantitative evolution of microbial populations over time. This is achieved to a great extent through models that include the mechanisms governing population dynamics. Traditionally, the models used in predictive microbiology are whole-system continuous models that describe population dynamics by means of equations applied to extensive or averaged variables of the whole system. Many existing models can be classified by specific criteria. We can distinguish between survival and growth models by seeing whether they tackle mortality or cell duplication. We can distinguish between empirical (phenomenological) models, which mathematically describe specific behaviour, and theoretical (mechanistic) models with a biological basis, which search for the underlying mechanisms driving already observed phenomena. We can also distinguish between primary, secondary and tertiary models, by examining their treatment of the effects of external factors and constraints on the microbial community. Recently, the use of spatially explicit Individual-based Models (IbMs) has spread through predictive microbiology, due to the current technological capacity of performing measurements on single individual cells and thanks to the consolidation of computational modelling. Spatially explicit IbMs are bottom-up approaches to microbial communities that build bridges between the description of micro-organisms at the cell level and macroscopic observations at the population level. They provide greater insight into the mesoscale phenomena that link unicellular and population levels. Every model is built in response to a particular question and with different aims. Even so, in this research we conducted a SWOT (Strength, Weaknesses, Opportunities and Threats) analysis of the different approaches (population continuous modelling and Individual-based Modelling), which we hope will be helpful for current and future
Membrane transport of several ions during peritoneal dialysis: mathematical modeling.
Galach, Magda; Waniewski, Jacek
2012-09-01
Peritoneal dialysis utilizes a complex mass exchange device created by natural permselective membranes of the visceral and abdominal muscle tissues. In mathematical modeling of solute transport during peritoneal dialysis, each solute is typically considered as a neutral, independent particle. However, such mathematical models cannot predict transport parameters for small ions. Therefore, the impact of the electrostatic interactions between ions on the estimated transport parameters needs to be investigated. In this study, transport of sodium, chloride, and a third ion through a permselective membrane with characteristics of the peritoneal transport barrier was described using two models: a model with the Nernst-Planck (NP) equations for a set of interacting ions and a model with combined diffusive and convective transport of each ion separately (DC). Transport parameters for the NP model were calculated using the pore theory, while the parameters for the DC model were estimated by fitting the model to the predictions from the NP model. Solute concentration profiles in the membrane obtained by computer simulations based on these two models were similar, whereas the transport parameters (diffusive mass transport parameters and sieving coefficients) were generally different. The presence of the third ion could substantially modify the values of diffusive mass parameter for sodium and chloride ions estimated using the DC model compared with those predicted by NP. The extent of this modification depended on the molecular mass and concentration of the third ion, and the rate of volumetric flow. Closed formulas for the transport parameters of the DC model in terms of the NP model parameters, ion concentration profiles in the membrane, and volumetric flow across the membrane were derived. Their reliable approximations, which include only boundary ion concentrations instead of spatial intramembrane concentration profiles, were formulated. The precision of this approximation
Mioni, Roberto; Mioni, Giuseppe
2015-10-01
In chemistry and in acid-base physiology, the Henderson-Hasselbalch equation plays a pivotal role in studying the behaviour of the buffer solutions. However, it seems that the general function to calculate the valence of acids, bases and ampholytes, N = f(pH), at any pH, has only been provided by Kildeberg. This equation can be applied to strong acids and bases, pluriprotic weak acids, bases and ampholytes, with an arbitrary number of acid strength constants, pKA, including water. By differentiating this function with respect to pH, we obtain the general equation for the buffer value. In addition, by integrating the titration curve, TA, proposed by Kildeberg, and calculating its Legendre transform, we obtain the Gibbs free energy of pH (or pOH)-dependent titratable acid. Starting from the law of electroneutrality and applying suitable simplifications, it is possible to calculate the pH of the buffer solutions by numerical methods, available in software packages such as Excel. The concept of buffer capacity has also been clarified by Urbansky, but, at variance with our approach, not in an organic manner. In fact, for each set of monobasic, dibasic, tribasic acids, etc., various equations are presented which independently fit each individual acid-base category. Consequently, with the increase in acid groups (pKA), the equations become more and more difficult, both in practice and in theory. Some examples are proposed to highlight the boundary that exists between acid-base physiology and the thermodynamic concepts of energy, chemical potential, amount of substance and acid resistance. PMID:26059505
Mioni, Roberto; Mioni, Giuseppe
2015-10-01
In chemistry and in acid-base physiology, the Henderson-Hasselbalch equation plays a pivotal role in studying the behaviour of the buffer solutions. However, it seems that the general function to calculate the valence of acids, bases and ampholytes, N = f(pH), at any pH, has only been provided by Kildeberg. This equation can be applied to strong acids and bases, pluriprotic weak acids, bases and ampholytes, with an arbitrary number of acid strength constants, pKA, including water. By differentiating this function with respect to pH, we obtain the general equation for the buffer value. In addition, by integrating the titration curve, TA, proposed by Kildeberg, and calculating its Legendre transform, we obtain the Gibbs free energy of pH (or pOH)-dependent titratable acid. Starting from the law of electroneutrality and applying suitable simplifications, it is possible to calculate the pH of the buffer solutions by numerical methods, available in software packages such as Excel. The concept of buffer capacity has also been clarified by Urbansky, but, at variance with our approach, not in an organic manner. In fact, for each set of monobasic, dibasic, tribasic acids, etc., various equations are presented which independently fit each individual acid-base category. Consequently, with the increase in acid groups (pKA), the equations become more and more difficult, both in practice and in theory. Some examples are proposed to highlight the boundary that exists between acid-base physiology and the thermodynamic concepts of energy, chemical potential, amount of substance and acid resistance.
Mathematical models for nonparametric inferences from line transect data
Burnham, K.P.; Anderson, D.R.
1976-01-01
A general mathematical theory of line transects is develoepd which supplies a framework for nonparametric density estimation based on either right angle or sighting distances. The probability of observing a point given its right angle distance (y) from the line is generalized to an arbitrary function g(y). Given only that g(O) = 1, it is shown there are nonparametric approaches to density estimation using the observed right angle distances. The model is then generalized to include sighting distances (r). Let f(y/r) be the conditional distribution of right angle distance given sighting distance. It is shown that nonparametric estimation based only on sighting distances requires we know the transformation of r given by f(O/r).
ERIC Educational Resources Information Center
Michelsen, Claus
2015-01-01
Mathematics plays a crucial role in physics. This role is brought about predominantly through the building, employment, and assessment of mathematical models, and teachers and educators should capture this relationship in the classroom in an effort to improve students' achievement and attitude in both physics and mathematics. But although there…
Mathematical Modelling of the Infusion Test
NASA Astrophysics Data System (ADS)
Cieslicki, Krzysztof
2007-01-01
The objective of this paper was to improve the well established in clinical practice Marmarou model for intracranial volume-pressure compensation by adding the pulsatile components. It was demonstrated that complicated pulsation and growth in intracranial pressure during infusion test could be successfully modeled by the relatively simple analytical expression derived in this paper. The CSF dynamics were tested in 25 patients with clinical symptoms of hydrocephalus. Basing on the frequency spectrum of the patient's baseline pressure and identified parameters of CSF dynamic, for each patient an "ideal" infusion test curve free from artefacts and slow waves was simulated. The degree of correlation between simulated and real curves obtained from clinical observations gave insight into the adequacy of assumptions of Marmarou model. The proposed method of infusion tests analysis designates more exactly the value of the reference pressure, which is usually treated as a secondary and of uncertain significance. The properly identified value of the reference pressure decides on the degree of pulsation amplitude growth during IT, as well as on the value of elastance coefficient. The artificially generated tests with various pulsation components were also applied to examine the correctness of the used algorithm of identification of the original Marmarou model parameters.
Use of artificial intelligence and simple mathematics to analyze a physiological model
Kunz, J.C.
1984-01-01
The objective of this research is to demonstrate a methodology for design and use of a physiological model in a computer program that suggests medical decisions. This methodology uses a physiological model based on first principles and facts of physiology and anatomy. The model includes inference rules for analysis of causal relations between physiological events. The model is used to analyze physiological behavior, identify the effects of abnormalities, identify appropriate therapies, and predict the results of therapy. This methodology integrates heuristic knowledge traditionally used in artificial intelligence programs with mathematical knowledge traditionally used in mathematical modeling programs. A vocabulary for representing a physiological model is proposed.
Evaluation of Limb Load Asymmetry Using Two New Mathematical Models
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
Andasari, Vivi; Gerisch, Alf; Lolas, Georgios; South, Andrew P; Chaplain, Mark A J
2011-07-01
The ability of cancer cells to break out of tissue compartments and invade locally gives solid tumours a defining deadly characteristic. One of the first steps of invasion is the remodelling of the surrounding tissue or extracellular matrix (ECM) and a major part of this process is the over-expression of proteolytic enzymes, such as the urokinase-type plasminogen activator (uPA) and matrix metalloproteinases (MMPs), by the cancer cells to break down ECM proteins. Degradation of the matrix enables the cancer cells to migrate through the tissue and subsequently to spread to secondary sites in the body, a process known as metastasis. In this paper we undertake an analysis of a mathematical model of cancer cell invasion of tissue, or ECM, which focuses on the role of the urokinase plasminogen activation system. The model consists of a system of five reaction-diffusion-taxis partial differential equations describing the interactions between cancer cells, uPA, uPA inhibitors, plasmin and the host tissue. Cancer cells react chemotactically and haptotactically to the spatio-temporal effects of the uPA system. The results obtained from computational simulations carried out on the model equations produce dynamic heterogeneous spatio-temporal solutions and using linear stability analysis we show that this is caused by a taxis-driven instability of a spatially homogeneous steady-state. Finally we consider the biological implications of the model results, draw parallels with clinical samples and laboratory based models of cancer cell invasion using three-dimensional invasion assay, and go on to discuss future development of the model.
The role of mathematical models in understanding pattern formation in developmental biology.
Umulis, David M; Othmer, Hans G
2015-05-01
In a Wall Street Journal article published on April 5, 2013, E. O. Wilson attempted to make the case that biologists do not really need to learn any mathematics-whenever they run into difficulty with numerical issues, they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilsons Principle No. 1: "It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations." This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson, mathematics is mere number crunching, but as Galileo said long ago, "The laws of Nature are written in the language of mathematics[Formula: see text] the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word." Mathematics has moved beyond the geometry-based model of Galileo's time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science (Both point and counter-point are available in Wilson and Frenkel in Notices Am Math Soc 60(7):837-838, 2013). We will take this a step further and show how mathematics has been used to make new and experimentally verified discoveries in developmental biology and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades-that of how organisms can scale in size. Mathematical analysis alone cannot "solve" these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. Herein, we discuss a few examples of the productive intercourse between mathematics and biology. PMID:25280665
Mathematical Modeling of the Induced Mutation Process in Bacterial Cells
NASA Astrophysics Data System (ADS)
Belov, Oleg V.; Krasavin, Evgeny A.; Parkhomenko, Alexander Yu.
2010-01-01
A mathematical model of the ultraviolet (UV) irradiation-induced mutation process in bacterial cells Escherichia coli is developed. Using mathematical approaches, the whole chain of events is tracked from a cell exposure to the damaging factor to mutation formation in the DNA chain. An account of the key special features of the regulation of this genetic network allows predicting the effects induced by the cell exposure to certain UV energy fluence.
Mathematical modeling and physical reality in noncovalent interactions.
Politzer, Peter; Murray, Jane S; Clark, Timothy
2015-03-01
The Hellmann-Feynman theorem provides a straightforward interpretation of noncovalent bonding in terms of Coulombic interactions, which encompass polarization (and accordingly include dispersion). Exchange, Pauli repulsion, orbitals, etc., are part of the mathematics of obtaining the system's wave function and subsequently its electronic density. They do not correspond to physical forces. Charge transfer, in the context of noncovalent interactions, is equivalent to polarization. The key point is that mathematical models must not be confused with physical reality. PMID:25697332
Mathematical model of a heterogeneous pulmonary acinus structure.
Koshiyama, Kenichiro; Wada, Shigeo
2015-07-01
The pulmonary acinus is a gas exchange unit distal to the terminal bronchioles. A model of its structure is important for the computational investigation of mechanical phenomena at the acinus level. We propose a mathematical model of a heterogeneous acinus structure composed of alveoli of irregular sizes, shapes, and locations. The alveoli coalesce into an intricately branched ductal tree, which meets the space-filling requirement of the acinus structure. Our model uses Voronoi tessellation to generate an assemblage of the alveolar or ductal airspace, and Delaunay tessellation and simulated annealing for the ductal tree structure. The modeling condition is based on average acinar and alveolar volume characteristics from published experimental information. By applying this modeling technique to the acinus of healthy mature rats, we demonstrate that the proposed acinus structure model reproduces the available experimental information. In the model, the shape and size of alveoli and the length, generation, tortuosity, and branching angle of the ductal paths are distributed in several ranges. This approach provides a platform for investigating the heterogeneous nature of the acinus structure and its relationship with mechanical phenomena at the acinus level.
Mathematical Modeling and the Redesign of a Teaching Ambulatory Clinic
ERIC Educational Resources Information Center
Baker, Duke H.; Mamlin, Joseph
1976-01-01
Mathematical modeling was utilized in the planning and decision-making process involved in reorganizing a teaching clinic to effect continuity of care. The model interrelated physicians, time, and space, facilitating value judgments and decisions. The reorganization was successful and the outcomes remarkably similar to model predictions.…
Mathematical Modelling in Physics and Engineering--Part 2.
ERIC Educational Resources Information Center
Oke, K. H.; Jones, A. L.
1982-01-01
Mathematical modelling and an example used with undergraduates were presented in part 1 (v17, n5, p212-18, 1982). A second example, Power from Windmills, is provided which has considerable potential for development both as a model and as a series of modelling experiences of increasing difficulty for students with different backgrounds. (Author/JN)
An Introduction to Mathematical Modelling for Ecologists and Environmental Scientists.
ERIC Educational Resources Information Center
Smith, I. R.; Henderson-Sellers, B.
1981-01-01
Describes the basic philosophy, nomenclature, and techniques used in mathematical modelling to enable biologists, engineers, land managers, and others to understand the concepts and usefulness of models. Contrasts conceptual and empirical approaches, using ecosystem models as an example of the former. (DC)
A Review on Mathematical Modeling for Textile Processes
NASA Astrophysics Data System (ADS)
Chattopadhyay, R.
2015-10-01
Mathematical model is a powerful tool in engineering for studying variety of problems related to design and development of products and processes, optimization of manufacturing process, understanding a phenomenon and predicting product's behaviour in actual use. An insight of the process and use of appropriate mathematical tools are necessary for developing models. In the present paper, a review of types of model, procedure followed in developing them and their limitations have been discussed. Modeling techniques being used in few textile processes available in the literature have been cited as examples.
A mathematical model for evolution and SETI.
Maccone, Claudio
2011-12-01
Darwinian evolution theory may be regarded as a part of SETI theory in that the factor f(l) in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor f(l) is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factors increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions (b-lognormals) constrained between the time axis and the exponential growth curve. Finally, since each b-lognormal distribution in the family may in turn be regarded as the product of a large number (actually "an infinity") of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation.
A Mathematical Model for Evolution and SETI
NASA Astrophysics Data System (ADS)
Maccone, Claudio
2011-12-01
Darwinian evolution theory may be regarded as a part of SETI theory in that the factor fl in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor fl is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factors increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions (b-lognormals) constrained between the time axis and the exponential growth curve. Finally, since each b-lognormal distribution in the family may in turn be regarded as the product of a large number (actually "an infinity") of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation.
A mathematical model for evolution and SETI.
Maccone, Claudio
2011-12-01
Darwinian evolution theory may be regarded as a part of SETI theory in that the factor f(l) in the Drake equation represents the fraction of planets suitable for life on which life actually arose. In this paper we firstly provide a statistical generalization of the Drake equation where the factor f(l) is shown to follow the lognormal probability distribution. This lognormal distribution is a consequence of the Central Limit Theorem (CLT) of Statistics, stating that the product of a number of independent random variables whose probability densities are unknown and independent of each other approached the lognormal distribution when the number of factors increased to infinity. In addition we show that the exponential growth of the number of species typical of Darwinian Evolution may be regarded as the geometric locus of the peaks of a one-parameter family of lognormal distributions (b-lognormals) constrained between the time axis and the exponential growth curve. Finally, since each b-lognormal distribution in the family may in turn be regarded as the product of a large number (actually "an infinity") of independent lognormal probability distributions, the mathematical way is paved to further cast Darwinian Evolution into a mathematical theory in agreement with both its typical exponential growth in the number of living species and the Statistical Drake Equation. PMID:22139521
ERIC Educational Resources Information Center
Tropper, Natalie; Leiss, Dominik; Hänze, Martin
2015-01-01
Empirical findings show that students have manifold difficulties when dealing with mathematical modeling problems. Accordingly, approaches for supporting students in modeling-based learning environments have to be investigated. In the research presented here, we adopted a scaffolding perspective on teaching modeling with the aim of both providing…
Mathematical modeling of plasma deposition and hardening of coatings-switched electrical parameters
NASA Astrophysics Data System (ADS)
Kadyrmetov, A. M.; Sharifullin, S. N.; Pustovalov, AS
2016-01-01
This paper presents the results of simulation of plasma deposition and hardening of coatings in modulating the electrical parameters. Mathematical models are based on physical models of gas-dynamic mechanisms more dynamic and thermal processes of the plasma jet. As an example the modeling of dynamic processes of heterogeneous plasma jet, modulated current pulses indirect arc plasma torch.
Jin, Rui; Zhang, Bing; Liu, Sen-mao; Xue, Chun-miao; Zhao, Qian
2011-08-01
Studying the essence of syndromes (Zheng) in traditional Chinese medicine (TCM) is a fundamental challenge in basic theoretical research of TCM. The relationship between any given syndrome and biochemical indicators is one of the important aspects of the study. As the indexes selected in each study are specific to a particular Western medical disease diagnosis, and the disease factor is inevitably introduced into the study, the effect of disease factor on the index changes cannot be assessed effectively by traditional data processing methods. This is known as "the same syndrome with different reasons", which has resulted in confusion in TCM research. This study aimed at providing a mathematical tool to address this issue. Based on information theory and the residual-split method, the syndrome information, which was covered in the index variation, was quantitatively calculated in this paper as an independent part of the disease factor. A mathematical model capable of objectively assessing and statistically testing the effect of the syndrome factor on the index changes was established. Applying this model to literature data of studies on the relationship between cyclic nucleotides and yang-deficiency syndrome showed following results. First, the values of yang-deficiency syndrome information were negative for cyclic adenosine monophosphate (cAMP) while positive for cyclic guanosine monophosphate (cGMP) in all included literature. This indicated that the group of yang-deficiency syndrome was correlated with an obvious trend of reduced cAMP levels and increased cGMP levels. Second, the statistical test results of yang-deficiency syndrome information of the two indexes were different among the literature included. The quality of original data was considered as a possible reason. Third, the significant differences between the yang-deficiency group of a specific disease and the normal group may, in some cases, be caused by a disease factor rather than a syndrome factor
Mathematical Modelling of a Helicopter Rotor Track and Balance: Theory
NASA Astrophysics Data System (ADS)
Rosen, A.; Ben-Ari, R.
1997-03-01
Non-uniformity of helicopter blades results in vibrations at low frequencies. These vibrations result in increased fatigue of the crew, discomfort to passengers and maintenance and reliability problems. Non-uniformities include geometric, mass, structural and aerodynamic aspects. Typical blades have special devices by which intentional non-uniformities can be introduced, in order to cancel the influence of “natural” non-uniformities of the blades. Non uniformities also result in out-of-track behavior of the blades. In many cases the corrections are aimed at decreasing the out-of-track behavior of the blades, based on the assumption that this effort will also decrease the vibrations that are transferred from the rotor to the hub. Unfortunately, tracking does not necessarily result in optimal reduction of the vibrations. The present paper presents a general mathematical definition of track and balance, and the relation between them. This mathematical model opens the way for a thorough investigation on optimal rotor tuning.
Mathematical framework for activity-based cancer biomarkers.
Kwong, Gabriel A; Dudani, Jaideep S; Carrodeguas, Emmanuel; Mazumdar, Eric V; Zekavat, Seyedeh M; Bhatia, Sangeeta N
2015-10-13
Advances in nanomedicine are providing sophisticated functions to precisely control the behavior of nanoscale drugs and diagnostics. Strategies that coopt protease activity as molecular triggers are increasingly important in nanoparticle design, yet the pharmacokinetics of these systems are challenging to understand without a quantitative framework to reveal nonintuitive associations. We describe a multicompartment mathematical model to predict strategies for ultrasensitive detection of cancer using synthetic biomarkers, a class of activity-based probes that amplify cancer-derived signals into urine as a noninvasive diagnostic. Using a model formulation made of a PEG core conjugated with protease-cleavable peptides, we explore a vast design space and identify guidelines for increasing sensitivity that depend on critical parameters such as enzyme kinetics, dosage, and probe stability. According to this model, synthetic biomarkers that circulate in stealth but then activate at sites of disease have the theoretical capacity to discriminate tumors as small as 5 mm in diameter-a threshold sensitivity that is otherwise challenging for medical imaging and blood biomarkers to achieve. This model may be adapted to describe the behavior of additional activity-based approaches to allow cross-platform comparisons, and to predict allometric scaling across species.
Mathematical framework for activity-based cancer biomarkers.
Kwong, Gabriel A; Dudani, Jaideep S; Carrodeguas, Emmanuel; Mazumdar, Eric V; Zekavat, Seyedeh M; Bhatia, Sangeeta N
2015-10-13
Advances in nanomedicine are providing sophisticated functions to precisely control the behavior of nanoscale drugs and diagnostics. Strategies that coopt protease activity as molecular triggers are increasingly important in nanoparticle design, yet the pharmacokinetics of these systems are challenging to understand without a quantitative framework to reveal nonintuitive associations. We describe a multicompartment mathematical model to predict strategies for ultrasensitive detection of cancer using synthetic biomarkers, a class of activity-based probes that amplify cancer-derived signals into urine as a noninvasive diagnostic. Using a model formulation made of a PEG core conjugated with protease-cleavable peptides, we explore a vast design space and identify guidelines for increasing sensitivity that depend on critical parameters such as enzyme kinetics, dosage, and probe stability. According to this model, synthetic biomarkers that circulate in stealth but then activate at sites of disease have the theoretical capacity to discriminate tumors as small as 5 mm in diameter-a threshold sensitivity that is otherwise challenging for medical imaging and blood biomarkers to achieve. This model may be adapted to describe the behavior of additional activity-based approaches to allow cross-platform comparisons, and to predict allometric scaling across species. PMID:26417077
Investigating and developing engineering students' mathematical modelling and problem-solving skills
NASA Astrophysics Data System (ADS)
Wedelin, Dag; Adawi, Tom; Jahan, Tabassum; Andersson, Sven
2015-09-01
How do engineering students approach mathematical modelling problems and how can they learn to deal with such problems? In the context of a course in mathematical modelling and problem solving, and using a qualitative case study approach, we found that the students had little prior experience of mathematical modelling. They were also inexperienced problem solvers, unaware of the importance of understanding the problem and exploring alternatives, and impeded by inappropriate beliefs, attitudes and expectations. Important impacts of the course belong to the metacognitive domain. The nature of the problems, the supervision and the follow-up lectures were emphasised as contributing to the impacts of the course, where students show major development. We discuss these empirical results in relation to a framework for mathematical thinking and the notion of cognitive apprenticeship. Based on the results, we argue that this kind of teaching should be considered in the education of all engineers.
NASA Technical Reports Server (NTRS)
Wada, B. K.; Kuo, C-P.; Glaser, R. J.
1986-01-01
For the structural dynamic analysis of large space structures, the technology in structural synthesis and the development of structural analysis software have increased the capability to predict the dynamic characteristics of the structural system. The various subsystems which comprise the system are represented by various displacement functions; the displacement functions are then combined to represent the total structure. Experience has indicated that even when subsystem mathematical models are verified by test, the mathematical representations of the total system are often in error because the mathematical model of the structural elements which are significant when loads are applied at the interconnection points are not adequately verified by test. A multiple test concept, based upon the Multiple Boundary Condition Test (MBCT), is presented which will increase the accuracy of the system mathematical model by improving the subsystem test and test/analysis correlation procedure.
On a Mathematical Model of Brain Activities
Fichtner, K.-H.; Fichtner, L.; Freudenberg, W.; Ohya, M.
2007-12-03
The procedure of recognition can be described as follows: There is a set of complex signals stored in the memory. Choosing one of these signals may be interpreted as generating a hypothesis concerning an 'expexted view of the world'. Then the brain compares a signal arising from our senses with the signal chosen from the memory leading to a change of the state of both signals. Furthermore, measurements of that procedure like EEG or MEG are based on the fact that recognition of signals causes a certain loss of excited neurons, i.e. the neurons change their state from 'excited' to 'nonexcited'. For that reason a statistical model of the recognition process should reflect both--the change of the signals and the loss of excited neurons. A first attempt to explain the process of recognition in terms of quantum statistics was given. In the present note it is not possible to present this approach in detail. In lieu we will sketch roughly a few of the basic ideas and structures of the proposed model of the recognition process (Section). Further, we introduce the basic spaces and justify the choice of spaces used in this approach. A more elaborate presentation including all proofs will be given in a series of some forthcoming papers. In this series also the procedures of creation of signals from the memory, amplification, accumulation and transformation of input signals, and measurements like EEG and MEG will be treated in detail.
On a Mathematical Model of Brain Activities
NASA Astrophysics Data System (ADS)
Fichtner, K.-H.; Fichtner, L.; Freudenberg, W.; Ohya, M.
2007-12-01
The procedure of recognition can be described as follows: There is a set of complex signals stored in the memory. Choosing one of these signals may be interpreted as generating a hypothesis concerning an "expexted view of the world". Then the brain compares a signal arising from our senses with the signal chosen from the memory leading to a change of the state of both signals. Furthermore, measurements of that procedure like EEG or MEG are based on the fact that recognition of signals causes a certain loss of excited neurons, i.e. the neurons change their state from "excited" to "nonexcited". For that reason a statistical model of the recognition process should reflect both—the change of the signals and the loss of excited neurons. A first attempt to explain the process of recognition in terms of quantum statistics was given in [1]. In the present note it is not possible to present this approach in detail. In lieu we will sketch roughly a few of the basic ideas and structures of the proposed model of the recognition process (Section). Further, we introduce the basic spaces and justify the choice of spaces used in this approach. A more elaborate presentation including all proofs will be given in a series of some forthcoming papers [2, 3]. In this series also the procedures of creation of signals from the memory, amplification, accumulation and transformation of input signals, and measurements like EEG and MEG will be treated in detail.
The Concept of Model. What is Remarkable in Mathematical Models
NASA Astrophysics Data System (ADS)
Bezruchko, Boris P.; Smirnov, Dmitry A.
Dictionaries tell us that the word "model" originates from the Latin word "modulus" which means "measure, template, norm". This term was used in proceedings on civil engineering several centuries BC. Currently, it relates to an enormously wide range of material objects, symbolic structures and ideal images ranging from models of clothes, small copies of ships and aeroplanes, different pictures and plots to mathematical equations and computational algorithms. Starting to define the concept of "model", we would like to remind about the difficulty to give strict definitions of basic concepts. Thus, when university professors define "oscillations" and "waves" in their lectures on this subject, it is common for many of them to repeat the joke of Russian academician L.I. Mandel'shtam, who illustrated the problem with the example of the term "heap": How many objects, and of which kind, deserve such a name? As well, he compared strict definitions at the beginning of studying any topic to "swaddling oneself with barbed wire". Among classical examples of impossibility to give exhaustive formulations, one can mention the terms "bald spot", "forest", etc. Therefore, we will not consider variety of existing definitions of "model" and "modelling" in detail. Any of them relates to the purposes and subjective preferences of an author and is valid in a certain sense. However, it is restricted since it ignores some objects or properties that deserve attention from other points of view.
A mathematical model for flight guidance in honeybee swarms.
Fetecau, R C; Guo, A
2012-11-01
When a colony of honeybees relocates to a new nest site, less than 5 % of the bees (the scout bees) know the location of the new nest. Nevertheless, the small minority of informed bees manages to provide guidance to the rest and the entire swarm is able to fly to the new nest intact. The streaker bee hypothesis, one of the several theories proposed to explain the guidance mechanism in bee swarms, seems to be supported by recent experimental observations. The theory suggests that the informed bees make high-speed flights through the swarm in the direction of the new nest, hence conspicuously pointing to the desired direction of travel. This work presents a mathematical model of flight guidance in bee swarms based on the streaker bee hypothesis. Numerical experiments, parameter studies, and comparison with experimental data are presented. PMID:22890574
Predictions of cardiovascular responses during STS reentry using mathematical models
NASA Technical Reports Server (NTRS)
Leonard, J. I.; Srinivasan, R.
1985-01-01
The physiological adaptation to weightless exposure includes cardiovascular deconditioning arising in part from a loss of total circulating blood volume and resulting in a reduction of orthostatic tolerance. The crew of the Shuttle orbiter are less tolerant to acceleration forces in the head-to-foot direction during the reentry phase of the flight at a time they must function at a high level of performance. The factors that contribute to orthostatic intolerance during and following reentry and to predict the likelihood of impaired crew performance are evaluated. A computer simulation approach employing a mathematical model of the cardiovascular system is employed. It is shown that depending on the severity of blood volume loss, the reentry acceleration stress may be detrimental to physiologic function and may place the physiologic status of the crew near the borderline of some type of impairment. They are in agreement with conclusions from early ground-based experiments and from observations of early Shuttle flights.
Mathematical modeling of fluid-electrolyte alterations during weightlessness
NASA Technical Reports Server (NTRS)
Leonard, J. I.
1984-01-01
Fluid electrolyte metabolism and renal endocrine control as it pertains to adaptation to weightlessness were studied. The mathematical models that have been particularly useful are discussed. However, the focus of the report is on the physiological meaning of the computer studies. A discussion of the major ground based analogs of weightlessness are included; for example, head down tilt, water immersion, and bed rest, and a comparison of findings. Several important zero g phenomena are described, including acute fluid volume regulation, blood volume regulation, circulatory changes, longer term fluid electrolyte adaptations, hormonal regulation, and body composition changes. Hypotheses are offered to explain the major findings in each area and these are integrated into a larger hypothesis of space flight adaptation. A conceptual foundation for fluid electrolyte metabolism, blood volume regulation, and cardiovascular regulation is reported.
Mathematical model of layered metallurgical furnaces and units
NASA Astrophysics Data System (ADS)
Shvydkiy, V. S.; Spirin, N. A.; Lavrov, V. V.
2016-09-01
The basic approaches to mathematical modeling of the layered steel furnaces and units are considered. It is noted that the particular importance have the knowledge about the mechanisms and physical nature of processes of the charge column movement and the gas flow in the moving layer, as well as regularities of development of heat- and mass-transfer in them. The statement and mathematical description of the problem solution targeting the potential gas flow in the layered unit of an arbitrary profile are presented. On the basis of the proposed mathematical model the software implementation of information-modeling system of BF gas dynamics is carried out. The results of the computer modeling of BF non-isothermal gas dynamics with regard to the cohesion zone, gas dynamics of the combustion zone and calculation of hot-blast stoves are provided
A mathematical model for mesenchymal and chemosensitive cell dynamics.
Häcker, Anita
2012-01-01
The structure of an underlying tissue network has a strong impact on cell dynamics. If, in addition, cells alter the network by mechanical and chemical interactions, their movement is called mesenchymal. Important examples for mesenchymal movement include fibroblasts in wound healing and metastatic tumour cells. This paper is focused on the latter. Based on the anisotropic biphasic theory of Barocas and Tranquillo, which models a fibre network and interstitial solution as two-component fluid, a mathematical model for the interactions of cells with a fibre network is developed. A new description for fibre reorientation is given and orientation-dependent proteolysis is added to the model. With respect to cell dynamics, the equation, based on anisotropic diffusion, is extended by haptotaxis and chemotaxis. The chemoattractants are the solute network fragments, emerging from proteolysis, and the epidermal growth factor which may guide the cells to a blood vessel. Moreover the cell migration is impeded at either high or low network density. This new model enables us to study chemotactic cell migration in a complex fibre network and the consequential network deformation. Numerical simulations for the cell migration and network deformation are carried out in two space dimensions. Simulations of cell migration in underlying tissue networks visualise the impact of the network structure on cell dynamics. In a scenario for fibre reorientation between cell clusters good qualitative agreement with experimental results is achieved. The invasion speeds of cells in an aligned and an isotropic fibre network are compared.
Redundancy management of electrohydraulic servoactuators by mathematical model referencing
NASA Technical Reports Server (NTRS)
Campbell, R. A.
1971-01-01
A description of a mathematical model reference system is presented which provides redundancy management for an electrohydraulic servoactuator. The mathematical model includes a compensation network that calculates reference parameter perturbations induced by external disturbance forces. This is accomplished by using the measured pressure differential data taken from the physical system. This technique was experimentally verified by tests performed using the H-1 engine thrust vector control system for Saturn IB. The results of these tests are included in this report. It was concluded that this technique improves the tracking accuracy of the model reference system to the extent that redundancy management of electrohydraulic servosystems may be performed using this method.
The Mathematical Analysis of Style: A Correlation-Based Approach.
ERIC Educational Resources Information Center
Oppenheim, Rosa
1988-01-01
Examines mathematical models of style analysis, focusing on the pattern in which literary characteristics occur. Describes an autoregressive integrated moving average model (ARIMA) for predicting sentence length in different works by the same author and comparable works by different authors. This technique is valuable in characterizing stylistic…
ERIC Educational Resources Information Center
Xia, Xiaogang; Lu, Chuanhan; Wang, Bingyi; Song, Yunming
2007-01-01
This research tends to make the experimental study on the mathematics teaching model of "situated creation and problem-based instruction" (SCPBI), namely, the teaching process of "creating situations--posing problems--solving problems--applying mathematics". It is aimed at changing the situation where students generally lack problem-based learning…
Applicability of mathematical modeling to problems of environmental physiology
NASA Technical Reports Server (NTRS)
White, Ronald J.; Lujan, Barbara F.; Leonard, Joel I.; Srinivasan, R. Srini
1988-01-01
The paper traces the evolution of mathematical modeling and systems analysis from terrestrial research to research related to space biomedicine and back again to terrestrial research. Topics covered include: power spectral analysis of physiological signals; pattern recognition models for detection of disease processes; and, computer-aided diagnosis programs used in conjunction with a special on-line biomedical computer library.
The Singing Wineglass: An Exercise in Mathematical Modelling
ERIC Educational Resources Information Center
Voges, E. L.; Joubert, S. V.
2008-01-01
Lecturers in mathematical modelling courses are always on the lookout for new examples to illustrate the modelling process. A physical phenomenon, documented as early as the nineteenth century, was recalled: when a wineglass "sings", waves are visible on the surface of the wine. These surface waves are used as an exercise in mathematical…
Metaphors and Models in Translation between College and Workplace Mathematics
ERIC Educational Resources Information Center
Williams, Julian; Wake, Geoff
2007-01-01
We report a study of repairs in communication between workers and visiting outsiders (students, researchers or teachers). We show how cultural models such as metaphors and mathematical models facilitated explanations and repair work in inquiry and pedagogical dialogues. We extend previous theorisations of metaphor by Black; Lakoff and Johnson;…
Mitochondrial DNA damage and efficiency of ATP biosynthesis: mathematical model.
Beregovskaya, N; Maiboroda, R
1995-01-21
The role of mitochondrial DNA (mtDNA) damage in ageing processes and in malignant transformation of a cell is discussed. A mathematical model of the mtDNA population in a cell and in tissue is constructed. The model describes the effects of mtDNA damages accumulated during ageing and some features of malignant transformation and regeneration.
PARCC Model Content Frameworks: Mathematics--Grades 3-11
ERIC Educational Resources Information Center
Partnership for Assessment of Readiness for College and Careers (NJ1), 2011
2011-01-01
As part of its proposal to the U.S. Department of Education, the Partnership for Assessment of Readiness for College and Careers (PARCC) committed to developing model content frameworks for mathematics to serve as a bridge between the Common Core State Standards and the PARCC assessments. The PARCC Model Content Frameworks were developed through a…
Teaching Mathematical Modelling: Demonstrating Enrichment and Elaboration
ERIC Educational Resources Information Center
Warwick, Jon
2015-01-01
This paper uses a series of models to illustrate one of the fundamental processes of model building--that of enrichment and elaboration. The paper describes how a problem context is given which allows a series of models to be developed from a simple initial model using a queuing theory framework. The process encourages students to think about the…
Mathematical model of an air-filled alpha stirling refrigerator
NASA Astrophysics Data System (ADS)
McFarlane, Patrick; Semperlotti, Fabio; Sen, Mihir
2013-10-01
This work develops a mathematical model for an alpha Stirling refrigerator with air as the working fluid and will be useful in optimizing the mechanical design of these machines. Two pistons cyclically compress and expand air while moving sinusoidally in separate chambers connected by a regenerator, thus creating a temperature difference across the system. A complete non-linear mathematical model of the machine, including air thermodynamics, and heat transfer from the walls, as well as heat transfer and fluid resistance in the regenerator, is developed. Non-dimensional groups are derived, and the mathematical model is numerically solved. The heat transfer and work are found for both chambers, and the coefficient of performance of each chamber is calculated. Important design parameters are varied and their effect on refrigerator performance determined. This sensitivity analysis, which shows what the significant parameters are, is a useful tool for the design of practical Stirling refrigeration systems.
NASA Astrophysics Data System (ADS)
Neves, Rui Gomes; Teodoro, Vítor Duarte
2012-09-01
A teaching approach aiming at an epistemologically balanced integration of computational modelling in science and mathematics education is presented. The approach is based on interactive engagement learning activities built around computational modelling experiments that span the range of different kinds of modelling from explorative to expressive modelling. The activities are designed to make a progressive introduction to scientific computation without requiring prior development of a working knowledge of programming, generate and foster the resolution of cognitive conflicts in the understanding of scientific and mathematical concepts and promote performative competency in the manipulation of different and complementary representations of mathematical models. The activities are supported by interactive PDF documents which explain the fundamental concepts, methods and reasoning processes using text, images and embedded movies, and include free space for multimedia enriched student modelling reports and teacher feedback. To illustrate, an example from physics implemented in the Modellus environment and tested in undergraduate university general physics and biophysics courses is discussed.
Mathematical model of galactose regulation and metabolic consumption in yeast.
Mitre, Tina M; Mackey, Michael C; Khadra, Anmar
2016-10-21
The galactose network has been extensively studied at the unicellular level to broaden our understanding of the regulatory mechanisms governing galactose metabolism in multicellular organisms. Although the key molecular players involved in the metabolic and regulatory processes of this system have been known for decades, their interactions and chemical kinetics remain incompletely understood. Mathematical models can provide an alternative method to study the dynamics of this network from a quantitative and a qualitative perspective. Here, we employ this approach to unravel the main properties of the galactose network, including equilibrium binary and temporal responses, as a way to decipher its adaptation to actively-changing inputs. We combine its two main components: the genetic branch, which allows for bistable responses, and a metabolic branch, encompassing the relevant metabolic processes that can be repressed by glucose. We use both computational tools to estimate model parameters based on published experimental data, as well as bifurcation analysis to decipher the properties of the system in various parameter regimes. Our model analysis reveals that the interplay between the inducer (galactose) and the repressor (glucose) creates a bistable regime which dictates the temporal responses of the system. Based on the same bifurcation techniques, we explain why the system is robust to genetic mutations and molecular instabilities. These findings may provide experimentalists with a theoretical framework with which they can determine how the galactose network functions under various conditions. PMID:27395401
Light driven microactuators: Design, fabrication, and mathematical modeling
NASA Astrophysics Data System (ADS)
Han, Li-Hsin
This dissertation is concerned with design, fabrication, and mathematical modeling of three different microactuators driven by light. Compared to electricity, electromagnetic wave is a wireless source of power. A distant light source can be delivered, absorbed, and converted to generate a driving force for a microactuator. The study of light-driven microsystems, still at its early stage, is already expanding the horizon for the research of microsystems. The microactuators of this dissertation include micro-cantilevers driven by pulsed laser, photo-deformable microshells coated with gold nanospheres, and a nano-particles coated micro-turbine driven by visible light. Experimental investigation and theoretical analysis of these microactuators showed interesting results. These microactuators were functioned based on cross-linked, multiple physics phenomenon, such as photo-heating, thermal expansion, photo-chemistry effect, plasomonics enhancement, and thermal convection in rarefied gas. These multiple physics effects dominate the function of a mechanical system, when the system size becomes small. The modeling results of the microactuators suggest that, to simulate a microscale mechanical system accurately, one has to take account the minimum dimension of the system and to consider the validity of a theoretical model. Examples of the building of different microstructures were shown to demonstrate the capacity of a digital-micromirror-device (DMD) based apparatus for three-dimensional, heterogeneous fabrication of polymeric microstructures.
ERIC Educational Resources Information Center
Psycharis, Sarantos
2016-01-01
Computational experiment approach considers models as the fundamental instructional units of Inquiry Based Science and Mathematics Education (IBSE) and STEM Education, where the model take the place of the "classical" experimental set-up and simulation replaces the experiment. Argumentation in IBSE and STEM education is related to the…
A full body mathematical model of an oil palm harvester
NASA Astrophysics Data System (ADS)
Tumit, NP; Rambely, A. S.; BMT, Shamsul; Shahriman A., B.; Ng Y., G.; Deros, B. M.; Zailina, H.; Goh Y., M.; Arumugam, Manohar; Ismail I., A.; Abdul Hafiz A., R.
2015-09-01
The main purpose of this article is to develop a mathematical model of human body during harvesting via Kane's method. This paper is an extension model of previous biomechanical model representing a harvester movement during harvesting a Fresh Fruit Bunch (FFB) from a palm oil tree. The ten segment model consists of foot, leg, trunk, the head and the arms segment. Finally, the inverse dynamic equations are represented in a matrix form.
Mathematically modelling proportions of Japanese populations by industry
NASA Astrophysics Data System (ADS)
Hirata, Yoshito
2016-10-01
I propose a mathematical model for temporal changes of proportions for industrial sectors. I prove that the model keeps the proportions for the primary, the secondary, and the tertiary sectors between 0 and 100% and preserves their total as 100%. The model fits the Japanese historical data between 1950 and 2005 for the population proportions by industry very well. The model also predicts that the proportion for the secondary industry becomes negligible and becomes less than 1% at least around 2080.
Mathematical modelling of undrained clay behavior
NASA Technical Reports Server (NTRS)
Prevost, J. H.; Noeg, K.
1976-01-01
The proposed general analytical model describes the anisotropic, elastoplastic, path-dependent, stress-strain properties of inviscid saturated clays under undrained conditions. Model parameters are determined by using results from strain-controlled simple shear tests on a saturated clay. The model's accuracy is evaluated by applying it to predict the results of other tests on the same clay, including monotonic and cyclic loading. The model explains the very anisotropic shear strength behavior observed for weak marine clays.
Mathematical models of magnetite desliming for automated quality control systems
NASA Astrophysics Data System (ADS)
Olevska, Yu.; Mishchenko, V.; Olevskyi, V.
2016-10-01
The aim of the study is to provide multifactor mathematical models suitable for use in automatic control systems of desliming process. For this purpose we described the motion of a two-phase environment regard to the shape the desliming machine and technological parameters of the enrichment process. We created the method for preparation of dependences of the enrichment process quality from the technological and design parameters. To automate the process we constructed mathematical models to justify intensive technological modes and optimal parameters for design of desliming machine.
Mathematical modelling in the computer-aided process planning
NASA Astrophysics Data System (ADS)
Mitin, S.; Bochkarev, P.
2016-04-01
This paper presents new approaches to organization of manufacturing preparation and mathematical models related to development of the computer-aided multi product process planning (CAMPP) system. CAMPP system has some peculiarities compared to the existing computer-aided process planning (CAPP) systems: fully formalized developing of the machining operations; a capacity to create and to formalize the interrelationships among design, process planning and process implementation; procedures for consideration of the real manufacturing conditions. The paper describes the structure of the CAMPP system and shows the mathematical models and methods to formalize the design procedures.
A mathematical look at a physical power prediction model
Landberg, L.
1997-12-31
This paper takes a mathematical look at a physical model used to predict the power produced from wind farms. The reason is to see whether simple mathematical expressions can replace the original equations, and to give guidelines as to where the simplifications can be made and where they can not. This paper shows that there is a linear dependence between the geostrophic wind and the wind at the surface, but also that great care must be taken in the selection of the models since physical dependencies play a very important role, e.g. through the dependence of the turning of the wind on the wind speed.
Mathematical model in controlling dengue transmission with sterile mosquito strategies
NASA Astrophysics Data System (ADS)
Aldila, D.; Nuraini, N.; Soewono, E.
2015-09-01
In this article, we propose a mathematical model for controlling dengue disease transmission with sterile mosquito techniques (SIT). Sterile male introduced from lab in to habitat to compete with wild male mosquito for mating with female mosquito. Our aim is to displace gradually the natural mosquito from the habitat. Mathematical model analysis for steady states and the basic reproductive ratio are performed analytically. Numerical simulation are shown in some different scenarios. We find that SIT intervention is potential to controlling dengue spread among humans population
Mathematical models of polymer solutions motion and their symmetries
NASA Astrophysics Data System (ADS)
Bozhkov, Yu. D.; Pukhnachev, V. V.; Pukhnacheva, T. P.
2015-10-01
We consider three mathematical models describing motion of aqueous polymer solutions. All of them are derived from equations of Maxwell type viscoelastic medium at small relaxation time. Distinction consists in the choice of time derivative in the rheological constitutive law. Namely, we can choose (a) connective, (b) partial or (c) objective derivative of the strain tensor in time. We found widest symmetry groups admitted by each of these models. Systems (a) and (c) admit the extended Galilei group containing four arbitrary functions of time while the group admitted by system (b) is rather poor. Wide classes of exact solutions are obtained and their behaviors are analyzed if the relaxation viscosity tends to zero. Asymptotic expansion in this solution's parameter describing the flow near a critical point in planar and axially symmetric cases is derived. Analogs of the classical Hagen-Poiseuille and Nusselt solutions are studied too. We found difference in the pressure distribution between solutions calculated on the base of model (c) and two other models.
Using mathematical models to understand the AIDS spidemic. [None
Hyman, J.M.; Stanley, E.A.
1987-01-01
The most urgent public health problem today is to devise effective strategies to minimize the destruction caused by the AIDS epidemic. This complex problem will involve medical advances and new public health and education initiatives. Mathematical models based on the underlying transmission mechanisms of the AIDS virus can help the medical/scientific community understand and anticipate its spread in different populations and evaluate the potential effectiveness of different approaches for bringing the epidemic under control. Before we can use models to predict the future, we must carefully test them against the past spread of the infection and for sensitivity to parameter changes. The long and extremely variable incubation period and the low probability of transmitting the AIDS virus in a single contact imply that population structure and variations in infectivity both play an important role in its spread. This structure occurs because of differences between people in numbers of sexual partners and the use of intravenous drugs and because of the way in which people mix among age, ethnic, and social groups. We use a simplified approach to investigate the effects of variation in incubation periods and infectivity specific to the AIDS virus and we compare a model of random partner choices with a model in which partners both come from similar behavior groups. 60 refs., 15 figs.
ERIC Educational Resources Information Center
McNamara, James F.
This mathematical programing model was developed to provide the State Board of Education with complete information for evaluating decisions about the efficient allocation of vocational education funds to local school districts. The model, based on a supply-demand criterion, was tested on a set of occupational training programs within a given Labor…
An applied mathematics perspective on stochastic modelling for climate.
Majda, Andrew J; Franzke, Christian; Khouider, Boualem
2008-07-28
Systematic strategies from applied mathematics for stochastic modelling in climate are reviewed here. One of the topics discussed is the stochastic modelling of mid-latitude low-frequency variability through a few teleconnection patterns, including the central role and physical mechanisms responsible for multiplicative noise. A new low-dimensional stochastic model is developed here, which mimics key features of atmospheric general circulation models, to test the fidelity of stochastic mode reduction procedures. The second topic discussed here is the systematic design of stochastic lattice models to capture irregular and highly intermittent features that are not resolved by a deterministic parametrization. A recent applied mathematics design principle for stochastic column modelling with intermittency is illustrated in an idealized setting for deep tropical convection; the practical effect of this stochastic model in both slowing down convectively coupled waves and increasing their fluctuations is presented here. PMID:18445572
Mathematical model of the neonatal mouse ventricular action potential
Wang, Linda J.; Sobie, Eric A.
2008-01-01
Therapies for heart disease are based largely on our understanding of the adult myocardium. The dramatic differences in action potential (AP) shape between neonatal and adult cardiac myocytes, however, indicate that a different set of molecular interactions in neonatal myocytes necessitates different treatment for newborns. Computational modeling is useful for synthesizing data to determine how interactions between components lead to systems-level behavior, but this technique has not been used extensively to study neonatal heart cell function. We created a mathematical model of the neonatal (day 1) mouse myocyte by modifying, based on experimental data, the densities and/or formulations of ion transport mechanisms in an adult cell model. The new model reproduces the characteristic AP shape of neonatal cells, with a brief plateau phase and longer duration than the adult (APD80=60.1 vs. 12.6 ms). The simulation results are consistent with experimental data, including: 1) decreased density, and altered inactivation, of transient outward K+ currents, 2) increased delayed rectifier K+ currents, 3) Ca2+ entry through T-type as well as L-type Ca2+ channels, 4) increased Ca2+ influx through Na+-Ca2+ exchange, and 5) Ca2+ transients resulting from transmembrane Ca2+ entry rather than release from the sarcoplasmic reticulum (SR). Simulations performed with the model generated novel predictions, including increased SR Ca2+ leak and elevated intracellular [Na+] in neonatal compared with adult myocytes. This new model can therefore be used for testing hypotheses and obtaining a better quantitative understanding of differences between neonatal and adult physiology. PMID:18408122
Mathematical Modelling in Engineering: An Alternative Way to Teach Linear Algebra
ERIC Educational Resources Information Center
Domínguez-García, S.; García-Planas, M. I.; Taberna, J.
2016-01-01
Technological advances require that basic science courses for engineering, including Linear Algebra, emphasize the development of mathematical strengths associated with modelling and interpretation of results, which are not limited only to calculus abilities. Based on this consideration, we have proposed a project-based learning, giving a dynamic…
ERIC Educational Resources Information Center
Soleimani, Ali
2013-01-01
Immersive 3D worlds can be designed to effectively engage students in peer-to-peer collaborative learning activities, supported by scientific visualization, to help with understanding complex concepts associated with learning science, technology, engineering, and mathematics (STEM). Previous research studies have shown STEM learning benefits…
Mathematical modeling of lithium iodine discharge data
Kim, J.S.; Brennen, K.R.
1980-01-01
An improved numerical model has been developed to project the capacities of Li/I/sub 2/ cardiac pacemaker batteries. The model uses accelerated rate discharge data, collected over a two year period, to project the capacities of batteries that will not be depleted in the field for approximately 8 years. Inclusion of new terms to account for self-discharge results in increased accuracy in this new model. Self-discharge is shown to be a small loss in the batteries modeled. 3 refs.
A mathematical space mapping model for ballistic carbon nanotube field-effect transistors
NASA Astrophysics Data System (ADS)
Emamifar, Farnousha; Yousefi, Reza
2016-11-01
In this study, a mathematical model is presented based on mathematical space mapping for ballistic carbon nanotube field-effect transistors. This model is generalized from another model that was based on the concept of neural space mapping to calculate the three parameters of a coarse model. These parameters were the threshold voltage, the Early voltage, and assumed constant k of a modified "level 1" MOSFET model in simulation program with integrated circuit emphasis (SPICE). In this work, three analytical relations are introduced to replace the neural networks of the main model. The comparisons between the proposed model and a well-known reference model, named FETToy, show that the proposed model had reasonable accuracy in terms of different biases and physical parameters.
Undergraduate Research: Mathematical Modeling of Mortgages
ERIC Educational Resources Information Center
Choi, Youngna; Spero, Steven
2010-01-01
In this article, we study financing in the real estate market and show how various types of mortgages can be modeled and analyzed. With only an introductory level of interest theory, finance, and calculus, we model and analyze three types of popular mortgages with real life examples that explain the background and inevitable outcome of the current…
A Mathematical Model for Segmenting ECG Signals
NASA Astrophysics Data System (ADS)
Feier, Horea; Roşu, Doina; Falniţǎ, Lucian; Roşu, Şerban; Pater, Liana
2010-09-01
This paper deals with the behavior of the modulus of the continuous wavelet transform (CWT) for some known mother wavelets like the Morlet wavelet and the Mexican Hat. By exploiting these properties, the models presented can behave as a segmentation/ recognition signal processing tool by modeling the temporal structure of the observed surface ECG.
A mathematical model of intestinal oedema formation.
Young, Jennifer; Rivière, Béatrice; Cox, Charles S; Uray, Karen
2014-03-01
Intestinal oedema is a medical condition referring to the build-up of excess fluid in the interstitial spaces of the intestinal wall tissue. Intestinal oedema is known to produce a decrease in intestinal transit caused by a decrease in smooth muscle contractility, which can lead to numerous medical problems for the patient. Interstitial volume regulation has thus far been modelled with ordinary differential equations, or with a partial differential equation system where volume changes depend only on the current pressure and not on updated tissue stress. In this work, we present a computational, partial differential equation model of intestinal oedema formation that overcomes the limitations of past work to present a comprehensive model of the phenomenon. This model includes mass and momentum balance equations which give a time evolution of the interstitial pressure, intestinal volume changes and stress. The model also accounts for the spatially varying mechanical properties of the intestinal tissue and the inhomogeneous distribution of fluid-leaking capillaries that create oedema. The intestinal wall is modelled as a multi-layered, deforming, poroelastic medium, and the system of equations is solved using a discontinuous Galerkin method. To validate the model, simulation results are compared with results from four experimental scenarios. A sensitivity analysis is also provided. The model is able to capture the final submucosal interstitial pressure and total fluid volume change for all four experimental cases, and provide further insight into the distribution of these quantities across the intestinal wall.
Molecular modeling: An open invitation for applied mathematics
NASA Astrophysics Data System (ADS)
Mezey, Paul G.
2013-10-01
Molecular modeling methods provide a very wide range of challenges for innovative mathematical and computational techniques, where often high dimensionality, large sets of data, and complicated interrelations imply a multitude of iterative approximations. The physical and chemical basis of these methodologies involves quantum mechanics with several non-intuitive aspects, where classical interpretation and classical analogies are often misleading or outright wrong. Hence, instead of the everyday, common sense approaches which work so well in engineering, in molecular modeling one often needs to rely on rather abstract mathematical constraints and conditions, again emphasizing the high level of reliance on applied mathematics. Yet, the interdisciplinary aspects of the field of molecular modeling also generates some inertia and perhaps too conservative reliance on tried and tested methodologies, that is at least partially caused by the less than up-to-date involvement in the newest developments in applied mathematics. It is expected that as more applied mathematicians take up the challenge of employing the latest advances of their field in molecular modeling, important breakthroughs may follow. In this presentation some of the current challenges of molecular modeling are discussed.
Mathematical Modeling Of Life-Support Systems
NASA Technical Reports Server (NTRS)
Seshan, Panchalam K.; Ganapathi, Balasubramanian; Jan, Darrell L.; Ferrall, Joseph F.; Rohatgi, Naresh K.
1994-01-01
Generic hierarchical model of life-support system developed to facilitate comparisons of options in design of system. Model represents combinations of interdependent subsystems supporting microbes, plants, fish, and land animals (including humans). Generic model enables rapid configuration of variety of specific life support component models for tradeoff studies culminating in single system design. Enables rapid evaluation of effects of substituting alternate technologies and even entire groups of technologies and subsystems. Used to synthesize and analyze life-support systems ranging from relatively simple, nonregenerative units like aquariums to complex closed-loop systems aboard submarines or spacecraft. Model, called Generic Modular Flow Schematic (GMFS), coded in such chemical-process-simulation languages as Aspen Plus and expressed as three-dimensional spreadsheet.
Cancer evolution: mathematical models and computational inference.
Beerenwinkel, Niko; Schwarz, Roland F; Gerstung, Moritz; Markowetz, Florian
2015-01-01
Cancer is a somatic evolutionary process characterized by the accumulation of mutations, which contribute to tumor growth, clinical progression, immune escape, and drug resistance development. Evolutionary theory can be used to analyze the dynamics of tumor cell populations and to make inference about the evolutionary history of a tumor from molecular data. We review recent approaches to modeling the evolution of cancer, including population dynamics models of tumor initiation and progression, phylogenetic methods to model the evolutionary relationship between tumor subclones, and probabilistic graphical models to describe dependencies among mutations. Evolutionary modeling helps to understand how tumors arise and will also play an increasingly important prognostic role in predicting disease progression and the outcome of medical interventions, such as targeted therapy.
Cancer Evolution: Mathematical Models and Computational Inference
Beerenwinkel, Niko; Schwarz, Roland F.; Gerstung, Moritz; Markowetz, Florian
2015-01-01
Cancer is a somatic evolutionary process characterized by the accumulation of mutations, which contribute to tumor growth, clinical progression, immune escape, and drug resistance development. Evolutionary theory can be used to analyze the dynamics of tumor cell populations and to make inference about the evolutionary history of a tumor from molecular data. We review recent approaches to modeling the evolution of cancer, including population dynamics models of tumor initiation and progression, phylogenetic methods to model the evolutionary relationship between tumor subclones, and probabilistic graphical models to describe dependencies among mutations. Evolutionary modeling helps to understand how tumors arise and will also play an increasingly important prognostic role in predicting disease progression and the outcome of medical interventions, such as targeted therapy. PMID:25293804
Mathematical analysis and numerical simulation of a model of morphogenesis.
Muñoz, Ana I; Tello, José Ignacio
2011-10-01
We consider a simple mathematical model of distribution of morphogens (signaling molecules responsible for the differentiation of cells and the creation of tissue patterns). The mathematical model is a particular case of the model proposed by Lander, Nie and Wan in 2006 and similar to the model presented in Lander, Nie, Vargas and Wan 2005. The model consists of a system of three equations: a PDE of parabolic type with dynamical boundary conditions modelling the distribution of free morphogens and two ODEs describing the evolution of bound and free receptors. Three biological processes are taken into account: diffusion, degradation and reversible binding. We study the stationary solutions and the evolution problem. Numerical simulations show the behavior of the solution depending on the values of the parameters.
ERIC Educational Resources Information Center
Carrejo, David; Robertson, William H.
2011-01-01
Computer-based mathematical modeling in physics is a process of constructing models of concepts and the relationships between them in the scientific characteristics of work. In this manner, computer-based modeling integrates the interactions of natural phenomenon through the use of models, which provide structure for theories and a base for…
Mathematical Modeling of Interleukin-35 Promoting Tumor Growth and Angiogenesis
Liao, Kang-Ling; Bai, Xue-Feng; Friedman, Avner
2014-01-01
Interleukin-35 (IL-35), a cytokine from the Interleukin-12 cytokine family, has been considered as an anti-inflammatory cytokine which promotes tumor progression and tumor immune evasion. It has also been demonstrated that IL-35 is secreted by regulatory T cells. Recent mouse experiments have shown that IL-35 produced by cancer cells promotes tumor growth via enhancing myeloid cell accumulation and angiogenesis, and reducing the infiltration of activated CD8 T cells into tumor microenvironment. In the present paper we develop a mathematical model based on these experimental results. We include in the model an anti-IL-35 drug as treatment. The extended model (with drug) is used to design protocols of anti-IL-35 injections for treatment of cancer. We find that with a fixed total amount of drug, continuous injection has better efficacy than intermittent injections in reducing the tumor load while the treatment is ongoing. We also find that the percentage of tumor reduction under anti-IL-35 treatment improves when the production of IL-35 by cancer is increased. PMID:25356878
Mathematical modeling of a single stage ultrasonically assisted distillation process.
Mahdi, Taha; Ahmad, Arshad; Ripin, Adnan; Abdullah, Tuan Amran Tuan; Nasef, Mohamed M; Ali, Mohamad W
2015-05-01
The ability of sonication phenomena in facilitating separation of azeotropic mixtures presents a promising approach for the development of more intensified and efficient distillation systems than conventional ones. To expedite the much-needed development, a mathematical model of the system based on conservation principles, vapor-liquid equilibrium and sonochemistry was developed in this study. The model that was founded on a single stage vapor-liquid equilibrium system and enhanced with ultrasonic waves was coded using MATLAB simulator and validated with experimental data for ethanol-ethyl acetate mixture. The effects of both ultrasonic frequency and intensity on the relative volatility and azeotropic point were examined, and the optimal conditions were obtained using genetic algorithm. The experimental data validated the model with a reasonable accuracy. The results of this study revealed that the azeotropic point of the mixture can be totally eliminated with the right combination of sonication parameters and this can be utilized in facilitating design efforts towards establishing a workable ultrasonically intensified distillation system.
Mathematical modeling of a Fermilab helium liquefier coldbox
Geynisman, M.G.; Walker, R.J.
1995-12-01
Fermilab Central Helium Liquefier (CHL) facility is operated 24 hours-a-day to supply 4.6{degrees}K for the Fermilab Tevatron superconducting proton-antiproton collider Ring and to recover warm return gases. The centerpieces of the CHL are two independent cold boxes rated at 4000 and 5400 liters/hour with LN{sub 2} precool. These coldboxes are Claude cycle and have identical heat exchangers trains, but different turbo-expanders. The Tevatron cryogenics demand for higher helium supply from CHL was the driving force to investigate an installation of an expansion engine in place of the Joule-Thompson valve. A mathematical model was developed to describe the thermo- and gas-dynamic processes for the equipment included in the helium coldbox. The model is based on a finite element approach, opposite to a global variables approach, thus providing for higher accuracy and conversion stability. Though the coefficients used in thermo- and gas-dynamic equations are unique for a given coldbox, the general approach, the equations, the methods of computations, and most of the subroutines written in FORTRAN can be readily applied to different coldboxes. The simulation results are compared against actual operating data to demonstrate applicability of the model.