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PubMed2005

Sex- and age-related differences in mathematics.

This study examined sex differences and age-related changes in mathematics based on Eccles's 1985 expectancy-value model of "achievement-related choices" and Dweck's 1986 motivation-process model. We have assessed motivational variables and performance in mathematics for youth in Grades 5, 7, and 9 in a German comprehensive secondary school. Significant sex differences in Grades 7 and 9 were observed even when school marks were controlled for. Furthermore, the results indicated differences between Grade 7 and Grade 9 on most of the motivational variables. Older students show a less favorable motivational pattern. Our results give evidence of the importance of motivational encouragement in mathematics classes, especially for girls and low achieving learners.

Adolescent↗
PubMed2004

SLEEP (Sleep Loss Effects On Everyday Performance) Model.

Sleep management affects human productivity, safety, health, and efficiency in the performance of various tasks. Most people seem to be unaware of the value and role of sleep and the various risks that can occur when less than desired amounts of sleep are obtained. People especially seem to be unaware of the dangers associated with the long-term accumulation of reduced sleep. Thus, a need exists to provide tools to enhance sleep education. This paper presents an overview of a sleep simulation and sleep education tool, the SLEEP (Sleep Loss Effects on Everyday Performance) Model. The SLEEP Model includes alcohol and caffeine along with sleep as variables that affect performance. Assumptions and modeling concepts are discussed, and the major mathematical functions are presented as part of this paper. The unique features of the SLEEP Model are: 1) it is based on conservation of REM sleep; 2) it uses a ratio of current day's sleep to sleep need for the day to adjust performance predictors; 3) it is designed for easy input and output of information; and 4) it has a wide range of applications, including sleep, alcohol, and caffeine management. Generally the mathematical functions used in the SLEEP Model fit the calibration data set with an R2 of 0.8 or better and have statistical significance at least at the 0.05 probability level. Several figures of simulated results are presented with a discussion of references that report similar measured results. The SLEEP Model appears to be a practical tool to teach people the value of proper sleep management.

Alcohol Drinking↗
PubMed2006

Verification of multiplication facts: an investigation using retrospective protocols.

Retrospective verbal protocols collected throughout participants' performance of a multiplication verification task (e.g., "7 x 3 = 28, true or false?") documented a number of different strategies and changes in strategy use across different problem categories used for this common experimental task. Correct answer retrieval and comparison to the candidate answer was the modal but not the only strategy reported. Experiment 1 results supported the use of a calculation algorithm on some trials and the use of the difference between the candidate and correct answers (i.e., split) on others. Experiment 2 clearly demonstrated that participants sometimes bypassed retrieval by relying on the split information. Implications for mental arithmetic theories and the general efficacy of retrospective protocols are discussed.

Algorithms↗
PubMed2005

The wave phenomena in smooth muscle syncytia.

Based on the concept of a functional unit, a mathematical model of a segment of the gut is developed. The model comprises real anatomical, histomorphological, physiological, and pharmacological information on the function of the organ. Numerical investigation into the dynamics of the electromechanical wave phenomenon reveals the fundamental principles of wave initiation, formation, and propagation along electrically anisotropic longitudinal and isotropic circular smooth muscle syncytia. A pattern of self-sustained electrical activity with the formation of spiral waves is discovered in the longitudinal syncytia and is attributed to the change in conductivity in the syncytia as a result of mechanical deformation of smooth muscle fibers. The model adequately predicts the effects of pharmacological interventions on the dynamics of myoelectrical activity. Although no direct experimental comparison to the theoretical findings is possible at this stage, the proposed mathematical model provides new insight onto the basics of physiological processes--slow wave activity, electromechanical conjugation, etc.--and a clinical entity--gastrointestinal dysrhythmias.

Algorithms↗
PubMed1991

Models of arithmetic fact retrieval: an evaluation in light of findings from normal and brain-damaged subjects.

Retrieval of basic arithmetic facts is a central aspect of almost any arithmetic performance. Furthermore, the arithmetic facts provide an opportunity to study memory processes in the context of a naturally occurring but circumscribed set of facts. This article examines current models of arithmetic fact retrieval in light of previously reported data from normal subjects, as well as the results from brain-damaged patients reported by Sokol, McCloskey, Cohen, and Aliminosa (1991) in the preceding article. The discussion serves to delineate the strengths and limitations of the models and, more generally, to identify important theoretical and empirical issues in the study of arithmetic fact retrieval.

Brain Damage, Chronic↗
PubMedDate not supplied

[Vector analytic evaluation of clinico-gerontologic data].

Using the concept of vector analysis and the mathematically theorized condition and age of patients as vectors in a right angle Cartesian coordinate system, the rate of aging and the functional age difference between males and females can be determined.

Adult↗
PubMed1986

[Effect of x-irradiation on the kinetics of 5-iodo-2'-deoxyuridine in a tumor].

Within the interval of 0.25-168 h after intraperitoneal administration of 125I-iodo-desoxyuridine (IDUR) to mice with inoculated melanoma B-16 or sarcoma-180 the kinetics of a radionuclide label (RL) in both tumors was almost the same; the difference were of quantitative nature only. X-ray radiation resulted in an increase in the radioactivity change rate on the first section of the curves of RL clearance, plotted in semilogarithmic coordinates, in both tumors. Differences in the rates in the study groups of animals irradiated at doses of 2; 10 and 20 Gy and their distinctions from the control group were significant. Proceeding from the modern concept of IDUR metabolism a simple mathematical model has been devised where it is assumed that at the initial moment t = 0.25 h general radioactivity measured in vivo over a tumor, results from radioactivity incorporated in DNA which is constant for each irradiation regimen up to a certain time, and the radioactivity of iodide which is released from the body by the exponential law. A formula has been deduced associating the rate of a decrease in general radioactivity on the first segment of a kinetic curve of RL clearance with the level of the label incorporation in DNA. Thus, the applicability of RL IDUR was shown for establishing the quantitative relations between the proliferative ability of a tumor and an irradiation dose.

Animals↗
PubMedDate not supplied

The probability of conception on different days of the cycle with respect to ovulation: an overview.

Several mathematical models have been developed over the past thirty years to investigate how the probability of conception changes on the different days of the cycle with respect to ovulation. A problem general to all models is to estimate the day of ovulation. Since the most fertile days are those close to ovulation, less precise estimates of this event will lead to less accurate estimates of the probability of conception on a given day of the cycle. Given that a reference point for ovulation is available, the first model considered conception as dependent only on the timing of intercourse. Conception was found to be most likely to occur on only six days in each cycle. However, the model is biologically unrealistic because it assumes that all ova can be fertilized and lead to a viable pregnancy. There are other factors that affect the probability of conception, including whether the ovum is viable or not. Recent models have extended the idea of cycle viability to allow for differences between cycles within couples and for the introduction of couple specific covariates. In a second group of models the probability of conception depends mainly on the time of intercourse and the survival times of sperm and ovum. A graphical summary of the results available in the literature is presented. Conception probabilities have been found to be significantly different from zero from five days before ovulation to the day of ovulation itself. On average, less than half of the cycles are viable in women, although recent studies suggest that different cycle viability between women should be taken into account. Survival times for sperm and the ovum have been estimated to be 1.4 days and 0.7 days, respectively. Sperm would have a 5% probability of surviving more than 4.4 days and a 1% probability of surviving more than 6.8 days.

Female↗
PubMed2002

Fractal characterization of complexity in temporal physiological signals.

This review first gives an overview on the concept of fractal geometry with definitions and explanations of the most fundamental properties of fractal structures and processes like self-similarity, power law scaling relationship, scale invariance, scaling range and fractal dimensions. Having laid down the grounds of the basics in terminology and mathematical formalism, the authors systematically introduce the concept and methods of monofractal time series analysis. They argue that fractal time series analysis cannot be done in a conscious, reliable manner without having a model capable of capturing the essential features of physiological signals with regard to their fractal analysis. They advocate the use of a simple, yet adequate, dichotomous model of fractional Gaussian noise (fGn) and fractional Brownian motion (fBm). They demonstrate the importance of incorporating a step of signal classification according to the fGn/fBm model prior to fractal analysis by showing that missing out on signal class can result in completely meaningless fractal estimates. Limitation and precision of various fractal tools are thoroughly described and discussed using results of numerical experiments on ideal monofractal signals. Steps of a reliable fractal analysis are explained. Finally, the main applications of fractal time series analysis in biomedical research are reviewed and critically evaluated.

Algorithms↗
PubMed2001

Topology of an intracellular transduction chain (phototropism of Phycomyces): 1. Joint review of functional, temporal, and spatial aspects.

Two light-induced growth reactions in a unicellular cylindrical sporangiophore of Phycomyces blakesleeanus-vertical growth acceleration under symmetrical irradiation (photomecism) and directional growth under unilateral irradiation (phototropism)-share common input light perception as well as common output growth mechanism but have strongly divergent dynamics and other distinctive features. This divergence culminates in the phototropic paradoxes the main of which states that photomecism shows total adaptation, while phototropism does not adapt. The basis for this contradiction is that the phototropic transduction chain, unlike that of photomecism, faces a spatially non-uniform stimulus and processes a series of spatial patterns (light and absorption profiles, adaptation profile, etc.). The only way to resolve the paradoxes and correlate features of both responses within a single transduction chain is to assume non-local signal transduction, e.g. a cross-talk between different azimuthal locations within the cylindrical cell. On the other hand, to establish the presence of an appropriate cross-talk is equivalent of gaining insight into the topology of the transduction chain. This series of two papers contains a review reconsidering the entire field from this viewpoint (Paper 1) and a mathematical model of pattern transduction which unifies features of phototropism and resolves the paradoxes (Paper 2). At the same time, this is the first "proof of concept" for the "activity/pooling (a/p) networks"-a specific mathematical apparatus designed to analyse systemic properties and control in metabolic pathways.

Absorption↗
PubMed1999

Language supports for children's understanding of numerical fractions: cross-national comparisons.

This study examined Croatian, Korean, and U.S. children's knowledge of numerical fractions prior to school instruction. The research is part of an ongoing project examining the influence of language characteristics on mathematical thinking and performance. The part-whole quantitative relation denoted by numerical fractions may be easier to understand in East Asian languages like Korean. In these languages, the concept of fractional parts is embedded in the mathematics terms used for fractions. The results from this study suggest that the Korean vocabulary of fractions may influence the meaning 6- to 7-year-old children ascribe to numerical fractions and that this results in children being able to associate numerical fractions with corresponding pictorial representations prior to formal instruction.

Child↗
PubMed2005

Pupils' liking for school: ability grouping, self-concept and perceptions of teaching.

BACKGROUND: Research indicates that affective aspects of development provide a basis for autonomous learning. Pupils' liking for school may be a useful indicator of their relationships with teachers and the school. AIMS: The aim of the research reported in this paper is to establish the properties of a measure of pupils' liking for school and to examine associations between this measure, pupils' experiences in lessons, their self-concepts and the amount of setting implemented in school. SAMPLE: A stratified sample of 45 mixed secondary comprehensive schools was selected for the research. Schools represented a variety of ability-grouping practices in the lower school (Years 7-9), from completely mixed-ability to setting in all academic subjects. All Year 9 pupils were included in the sample. METHODS: Pupils completed a questionnaire containing items on their self-concept, liking for school, and their perceptions of teaching in English, mathematics, and science. Data on pupils' gender, ethnic origin, social disadvantage and attainment was also collected. RESULTS AND CONCLUSIONS: The properties and correlates of scales indicating pupils' liking for school and their perceptions of teaching in English, mathematics, and science are established. Liking for school is greater among girls, pupils with higher academic self-concepts, and those with more positive perceptions of teaching. Pupils are more positive about teaching they experience in English than in mathematics or science. When other variables are statistically controlled, there is no significant effect of the extent of ability grouping in the school as a whole. Affective aspects of learning should not be neglected in the drive to raise standards.

Achievement↗
PubMed1992

Concepts and models of sleep regulation: an overview.

Various mathematical models have been proposed to account for circadian, ultradian and homeostatic aspects of sleep regulation. Most circadian models assume that multiple oscillators underlie the differences in period and entrainment properties of the sleep/wake cycle and other rhythms (e.g. body temperature). Interactions of the oscillators have been postulated to account for multimodal sleep/wake patterns. The ultradian models simulate the cyclic alternation of nonREM sleep and REM sleep by assuming a reciprocal interaction of two cell groups. The homeostatic models propose that a sleep/wake dependent process (Process S) underlies the rise in sleep pressure during waking and its decay during sleep. The time course of this process has been derived from EEG slow-wave activity, an indicator of nonREM sleep intensity. The predictions of homeostatic models have been most extensively tested in experiments. The interaction of Process S with a single circadian process can account for multimodal sleep/wake patterns, internal desynchronization and the time course of daytime sleepiness. Close links have emerged between the processes postulated by the various models and specific brain mechanisms. Due to its recent quantitative elaboration and experimental validation, the modelling approach has become one of the potent research strategies in sleep science.

Journal Article↗
PubMed1999

Hypervolemic hemodilution: an alternative to acute normovolemic hemodilution? A mathematical analysis.

BACKGROUND: Hypervolemic hemodilution has been proposed as an alternative to normovolemic hemodilution to reduce homologous blood transfusions. So far, convincing data supporting this concept are unknown. MATERIALS AND METHODS: We therefore present a mathematical model calculating the efficacy of hypervolemic, normovolemic, and "no" hemodilution. Hypervolemic hemodilution constituted volume expansion (20% of estimated blood volume) maintained throughout surgery. Normovolemic hemodilution contained isovolemic exchange of blood (40% of estimated blood volume) vs colloid as well as retransfusing blood plus colloid to maintain minimal acceptable hematocrit, e.g., transfusion trigger. To determine the efficacy of each technique maximal allowable blood loss and final postoperative hematocrit were calculated. Maximal allowable blood loss referred to the amount of blood lost during surgery after which homologous blood transfusion became necessary. RESULTS: Recalculating published clinical data strongly validated the formulas used for our model. Hypervolemic hemodilution always revealed lowest maximal allowable blood losses. Normovolemic hemodilution constantly ensured highest maximal allowable blood losses. For blood losses <40% of blood volume, hypervolemic and normovolemic hemodilution provided almost identical final postoperative hematocrits. But in contrast to normovolemic hemodilution, hypervolemic hemodilution did not carry the risk of severe transient, retransfusion-induced hypervolemia. "No" hemodilution always gave lowest final postoperative hematocrits. CONCLUSIONS: Thus, hypervolemic hemodilution cannot replace normovolemic hemodilution to reduce homologous transfusions, but for blood losses <40% of blood volume hypervolemic hemodilution appears to be superior.

Blood Loss, Surgical↗