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PubMed1990

A scale model study of the effects of meteorological, soil, and house parameters on soil gas pressures.

To assess the contribution of various environmental parameters to the entry of Rn into basements, it is advantageous to simplify and control the important variables present in the field situation. A scale model system, simulating a house in soil, has been constructed to investigate the effect of meteorological parameters and house and soil characteristics on soil gas flow around houses. The house walls and soil are of variable permeability. Wind is simulated by applying a static pressure distribution to the soil surface. The effect of temperature differences and appliances is simulated by depressurizing the model house. Soil gas pressures at various locations around the house are measured under different conditions. The results show that the ratio of wall to soil permeability is the determining factor in soil gas flow patterns. For a wind of 8.94 m s-1 (20 mph), the horizontal pressure gradients are about 99 Pa m-1 in the model when the wall is at least as permeable as the soil. This corresponds to 3.3 Pa m-1 in the field. When the soil is two or more orders of magnitude more permeable than the wall, the gradient is about 19.8 Pa m-1 in the model, or 0.66 Pa m-1 in the field. There is a logarithmic dependence of pressure gradient on the ratio of wall to soil permeability in the range -2 less than log (kw/ks) less than 0. Conversely, it takes a large temperature difference of 27 degrees C to cause a 99 Pa m-1 horizontal pressure gradient in model systems with wall permeability greater than soil permeability. The effects of changes in the model system on soil gas flow patterns are investigated for the cases of lowered soil surface permeability, partial surface capping, and presence of a subfloor gravel bed. Partial surface capping, as would occur with driveways and patios, was found to have a minor effect on soil gas pressures. However, lowered surface permeability, caused by precipitation, can significantly change soil gas flow patterns. The only change in soil pressure gradients or pressure differences in the presence of a gravel bed is in the system with the highest wall-to-soil permeability ratio. In this system, under all conditions (house depressurization, wind, and wind with house depressurization), there is an increase in the absolute value of both upwind and downwind pressure differences and pressure gradients with the addition of a gravel bed.

Air Pollutants↗
PubMed2004

Models of social networks based on social distance attachment.

We propose a class of models of social network formation based on a mathematical abstraction of the concept of social distance. Social distance attachment is represented by the tendency of peers to establish acquaintances via a decreasing function of the relative distance in a representative social space. We derive analytical results (corroborated by extensive numerical simulations), showing that the model reproduces the main statistical characteristics of real social networks: large clustering coefficient, positive degree correlations, and the emergence of a hierarchy of communities. The model is confronted with the social network formed by people that shares confidential information using the Pretty Good Privacy (PGP) encryption algorithm, the so-called web of trust of PGP.

Algorithms↗
PubMed1986

Two noninvasive methods to measure female maturation.

Data from a sample (n = 278) of female subjects, ages seven-13, from a cross-sectional study were used to compare two methods of measuring maturation. The methods were self-assessment of secondary sex characteristics and prediction of adult height. Breast and pubic hair assessments were correlated significantly (r = 0.615 and r = 0.696, p less than 0.001) with predicted adult height estimates, indicating the practical use of either method. Assessment of maturation in childhood is strongly recommended to further understanding of the timing and sequence of physical, physiological, social, and behavioral characteristics of children during growth and maturation.

Adolescent↗
PubMedDate not supplied

A cross-sectional study of mathematics achievement, estimation skills, and academic self-perception in students of varying ability.

This study investigated students' mathematics achievement, estimation ability, use of estimation strategies, and academic self-perception. Students with learning disabilities (LD), average achievers, and intellectually gifted students (N = 135) in fourth, sixth, and eighth grade participated in the study. They were assessed to determine their mathematics achievement, ability to estimate discrete quantities, knowledge and use of estimation strategies, and perception of academic competence. The results indicated that the students with LD performed significantly lower than their peers on the math achievement measures, as expected, but viewed themselves to be as academically competent as the average achievers did. Students with LD and average achievers scored significantly lower than gifted students on all estimation measures, but they differed significantly from one another only on the estimation strategy use measure. Interestingly, even gifted students did not seem to have a well-developed understanding of estimation and, like the other students, did poorly on the first estimation measure. The accuracy of their estimates seemed to improve, however, when students were asked open-ended questions about the strategies they used to arrive at their estimates. Although students with LD did not differ from average achievers in their estimation accuracy, they used significantly fewer effective estimation strategies. Implications for instruction are discussed.

Achievement↗
PubMed2005

Mathematical models of oxygen and carbon dioxide storage and transport: the acid-base chemistry of blood.

This article describes a mathematical model of the acid-base chemistry of blood. The model is formulated from first principles by considering the "components" of blood and the reaction equations in the plasma and erythrocyte fractions. Equations are formulated to describe the total concentration of blood components, the physicochemical properties, and the equilibrium position of reactions. The model includes 28 equations and 12 parameters. All equations can be solved from six variables included in the model. The model uses simple mathematics, without introducing intermediate concepts or linear coefficients necessary for algebraic solution. Model equations are solved simultaneously using numerical methods. Model parameters are estimated and the model verified for plasma, fully oxygenated blood, and deoxygenated blood. Published data are used to estimate model parameters and normal conditions and to verify model simulations. The model reproduces experimental results, including addition or removal of CO2, or strong acid to plasma; CO2, strong acid or haemoglobin to blood; and the effects of deoxygenating blood. The model can also be used as the basis for models of whole body CO2 transport as illustrated in the accompanying article. As such, it is possible to simulate the effects on blood of physiological changes in ventilation or metabolism.

Acid-Base Equilibrium↗
PubMed1988

Evidence and scientific research.

This commentary reviews the arguments for and against the use of p-values put forward in the Journal and other forums, and shows that they are all missing both a measure and concept of "evidence." The mathematics and logic of evidential theory are presented, with the log-likelihood ratio used as the measure of evidence. The profoundly different philosophy behind evidential methods (as compared to traditional ones) is presented, as well as a comparative example showing the difference between the two approaches. The reasons why we mistakenly ascribe evidential meaning to p-values and related measures are discussed. Unfamiliarity with the technology and philosophy of evidence is seen as the main reason why certain arguments about p-values persist, and why they are frequently contradictory and confusing.

Bayes Theorem↗
PubMed2002

Math = male, me = female, therefore math not = me.

College students, especially women, demonstrated negativity toward math and science relative to arts and language on implicit measures. Group membership (being female), group identity (self = female), and gender stereotypes (math = male) were related to attitudes and identification with mathematics. Stronger implicit math = male stereotypes corresponded with more negative implicit and explicit math attitudes for women but more positive attitudes for men. Associating the self with female and math with male made it difficult for women, even women who had selected math-intensive majors, to associate math with the self. These results point to the opportunities and constraints on personal preferences that derive from membership in social groups.

Attitude↗
PubMedDate not supplied

A mutational model of carcinogenesis.

A model of carcinogenesis based on spontaneous somatic mutation in expanding cell clones is presented and compared with previous mathematical treatments of this concept. The model shows that if cancer is purely a consequence of gene mutation then four independent mutations are required. To explain the marked increase in the incidence of cancer with age it is necessary to postulate that stem cells with a subset of the four key mutations show some loss of growth suppression and expand relative to unaffected stem cells. The model also predicts that for carcinogens acting during extrauterine life the incidence of cancer will be proportional to the dose of carcinogen raised to a power between one and two, even though the carcinogen increases the chance of all four mutations. This power relationship accords with data on human cancer and experimentally induced tumours in animals, but is hitherto unexplained.

Age Factors↗
PubMed1988

[Phase coordination of the rhythms of changes in solar activity and of the monthly biorhythms of altered cholesterol levels of the blood serum in rabbits].

The concentration of total, free and bound cholesterol in the blood serum of 13 intact Chinchilla male rabbits was determined in two four-month experiments carried out in 1973-1974 and in 1984-1985 during a "minimum" phase of an 11-year solar activity cycle. A hierarchy of ten cholesterol biorhythms and solar activity rhythms were singled out on a computer, using an original algorithm, in the individual changes in cholesterol concentration in each rabbit and in changes in seven environmental indexes. A statistical stability of the frequency and phase of low-frequency cholesterol biorhythms and solar activity rhythms has been established within an 11-year period, the fluctuation amplitude of the indexes studied being, on the contrary, statistically unstable.

Animals↗
PubMed2001

Mental organization according to the metabolism of information model and its mathematical description.

This paper outlines the concept of information metabolism, based on the structural organization of the biological cell. It was considered a model of states of consciousness (Kokoszka, 1993b) and human experiences (Kokoszka, 1999) reported earlier. The improved version of the graphical model is presented along with its preliminary description in the terms of dynamic systems. The possible application of the model to the design of artificial networks and into psychotherapeutic diagnosis discussed.

Brain↗
PubMed1965

On the mathematical analysis of schistosome populations.

The concept of the stationary ecological life-table has been applied to populations of the three main species of schistosomes affecting man. In such a system, the net reproductive rate should be equal to 1.0, with reproduction and mortality balancing each other. Calculations are made of net reproduction in both snail and mammal hosts and of the probabilities of transmission from each host to the other. By far the most complete data are those for Schistosoma japonicum, for which the net reproductive rate is calculated as 0.588. The error probably represents the inadequacy of information on rat populations. Using much less complete data, the net reproductive rate for S. mansoni is calculated as 1.85 and for S. haematobium as 2.74. The relative departure from the expected value of 1.0 thus reflects the lack of complete information on the respective parasites. Details of the method and examples of each kind of calculation are given.It is estimated that with adequate data from three or four areas with a range of transmission rates, a predictive model could be constructed for the epidemiology of one species of parasite, and that adequate staff could obtain the necessary data in two-and-a-half years.

Animals↗
PubMed1999

Local similarity in organic crystals and the non-uniqueness of X-ray powder patterns.

Two new concepts for molecular solids, 'local similarity' and 'boundary-preserving isometry', are defined mathematically and a theorem which relates these concepts is formulated. 'Locally similar' solids possess an identical short-range structure and a 'boundary-preserving isometry' is a new mathematical operation on a finite region of a solid that transforms mathematically a given solid to a locally similar one. It is shown further that the existence of such a 'boundary-preserving isometry' in a given solid has infinitely many 'locally similar' solids as a consequence. Chemical implications, referring to the similarity of X-ray powder patterns and patent registration, are discussed as well. These theoretical concepts, which are first introduced in a schematic manner, are proved to exist in nature by the elucidation of the crystal structure of some diketopyrrolopyrrole (DPP) derivatives with surprisingly similar powder patterns. Although the available powder patterns were not indexable, the underlying crystals could be elucidated by using the new technique of ab initio prediction of possible polymorphs and a subsequent Rietveld refinement. Further ab initio packing calculations on other molecules reveal that 'local crystal similarity' is not restricted to DPP derivatives and should also be exhibited by other molecules such as quinacridones. The 'boundary-preserving isometry' is presented as a predictive tool for crystal engineering purposes and attempts to detect it in crystals of the Cambridge Structural Database (CSD) are reported.

Journal Article↗
PubMed1987

Parasitic contamination cycles and mathematical epidemiology.

Mathematics plays an essential role in epidemiology. Whether simple questions are asked about simple relations, or complicated questions about complicated relations, the best fitting mathematical figures are always searched for. In a holistic approach, it may often be necessary to assess complicated relations by using (real) mathematical models (simulation models). Examples are presented of parasitic contamination cycles which require more or less complicated mathematics to answer epidemiological questions regarding prevalence and incidence of infection in the human population: Trichinella, Toxocara and Toxoplasma. Some general remarks on epidemiological insights which are necessary to understand abstract concepts of the 'real world' ('mathematical modelling'), are discussed.

Animals↗