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PubMed1992

Confirmatory factor analysis of reading and mathematics performance: a twin study.

Reading and mathematics performance data from a sample of 264 reading-disabled twin pairs and 182 matched control twin pairs were subjected to multivariate behavior genetic analysis. The factor structure of reading and math performance measures was found to be highly similar for both groups. Consistent with previous findings obtained using alternative methods, a significant heritable component to individual differences in reading performance was found both within the reading-disabled (h2 = 0.78) and control (h2 = 0.74) twin samples. In addition, a substantial genetic influence on mathematics performance was found (h2 = 0.51 and 0.60 in the reading-disabled and control samples, respectively), although shared environmental influences common to both members of a twin pair also contribute significantly to the variance in math scores of both groups (c2 = 0.44 and 0.37). Moreover, genetic influences accounted for 98% of the observed correlation between reading and math performance within the sample of reading-disabled twin pairs, and for 55% of the observed correlation in the control sample. Thus, individual differences in both reading and mathematics performance are highly heritable and appear to be caused by many of the same genetic influences.

Adolescent↗
PubMedDate not supplied

Mathematical programming assisted drug design for nonclassical antifolates.

A concept from optimization theory, specifically, mathematical programming, is proposed for designing drugs with desired properties. The mathematical programming formulation is solved to obtain the optimal descriptor values, which are employed in the Cerius(2) modeling environment to infer the optimal lead candidates, in the sense that they exhibit both high selectivity and activity while ensuring low toxicity. It has been observed that unique substituent groups and their molecular conformations are responsible for attaining the goal of simultaneous high selectivity and activity. Both linear and nonlinear quantitative structure activity relationships (QSARs) have been developed for use in the proposed approach. A comparative study of these models is done, and it is shown that the QSARs are well represented by nonlinear models. The proposed mathematical programming strategy has been demonstrated for a class of nonclassical antifolates for Pneumocistis carinii and Toxoplasma gondii dihydofolate reductase. Some of the potential leads found in this study have biological properties similar to those in the open literature. We believe the technique proposed is general and can be applied to other structure based drug design.

Algorithms↗
PubMed1993

Mathematical disabilities: cognitive, neuropsychological, and genetic components.

Cognitive, neuropsychological, and genetic correlates of mathematical achievement and mathematical disability (MD) are reviewed in an attempt to identify the core deficits underlying MD. Three types of distinct cognitive, neuropsychological, or cognitive and neuropsychological deficits associated with MD are identified. The first deficit is manifested by difficulties in the representation or retrieval of arithmetic facts from semantic memory. The second type of deficit is manifested by problems in the execution of arithmetical procedures. The third type involves problems in the visuospatial representation of numerical information. Potential cognitive, neuropsychological, and genetic factors contributing to these deficits, and the relationship between MD and reading disabilities, are discussed. Finally, suggestions for the subtyping of mathematical disorders are offered.

Brain Damage, Chronic↗
PubMed2006

Does learning about the mathematics of gambling change gambling behavior?

The present research examined the influence of improved knowledge of odds and mathematical expectation on the gambling behavior of university students. A group of 198 students in an introductory statistics class received instruction on probability theory using examples from gambling. A comparison group of 134 students received generic instruction on probability, and another group of 138 students in classes on unrelated topics received no mathematical instruction. Students receiving the intervention demonstrated superior ability to calculate gambling odds as well as resistance to gambling fallacies 6 months after the intervention. Unexpectedly, this improvement in knowledge and skill was not associated with any decreases in actual gambling behavior. The implication of this research is that enhanced mathematical knowledge on its own may be insufficient to change gambling behavior.

Adult↗
PubMed1999

Herbart's mathematical psychology.

J.F. Herbart (1824/1890b) provided a mathematical theory about how mental ideas (Vorstellungen) in consciousness at Time 1 (T1) could compete, possibly driving 1 or more Vorstellungen below a threshold of consciousness. At T1 a Vorstellung A could also fuse with another, B. If at a later T2, A resurfaced into consciousness, it could help B to re-resurface into consciousness. This article describes the historical and mathematical background of Herbart's theory, outlines the mathematical theory itself with the aid of computer graphics, and argues that the theory can be applied to the modern problem of predicting recognition latencies in short-term memory (Sternberg's task; Sternberg, 1966)

Germany↗
PubMed2000

Descartes's Regulae, mathematics, and modern psychology: "the Noblest example of all" in Light of Turing's (1936) On computable Numbers.

There are surprisingly strong connections between the philosophy of mind and the philosophy of mathematics. One particular important example can be seen in the Regulae (1628) of Descartes. In "the noblest example of all," he used his new abstract understanding of numbers to demonstrate how the brain can be considered as a symbol machine and how the intellect's algebraic reasoning can be mirrored as operations on this machine. Even though his attempt failed, it is illuminating to explore it because Descartes launched 2 traditions--mechanistic philosophy of mind and abstract mathematics--that would diverge until A. Turing (1936) approached symbolic reasoning in a similar "symbol machine-existence proof" way. Descrates's and Turing's thought experiments, which mark the beginning of modern psychology and cognitive science, respectively, indicate how important the development of mathematics has been for the constitution of the science of mind.

History, 17th Century↗
PubMed1983

Computing, mathematics, and the nephrologist.

The potential of computing and mathematics to make major contributions to nephrology by making information retrieval and presentation more accurate, more complete, and more rapid and by providing immediate access to computational and graphic facilities is emphasized in this symposium issue. The realization that disordered physiology due to disease may not prevent the course of an illness being described in mathematical terms should encourage physicians, and others interested in pathophysiology, to integrate mathematics and statistics into their thinking and their practice.

Computers↗
PubMed1997

Mathematical considerations in the practice of acute normovolemic hemodilution.

BACKGROUND: Acute normovolemic hemodilution (ANH) is recommended as a simple and cost-effective method of autologous transfusion. The present mathematical model, based on the current clinical practice of removing 2 to 3 units of fresh whole blood, defines the indications for ANH. STUDY DESIGN AND METHODS: A mathematical model and subsequent nomograms were developed to define patients for whom removal of 2 to 3 units (450 mL each) would allow a theoretical red cell savings equivalent to 1 unit of packed red cells (volume, 250 mL; hematocrit, 60%), that is, a successful application of the technique. Minimal safe target hematocrits were defined as 30, 26, and 22 percent. RESULTS: The minimal initial hematocrits required for given patient weights are displayed on nomograms derived from the mathematical model. The nomograms also indicate the surgical blood loss allowed without ANH: for example, a 75-kg man, (2-unit ANH, minimal safe hematocrit 22%) requires a minimal initial hematocrit of 42 percent (surgical blood loss of 0.64 x estimated blood volume = 3100 mL). CONCLUSION: ANH involving the removal of 2 to 3 units (450 mL each) may be useful in patients with anticipated blood loss exceeding 50 percent of estimated blood volume, high initial hematocrit, and a capacity to tolerate dilution-induced anemia.

Decision Making↗
PubMed1999

The value of oxygen-carrying solutions in the operative setting, as determined by mathematical modeling.

BACKGROUND: The use of oxygen carriers (red cell [RBC] substitutes) in acute trauma and in surgery, with or without the use of acute normovolemic hemodilution (ANH), is being investigated. Mathematical modeling was used to assess the impact of RBC substitutes, with or without ANH, in the elective surgical setting. STUDY DESIGN AND METHODS: Mathematical equations and computer models were developed on the basis of previously described mathematical principles, for better understanding of the potential efficacy of RBC substitutes for blood needs with or without ANH. Savings were calculated for a patient with a blood volume of 5000 mL and an initial hematocrit (Hct) of 45 or 30 percent. RESULTS: Substantial increases in the tolerable blood losses (or reduced allogeneic RBC needs) were most evident when the use of an RBC substitute to achieve severe ANH to a Hct that the patient might not otherwise have been able to tolerate was combined with the use of RBC substitutes as replacement for the surgical blood subsequently lost. However, the benefit was greatly dependent on the patient's initial Hct. For example, for a patient with a blood volume of 5000 mL and an initial Hct of 45 percent, a blood loss of approximately 2500 mL resulted in a final Hct of 28 percent without the use of an RBC substitute or ANH. In contrast, with the combined use of staged ANH with an RBC substitute and the RBC substitute for lost surgical blood, a blood loss of up to 14.5 L could be tolerated. However, in an anemic patient (blood volume 5000 mL, initial Hct 30%), a Hct of 28 percent cannot be sustained without the use of allogeneic RBCs for any of the described strategies, even when blood losses were as low as 1 L. CONCLUSION: The use of RBC substitutes has the potential to result in a substantial reduction in allogeneic RBC exposure. This benefit is essentially limited to the nonanemic patient when the use of an RBC substitute is combined with severe ANH and there is concomitant large perioperative blood loss. Anemic patients can be expected to have only limited benefit, because of an inability to sequester an adequate volume of autologous RBCs via ANH.

Blood Substitutes↗
PubMed2006

Large sex difference in adolescents on a timed line judgment task: attentional contributors and task relationship to mathematics.

Visuospatial performance, assessed with the new, group-administered Judgment of Line Angle and Position test (JLAP-13), varied with sex and mathematical competence in a group of adolescents. The JLAP-13, a low-level perceptual task, was modeled after a neuropsychological task dependent upon functioning of the posterior region of the right hemisphere [Benton et al, 1994 Contributions to Neuropsychological Assessment: A Clinical Manual (New York: Oxford University Press)]. High-school boys (N = 52) performed better than girls (N = 62), with a large effect for sex (d = 1.11). Performance increased with mathematical competence, but the sex difference did not vary significantly across different levels of mathematics coursework. On the basis of earlier work, it was predicted that male, but not female, performance in line judgment would decline with disruptions to task geometry (page frame), and that the sex difference would disappear with disruptions to geometry. These predictions were supported by a number of univariate and sex-specific analyses, although an omnibus repeated-measures analysis did not detect the predicted interaction, most likely owing to limitations in power. Thus, there is partial support for the notion that attentional predispositions or strategies may contribute to visuospatial sex differences, with males more likely than females to attend to, and rely upon, internal or external representations of task geometry. Additional support for this hypothesis may require development of new measures or experimental manipulations with more powerful geometrical disruptions.

Adolescent↗
PubMed2004

Digit span in dyslexia: variations according to language comprehension and mathematics skills.

The aim of this study was to investigate digit span performance in dyslexia. It was hypothesised that differences would be found in accordance with subgrouping by language comprehension and mathematic skills, and by analyses of how the digit span scores were attained. Two digit span tasks were given to a group of dyslexic children and controls (n = 57), mean age 12.62 (SD = 1.43). The tasks were "Digit Span" of the WISC-R, and "Digit Span 2," where the use of back-up strategies like finger counting and lip reading were restricted. As expected, the digit span scores were significantly lower in the dyslexia group than in the control group. Restrictions of back-up strategies did not alter the scores in the control group, while the scores were lowered in the dyslexia group. Further analyses of longest digit span, serial recall, and serial position indicated different retrieval patterns in the subgroups. The subgroup with good language comprehension and mathematic skills (n = 12), showed impaired serial recall especially in backward recall. The subgroup with good language comprehension skills, but with mathematics impairment (n = 9), showed impaired serial recall in both forward and backward recall. The subgroup with language impairments (n = 16), recalled fewer digits than the two other subgroups. The findings were discussed in relation to the "Phonological loop" of the Multi Component Model of Working Memory, and implications for intervention were discussed.

Adolescent↗
PubMed2001

Effect of teachers' stereotyping on students' stereotyping of mathematics as a male domain.

This multilevel analysis used data from a representative sample from Grades 6, 7, and 8 in public schools in Switzerland. The data included information on (a) 6,602 students (3,307 girls, 3,295 boys) nested within 338 classes and (b) 321 mathematics teachers of these classes. The teachers and the students tended to stereotype mathematics as a male domain, and the teachers' stereotypes significantly affected the students' stereotypes after the author controlled for achievement, interest, and self-confidence in mathematics and for school grade and schooling track.

Achievement↗
PubMed1993

A mathematical model of the intracerebral steal phenomenon in regional and focal ischaemia.

The objective of the present work was to mathematically estimate the extent and dynamics of intracerebral steal which may occur in response to cerebral vasodilation in regional and focal cerebral ischaemia. To this end, a spatially distributed mathematical model of regional cerebral blood flow (rCBF) was developed. The model contained a parallel system of intracerebral vascular resistances which were connected in series to a lumped extracerebral artery resistance and, for the focal ischaemia model, also a lumped pial collateral resistance. The rCBF was measured at 30 min of ischaemia in the following models: (1) bilateral carotid occlusion in spontaneously hypertensive rats (SHR), and (2) occlusion of the middle cerebral artery (MCA) in normotensive rats. The measured 3-dimensional rCBF data were used to set up the initial values of intracerebral resistance components. Cerebral vasodilation induced by inhalation of CO2 was simulated in the model by decreasing the values of both intracerebral and collateral resistance. Vascular responsiveness was specified to decrease with the ischaemic rCBF. In addition, a long term change in rCBF and resistance distribution was introduced to account for: (1) gradual rise in intracerebral resistance due to ischaemic oedema, and (2) adaptive decrease in collateral resistance. The following were predicted by the mathematical model. (1) At 60% maximum intracerebral dilatation a small intracerebral steal (5-10%) occurs at flow levels below 30-50 ml/100 g/min in both ischaemic models. (2) In focal ischaemia, the steal can be compensated by the 5% to 20% decrease in the collateral vascular resistance. (3) The rate of collateral adaptation overcomes the rate of intracerebral resistance rise and, therefore, eliminates the intracerebral steal after an adequately long period of time (on the order of a few hours). (4) An inverse steal effect can be demonstrated at the end of vasodilatation, provided that the time constant of collateral adaptation selected is longer (about 5:1) than the time constant of the intracerebral resistance rise. We conclude that the prediction of rCBF response to vasodilatation in cerebral ischaemia requires a knowledge of resting rCBF and of the response characteristics of both intracerebral and pial arterial segments.

Animals↗
PubMed2004

Mathematical modeling reveals threshold mechanism in CD95-induced apoptosis.

Mathematical modeling is required for understanding the complex behavior of large signal transduction networks. Previous attempts to model signal transduction pathways were often limited to small systems or based on qualitative data only. Here, we developed a mathematical modeling framework for understanding the complex signaling behavior of CD95(APO-1/Fas)-mediated apoptosis. Defects in the regulation of apoptosis result in serious diseases such as cancer, autoimmunity, and neurodegeneration. During the last decade many of the molecular mechanisms of apoptosis signaling have been examined and elucidated. A systemic understanding of apoptosis is, however, still missing. To address the complexity of apoptotic signaling we subdivided this system into subsystems of different information qualities. A new approach for sensitivity analysis within the mathematical model was key for the identification of critical system parameters and two essential system properties: modularity and robustness. Our model describes the regulation of apoptosis on a systems level and resolves the important question of a threshold mechanism for the regulation of apoptosis.

Apoptosis↗
PubMed1996

A mathematical solution to a network designing problem.

One of the major open issues in neural network research includes a Network Designing Problem (NDP): find a polynomial-time procedure that produces minimal structures (the minimum intermediate size, thresholds and synapse weights) of multilayer threshold feed-forward networks so that they can yield outputs consistent with given sample sets of input-output data. The NDP includes as a subproblem a Network Training Problem (NTP) where the intermediate size is given. The NTP has been studied mainly by use of iterative algorithms of network training. This paper, making use of both rate distortion theory in information theory and linear algebra, solves the NDP mathematically rigorously. On the basis of this mathematical solution, it furthermore develops a mathematical solution procedure to the NDP that computes the minimal structure straightforwardly from the sample set. The procedure precisely attains the minimum intermediate size, although its computational time complexity can be of nonpolynomial order at worst cases. The paper also refers to a polynomial-time shortcut of the procedure for practical use that can reach an approximate minimum intermediate size with its error measurable. The shortcut, when the intermediate size is prespecified, reduces to a promising alternative as well to current network training algorithms to the NTP.

Algorithms↗
PubMed2000

Mathematical models of the transmission and control of sexually transmitted diseases.

BACKGROUND: The development of mathematical models to describe and interpret the epidemiology of sexually transmitted infections has involved the incremental addition of various forms of biological and behavioral complexity to simple mathematical templates. GOAL: To review simple and complex models used in study of observed epidemiologic pattern. STUDY DESIGN: An overview of modeling in sexually transmitted disease epidemiology identifies the function of different types of models. RESULTS: Simple models have the advantage of transparency and analytical tractability and can illustrate the relative merits of different intervention options. However, real life is replete with complexities that can have effects that are difficult to predict in the absence of a mathematical framework. CONCLUSIONS: Research should increasingly be based on robust parameterization of model structures and try to capture individual behaviors. Progress will be most rapid by interdisciplinary work where the clinician, epidemiologist, and mathematician work collaboratively to help improve our knowledge of how to best control infection and disease.

Female↗
PubMed2000

Sex differences in mathematical reasoning ability at age 13: their status 20 years later.

Reported is the 20-year follow-up of 1,975 mathematically gifted adolescents (top 1%) whose assessments at age 12 to 14 revealed robust gender differences in mathematical reasoning ability. Both sexes became exceptional achievers and perceived themselves as such; they reported uniformly high levels of degree attainment and satisfaction with both their career direction and their overall success. The earlier sex differences in mathematical reasoning ability did predict differential educational and occupational outcomes. The observed differences also appeared to be a function of sex differences in preferences for (a) inorganic versus organic disciplines and (b) a career-focused versus more-balanced life. Because profile differences in abilities and preferences are longitudinally stable, males probably will remain more represented in some disciplines, whereas females are likely to remain more represented in others. These data have policy implications for higher education and the world of work.

Adolescent↗
PubMed1997

The effect of social comparison on mathematics self-concept.

Implicit in the frame of reference hypothesis is the assumption that social comparison is one of the causal determinants of self-concept. The present study of Norwegian sixth-grade elementary school students showed that students of low-, medium-, and high-achievement classes did not differ in mathematics self-concept. Mathematics self-concept was, however, significantly influenced by the students' within-classroom position in mathematics. The results support the frame of reference hypothesis, and the support was consistent over gender.

Achievement↗