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PubMed1990

Epigenesis theory: a mathematical model relating causal concepts of pathogenesis in individuals to disease patterns in populations.

A mathematical modeling approach called epigenesis theory is presented which relates three aspects of pathogenesis to the population distribution of disease. The three aspects of pathogenesis involve how two or more measured variables interact. They are 1) whether the measured variables are related to the same causal action, 2) whether there is only one pathogenic process leading to disease, and 3) whether the measured variables contribute to the same pathogenic process. Epigenesis theory defines the following multivariable relations between two disease causes: 1) "Complementary" causes contribute different causal actions to the sole pathogenic process leading to disease. They have multiplicative relations. 2) "Separate process" causes contribute different causal actions to different pathogenic processes. They have the relations of simple independent action which are slightly less than additive. 3) "Intermediate" causes contribute different causal actions to the same pathogenic process in the presence of additional pathogenic processes where at most one of them may also participate. They have relations somewhere between multiplicative and simple independent actions. 4) "Cooperative-competitive" causes share the same causal action and act within the same pathogenic process. Their relations can change from greater than multiplicative to less than simple independent action at increasing dichotomization points of the measured variables. Epigenesis theory unifies the sufficient-component causes model and the simple independent action model and exceeds either model in the range of observations it can explain. It is most useful given directly causal measured variables and specific disease outcomes, but it will assist in etiologic investigations of nonspecific outcomes in which new disease classifications are proposed. While it is less useful given surveillance-type variables such as age or sex or outcomes resulting from numerous pathogenic processes such as death, it gains utility as more causal variables are entered into an analysis and as more cut points of continuous complementary, independent, or intermediate variables are distinguished.

Adult↗
PubMed2000

Conceptions of and approaches to learning mathematics.

Pearson correlation coefficients indicated a different relationship between conceptions of mathematics and approaches to learning mathematics to that reported in literature. It was concluded that the 154 students (82 women and 72 men) followed a strategic approach to learning mathematics.

Adolescent↗
PubMed1991

Cardiac electrophysiological experiments in numero, Part I: Concepts and strategies of mathematical and computer models.

This article is the first of three articles that review mathematical and computer models of the heart and describe their construction, development, research potential, and clinical utility. This article explains the methodological principles of mathematical and computer simulation of biomedical systems. The strategies of model construction, testing, and application are presented; the advantages and limitations of computer simulation studies are explained, and the basic value of computer simulation for cardiological research and practice is discussed.

Cardiac Pacing, Artificial↗
PubMed2000

Motivational Beliefs, Study Strategies, and Mathematics Attainment in High- and Low-Achieving Chinese Secondary School Students.

In order to examine the relationship between cognitive and motivational variables and their relationship to mathematics attainment, Hong Kong-Chinese students enrolled in schools for high-, average-, and low-achievers completed questionnaires in Year 10 and in Year 11. Low-achievers perceived academic learning as being less useful over time and reported spending less time studying in Year 10 than in Year 11 but high- and low-achievers did not differ on their use of self-regulated learning strategies. Performance on the public examination in mathematics was predicted by prior achievement and Self-Concept of Mathematics Ability. Results underscore the importance of considering cultural beliefs systems and educational systems in models of academic motivation. Copyright 2000 Academic Press.

Journal Article↗
PubMed1987

Efficient pharmacokinetic modeling of complex clinical dosing regimens: the universal elementary dosing regimen and computer algorithm EDFAST.

Dosing regimens used in clinical practice are often complex, involving several different routes of administration, dose sizes, dosing rates, and dosing intervals and durations. A novel universal elementary dosing regimen (uedr), that allows general pharmacokinetic modeling of these clinical regimens, is presented and developed mathematically. The uedr concept is computationally efficient, mathematically exact, and logically simple, and can replace the disparate standard concepts and equations of elementary infusion, "bolus" injection, multiple injection, oral dosing, zero-order-release dosing, etc. An optimized computer algorithm (EDFAST) based on the uedr approach, that readily permits the creation of a single fast and versatile microcomputer program for the analysis of all complex dosing regimens in any set of linear compartmental models, is presented. This is of particular relevance to three areas of application in clinical pharmacokinetics: compartmental drug concentration or amount versus time course prediction (simulation) with known model parameter values; parameter estimation (curve-fitting) from measured concentration versus time data; and individualized complex dosing regimen calculation (optimization) for target sets of concentration-time points. Application examples that show the versatility of the uedr approach are presented in detail.

Algorithms↗
PubMed2003

Evaluating change in attitude towards mathematics using the 'then-now' procedure in a cooperative learning programme.

BACKGROUND: Tertiary students' attitudes to mathematics are frequently negative and resistant to change, reflecting low self-efficacy. Some educators believe that greater use should be made of small group, collaborative teaching. However, the results of such interventions should be subject to assessments of bias caused by a shift in the frame of reference used by students in reporting their attitudes. AIMS: This study was designed to assess whether traditional pretest-post-test procedures would indicate positive changes in mathematics attitude during a programme of cooperative learning, and whether an examination of any attitudinal change using the 'then-now' procedure would indicate bias in the results due to a shift in the internal standards for expressing attitude. SAMPLE: Participants were 141 undergraduate students enrolled in a 12-week statistics and research design component of a course in educational psychology. METHOD: Using multivariate procedures, pretest, post-test, and then-test measures of mathematics self-concept and anxiety were examined in conjunction with a cooperative learning approach to teaching. RESULTS: Significant positive changes between pretest and post-test were found for both mathematics self-concept and mathematics anxiety. There were no significant differences between the actual pretest and retrospective pretest measures of attitude. The results were not moderated by prior level of mathematics study. CONCLUSION: Conclusions about the apparent effectiveness of a cooperative learning programme were strengthened by the use of the retrospective pretest procedure.

Anxiety↗
PubMed1993

The impact of HIV and other STDs on human populations. Are predictions possible?

This article presents an overview of the use of mathematical models to study the demographic impact of STDs. Written for the nonmathematician, the article introduces the basic concepts of mathematical epidemiology for infectious diseases, such as the mass-action principle, the threshold density concept, and the basic reproductive rate. Described are the main features that characterize the epidemiology of STDs and those features that differentiate them from other directly transmitted diseases, such as measles, rubella, and others. Also presented are major findings concerning the importance of sexual behavior on the dynamics of STD transmission, and the numerical analysis of the demographic impact on gonococcal and HIV infections using a mathematical model. The epidemiology of these two STDs is explored, as well as how the growth rate of the population can influence the epidemiology of these STDs. Finally, the authors demonstrate how, under some circumstances, early treatment of gonorrhea can reduce the demographic impact of HIV in regions most affected by both diseases.

Female↗
PubMed1991

Human exposure assessment: a graduate level course.

The course has been offered three times. The content and the approach to each lecture has evolved after each time it was given. This is not unexpected since the field has been undergoing major transformations, and new approaches to measurement and modeling are being applied to current problems. The most recent student evaluation, 1990, indicates a difficulty rating of "just right" (70%) to "difficult" (30%). Most felt the course stimulated their interest in the topic (72%) and the examinations were learning experiences as well as a grading exercise. The major need for the discipline is an adequate text book. The GRAPE program has excellent potential as an educational took, but it needs to make more interactions and allow introduction of activities and data. The major strengths of the course are the problems provided to the students for homework. These give the student quantitative perspective on the concepts, range in values, variables, and uncertainties necessary to complete an assessment. In addition, the development of the mathematical and conceptional continuum for placing exposure assessment in the context of toxicology, environmental science, epidemiology, and clinical intervention provides a basic framework for the discipline.

Air Pollutants↗
PubMed2005

The quantitation of buffering action I. A formal & general approach.

BACKGROUND: Although "buffering" as a homeostatic mechanism is a universal phenomenon, the quantitation of buffering action remains controversial and problematic. Major shortcomings are: lack of a buffering strength unit for some buffering phenomena, multiple and mutually incommensurable units for others, and lack of a genuine ratio scale for buffering strength. Here, I present a concept of buffering that overcomes these shortcomings. THEORY: Briefly, when, for instance, some "free" H+ ions are added to a solution (e.g. in the form of strong acid), buffering is said to be present when not all H+ ions remain "free" (i.e., bound to H2O), but some become "bound" (i.e., bound to molecules other than H2O). The greater the number of H+ ions that become "bound" in this process, the greater the buffering action. This number can be expressed in two ways: 1) With respect to the number of total free ions added as "buffering coefficient b", defined in differential form as b = d(bound)/d(total). This measure expresses buffering action from nil to complete by a dimensionless number between 0 and 1, analogous to probabilites. 2) With respect to the complementary number of added ions that remain free as "buffering ratio B", defined as the differential B = d(bound)/d(free). The buffering ratio B provides an absolute ratio scale, where buffering action from nil to perfect corresponds to dimensionless numbers between 0 and infinity, and where equal differences of buffering action result in equal intervals on the scale. Formulated in purely mathematical, axiomatic form, the concept reveals striking overlap with the mathematical concept of probability. However, the concept also allows one to devise simple physical models capable of visualizing buffered systems and their behavior in an exact yet intuitive way. CONCLUSION: These two measures of buffering action can be generalized easily to any arbitrary quantity that partitions into two compartments or states, and are thus suited to serve as standard units for buffering action. Some exemplary treatments of classical and non-classical buffering phenomena are presented in the accompanying paper.

Buffers↗
PubMed2005

Mathematical modelling and controlled drug delivery: matrix systems.

This paper deals with the physical and mathematical modelling description of drug release from matrix systems. In the introduction, matrix systems are considered in the wide frame of the controlled release systems and the concept of mathematical model is briefly discussed. Then, matrix structure and topology are matched, analysing the characteristics of the three-dimensional network constituting them. In this context, drug release mechanisms are considered with particular emphasis on the key factors ruling the release kinetics, such as matrix swelling, erosion, drug dissolution (re-crystallisation), drug diffusion, drug - polymer interaction, initial drug distribution and particle size distribution (for powdered matrix systems). The mathematical modelling section firstly considers the empirical and semi-empirical models that have the great advantage of showing analytical solutions. Then, the attention is focused on theoretical approaches regarding matrix swelling equilibrium and kinetics, drug dissolution, drug diffusion, drug - polymer interaction, initial drug distribution and matrix erosion. Finally, release kinetics from polydispersed spherical particles is studied. This review points out the fact that the comprehension of the phenomena ruling drug release from matrix systems is appropriate from both the physical and modelling point of view, although further improvements are always possible and desirable.

Algorithms↗
PubMed2000

Minimization of Boolean complexity in human concept learning.

One of the unsolved problems in the field of human concept learning concerns the factors that determine the subjective difficulty of concepts: why are some concepts psychologically simple and easy to learn, while others seem difficult, complex or incoherent? This question was much studied in the 1960s but was never answered, and more recent characterizations of concepts as prototypes rather than logical rules leave it unsolved. Here I investigate this question in the domain of Boolean concepts (categories defined by logical rules). A series of experiments measured the subjective difficulty of a wide range of logical varieties of concepts (41 mathematically distinct types in six families--a far wider range than has been tested previously). The data reveal a surprisingly simple empirical 'law': the subjective difficulty of a concept is directly proportional to its Boolean complexity (the length of the shortest logically equivalent propositional formula)--that is, to its logical incompressibility.

Humans↗
PubMed1993

Hyperinsulinemia after pancreatic transplantation. Prediction by a novel computer model and in vivo verification.

OBJECTIVE: The authors evaluated systemic venous insulin release as a cause of the hyperinsulinemia (HNS) associated with pancreatic transplantation (PTX) with respect to the mechanism and metabolic consequences. SUMMARY BACKGROUND DATA: Many investigators believe the postoperative anatomy associated with common PTX techniques to be the sole cause of the two- to threefold posttransplantation HINS. However, this concept remains to be conclusively proved and characterized quantitatively. METHODS: The authors used three approaches to achieve their objectives. First, a computer model was generated based on established data concerning blood flow and tissue insulin extraction to determine whether it was mathematically possible for HINS to be caused by systemic insulin release. Second, HINS clamps were applied to normal dogs using the Andres clamp technique to quantify the in vivo differences in peripheral insulin levels and the metabolic consequences of systemic versus portal insulin infusion. Third, prolonged insulin half-life was evaluated as a possible mechanism of HINS from systemic insulin release by determination of biexponential rates of plasma disappearance from an endogenous pulse of insulin in surgically induced dog models of systemic and portal insulin release. RESULTS: First, the computer model calculated a 1.4- to 2.9-fold increase in peripheral venous insulin levels with systemic versus portal insulin release, verifying mathematically the concept of HINS resulting from systemic insulin release. Second, the actual systemic insulin infusion produced a 1.3- to 1.4-fold increase in peripheral venous insulin levels compared with portal infusion (p < 0.05). No significant differences in hepatic glucose output, total glucose disposal, or glucose infusion requirements were seen. Third, although the basal insulin level was twofold higher in the surgically induced animal models with systemic insulin release (p < 0.003), there were no differences in biexponential insulin clearance parameters. CONCLUSIONS: The HINS produced by systemic insulin release did not significantly alter glucose metabolism and was not the result of altered peripheral insulin clearance parameters. In vivo systemic venous insulin infusion studies produce HINS, but not to the degree calculated by mathematic modeling or that occurs after clinical PTX, making it likely that other factors also play a role in the HINS after PTX.

Animals↗
PubMed2005

[Risk evaluation in sleeping sickness: a mathematical contribution].

The concept of "risk" is important in epidemiology but is often used in a confused way for sleeping sickness. Using a rigorous approach resulting from mathematical modelling, new virtual entomological risk indicators and parasitological transmission indexes derived from the basic reproduction rate R0 are proposed and discussed.

Animals↗
PubMed1988

System approaches in pharmacokinetics: I. Basic concepts.

System approaches mathematically describe a general property of a pharmacokinetic system without modeling in specific terms the kinetic processes responsible for the general property considered. Definitions, basic concepts, kinetic basis, and rationale for system approaches as well as advantages and disadvantages of system approaches are presented and discussed. It appears that the system approaches may offer certain advantages over more traditional methods for many practical applications.

Pharmacokinetics↗
PubMedDate not supplied

Measuring human aging using a two-compartmental mathematical model and the vitality concept.

We calculated a theoretical vitality function as a reference curve, based on experimental results from 226 healthy individuals. This can be used to assess biological aging rates of geographically separate human populations. Only six parameters were used to assess vitality. Each parameter is associated with one of the two physiological compartments. We assume that one compartment keeps the system stable and the other maintains system fidelity. The results permit us to compare vitality curves within populations as well as to determine the age at which maximum vitality appears in each population. The differences between biological and chronological ages in each population and possible etiological interpretations are discussed. This mathematical model can be useful as a method to measure differences in aging rates and effects of aging in several human populations.

Journal Article↗
PubMed1989

A causal model of mathematics performance in early adolescence: the role of sex.

Using path analysis, the present investigation was done to clarify possible causal linkages among general scholastic aptitude, academic achievement in mathematics, self-concept of ability, and performance on a mathematics examination. Subjects were 122 eighth-grade students who completed a mathematics examination as well as a measure of self-concept of ability. Aptitude and achievement measures were obtained from school records. Analysis showed sex differences in prediction of performance on the mathematics examination. For boys, this performance could be predicted from scholastic aptitude and previous achievement in mathematics. For girls, performance only could be predicted from previous achievement in mathematics. These results indicate that the direction, strength, and magnitude of relations among these variables differed for boys and girls, while mean levels of performance did not.

Achievement↗