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 19 recordsLinked to original sources
PubMed1979

Role of mathematical concepts in cancer research.

The role of mathematics in cancer research is not confined to epidemiology (population level). The expected contribution of it in various levels is exemplified stepwise. At the individual level, prediction of life expectancy of a cancer case or psychological analysis of life-threatened patient; at the tissue level, stochastic estimation of future metastases; at the cellular level, model contruction for abnormal metabolic processes in malignant cell; at the molecular level, elucidation of carcinogenetic mechanism from a thermodynamic standpoint of view.

Forecasting↗
PubMed1977

[Critical remarks on an essay by K.T. Kalveram, "Factor analysis. Critical comments on a theoretical concept and its mathematical reformulation"].

The following contribution is a critical discussion of a paper by K. T. Kalveram Uber Faktorenanalyse. Kritik eines theoretischen Konzepts und seine mathematische Neuformulierung", which was published in this journal in 1970. In the following it is shown that Kalveram's attempt of a mathematical reformulation must be considered a failure, even if mathematical misrepresentations are not taken into account.

Factor Analysis, Statistical↗
PubMed2026

Modelling the effects of biological intervention in a dynamical gene network.

Cellular response to environmental and internal signals can be modeled by dynamical gene regulatory networks (GRN). In the literature, three main classes of gene network models can be distinguished: (1) non-quantitative (or data-based) models which do not describe the probability distribution of gene expressions; (2) quantitative models which fully describe the probability distribution of all genes co-expression; and (3) mechanistic models which allow for a causal interpretation of gene interactions. We propose two rigorous frameworks to model gene alteration in a dynamical GRN, depending on whether the network model is quantitative or mechanistic. We explain how these models can be used for design of experiment, or, if additional alteration data are available, for validation purposes or to improve the parameter estimation of the original model. We apply these methods to the Gaussian graphical model, which is quantitative but non-mechanistic, and to mechanistic models of Bayesian networks and penalized linear regression.

Gene Regulatory Networks↗
PubMed2025

Beyond Level-1: Identifiability of a Class of Galled Tree-Child Networks.

Inference of phylogenetic networks is of increasing interest in the genomic era. However, the extent to which phylogenetic networks are identifiable from various types of data remains poorly understood, despite its crucial role in justifying methods. This work obtains strong identifiability results for large sub-classes of galled tree-child semidirected networks. Some of the conditions our proofs require, such as the identifiability of a network's tree of blobs or the circular order of 4 taxa around a cycle in a level-1 network, are already known to hold for many data types. We show that all these conditions hold for quartet concordance factor data under various gene tree models, yielding the strongest results from 2 or more samples per taxon. Although the network classes we consider have topological restrictions, they include non-planar networks of any level and are substantially more general than level-1 networks - the only class previously known to enjoy identifiability from many data types. Our work establishes a route for proving future identifiability results for tree-child galled networks from data types other than quartet concordance factors, by checking that explicit conditions are met.

Mathematical Concepts↗
PubMed2026

Polyploidy Arithmetic.

Polyploidy occurs in plants and animals, and is an important force in speciation and genome evolution. The main focus of this paper is the following fundamental question that was recently posed by Huber and Maher: Given the ploidy numbers of a collection of extant species, or their ploidy profile, what is the smallest number of hybridizations needed in any evolutionary history for these species to completely represent these numbers? In this paper, we shall show that this question can be rephrased in terms of addition chains and the closely related addition sequences, which have been studied for over a century in mathematics and computer science. These are sequences of natural numbers that start with 1, so that each number in the sequence larger than 1 is the sum of two other numbers arising earlier in the sequence. In our first main result, we show that finding the smallest number of hybridization events to explain a ploidy profile, or the hybrid number, is equivalent to solving the so-called addition sequence problem. This immediately implies that computing the hybridization number is computationally intractable. Even so, it also leads to new connections to representing polyploid evolution using networks. More specifically, in our second main result we show that ploidy profiles representable by tree-child networks are exactly the addition chains, implying a polynomial-time algorithm for identifying these profiles. We then consider beaded tree-child networks, which permit the representation of autopolyploidy events, and in our third main result we provide a greedy polynomial-time algorithm to decide whether a given profile can be realized by such a network. We expect that our results can be leveraged in future work through, for example, making use of known algorithms for computing short addition sequences to give bounds for the hybrid number, and in guiding network reconstruction for polyploid species.

Polyploidy↗
PubMed2026

Pattern Formation in a Spatial Public Goods Dilemma due to Diffusive or Directed Motion.

The costly provision of public goods serves as a model problem for the evolution of cooperative behavior, presenting a social dilemma between the collective benefits of shared resources and the individual incentive to free-ride in resource production. The spatial structure of populations can also impact cooperation over public goods, as diffusion of public goods and intentional motion of individuals towards regions with greater resources can interact with population and public goods dynamics to produce heterogeneous patterns in the spatial distribution of strategies and resources. In this paper, we build off a model introduced by Young and Belmonte for the reaction dynamics of interacting individuals and an explicit public good, deriving a system of PDEs that describes the spatial profiles of strategies and the public good in the presence of both diffusive motion of individuals and resources and chemotaxis-like directed motion of individuals in response to gradients in the concentration of public goods. Through linear stability analysis, we show that spatial patterns in strategic and public goods profiles can emerge due to either Turing instability with high defector diffusivity or a directed-motion instability through strong sensitivity of cooperators towards increasing resource concentration. We further explore the emergent spatial patterns with a mix of weakly nonlinear stability analysis and numerical simulation, showing that, for a wide range of reaction parameters, diffusion-driven instability appears to increase cooperation and public goods across the spatial domain, while directed motion of cooperators towards public goods tends to decrease cooperation and environmental quality across the environment.

Models, Biological↗
PubMed1979

A model of potassium ion efflux during exercise of skeletal muscle.

Potassium (K+) is a vasoactive agent and is released from muscle cells during exercise. A simple diffusion model does not predict the time course of K+ efflux during exercise, which decreases as the exercise progresses. We constructed a mathematical model using the concept of an active Na+-K+ ion pump to account for the decreased efflux during and uptake after exercise. Passive fluxes are calculated by the Nernst equation. Active fluxes are constrained to balance these passive fluxes at rest. The pump activity increases as either extracellular K+ or intracellular Na+ concentration increases. To test the model, the venous K+ efflux profile was simulated for direct stimulation (4/s) of the anterior calf mus cles of dogs. The model simulated the K+ release during the stimulation period and [K+] undershoot after the stimulation. The active Na+-K+ ATPase transport concept used in the model was further tested by observing K+ efflux after administration of ouabain. Ouabain infusion decreased K+ uptake during exercise slightly and abolished [K+] undershoot after the stimulation. These experimental data were matched by the model only if a discontinuous effect of ouabain is assumed. This suggests that ouabain may more completely block the sensitivity of the pump to intracellular [Na+] than to extracellular [K+].

Animals↗
PubMed1976

Mathematical aspects of dose-response studies in carcinogenesis--the concept of thresholds.

Many of the previously proposed theories of carcinogenesis which relate the exposure level of a carcinogen to expected tumor response, are summarized and it is pointed out that these theories assume the existence of no threshold level. A modification of the one-hit carcinogenic model which would incorporate a threshold, is proposed along with a generalization to variable thresholds over the population at risk. The statistical problems of discriminating between threshold and non-threshold models from experimental bioassay data are discussed and an example is given.

Animals↗
PubMed1977

Concept of visual sensation.

A direct-realist account of visual sensation is outlined. The explanatory notion of elements in visual sensation (atomic sensations) is reinterpreted, and the suggested interpretation is formally justified by constructing a Boolean algebra for visual sensations. The related notion of sensory levels (visual field vs visual world) is discussed.

Color Perception↗
PubMed1977

Relationships between area-specific measures of self-concept, self-esteem and academic achievement for junior high school students.

Physical maturity, peer relations, academic success and school adaptiveness self-concept and self-esteem measures were correlated with reading, language, mathematics, and composite achievement scores for 26 male and 48 female junior high school students. Academic success self-concept was significantly correlated with each of the achievement measures. Peer relations self-concept and self-esteem correlated with language, math, and composite achievement. Academic success self-esteem measures did not correlate with any of the measures of achievement.

Achievement↗
PubMed1977

[Instability and stability in biological morphogenesis].

The concept of morphogenesis is determined and the mathematical image of the developing system is considered. A certain amount of stable and unstable states and slow changes of the potential relief (parameters) are inherent in the latter. The developing systems are intermediate between the deterministic and statistic ones. They are distinctly multiple-levelled. The microprocesses of morphogenesis and the laws of macromorphogenesis are described, the instabilities and stable periods of morphogenesis are considered. All of them in the multiple-leveled system tend to the formation of through hierarchies, or cascades, where the upper levels parametrize the lower ones. This tendency increases as the evolutionary progress proceeds. The genetic regulation is considered also as a parametric regulation in the domains of instabilities. The approach contemplated may be considered both as the generalization of the available data and as the programme of investigation, more adequate to the biological reality than the causal-analytical methodology.

Animals↗
PubMed1979

Seasonal migration and seasonal variation in fecundability: effects on birth rates and birth intervals.

Seasonal patterns in conception rates have been documented in several recent studies. In this paper, a mathematical model of the reproductive process is developed through which the impact of such variation in conception rates is assessed. It is found that the effect on fertility can be quite substantial, but that the birth rate when seasonal variation is occurring is approximated well by the birth rate calculated when conception rates are constant at their mean. These results indicate that further documentation of seasonality in conception rates and exploration of the causes of these patterns and their change is an important area for demographic research.

Birth Rate↗
PubMed1978

An analytical approach to the determination of optimal phasing for external counterpulsation.

An inhomogeneous linear one-dimensional mathematical model is constructed as a conceptual approach to the study of the effects of External Counterpulsation (ECP) on the pressure and flow at the root of the aorta. The optimal operation of ECP is defined by two conditions: (1) minimization of the mean systolic pressure; and (b) maximization of the ratio of diastolic area over systolic area under the total pressure curve. The phase shift of the external pressure is determined so as to satisfy these two requirements. It is demonstrated within our approximation that with a given magnitude of external pressure, the phase shifts that satisfy these two requirements are the same. These phase shifts are linear functions of the systolic fraction of the total cardiac period, and depend on the time for the external wave to travel from the site of application up the vascular bed to the root of the aorta, plus the reflection contributions. Even though these results are derived from a simple model far from the complexity of the actual vasculature, the basic concepts would remain valid even if more complex mathematical treatments would have been used.

Aorta↗
PubMed1978

Computers in nuclear medicine: introductory concepts.

Computers play an important role in image and data processing in nuclear medicine. Applications extend from relatively simple mathematical processing of in vitro specimen assays to more sophisticated image reconstruction procedures for emission tomography. The basic concepts and terminology associated with computer applications in image and data processing in nuclear medicine are presented here.

Computers↗
PubMed1978

Mathematical modeling of lag phases in microbial growth.

This paper describes a mathematical method of the lap phases of Saccharomyces cerevisiae that incorporates the basic concepts previously presented in a two-stage deterministic model for the growth of this organism under conditions of oxygen excess with a sugar as the growth-limiting substrate. The model structure was suggested by an extensive investigation of the causes of the lap phases of S. cerevisiae which found that, in contrast to the traditionally accepted trends, the length of the lap phase was not inoculum-size dependent. This was consistent with other previously published work which suggested that a major factor in the length of the lag phases in S. cerevisiae was the need to synthesize adequate levels of glycolytic and respiratory enzymes. These suggestions were confirmed experimentally with lag-age data. Based on this conclusion a mathematical model was developed incorporating a description of the levels of glycolytic and respiratory enzymes and their effect on the growth rate and metabolism. This model was tested experimentally and the initial results indicate that many aspects of the lag phase of this organism may be described mathematically. The experimental findings further support the concept of primary regulatory control proposed by Bijkerk and Hall.

Glycolysis↗