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PubMed1993

Psychological profiles of the mathematically talented: some sex differences and evidence supporting their biological basis.

For over 20 years, above-level testing with the College Board Scholastic Aptitude Test (SAT) has been used to assess the abilities of well over 1,000,000 highly able 12-13-year-olds (students in the top 3% in intellectual ability). In this population, the predictive validity of the mathematical part of the SAT, SAT-M, for academic and vocational criteria has been demonstrated over 10-year gaps. Here, we document aspects of the psychological and achievement profiles of these highly able students, paying particular attention to sex differences. Males score higher on SAT-M (i.e., mathematical reasoning ability) than females; this difference is accompanied by differences between the sexes in spatial-mechanical reasoning abilities and in a number of lifestyle and vocational preferences. Collectively, these attributes appear to play a key role in structuring male-female disparities in pursuing advanced educational credentials and careers in the physical sciences. After profiling a number of the behavioural characteristics of the highly able, we examine some underlying biological correlates of these phenotypic manifestations. These include hormonal influences, medical and bodily conditions and enhanced right hemispheric activation.

Adolescent↗
PubMed1979

A comparison of mathematical models for estimating right ventricular volumes in animals and man.

Volume of 19 right ventricular canine casts and 11 right ventricular human casts were obtained by water displacement and compared to three different mathematical models for estimating right ventricular volumes by biplane cineangiography. In the canine studies, significant linear correlation coefficients were obtained using the longest measured length method (r = 0.92), the triangular modification of Simpson's rule (r = 0.93), and the elliptical modification of Simpson's rule (r = 0.93). The human studies resulted in similar significant correlation coefficients of 0.96, 0.97, and 0.97, respectively. Although the highest correlation with the lowest standard error of estimate was obtained using the triangular model, all three mathematical models produced volume estimations that feel within acceptabe biological limits of accuracy.

Animals↗
PubMed1989

Mutagenesis and mathematics: the allure of numbers.

This paper sets out the "formal," "empirical," and "mechanistic" equations that my colleagues and I have developed for the description and analysis of dose-response data on the lethal and genetic effects of mutagens in microorganisms. These three types of equations are interrelated inasmuch as they are all based ultimately on the use of the Poisson distribution in the formal definition of lethal and mutational hit functions. Explicit mathematical expressions for these functions can be written down in either empirical or mechanistic terms. The empirical equations are obtained simply by writing the hit functions as finite polynomials with adjustable coefficients. The mechanistic equations are based on the assumptions of the "DNA damage-repair hypothesis." The mathematical formulation of this hypothesis entails an important change in the definition of the word "hit" from that used in the classical hit/target theory of radiation biology. The theoretical and practical applications of these various equations in mutation research are summarized briefly and their merits are assessed in light of recent advances in our understanding of the biochemical basis of mutagenesis.

DNA Damage↗
PubMed2006

Is there a problem with mathematical psychology in the eighteenth century? A fresh look at Kant's old argument.

Common opinion ascribes to Immanuel Kant the view that psychology cannot become a science properly so called, because it cannot be mathematized. It is equally common to claim that this reflects the state of the art of his times; that the quantification of the mind was not achieved during the eighteenth century, while it was so during the nineteenth century; or that Kant's so-called "impossibility claim" was refuted by nineteenth-century developments, which in turn opened one path for psychology to become properly scientific. These opinions are often connected, but they are misguided nevertheless. In Part I, I show how the issue of a quantification of the mind was discussed before Kant, and I analyze the philosophical considerations both of pessimistic and optimistic authors. This debate reveals a certain progress, although it remains ultimately undecided. In Part II, I present actual examples of measuring the mind in the eighteenth century and analyze their presuppositions. Although these examples are limited in certain ways, the common view that there was no such measurement is wrong. In Part III, I show how Kant's notorious " impossibility claim" has to be viewed against its historical background. He not only accepts actual examples of a quantitative treatment of the mind, but also takes steps toward an explanation of their possibility. Thus, he does not advance the claim that the mind as such cannot be mathematized. His claim is directed against certain philosophical assumptions about the mind, assumptions shared by a then-dominating, strongly introspectionist conception of psychology. This conception did and could not provide an explanation of the possibility of quantifying the mind. In concluding, I reflect on how this case study helps to improve the dispute over when and why psychology became a science.

Attitude↗
PubMed2006

A mathematical model of Saccharomyces cerevisiae growth in response to cadmium toxicity.

Microbial growth can be described using models derived by differential equations, but available mathematical models have yet to adequately describe lag phase related cell growth or cell mortality in response to chemical toxicity. Lag phase cell behavior, however, dictates the onset of exponential growth and the number of actively growing cells available to initiate exponential growth, important factors in the success of remediation efforts. In this study, a five-parameter polynomial ratio (PR) model was used to characterize the growth, from lag through stationary phase, of the yeast Saccharomyces cerevisiae in response to cadmium toxicity. The PR model used in this study has the advantages over standard mathematical models in the ability to represent the initial cell mortality observed when S. cerevisiae is exposed to increasing cadmium levels, up to 12 mg/l Cd, as well as following cell recovery and growth to stationary levels.

Cadmium↗
PubMed1995

Mathematical model for repair of fatigue damage and stress fracture in osteonal bone.

This paper assembles current concepts about bone fatigue and osteonal remodeling into a mathematical theory of the repair of fatigue damage and the etiology of stress fracture. The model was used to address three questions. (a) How does the half-life of fatigue damage compare with the duration of the remodeling cycle? (b) Does the porosity associated with the remodeling response contribute to stress fracture? (c) To what extent is a periosteal callus response necessary to augment repair by remodeling? To develop the theory, existing experimental data were used to formulate mathematical relationships between loading, damage, periosteal bone formation, osteonal remodeling, porosity, and elastic modulus. The resulting nonlinear relationships were numerically solved in an iterative fashion using a computer, and the behavior of the model was studied for various loading conditions and values of system parameters. The model adapted to increased loading by increasing remodeling to repair the additional damage and by adding new bone periosteally to reduce strain. However, if too much loading was encountered, the porosity associated with increased remodeling caused the system to become unstable; i.e., damage, porosity, and strain increased at a very high rate and without limit. It is proposed that this phenomenon is the equivalent of a stress fracture and that its biological and mechanical elements are significant in the etiology of stress fractures. Additional experiments must be done to test the model and provide better values for its parameters. However, the instability characteristic is relatively insensitive to changes in model parameters.

Animals↗
PubMed2006

Mathematical explanation of the buckling of the vessels after twisting of the microanastomosis.

BACKGROUND: To obtain free flap success, microvascular anastomosis must be perfectly constructed. External compression, twisting (torsion) of the anastomosis site, tension on the anastomosis site, and kinking of the pedicle must be avoided. Few experimental studies report the patency rates of rat vessels after twisting (torsion) of the microanastomosis: these results recently opened a discussion for the maximal angle of torsion, which can be impressed to a vessel in order to have the best patency rates. MATERIALS AND METHODS: To describe specifically the changing of shape of the vessels after the twisting of the microanastomosis, we extrapolate, to our experimental model (constituted by the femoral vessels of Wistar rats), the mathematical formula that engineers use to calculate the torsion of a beam when a torsion force is applied. The mathematical model used is the shell theory. Then, with a computer program using MATLAB, we could obtain the representation of these shapes at any degree of torsion. RESULTS: If a small load is applied to the vessels, it maintains its straight geometry. However, as soon as the load exceeds a critical value, which is a function of the vessel geometry and its mechanical characteristics, it snaps suddenly to a different equilibrium configuration. This phenomenon is called "buckling." When buckling occurs, wave-like deformations appear on the wall of the vessels. We calculate, in our experimental rat model, the critical twisting angle that induces buckling: maintaining a constant length of dissection of 25 mm, a minimum twisting angle of 360 degrees + 161 degrees, or 105 degrees, is required, respectively, for the femoral artery or vein, to have the buckling phenomenon and the appearance of two waves and decreased section area. CONCLUSIONS: In surgical practice, with the parameters of our experimental Wistar rats model (vessel diameter, length of dissection), it is fundamental to be below 105 degrees of torsion angle for the vein microanastomosis, in order to decrease its risk of failure.

Anastomosis, Surgical↗
PubMed2005

Mathematical framework for simulating diffusion tensor MR neural fiber bundles.

White matter (WM) fiber tractography (i.e., the reconstruction of the 3D architecture of WM fiber pathways) is known to be an important application of diffusion tensor magnetic resonance imaging (DT-MRI). For the quantitative evaluation of several fiber-tracking properties, such as accuracy, noise sensitivity, and robustness, synthetic ground-truth DT-MRI data are required. Moreover, an accurate simulated phantom is also required for optimization of the user-defined tractography parameters, and objective comparisons between fiber-tracking algorithms. Therefore, in this study a mathematical framework for simulating DT-MRI data, based on the physical properties of WM fiber bundles, is presented. We obtained a model of a WM fiber bundle by parameterizing the various features that characterize this bundle. We then evaluated three different synthetic DT-MRI models using experimental data in order to test the proposed methodology, and to determine the optimum model and parameter settings for constructing a realistic simulated DT-MRI phantom. Several examples of how the mathematical framework can be applied to compare fiber-tracking algorithms are presented.

Algorithms↗
PubMed1999

A mathematical model for simulating virus transport through synthetic barriers.

Synthetic barriers such as gloves, condoms and masks are widely used in efforts to prevent disease transmission. Due to manufacturing defects, tears arising during use, or material porosity, there is inevitably a risk associated with use of these barriers. An understanding of virus transport through the relevant passageways would be valuable in quantifying the risk. However, experimental investigations involving such passageways are difficult to perform, owing to the small dimensions involved. This paper presents a mathematical model for analyzing and predicting virus transport through barriers. The model incorporates a mathematical description of the mechanisms of virus transport, which include carrier-fluid flow, Brownian motion, and attraction or repulsion via virus-barrier interaction forces. The critical element of the model is the empirically determined rate constant characterizing the interaction force between the virus and the barrier. Once the model has been calibrated through specification of the rate constant, it can predict virus concentration under a wide variety of conditions. The experiments used to calibrate the model are described, and the rate constants are given for four bacterial viruses interacting with a latex membrane in saline. Rate constants were also determined for different carrier-fluid salinities, and the salt concentration was found to have a pronounced effect. Validation experiments employing laser-drilled pores in condoms were also performed to test the calibrated model. Model predictions of amount of transmitted virus through the drilled holes agreed well with measured values. Calculations using determined rate constants show that the model can help identify situations where barrier-integrity tests could significantly underestimate the risk associated with barrier use.

Condoms↗
PubMed1999

Numerical and arithmetical cognition: patterns of functions and deficits in children at risk for a mathematical disability.

Based on performance on standard achievement tests, first-grade children (mean age = 82 months) with IQ scores in the low-average to high-average range were classified as at risk for a learning disability (LD) in mathematics, reading, or both. These at-risk children (n = 55) and a control group of academically normal peers (n = 35) were administered experimental tasks that assessed number comprehension and production skills, counting knowledge, arithmetic skills, working memory, and ease of retrieving information from long-term memory. Different patterns of intact cognitive functions and deficits were found for children in the different at-risk groups. As a set, performance on the experimental tasks accounted for roughly 50% and 10% of the group differences in mathematics and reading achievement, respectively, above and beyond the influence of IQ. Performance on the experimental tasks thus provides insights into the cognitive deficits underlying different forms of LD, as well as into the sources of individual differences in academic achievement.

Case-Control Studies↗
PubMed1994

Mathematical model of antiviral immune response. III. Influenza A virus infection.

We present an approach to studying theoretically the regularities and the kinetic characteristics of influenza A virus (IAV) infection in man. The estimates of the "numbers" (Zinkernagel et al., 1985) characterizing evolutionary established interferon and immune responses in uncomplicated IAV infection are explored by developing a multiparameter mathematical model which allows direct quantitative references to the biological reality. The system of equations of the mathematical model of antiviral immune response, applied earlier to acute hepatitis B virus infection (Marchuk et al., 1991a, b), is modified and extended to describe the joint reaction of the interferon and immune systems in IAV infection. Macrophages infiltrating the airway's epithelium are considered to be the principal source of interferon that induces antiviral resistance in lung epithelial cells. The model is formulated as a delay-differential system with about 60 parameters characterizing the rates of various processes contributing to the typical course of IAV infection. The key aspect of the adjustment between the model and various data on the immunity to influenza is the derivation of a consistent data set--the generalized picture of uncomplicated IAV infection. It serves as a consistent theoretical definition of the structure of the normal course of the infection and the antiviral immune response suitable for model fitting. The parameter estimates for the processes considered in the model are carefully discussed. The quantitative model is used to study the organization and dynamic properties of the processes contributing to IAV infection. The threshold condition for immune protection of virus-free host to infection with IAV is analyzed. The relative roles of humoral, cellular and interferon reactions for the kinetics of the uncomplicated IAV infection are studied. The contribution of parameters of virus-sensitive tissue, interferon and IAV-specific immune processes to the variations of duration and severity of the infection is quantitatively estimated by sensitivity studies. It is shown that the variations in the parameters of a virus-epithelial cell system are more influential on the severity of the infection rather than that of the antiviral immune response. The need for fine co-ordination of the kinetics of the non-specific interferon response and the adaptive antigen-specific immune reactions to provide recovery from the infection is illustrated.

Humans↗
PubMed1995

A mathematical model explaining the molecular weights and distribution of very long chain dicarboxylic acids formed during the adaptive response of Sarcina ventriculi.

A simple mathematical model is presented to explain a recent new discovery of an unusual membrane adaptive response in Sarcina ventriculi. In this response, this organism synthesizes very long chain alpha, omega-dicarboxylic acids ranging from 28 to 36 carbon atoms in length. The distribution of chain lengths of the new fatty acid species is not consistent with de novo synthesis but suggests elaboration from the existing regular-chain fatty acids by a coupling process. Here, we demonstrate, using a mathematical model, that if the molecular weights and relative abundances of regular chain fatty acids are known, the molecular weights and relative abundances of the new, very long chain dicarboxylic fatty acid species can be predicted using a model based on the random, pairwise combination of regular chain species. This combination takes place across the bilayer leaflet to form transmembrane fatty acids. It is proposed that this coupling phenomenon is regulated by the motional dynamics of the membrane.

Cell Membrane↗
PubMed1995

Mathematical modeling of the loss of telomere sequences.

hortening of telomeres is one of the supposed mechanisms of cellular aging and death. An important question related to this so-called "end-replication" hypothesis is whether it can explain in quantitative detail the dynamic of cell sensescence in vitro and in vivo. A natural way to answer this question is to use mathematical modeling. In this paper, the models were successfully fitted to data on cultured fibroblasts from two different sources assuming that after reaching the Hayflick checkpoint on a single chromosome cells cease to proliferate. The main conclusion is that the end-replication hypothesis provides an explanation for the cell aging process which is quantitatively consistent with the data. As a secondary outcome, estimates were obtained of the rate of shortening of telomeres and several interesting mathematical results for branching processes with infinite type spaces arise.

Animals↗
PubMed2000

A mathematical model of drug transport in human breast cancer.

A mathematical model of drug transport in tissue has been developed on the basis of a clinical study of patients with breast cancer, treated with the drug doxorubicin and of drug transport experiments using cultured human breast cancer cells. The clinical study revealed doxorubicin gradients in tumor islets of densely packed cancer cells. The mathematical model allows simultaneous drug transport through the cellular network (transcellular pathway), through the intercellular interstitium (paracellular pathway), and across the boundary between the two networks. The effective diffusion coefficient of the interstitial network is found to be much higher than that of the cellular network, in spite of the fact that the interstitium thickness is only 20-40 nm. The model simulations can be made to fit the results of the clinical study. A long-continued simulation (40 days) of drug transport into a spherical islet with a radius of 150 microm, after a bolus injection of doxorubicin, reveals that the maximum average drug concentration at the islet centre is only reached after 224 h, while it decreases by a factor 15 from the boundary to the centre of the islet. The area under the curve in a plot of the average drug concentration versus time only decreases by 10% from the boundary to the centre of the islet.

Antineoplastic Agents↗
PubMed1986

Membrane transport: a mathematical investigation.

It is known that the primary constituents of the membranes of cells are lipids. These lipids are arranged in two layers and the membrane is frequently called a bilipid layer. Recent low intensity scanning electron micrographs of the bilipid layer has revealed that the bilipid layer has revealed that the bilipid membrane layer also contains proteins. The proteins in the bilipid membrane layer pass from one side of the layer to the other and thus constitute a "hole" in the membrane layer. The structure of the proteins is such that an essentially void space exists surrounded by the molecular structures of the protein. The exact functioning of the proteins has not yet been determined. The thesis of this paper is that the proteins act as mediators for the transport of specific catabolites. The supporting arguments for the thesis are in the form of mathematical models for the catabolite - protein interactions, and the results of simulations based upon the mathematical models. Physical verifications of the results presented in this paper await physiological experimental data. However the results of this work indicate that modest changes in the membrane proteins result in a significant change in the amount of catabolite transported across the cell membrane. The mediation of the catabolite transport by the proteins has the pathological implications that long term post-disease states of the cells may be linked closely to the altered states of the membrane proteins: which may occur during the period of the disease state.

Biological Transport↗
PubMed1987

Mathematical model and simulation of retina and tectum opticum of lower vertebrates.

The processing of information within the retino-tectal visual system of amphibians is decomposed into five major operational stages, three of them taking place in the retina and two in the optic tectum. The stages in the retina involve (i) a spatially local high-pass filtering in connection to the perception of moving objects, (ii) separation of the receptor activity into ON- and OFF-channels regarding the distinction of objects on both light and dark backgrounds, (iii) spatial integration via near excitation and far-reaching inhibition. Variation of the spatial range of excitation and inhibition allows to account for typical activities observed in a variety of classes of retina ganglion cells. Mathematical description of the operations in the tectum opticum include (i) spatial summation of retinal output (mainly of class-2 and class-3 retina ganglion cells), and (ii) direct or indirect lateral inhibition between tectal cells. In the computer simulation, first the output of the mathematical retina model is computed which, then, is used as the input to the tectum model. The full spatio-temporal dynamics is taken into account. The simulations show that different combinations of strength of lateral inhibition on the one side and the response properties of the retina ganglion cells on the other side determine the response properties of tectal cell types involved in object recognition.

Amphibians↗
PubMed1978

The evolution of sexual reproduction as a repair mechanism. Part II. Mathematical treatment of the wheel model and its significance for real systems.

The dynamics of populations of self-replicating, hierarchically structured individuals, exposed to accidents which destroy their sub-units, is analyzed mathematically, specifically with regard to the roles of redundancy and sexual repair. The following points emerge from this analysis: 1. A population of individuals with redundant sub-structure has no intrinsic steady-state point; it tends to either zero or infinity depending on a critical accident rate alpha c. 2. Increased redundancy renders populations less accident prone initially, but population decline is steeper if alpha is greater than a fixed value alpha d. 3. Periodic, sexual repair at system-specific intervals prevents continuous decline and stabilizes the population insofar as it will now oscillate between two fixed population levels. 4. The stabilizing sexual interval increases with increased complexity provided this is accompanied by appropriate levels of redundancy. 5. The model closely simulates the dynamics of heterosis effects. 6. Repair fitness is a population fitness: the chance of an individual being repaired is a function of the statistical make-up of the population as a whole at the particular period. Populations living at alpha greater than alpha c either engage in sexual repair at the appropriate time or they die out. 7. The mathematical properties of the model illustrate mechanisms which possibly played a role in the evolution of a mortal soma in relation to sexual reproduction.

Animals↗
PubMed1978

Mathematical optimization of glaucoma visual field screening protocols.

There is potential for significantly shortening the time required for visual field screening protocols by a precise specification of the number, exact location, and sequence of points to be tested. Through statistical and mathematical methods, protocols have been developed for maximizing the probability of detecting at least one visual field defect in a subject who is a risk for early glaucomatous field loss. The mathematical formulation was derived in a generalized manner so that it could be applied to most kinetically or statically determined visual field screening methods.

Glaucoma↗