Strong Mathematical Background Research Articles

An Optimization Problem with a Surprisingly Simple Solution

Click to increase image sizeClick to decrease image size Additional informationNotes on contributorsD. DrinenDOUG DRINEN is an associate professor at the University of the South. He received a B.A. from Trinity University (TX) in 1993 and a Ph.D. from Arizona State in 1999. He only very occasionally thinks about anything other than sports or math, so he is always excited when he can save some time by thinking about both simultaneously.K. G. KennedyK. GRACE KENNEDY graduated from the University of the South in 2006, majoring in mathematics and French literature. In 2008 she received her masters (M2) in Algebra, Number Theory, and Applications from the Université de Picardie in Amiens, France, and she is currently at the University of California in Santa Barbara. She hopes to continue studying topics related to her masters work in Coxeter Groups, Hecke Algebras, and Temperley-Lieb algebrasW. M. PriestleyMAC PRIESTLEY has taught at the University of the South since 1967, having received a B.A. there in 1962. His Ph.D. degree is from Princeton. He wrote an elementary text, Calculus: A Liberal Art (SpringerVerlag, 1998), to support a one-semester general education course for liberal arts majors who may lack a strong background in mathematics. In 2006 he received the Distinguished Teaching Award from the Southeastern Section of the MAA.

A practical guide for optimal designs of experiments in the Monod model

The Monod model is a classical microbiological model often used in environmental sciences, for example to evaluate biodegradation processes. The model describes microbial growth kinetics in batch culture experiments using three parameters: the maximal specific growth rate, the saturation constant and the yield coefficient. However, identification of these parameter values from experimental data is a challenging problem. Recently, it was demonstrated theoretically that the application of optimal design theory in this model is an efficient method for both parameter value identification and economic use of experimental resources [Dette, H., Melas, V.B., Pepelyshev, A., Strigul, N., 2003. Efficient design of experiments in the Monod model. J. R. Stat. Soc. B 65 (Part 3), 725–742]. The purpose of this paper is to provide this method as a computational “tool” such that it can be used by practitioners without a strong mathematical and statistical background for the efficient design of experiments in the Monod model. The paper presents careful explanations of the principal theoretical concepts, and a simple algorithm for practical optimal design calculations.

Gustav Mie and the scattering and absorption of light by particles: Historic developments and basics

Gustav Mie was a professor of physics with a strong background in mathematics. After moving to the University of Greifswald in North-Eastern Germany he became acquainted with colloids, and one of his PhD students investigated the scattering and attenuation of light by gold colloids experimentally. Mie used his previously acquired knowledge of the Maxwell equations and solutions of very similar problems in the literature to concisely treat the theoretical problem of scattering and absorption of light by a small absorbing sphere. He also presented many numerical examples which completely explained all the effects that had been observed until then. Since all calculations were done by hand, Mie had to limit his theoretical results to three terms in infinite expansions, thus he only could treat particles smaller than 200 nm at visible wavelengths. Mie's paper had remained hardly noticed for the next 50 years, most likely because of the lack of computers. It experienced a revival later and up to now it has been referenced more than 4000 times, owing to the widespread use of Mie's approach in sciences such as astronomy, meteorology, fluid dynamics and many others. Gustav Mie did not consider his work on scattering of light by small particles as very important, since he just tried to explain the effects which his students had observed. He concentrated on hot topics in theoretic physics, e.g., the theory of matter. He wrote several textbooks, e.g., on relativity, gravitation theory, and electromagnetism, and all of them had run into several editions.

REFLECTION ON THE NEW INNOVATIONS FOR 'MAXIMISING' THE LEARNING IN TEACHING OF MATHEMATICS

Though Mathematics is being so important subject and occupying a central position since the Ancient period still it has not been the interest of many students. The gaps are found between aspiration and achievement. Mathematics is highly abstract. It is concerned with ideas rather than objects; with the manipulation of symbols rather than the manipulation of object. It is a closely knit structure in which ideas are interrelated. Mathematical concepts are hierarchical and interconnected, much like a house of cards. Unless lower level concepts are mastered, higher level concepts cannot be understood. Students, who discover some of the structures of mathematics, are often impressed by its beauty. Teaching mathematical concepts to students who do not have a very strong background in mathematics is always challenging. This experience is also extremely rewarding when these students begin enjoying the journey, which leads to mastering the concepts. This paper will demonstrate how we can make it possible for learners with an average secondary education level of mathematical skills to make the transition to a more advanced level more successfully.

Stochastic modeling of the vibro-acoustic behavior of production cars

Production cars -as any industrial product- are subject to various causes of variability including process uncertainties or product diversity. Many authors have shown that vibroacoustic problems sensitivity to small uncertainties increases dramatically with frequency until only statistical approaches remain relevant in the high frequency range. Moreover, modeling uncertainties due to numerous model simplifications induce similar dispersion effects on the computed responses. Both kind of uncertainties may be addressed when using a non-parametric stochastic modeling, based on the random matrices theory. Such a modeling, appears to be very practicable for industrial vibroacoustic problems while relying on a strong mathematical background. In a first part, the application of the non-parametric modeling of uncertainties to vibro-acoustics problems will be addressed. Stochastic aspects are controlled by only 7 dispersion parameters that provide most of the dynamic behaviors that can be observed experimentally. A Monte-Carlo simulation is performed to provide converged statistics of the stochastic problem solution. In a second part, the dispersion parameters are identified so that the stochastic model fits experimental data. Frequency Response Functions of 25 production vehicles were measured for this purpose and compared to the computed results in the low frequency range (<200 Hz).

Deploying defeasible logic rule bases for the semantic web

Logic is currently the target of the majority of the upcoming efforts towards the realization of the Semantic Web vision, namely making the content of the Web accessible not only to humans, as it is today, but to machines as well. Defeasible reasoning, a rule-based approach to reasoning with incomplete and conflicting information, is a powerful tool in many Semantic Web applications. Despite its strong mathematical background, logic, in general, and defeasible logic, in particular, may overload the user with tons of additional complex semantic relationships among data and metadata of the Semantic Web. To this end, a comprehensible, visual representation of these semantic relationships (rules) would help users understand them and make more use of them. This paper presents VDR-DEVICE, a defeasible reasoning system, designed specifically for the Semantic Web environment. VDR-DEVICE is an integrated development environment for deploying and visualizing defeasible logic rule bases on top of RDF Schema ontologies. The system consists of a number of sub-components, which, though developed autonomously, are combined efficiently, forming a flexible framework. The system employs a defeasible reasoning system that supports direct importing and processing of RDF data and RDF Schema ontologies as well as a number of user-friendly rule base and ontology visualization modules.

Historical Perspectives

When neonatology was emerging as a clinical discipline in the late 1950s and early 1960s, it had the advantage of a strong foundation of basic research in fetal and neonatal physiology. In particular, the new clinical enterprise (it was not yet a subspecialty) focused on cardiorespiratory pathophysiology. This foundation came from a few distinguished research laboratories studying fetal and neonatal physiology and the processes of the transition from fetal to neonatal life. The preeminent laboratory in the field was the Nuffield Institute for Medical Research at Oxford, directed by Geoffrey S. Dawes. Geoffrey Dawes became the director of the Institute in 1948. He received his medical degree in 1943, and in the following 5 years, he gained recognition as a prominent investigator in pharmacology and physiology. The very short interval between receiving his degree and being named director of an important research institute indicates how quickly the academic leadership recognized his exceptional qualities. As the new director, Dawes set the primary focus of research for the Nuffield Institute as developmental physiology. In this role, the Nuffield became the successor to the path of research started by Sir Joseph Barcroft at Cambridge early in the twentieth century. Dawes and his coinvestigators concentrated particularly on the preparations for and mechanisms of adaptation to extrauterine life. A central focus of the research was the adaptive mechanisms in the circulatory and respiratory systems, including placental function, establishment of lung function, and changes in the pulmonary and systemic circulations. Although most of the work examined cardiorespiratory physiology and its neurohumoral regulation, researchers also studied fetal growth and metabolism, and their studies included the responses to stresses such as hypoxia and hemorrhage. One of the hallmarks of the research of this highly productive group was the elegance of their experimental designs. The clinical implications of this …

Profile

BioTechniquesVol. 39, No. 3 ScientistsOpen AccessProfile of John Yates III, Ph.D.Professor of Cell Biology and head of the Proteomic Mass Spectrometry Lab, The Scripps Research Institute, La Jolla, CALaura BonettaLaura BonettaSearch for more papers by this authorPublished Online:30 May 2018https://doi.org/10.2144/05393SP01AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinkedInReddit Getting SidetrackedWhen I started my undergraduate studies at the University of Maine, I was thinking about going to medical school. I had injured my leg playing football in high school and became interested in medicine while I was convalescing in the hospital. But I was eventually sidetracked by the biology and chemistry courses I took. Given the state of medical finances these days, I am glad things turned out the way they did.I got my first taste of mass spectrometry during an undergraduate chemistry course. Right away, I thought that the technique was the future—mostly because the instrument had a computer attached to it. To me, that was so cool. I guess I had the right insight, if not necessarily for the right reasons.I decided to do my graduate work at the University of Virginia in a mass spectrometry lab. We were developing and applying tandem mass spectrometry to the sequence analysis of proteins. At that time, it would take a year just to sequence one protein. Twenty years later, mass spectrometry is able to tackle much more complex questions.What appeals to me are technically difficult problems. One of my favorite papers was the one we published in Nature in 2002 on the proteome of the malaria pathogen, Plasmodium falciparum. The study identified more than 2400 proteins.Daniel Carucci, formerly of the Naval Medical Research Center, and one of the people who had gotten the malaria genome project off the ground, had heard me give a talk about my work identifying complex mixtures of proteins in different systems. He asked me, “Could what you talked about work with malaria?”It was a tough problem, because you can never isolate pure Plasmodium proteins. With the life cycle of the parasite, you always get a high background of mosquito or human components. Therefore, we had to spend a lot of time working on strategies to distinguish among different proteins, and we had to do this while the Plasmodium genome sequence was being completed. There were many technical challenges to sort through, but that was part of the attraction.I was also drawn to the project because malaria is such a huge problem in terms of the number of people who are affected by the disease. I tend to gravitate toward issues that affect the developing world.In my mind, the development of the SEQUEST algorithm for correlating tandem mass spectrometry data to protein sequences was a critical step in enabling us to do the things we are doing today. When I started with mass spectrometry, a major bottleneck was throughput of data analysis. You could not do any large-scale projects. SEQUEST, which I developed about 12 years ago when I was a faculty member at the University of Washington, allowed us to take protein mixtures in solution or from cell lysates and obtain a fairly accurate identification of the proteins in the mix.Because of the patent arrangements with the University of Washington, SEQUEST is now distributed through a company. But we have developed other programs that are freely available. We spend a fair amount of time supporting people who use our software. Support is a lot of work, but I believe that if you write software, you need to take responsibility for it.The applications of mass spectrometry have changed a lot over the years, and my knowledge has gotten a lot broader to keep up with these changes. But you know what they say about generalists: you end up knowing nothing about everything.I currently have about 20 people working with me, and most are postdocs. Chemists, computer scientists, physicists, and biologists work side-by-side in my lab. It is to their advantage to have access to all these different kinds of expertise. For example, if one of the biologists is having problems with statistical analysis, he or she can ask one of the people with a strong mathematical background for help.I enjoy being the head of the lab. It is a bit like having a small business—making decisions, setting direction, taking responsibility for what happens. All these things appeal to me. Outside of work, most of what I do revolves around the lives of my three sons. It means I spend a lot of time at baseball games.FiguresReferencesRelatedDetails Vol. 39, No. 3 Follow us on social media for the latest updates Metrics History Published online 30 May 2018 Published in print September 2005 Information© 2005 Author(s)PDF download

An Introduction to Multivariate Statistical Analysis, 3rd ed. T.W. Anderson. Hoboken, NJ: John Wiley & Sons, 2003, 742 pp., $99.95, hardcover. ISBN 0-471-36091-0.

This third edition is a wonderful textbook for graduate students studying statistics or professional statisticians interested in a thorough introduction to the mathematical theory underlying many common multivariate statistical methods. However, if you are a laboratory scientist lacking a strong mathematical background, this book is not for you. The author earned his PhD in mathematics at Princeton in 1945 and has been an influential figure in the statistical field for many decades. In addition to this book, he is also the author of The Statistical Analysis of Time Series. The first edition of An Introduction to …

A Fun General Education Physics Course: Physics of Sports

During a two-year visiting appointment at Oberlin College in Oberlin, OH, I offered a course called Physics of Sports for the fall 2000 semester and the fall 2001 semester. While preparing the course, I faced a challenge that confronts many physics teachers: How can I make a general education physics course fun for nonscience students? With only an algebra prerequisite for the course, the typical student did not have a particularly strong mathematical background. My goal was to not only teach those students a little physics, but also show them how physicists try to understand and describe the world of sports. I also wanted to make the course sufficiently enjoyable that the students had a positive experience in what may have been the last science course some of them ever took. After discussions with the students, I feel the course succeeded in fulfilling my goals.

Jozef Zwislocki in the post‐von Bekesy era of cochlear physiology

Professor Joe Zwislocki is a rare individual who has a strong background in mathematics and hydrodynamics that he applied to the physiological characterization of cochlear function. Realizing the preeminent need for more accurate measurements of cochlear mechanical properties, he undertook the study of properties of the tectorial membrane (TM). His measurements are unique in that they remain the only in vivo measurements of stiffness of the TM. In 1979, he introduced longitudinal effects into cochlear modeling that today has been shown to result in realistic cochlear mechanical transfer curves. A difference between the filter properties seen in auditory nerve fibers and basilar membrane (BM) mechanics led to a leading theory of separate resonances for organ of Corti and TM. He developed a model of how this would affect the shear motion between the TM and reticular lamina. Additional studies were undertaken that substituted recordings in the cells of Hensen for the very difficult direct observation of BM mechanics that epitomize the ingenuity and resourcefulness of Joe Zwislocki.

Fuzzy Model for Real-Time Reservoir Operation

A fuzzy rule-based control model for multipurpose real-time reservoir operation is constructed. A new, mathematically justified methodology for fuzzy inference—total fuzzy similarity—is used and compared with the more traditional Sugeno-style method. Specifically, the seasonal variation in both hydrological variables and operational targets is examined by considering the inputs as season-dependent relative values, instead of using absolute values. The inference drawn in several stages allows a simple, accessible model structure. The control model is illustrated using Lake Paijanne, a regulated lake in Finland. The model is calibrated to simulate the actual operation, but also to better fulfill the new multipurpose operational objectives determined by experts. Relatively similar results obtained with the inference methods and the strong mathematical background of total fuzzy similarity put fuzzy reasoning on a solid foundation.

An Algorithm for the 2-Median Problem on Two-Dimensional Meshes

The mesh (and its variant, the torus) is a popular topology for processor interconnection in parallel computers. It has practical advantages such as low degree and perfectly compact layout when compared to other well-known topologies, for example the hypercube. A notable example of parallel computers based on the mesh topology is the iWarp system [1]. Dally has shown that low-dimensional networks have lower latency and higher hot-spot throughput than high-dimensional networks [2]. In this paper, we study the problem of finding a 2-median set in a two-dimensional mesh. The p-median problem is a well-known problem in location theory, which is to locate p identical facilities in a network so that the sum of the distance between every client in the network and its nearest facility is minimized. This has practical application in real mesh-connected parallel computers, which is to locate servers in selected nodes so that service requests from client nodes can be directed to different servers to achieve load balancing, and the traffic so generated can be more spread out over the links. The problem has been proved to be NP-hard for general networks. For a survey on the NP-hardness and algorithms developed in recent years, one can refer to [3]. Mirchandani [4] gives a strong mathematical background for the problem, which also gathers many of the results before 1989. An early survey [5, 6] by Tansel et al. is still very useful, especially for beginners. Shmoys et al. [7] includes a short summary of some of the results. Recently, Guha and Khuller used the greedy approach to handle the problem [8]. Hamacher et al. dealt with a variation of the problem with multicriteria, instead of single criteria [9]. Lai and Chang proposed a

An Introduction to the World's Oceans, 6th Edition

This book is a significantly updated sixth edition of a popular and widely used introductory text in ocean sciences. The audience—students without a strong background in mathematics, chemistry, physics, geology, or biology, but with a basic curiosity and interest in the oceans—is an increasingly large group at most universities, where such introductory courses are offered to fulfill distributional requirements in physical science. In this latest version, the Duxburys have teamed up with Keith Sverdrup to expand sections on geology, tectonics, and seismology, and add descriptions of major interdisciplinary research programs. Almost every subject about the ocean is addressed in some way, and a rich array of additional sources of information is provided through sidebars on special topics, Internet links, and a text Web site.

Australasian Society of Clinical and Experimental Pharmacologists and Toxicologists, 1994: THE ALLOMETRIC APPROACH FOR INTERSPECIES SCALING OF PHARMACOKINETICS AND TOXICITY OF ANTI‐CANCER DRUGS

1. The rationale for extrapolation or 'scaling' across animal species is based on their underlying anatomical, physiological and biochemical similarities. 2. Research carried out in the 19th and early 20th century resulted in Benedict's famous 'mouse-to-elephant' graph which showed that the log of the basal metabolic rate plotted against the log of bodyweight (W) produced a straight line with a slope of 0.76. Since then it has become apparent that a number of other physiological variables (Y) exhibit a similar relationship which can be represented by the general allometric equation, Y = alpha W beta; where beta is the slope of the log-log plot and alpha is the intercept on the y axis. 3. The major pharmacokinetic parameters such as clearance and volume of distribution of many drugs are also related to W in a similar manner. 4. This empirical approach does not require a strong mathematical background and offers a relatively simple method of predicting the kinetics of anti-cancer drugs in patients from pre-clinical animal data. 5. The occurrence of major qualitative and quantitative differences in the metabolism of drugs between species is probably the single greatest complicating factor in the use of animals as predictors of drug toxicity and kinetics in patients. 6. Despite this, the allometric approach is useful for allowing the estimation of a more appropriate starting dose for some drugs in a Phase I trial, which might result in potential savings in escalation steps and maximize the chance that the dose which an individual receives has the potential for therapeutic value.

Predictors of math anxiety and its influence on young adolescents' course enrollment intentions and performance in mathematics.

We used structural modeling procedures to assess the influence of past math grades, math ability perceptions, performance expectancies, and value perceptions on the level of math anxiety reported in a sample of 7th- through 9th-grade students (N = 250). A second set of analyses examined the relative influence of these performance, self-perception, and affect variables on students' subsequent grades and course enrollment intentions in mathematics. The findings indicated that math anxiety was most directly related to students' math ability perceptions, performance expectancies, and value perceptions. Students' performance expectancies predicted subsequent math grades, whereas their value perceptions predicted course enrollment intentions. Math anxiety did not have significant direct effects on either grades or intentions. The findings also suggested that the pattern of relations are similar for boys and girls. The results are discussed in relation to expectancy-value and self-efficacy theories of academic achievement. A strong background in mathematics is critical for many career and job opportunities in today's increasingly technological society. However, many academically capable students prematurely restrict their educational and career options by discontinuing their mathematical training early in high school. Several recent surveys (National Assessment of Educational Progress [NAEP], 1988; National Center for Educational Statistics [NCES], 1984) indicate that only half of all high school graduates enroll in mathematics courses beyond the 10th grade. These reports also indicate that fewer women than men enroll in the more advanced courses in high school mathematics (NAEP, 1988; NCES, 1984), although the gender gap is beginning to narrow (Chipman & Thomas, 1985; Eccles, 1987). Furthermore, students of both sexes, but particularly women, do not attain a high level of mathematical competency, even if they have completed 4 years of high school math (NAEP, 1988).

The outerproduct: a tool to overcome the annoyance of indexing in mathematical education

While the way indexing is expressed in traditional mathematical formulas provides a useful abbreviation for mathematicians solving mathematical problems, it can be difficult to understand for students who lack a strong mathematical background. This teaching note uses two examples to illustrate the use of an ‘outerproduct’ which can overcome the annoyance of indexing and therefore improve the efficiency of mathematical education. Computer program implementation using the outerproduct is also shown.

A Study of Basic Numeracy Skills: Primary Education Student Teachers at the Institute of Education (Singapore)

ABSTRACT This study concerns the basic mathematical skills and attitudes of prospective primary school teachers at the Institute of Education, Singapore. The study was prompted by a concern for basic standards in mathematics education. As these trainees are admitted to the Institute of Education on the basis of their overall Cambridge A-Level Examination results, it is conceivable that not all of them possess a strong mathematical background. At the Institute, they take a compulsory methodology course — Teaching Mathematics in the Primary School, preparing them to teach Mathematics in the Primary school. Despite the varying mathematical background, there is no optional or compulsory mathematics content course available in the curriculum to equip the needy and neither are they required to pass any mathematics test before graduating from their teacher training programme. A test comprising 40 testing skills items adapted from the Primary Teacher Education program of the St George Institute of Education (SGIE) in Sydney was administered to 173 (15 male and 158 female) 2nd year Certificate-in-Education students at the Institute of Education in February 1990. At the SGIE, all students of the Primary Teacher Education Program are required to pass a basic skills test in mathematics at the 75% mastery level. At the Institute of Education, 18.5% (or 32) of the students failed to obtain a pass at the 75% mastery level although the mean score for the sample was 33.68. The study also shed light on the trainee teachers' perceptions of mathematics as a subject, and personal confidence in doing and teaching mathematics.

Applications of the Numerical Method of Lines (NMOL) in Soil Hydrology

ABSTRACT Anew technique, called the numerical method of lines (NMOL), is described. It can be used to obtain numerical solutions of initial-boundary value problems in soil hydrology in a very short time. The method is very simple and does not require a strong background in advanced mathematics or computer programming. The implementation of the method does not change from problem to problem and the method is also applicable to multi-dimensional problems. A software package that implements this technique has been developed for the IBM PC or compatible computers. The technique is illustrated by solving the initial-boundary value problems in the design of drainage and sub-irrigation systems. The nonlinear Boussinesq equation is solved numerically, subject to appropriate initial and boundary conditions. Results are compared with those of Skaggs (1975, 1979). The advantages of NMOL over other conventional numerical methods are discussed.

Methods for determining the order of an autoregressive-moving average process: a survey: Jan G. De Gooijer, Bovas Abraham, Ann Gould and Lecily Robinson, International Statistical Review 53 (1985) 301–329

Today’ real world data bases witnessed significant increase in the amount of data in digital format, due to the widespread use of datasets and storage system. There is a need to developing fast and highly accurate algorithms to automatically classify large data. It becomes a vital part of the machine learning and knowledge discovery. The main intention of this paper is however data sizes increases, our proposed method make faster computation and scalable machine learning algorithm is used to learn faster from the labelled training data. Due to its strong mathematical background and theoretical foundation and good generalization performance, Support Vector Machine (SVM) Classification becomes more feasible options for large datasets. A major research goal of SVM is to improve the speed in training and testing phase. In this paper We introduce a proposed algorithm to speed up the training time of SVM is presented. It is highly accurate classification method. However SVM classifiers suffer from slow processing, when training with a large set of data tuples. Our novel approach selects a small representative amount of data from large datasets to enhance training time of SVM. This method uses an induction tree to reduce the training dataset for SVM classification, it generate faster results with improving accuracy rates than the current SVM implementations.