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PubMed1989

Self-concepts, domain values, and self-esteem: relations and changes at early adolescence.

We assessed how children's self-concepts of ability for mathematics, English, social, and physical skills activities, ratings of the importance of these activities, and general self-esteem change across the transition to junior high school. Three types of change were assessed: change in mean levels, change in stability, and change in relationships. Twice each year during the sixth and seventh grades, 1,450 children completed questionnaires. Mean levels of children's self-esteem were lowest immediately after the transition, but recovered during seventh grade. Self-concept of ability and importance ratings for math and sports activities showed linear declines. Self-concept of ability for social activities showed a cubic trend, but importance ratings for social activities declined in a linear fashion. Children's self-concepts of ability for math and English became less stable across the junior high transition, whereas beliefs about other activities and general self-esteem were more stable in seventh grade.

Adolescent↗
PubMed1989

A mathematical model of physiological processes and its application to the study of aging.

The behavior of a physiological system which, after displacement, returns by homeostatic mechanisms to its original condition can be described by a simple differential equation in which the "recovery time" is a parameter. Two such systems, which influence one another, can be linked mathematically by the use of "coupling" or "feedback" coefficients. These concepts are the basis for many mathematical models of physiological behavior, and we describe the general nature of such models. Next, we introduce the concept of a "fatal limit" for the displacement of a physiological system, and show how measures of such limits can be included in mathematical models. We show how the numerical values of such limits depend on the values of other system parameters, i.e., recovery times and coupling coefficients, and suggest ways of measuring all these parameters experimentally, for example by monitoring changes induced by X-irradiation. Next, we discuss age-related changes in these parameters, and show how the parameters of mortality statistics, such as the famous Gompertz parameters, can be derived from experimentally measurable changes. Concepts of onset-of-aging, critical or fatal limits, equilibrium value (homeostasis), recovery times and coupling constants are involved. Illustrations are given using published data from mouse and rat populations. We believe that this method of deriving survival patterns from model that is experimentally testable is unique.

Aging↗
PubMed2000

From autopoiesis to semantic closure.

This article addresses the question of providing an adequate mathematical formulation for the concepts of autopoiesis and closure under efficient cause. What is required is metaphorically equivalent to reducing the act of writing to a set of mathematical equations, habitually effected by a human mathematician, within the ongoing function of the system itself. This, in turn, raises the question of the relationship between autopoiesis and semantics. The hypothesis suggested is that whereas semantics clearly requires autopoiesis, it may be also be the case that autopoiesis itself can only be materially realized in a system that is characterized by a semantic dimension.

Humans↗
PubMed1997

[Biomechanical problems of the maxillodental system in children].

The biomechanical regularities of the function of anatomic blocks of the maxillodental system were studied using mathematical simulation and mathematical models. The biological concept of the structure and biomechanics of human masticatory system is presented. Methods of rapid diagnosis, based on the anthropometric characteristics of the face, and a mathematical model of the function of the maxillodental system intended for the orthodontic treatment of maxillodental abnormalities in children have been developed.

Biomechanical Phenomena↗
PubMed1986

A dynamic model of smooth muscle contraction.

A dynamic model of smooth muscle contraction is presented and is compared with the mechanical properties of vascular smooth muscle in the rat portal vein. The model is based on the sliding filament theory and the assumption that force is produced by cross-bridges extending from the myosin to the actin filaments. Thus, the fundamental aspects of the model are also potentially applicable to skeletal muscle. The main concept of the model is that the transfer of energy via the cross-bridges can be described as a 'friction clutch' mechanism. It is shown that a mathematical formulation of this concept gives rise to a model that agrees well with experimental observations on smooth muscle mechanics under isotonic as well as isometric conditions. It is noted that the model, without any ad hoc assumptions, displays a nonhyperbolic force-velocity relationship in its high-force portion and that it is able to maintain isometric force in conditions of reduced maximum contraction velocity. Both these findings are consistent with new experimental observations on smooth muscle mechanics cannot be accounted for by the classical Hill model.

Animals↗
PubMedDate not supplied

[Small doses and synergistic interaction of environmental factors].

Methodology approach demonstrating a principle importance of mutual increase of damaging action of physical and chemical environmental factors at low doses and intensities was described. A generalize conceptual basis of synergism was suggested which was appropriate both for combined action of ionizing radiation with other agents and for combined action of any other harmful environmental factors. The main idea of the concept described here is in the formation of additional effective damages under combined action due to interaction of sublesions induced by every agent and which are not effective under separate action of each agent employed. Mathematical presentation of this concept allowed to make some new non-trivial conclusions. It was shown theoretically the existence of optimal ratio of damages induced by acting agents under which the highest synergism must be obtained. The effect of synergistic interaction has to be dependent on intensities of agents: the less intensity of one agent used, the small intensity of another factor must be applied for the greatest synergistic effect expression. The test of these consequences was performed for a number of experiments described in this paper. The results presented here have of principle importance for interpretation of the higher effectiveness of low dose and dose rate of ionizing radiation observed in some cases.

Animals↗
PubMed2006

The belief in a negative interdependence of math and verbal abilities as determinant of academic self-concepts.

BACKGROUND: The internal/external frame of reference (I/E) model by Marsh (1986) assumes intra-individual dimensional comparisons in which students compare their own achievements in one subject with their achievements in other subjects. These comparison processes should lead to negative paths from achievement in one subject (e.g. maths) on self-concept in another subject (e.g. verbal domains). AIMS: Within this study, we investigated the impact of students' belief in a negative interdependence of maths and verbal abilities, that is, whether students think of maths and verbal abilities as negatively correlated or not, on the impact of dimensional comparisons. METHODS: Maths and German grades, academic self-concepts in maths and German, and a new scale on the beliefs in a negative interdependence of maths and verbal abilities students were assessed (N = 1,443). RESULTS: The importance of the negative interdependence beliefs could be shown: stronger beliefs in a negative interdependence of maths and verbal ability are accompanied by more negative path coefficients from grades in one subject to academic self-concepts in the other subject. CONCLUSIONS: Dimensional comparisons seem to be of particular importance for students with negative interdependence beliefs.

Adolescent↗
PubMed1989

Time to steady state following a change in dosing rate.

Drugs administered at fixed intervals or by continuous infusion will accumulate in the body until steady state is achieved. The time to a given percentage of the eventual steady-state concentration has previously been considered to be dependent only on the elimination half-life. This is incorrect. Although the rate of drug accumulation in the body is dependent only on the elimination half-life, the time to a given percentage of steady state is dependent on both the elimination half-life of the drug and the initial concentration. This paper presents the mathematical proof of this concept, computer simulations demonstrating the use of these equations, and nomograms for use in clinical practice. The use of this method allows serum drug concentrations to be evaluated earlier than previously predicted after changes in the dosing rate.

Adult↗
PubMed1977

Mathematical description of molecular structure: Molecular topology.

The concepts of the topology of finite point sets are applied to a mathematical description of molecular structure. The combinatorial properties of the "bond topology," which arises naturally from atomic adjacency relationships within a molecule, are investigated in detail. The collection of closed sets, the cotopology, is found to be related to bonding. Combinatorial weights of bonds over the cotopology are defined and explicit expressions for a general molecule are derived. The bond weights are found to parallel molecular orbital bond orders. It is concluded that much of the variation in pi bond orders is topological in origin.

Journal Article↗
PubMed2005

Mathematical modeling of the course and prognosis of factitious disorders: a game-theoretic approach.

A mathematical model using simple concepts of repeated games is proposed to model the course and prognosis of factitious disorders. Although simple, the model seems capable of explaining the yet unknown mechanisms underlying the variable course of factitious disorders. One of the notable results of this study is the significant effect of involved physicians in the treatment process on the course of the disease. Particularly, the doctor's error rate in realizing whether the symptoms are real or factitious can considerably affect the course of the disease. This is the first paper to apply a mathematical model to factitious disorders.

Factitious Disorders↗
PubMed1983

[The economy of protein maintenance in the living cell].

On the economy of proteins in living cells Each synthesized protein of a cell is of certain metabolic advantage, but at the same time also a load on the energy and material metabolism. "Costs" as well as "profit" vary with the amount of protein formed, and the optimal amount would maximize the profitability, i.e. profit minus cost. The paper deals with the special case of an enzyme necessary for substrate uptake, which is therefore of advantage for the energy budget of the cell, whose biosynthesis, however, drains this budget at the same time. This example allows a mathematical formulation of the concept of profitability and shows, with the help of a basic kinetic model that indeed an optimum exists. Its existence follows from the rather general fact that the advantage of an enzyme reaches a saturation value, if its amount increases, while the "cost factor" continues to increase in a linear manner.

Adenosine Triphosphate↗
PubMed1999

Cooperative Solutions for Sustainable Resource Management.

/ Many environmental management issues can be defined as allocation problems, e.g., the allocation of rights to use common-pool resources or the allocation of the cost of regional resource development projects. The allocation methods developed in the area of cooperative n-person game theory are most appropriate for these problems because they focus on the conditions for engendering and sustaining the necessary cooperation among the involved stakeholders. These solution concepts seek to ensure that the allocation is based on some norm of equity and, most often, also to minimize the incentive for any player to defect from the cooperative venture. We illustrate these solution concepts with an application to a water resource project in Southern California. We argue how the rigorous mathematical nature of these solution concepts should not hinder their application to actual situations and how, with the use of heuristic rules and inexact notions of comparable worths, we can employ these concepts even in approximate fashion. We remind ourselves that the goal of such an endeavor is to convince stakeholders of the equity of a proposed solution and, in so doing, maximize the prospect of sustained cooperation. The alternative to cooperation, on the other hand, may be endless stalemate.KEY WORDS: Core; Game theory; Equity; Common-pool resources; Sustainabilityhttp://link.springer-ny.com/link/service/journals/00267/bibs/24n2p167.html

Journal Article↗
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↗
PubMedDate not supplied

[Theoretical analysis of possible construction of biomechanical parameters of energy expenditures in heart muscle].

Proceeding from the data that overall efficiency of the heart muscle under constant level of contraction is estimated by the rate of fibre shortening a total expression for energy losses in the wall of the heart left ventricle is proposed. It is a concrete mathematical expression of modern concepts about the factors responsible for energy consumption by the heart. With certain assumptions the known parameters of energy expenditures are obtained: the index of heart tension (IHT known as "double product" index) and the index of time - tension TTI. More exact fulfillment of IHT is explained by the fact that it assumes certain changes of the heart contraction, while TTI is valid only at its constants level.

Chemical Phenomena↗
PubMed2006

Metabolomic database annotations via query of elemental compositions: mass accuracy is insufficient even at less than 1 ppm.

BACKGROUND: Metabolomic studies are targeted at identifying and quantifying all metabolites in a given biological context. Among the tools used for metabolomic research, mass spectrometry is one of the most powerful tools. However, metabolomics by mass spectrometry always reveals a high number of unknown compounds which complicate in depth mechanistic or biochemical understanding. In principle, mass spectrometry can be utilized within strategies of de novo structure elucidation of small molecules, starting with the computation of the elemental composition of an unknown metabolite using accurate masses with errors <5 ppm (parts per million). However even with very high mass accuracy (<1 ppm) many chemically possible formulae are obtained in higher mass regions. In automatic routines an additional orthogonal filter therefore needs to be applied in order to reduce the number of potential elemental compositions. This report demonstrates the necessity of isotope abundance information by mathematical confirmation of the concept. RESULTS: High mass accuracy (<1 ppm) alone is not enough to exclude enough candidates with complex elemental compositions (C, H, N, S, O, P, and potentially F, Cl, Br and Si). Use of isotopic abundance patterns as a single further constraint removes >95% of false candidates. This orthogonal filter can condense several thousand candidates down to only a small number of molecular formulas. Example calculations for 10, 5, 3, 1 and 0.1 ppm mass accuracy are given. Corresponding software scripts can be downloaded from http://fiehnlab.ucdavis.edu. A comparison of eight chemical databases revealed that PubChem and the Dictionary of Natural Products can be recommended for automatic queries using molecular formulae. CONCLUSION: More than 1.6 million molecular formulae in the range 0-500 Da were generated in an exhaustive manner under strict observation of mathematical and chemical rules. Assuming that ion species are fully resolved (either by chromatography or by high resolution mass spectrometry), we conclude that a mass spectrometer capable of 3 ppm mass accuracy and 2% error for isotopic abundance patterns outperforms mass spectrometers with less than 1 ppm mass accuracy or even hypothetical mass spectrometers with 0.1 ppm mass accuracy that do not include isotope information in the calculation of molecular formulae.

Algorithms↗