PubMed Health⌕ Search

SEARCH · PubMed Health

Results for “Mathematical Concepts”

Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 199 records · Page 11Linked to original sources
PubMed1998

[Computer technology for genogenographic study of the gene pool. V. Evaluation of the reliability of maps].

An important aspect of gene geography, the estimation of the reliability of interpolation maps, is considered. The introduced quantitative parameter, map reliability, was estimated as the probability of predicted character values in interpolated map regions. The obtained estimates characterize the statistic significance of the mapped values of the character. The estimation algorithm is based on concepts and mathematical methods of the reliability theory. The proposed approach involved the estimation of the reliability at each point of the mapped area and resulted in a new map (a reliability map) expressing the reliability of gene geographic mapping in probability terms. Approaches to estimate the reliability of mapping, as dependent on various parameters of the initial data, were proposed, a general computer-based technology was elaborated, and a standardized reliability scale was proposed. Reliability maps are considered necessary for the correct interpretation of gene geographic maps. The estimation of reliability as dependent on the number and distribution of initially tested populations was illustrated by the example of frequency maps of individual genes (HP*1, HLA*A1) and synthetic maps (100 alleles of 34 polymorphic loci) of Eastern Europe.

Algorithms↗
PubMed1985

Relationship of uteroplacental blood flow to placental clearance of maternal plasma C-19 steroids: evaluation of mathematical models.

The concept that the placental clearance of maternal plasma dehydroepiandrosterone sulfate through estradiol formation is a function of uteroplacental blood flow in women has been disputed. We obtained data on the clearance of maternal plasma dehydroepiandrosterone through placental estradiol formation in the baboon and used these data to evaluate some mathematical models of placental clearance. Our evaluation shows that the placental clearance of dehydroepiandrosterone is proportional to uteroplacental blood flow in the baboon.

Animals↗
PubMed2004

Frames of reference for self-evaluation of ability in mathematics.

Measures of eight frame-specific self-evaluations of ability in mathematics were used to predict general mathematics self-concept and self-efficacy. Participants were 900 Norwegian students in Grade 6 (n = 277), Grade 9 (n = 236), Grade 11 (n = 263), and adult students attending senior high school (n = 124). Four items measured frame-specific self-evaluation of achievement based on external frames of reference whereas four items measured frame-specific self-evaluation based on internal frames of reference. Regression analyses were used to test relations between the frame-specific self-evaluations and general mathematics self-concept and self-efficacy. The analyses indicated that self-evaluation based on comparison with other students in class (an external frame of reference) and on comparison of mathematics achievement with achievement in other school subjects (an internal frame of reference) were robust predictors of both mathematics self-concept and self-efficacy. The analyses also indicated that students are using multiple frames of reference when evaluating their mathematics ability. Implications of the result for the internal-external frame of reference model are discussed.

Achievement↗
PubMed1987

Early function concepts: their development and relation to certain mathematical and logical abilities.

Cognition of functions (i.e., y = f(x)) has been identified as an achievement of early childhood. To investigate the development of function concepts and their relation to mathematical and logical abilities typically acquired during the age period of 5-7 years, 72 children in this age range were tested on nonnumerical function tasks (functions as exchange of properties, functions as displacement of positions, and functions as preservation of structure), numerical tasks (number conservation and arithmetic problems), and aspects of logical reasoning (class inclusion, class vicariance, and seriation). Orderly developmental trends were found in function task performance, with younger children manifesting limited success through trial-and-error strategies and older children achieving substantial success with anticipatory strategies. Moreover, certain function abilities were associated with the numerical domain, whereas others were associated with the logical domain. The findings are consistent with the developmental model of Piaget et al. according to which cognition of functions lays the groundwork for reversible operations, but also suggest that this development occurs through parallel processes within separate conceptual domains.

Child↗
PubMed2003

New data on chemotherapy in the adjuvant setting.

In the last few months, there have been three sets of new, provocative data that might have important implications for the daily prescription of adjuvant chemotherapy (CT) in the future. (1) Urokinase-type plasminogen activator (UPA) and type 1 plasminogen activator inhibitor (PAI-1), two molecular markers of invasion already known for their powerful prognostic value in node-negative breast cancer, seem to predict for enhanced benefit from adjuvant CT, while the benefit from adjuvant endocrine therapy seems independent of them. The predictive value of these markers, however, remains suboptimal and an important limitation lies in their evaluation through a cytosolic assay, which is compromised for small tumours (<1cm). (2) Breast cancer 'gene expression profiles' have been identified through DNA-microarray technology and seem to be better predictors of clinical outcome in young women (less than 55 years old) with stage I or II breast cancer, when compared to the currently used clinical-pathological criteria. Remarkably, these molecular data suggest that the prognostic profile of breast cancer does not depend on lymph node status and that it is possible to identify a group of node-positive breast cancer patients with an unexpectedly good prognosis. Prospective and independent confirmation is needed, but these data are fascinating and carry the hope that CT decision-making in breast cancer will be greatly facilitated in the future. (3) The recently reported CALGB 9741 (or INT 69741) trial shakes our belief that 'one cycle of CT every 3 weeks' is the adequate adjuvant treatment for node-positive breast cancer. Launched in 1999, it aimed to test two novel concepts based on mathematical models of tumour cell growth kinetics. Concept 1 implies that dose-densification of CT, i.e., delivering drugs at reduced intervals, will maximize the chances of eradicating the tumour; and concept 2 extends the first one to encompass situations of heterogeneous drug sensitivity through the use of sequential dose-dense, non-cross-resistant single agents or regimens. The 3-year results of this trial strongly support concept 1; a longer follow-up and a confirmation study are desirable before recommending changes in routine patient care.

Biomarkers, Tumor↗
PubMed1996

The development and use of demographic models.

In this review, we first examine two classical demographic models - conventional life tables and stable populations - and a modern generalization of stable population theory; we then discuss mathematical models of conception and birth. These models involve purely mathematical relations in formal demography as opposed to empirical regularities. Next we consider model age schedules of mortality, nuptialitiy, marital fertility, fertility, and migration that are explicitly based on such empirical patterns. We close this empirical section with a discussion of model stable populations, which are based on model life tables. We next examine the use of demographic models in forecasting future mortality, nuptiality, and fertility and in population projection. Following a discussion of microsimulation models, which gives us the opportunity to mention model age schedules of post partum amenorrhoea and of sterility, we close with observations about the purposes and uses of demographic models.

Demography↗
PubMed2000

Aspects of self-concept and their relationship to language performance and verbal reasoning ability.

It has been claimed that self-concept is multidimensional, with dimensions such as mathematical self-concept and self-concept in language. The present study investigated the relationship of academic self-concept in language with performance on school-related language tasks and verbal reasoning ability. A total of 512 students in grades 7, 9, and 11 rated four aspects of their academic self-concept in language: self-perception, self-efficacy, self-esteem, and others' perception of their abilities. Verbal reasoning ability and performance on language tasks were assessed. Path analysis showed that performance on language tasks was influenced strongly by verbal reasoning abilities. Self-esteem and others' perception of one's abilities were affected directly by language performance. No direct relationship was found between academic self-concept in language and verbal reasoning ability. The results suggest that adolescents do not construe their academic self-concept according to their abilities but according to their performance in school and others' response to it.

Adolescent↗
PubMed1991

Statistical evaluation of the evidential value of human hairs possibly coming from multiple sources.

A concept of the mathematical evaluation of human hair evidence is derived. This concept can be realized in a special computer program, the output of which is an incrimination probability. The problems of not knowing the true number of sources and the correct partition of hairs corresponding to their sources are solved from the point of view of avoiding an unjustified incrimination.

Forensic Medicine↗
PubMedDate not supplied

[A new mathematical model of the dynamics of an age cohort population].

A new generalized conception of an organism is given. Based on this conception, a new mathematical model of ontogenesis of an individual and the survival of the age cohort of population was proposed. By using real data on the dynamics of the survival of the age cohort of population, the model enables one to determine the parameters characterizing the relationship man-environment in the context of survival and calculate the dynamics (from birth to death) of the model variables of the state of the organism.

Age Distribution↗
PubMed1997

Comparison of mechanistic rumen models on mathematical formulation of extramicrobial and microbial processes.

This study investigated the consequences of differences in applied concepts and individual mathematical formulations on steady-state behavior of three important mechanistic rumen models. In the models of Baldwin et al. (2) and Danfaer (6), the formulation of passage rate, nondietary inputs, defined rumen substrate pools, absorption rates, degradation rates, molecular weights, parameterization of VFA production, and physical compartmentalization were sequentially exchanged for the formulation of the model of Dijkstra et al. (9). Most of these adaptations had a considerable influence on model behavior, indicating large qualitative differences in formulation and sensitivity to concept choice. Because microbial substrate environments were similar after all adaptations, the microbial mechanisms could be compared objectively without being concealed by differences in extramicrobial formulation. None of the microbial functions were altered except for substrate degradation, which gave rise to a similar rate of substrate entrance to soluble rumen pools that are available for microbial utilization. Large differences remained in microbial functions of substrate fermentation, substrate incorporation, and microbial synthesis. Differences in extramicrobial rumen functions and microbial mechanisms had important consequences for simulated nutrient outputs from the rumen, illustrating the necessity for further validation of individual formulations.

Absorption↗
PubMed2002

Mathematical consequences of the genealogical species concept.

A genealogical species is defined as a basal group of organisms whose members are all more closely related to each other than they are to any organisms outside the group ("exclusivity"), and which contains no exclusive group within it. In practice, a pair of species is so defined when phylogenies of alleles from a sample of loci shows them to be reciprocally monophyletic at all or some specified fraction of the loci. We investigate the length of time it takes to attain this status when an ancestral population divides into two descendant populations of equal size with no gene exchange, and when genetic drift and mutation are the only evolutionary forces operating. The number of loci used has a substantial effect on the probability of observing reciprocal monophyly at different times after population separation, with very long times needed to observe complete reciprocal monophyly for a large number of loci. In contrast, the number of alleles sampled per locus has a relatively small effect on the probability of reciprocal monophyly. Because a single mitochondrial or chloroplast locus becomes reciprocally monophyletic much faster than does a single nuclear locus, it is not advisable to use mitochondrial and chloroplast DNA to recognize genealogical species for long periods after population divergence. Using a weaker criterion of assigning genealogical species status when more than 50% of sampled nuclear loci show reciprocal monophyly, genealogical species status depends much less on the number of sampled loci, and is attained at roughly 4-7 N generations after populations are isolated, where N is the historically effective population size of each descendant. If genealogical species status is defined as more than 95% of sampled nuclear loci showing reciprocal monophyly, this status is attained after roughly 9-12 N generations.

Alleles↗
PubMed2002

Model-based evaluation of a new upgrading concept for N-removal.

Mathematical modelling is considered a time and cost-saving tool for evaluation of new wastewater treatment concepts. Modelling can help to bridge the gap between lab and full-scale application. Bio-augmentation can be used to obtain nitrification in activated sludge systems with a limited aerobic sludge retention time. In the present study the potential for augmenting the endogenous nitrifying population is evaluated. Implementing a nitrification reactor in the sludge return line fed with sludge liquor with a high ammonia concentration leads to augmentation of the native nitrifying population. Since the behaviour of nitrifiers is relatively well known, a choice was made to evaluate this new concept mainly based on mathematical modelling. As an example an existing treatment plant (WWTP Walcheren, The Netherlands) that needed to be upgraded was used. A mathematical model, based on the TUDP model and implemented in AQUASIM was developed and used to evaluate the potential of this bioaugmentation in the return sludge line. A comparison was made between bio-augmentation and extending the existing aeration basins and anoxic tanks. The results of both modified systems were compared to give a quantitative basis for evaluation of benefits gained from such a system. If the plant is upgraded by conventional extension it needs an increase in volume of about 225%; using a bioaugmentation in the return sludge line the total volume of the tanks needs to be expanded by only 75% (including the side stream tanks). Based on the modelling results a decision was made to implement the bioaugmentation concept at full scale without further pilot scale testing, thereby strongly decreasing the scale-up period for this process.

Ammonia↗
PubMed1989

Biological priority and psychological supremacy: a new integrative paradigm derived from process theory.

Process theory is a comprehensive theory of physical and psychological processes that can serve to integrate biological, social, and psychodynamic psychiatry. Process theory uses concepts derived from mathematical dynamics and Heraclitus's process philosophy. It provides three novel and clinically applicable concepts: 1) biological priority and psychological supremacy (as contrasted to theories of biological or psychological primacy), 2) union of opposites (as contrasted to psychoanalytic and dialectic conflicts and to systems homeostasis), and 3) creative bifurcations (as contrasted to determinism and developmental theories).

Biological Psychiatry↗
PubMed1965

OBSERVABLE CHANGES OF HYPOTHESES UNDER POSITIVE REINFORCEMENT.

In mathematical models of concept learning it has consistently been assumed that positive reinforcement cannot lead to a change of the hypothesis determining the overt response. When hypotheses are experimentally identified and recorded along with positive and negative reinforcements of stimulus-response pairs, it can be shown that hypotheses may change after a positive reinforcement. Positive reinforcement has an information content for subjects that has not yet been adequately recognized in concept formation studies.

Humans↗
PubMed1990

Fascinating rhythm: a primer on chaos theory and its application to cardiology.

Nonlinear dynamics is an exciting new way of looking at peculiarities that in the past have been ignored or explained away. We have attempted to give a general introduction to the basics of the mathematics, applications to cardiology, and a brief review of the new tools needed to use the concepts of nonlinear mathematics. The careful mathematical approach to problems in cardiac electrical dynamics and blood flow is opening a window on behaviors and mechanisms previously inaccessible.

Animals↗