SEARCH · Search PubMed

Results for “MATHEMATICS”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

SourceResearch connectionFrom yearThrough year

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

At least 757 records · Page 42Linked to original sources

PubMed2004

Can the genetic code be mathematically described?

From a mathematical point of view, the genetic code is a surjective mapping between the set of the 64 possible three-base codons and the set of 21 elements composed of the 20 amino acids plus the Stop signal. Redundancy and degeneracy therefore follow. In analogy with the genetic code, non-power integer-number representations are also surjective mappings between sets of different cardinality and, as such, also redundant. However, none of the non-power arithmetics studied so far nor other alternative redundant representations are able to match the actual degeneracy of the genetic code. In this paper we develop a slightly more general framework that leads to the following surprising results: i) the degeneracy of the genetic code is mathematically described, ii) a new symmetry is uncovered within this degeneracy, iii) by assigning a binary string to each of the codons, their classification into definite parity classes according to the corresponding sequence of bases is made possible. This last result is particularly appealing in connection with the fact that parity coding is the basis of the simplest strategies devised for error correction in man-made digital data transmission systems.

Algorithms↗

PubMedDate not supplied

[Mathematical modeling of optimal dose fields in radiotherapy of malignant tumors. Part 2 (Contact methods of radiotherapy)].

The principles of mathematical modeling of optimal dose fields in contact radiotherapy (RT) of malignant tumors are investigated. The point dose additivity provides for presetting the permissible dose field in an irradiated organism as a system of linear limitations to doses in the control points (CP) distributed in the lesion focus and in healthy organs and tissues. It was shown as impossible to shape a dose field by linear limitations to doses in CP in using the RT contact methods with the irradiation sources being implanted into lesion focus. A mathematic interpretation was suggested for the task (with its solution by an iterative algorithm) of forming an optimal dose field in the lesion focus with implanted irradiation sources, which is based on maximizing the factor of dose-field homogeneity. It was further demonstrated that linear limitations, if added to the dose in healthy organs and tissues, make the task even more complicated if not insoluble. Finally, it is suggested to use the method of shaping an effective dose field by the iterative method with interactive visual optimization of the dose field.

Algorithms↗

PubMed2005

[How should we perform acute normovolemic hemodilution during radical prostatectomy? Comparison with a mathematical model].

BACKGROUND: Although allogenic blood transfusion has become safer than ever, there still exist some risks such as infection and immunomodulation. The importance of autologous blood transfusion is emphasized. METHODS: Fourteen cases of radical prostatectomy performed with the use of acute normovolemic hemodilution (ANH) were examined retrospectively. The efficacy of ANH was evaluated in comparison with a mathematical model. RESULTS: The average blood loss was 1321 ml and the average blood volume collected during ANH was 637 ml. In no cases, allogenic blood transfusion was necessary. According to a mathematical model, however, the actual blood loss was smaller than the calculated allowable blood loss in all the cases, which implied allogenic blood transfusion would have been avoidable even without ANH. It was also suggested that only a limited efficacy was obtained due to a relatively small blood volume collected during ANH. CONCLUSIONS: Our way of performing ANH was considered suboptimal in that no efficacy was found as to avoidance of allogenic blood transfusion and the extent of ANH was not sufficient to prepare for unexpected massive blood loss. It seemed necessary to reconsider the indications for ANH to increase the efficacy. The importance of the informed consent was also recognized.

Blood Transfusion, Autologous↗

PubMed2005

[The release behavior of the combined system of diltiazem hydrochloride delayed-onset sustained-release pellets and modeling by mathematics method].

AIM: To prepare the combined system of diltiazem hydrochloride delayed-onset sustained-release pellets in order to make time-specific drug delivery system. The drug can release from the system sustained after a predetermined lag time, and the release behavior can continue till 24 hour after administrating the formulation. According to the concept of chronotherapy, the combined system is useful to improve the pharmacotherapy of cardiovascular diseases. METHODS: The velocity-time curve of the drug release from the multiple-unit system containing pellets was consistent with the fluctuation curve following time of blood pressure and heart ratio. So the velocity-time curve was selected to describe the release behavior of the combined system. The velocity-time equation describing the release behavior of two kinds of pellets was deduced by non-linear least square model fit. And zero-order kinetics equation was adopted to fit the release behavior of different combinations which were composed of different proportion of two kinds of pellets. The velocity-time equation describing the release behavior of the combinations was deduced by non-linear least square model fit, too. The difference of combinations in velocity-time curves between theoretical value and test value was compared. RESULTS: The results showed that the test values were closely approximate to the theoretical values. Therefore, the multiple unit drug delivery system can be described by adding the velocity-time equations of different pellets to calculate the theoretical equations. CONCLUSION: A multiple-unit combined system containing different coated pellets, as a novel delayed-onset sustained-release system, was prepared. Then a time-specific drug delivery system has been made. The programmed drug delivery system could be predicted by adding the velocity-time equation of each kind of pellets to calculate the theoretical equations. characterized by mathematics equation. The release behavior of pellets system could be characterized by mathematics equation.

Capsules↗

PubMed2006

[Difficulties in learning mathematics].

AIMS: To discuss our concern for some aspects of mathematics learning disorders related to the nomenclature employed and their diagnosis; these aspects refer to the term 'dyscalculia' and to its diagnosis (especially syndromatic diagnosis). We also intend to propose a classification that could help to define the terminology. Lastly we are going to consider the different aspects of diagnosis and to determine which of them are indispensable in the diagnosis of primary and secondary disorders. DEVELOPMENT: As far as the nomenclature is concerned, we refer to the term 'dyscalculia'. The origins of the term are analysed along with the reasons why it should not be used in children with difficulties in learning mathematics. We propose a classification and denominations for the different types that should undoubtedly be discussed. With respect to the diagnosis, several problems related to the syndromatic diagnosis are considered, since in our country there are no standardised tests with which to study performance in arithmetic and geometry. This means that criterion reference tests are conducted to try to establish current and potential performance. At this stage of the diagnosis pedagogical and psychological studies must be conducted. The important factors with regard to the topographical and aetiological diagnoses are prior knowledge, results from the studies that have been carried out and findings from imaging studies. The importance of a genetic study must be defined in the aetiological diagnosis. CONCLUSIONS: We propose a nomenclature to replace the term 'dyscalculia'. Standardised tests are needed for the diagnosis. The need to establish current and potential performance is hierarchized. With regard to the topographical diagnosis, we highlight the need for more information about geometry, and in aetiological studies the analyses must be conducted with greater numbers of children.

Child↗

PubMed2006

The consequences of idiopathic partial epilepsies in relation to neuropsychological functioning: a closer look at the associated mathematical disability.

Although the seizure prognosis is mostly favorable in idiopathic partial epilepsies, there is some empirical evidence showing that subtle neuropsychological impairments, with a consequent risk of academic underachievement, are not rare. We investigated neuropsychological functioning including attention, memory, visuomotor ability, and executive functioning with a closer look at the associated mathematical ability in patients with idiopathic partial epilepsies. A battery of age-appropriate, neuropsychological and mathematics achievement tests was administered to 30 participants with idiopathic partial epilepsy [13 children with benign epilepsy with centrotemporal spikes (BECTS), 17 children with idiopathic childhood occipital epilepsies (ICOE)], and to 30 healthy participants matched for age, sex, handedness, and socioeconomic status. Results did not support any impairment in overall neuropsychological functioning in participants with idiopathic partial epilepsies, whereas, isolated deficits did exist. The mean performance of the IPE group was significantly lower than the control group in six out of 12, neuropsychological measures: drawing (p < 0.01), digit span (p < 0.05), verbal learning (p < 0.01), object assembly (p < 0.01), similarities (p < 0.05), and vocabulary (p < 0.001). Results suggested that one should be cautious regarding neuropsychological and academic prognosis in the so-called benign idiopathic partial epilepsies of childhood.

Adolescent↗

PubMed2006

[Combating infectious disease using mathematical modelling].

When determining interventions against threatening infectious diseases such as HIV-infection, severe acute respiratory syndrome (SARS), smallpox and pandemic influenza, the use of mathematical models of the spread of infectious diseases is becoming increasingly popular. These models contribute to the structuring of the knowledge already available in various disciplines, to finding epidemiological connnections, to demonstrating lacunas within the pool of knowledge and to the comparison of the expected effects and costs of preventative and intervention measures. The use of models leads to a 'made-to-measure' analysis ofthe effects and costs of preventative and intervention measures which takes account of the specific characteristics of infectious diseases. The integration of knowledge from various disciplines can be supported by more research into the theoretical epidemiology of infectious disease and by better integration of mathematical models into policy development. The resulting and better foundations of this policy that are achieved by means of infectious disease modelling translate into more effective combating of infectious disease.

Cost-Benefit Analysis↗

PubMed1991

[The use of computers and mathematical methods for optimizing epidemic control measures with respect to measles infection].

The potentialities of computers for the study of the effectiveness of immunization have been demonstrated and the mathematical model for the prediction of the proportion of children, seronegative to measles, derived on the basis of the data on the average measles morbidity in different groups for a given period. A multifactor analysis of a large scope of data obtained in seroepidemiological survey and a retrospective analysis of measles morbidity on the basis of data collected in two districts of Moscow have been carried out with the use of computers and mathematical methods.

Age Factors↗

PubMed1991

Mathematical approach to horizontal and vertical magnification factors in rotational panoramic radiography--with attention to redundant shadows.

Rotational panoramic radiographs consist of two different images, the tomographic image and redundant shadows. Many authors have reported magnification factors for the tomographic image which include the term "real image", as proposed by McDavid et al. in 1983. However, a mathematical formula has never been proposed for ghost images, which redundant shadows projected only when the object is located between the center of rotation and the X-ray source. The purpose of this study was to propose a new mathematical approach for calculating the horizontal and the vertical magnification factors for ghost images. Using this approach, we investigated the effect of variations in the position of the object, its length, and its placement angle with respect to the X-ray beam. Since the object was assumed to be small, an approximated expression for film speed was integrated to determine the length of the object on the film in the horizontal dimension. The approximated and the geometric expressions proposed by Wakoh in 1988 were used to calculate the vertical dimension. Differences between the scanning and the film speeds were assumed to affect the horizontal magnification factors of the ghost image. In addition, differences in the setting position, length, and angle of the object affected the calculated values. Vertical magnification factors were considerably influenced by the Z coordinate of the position, even though the length and angle remained constant.

Artifacts↗

PubMed1991

[Development and analysis of mathematical models of the relationship "water pollution--health of the population"].

Hygienic aspects of building and analysis of mathematical models of the relationship water chemical stress--health of the population are presented in the article. The developed methodological approaches are approved at the example of two water objects--sources of centralized water supply of a big industrial city in the West Urals. The proposed methods of mathematical modelling make it possible to significantly broaden and deepen hygienic analysis and tasks for the development of further studies in the field of investigation of health effects of actual body burden of pollutants.(ABSTRACT TRUNCATED AT 400 WORDS)

Adolescent↗

PubMed1991

[A mathematical model of the regulation mechanism of Ca2+ concentration in lens in vivo].

In order to elucidate the regulation mechanism of homeostasis on intracellular Ca2+ concentration in lens in vivo, the authors proposed a new mathematical model based upon the model of Ca2+ active transport. The mathematical model has new factors: Ca2+ efflux and Ca2+ influx across the cell membrane related to the difference between intracellular and extracellular Ca2+ concentration. Changes in intracellular Ca2+ concentration were investigated by numerical simulation using this model. Ca2+ efflux (active transport) is increased with intracellular Ca2+ concentration and their relationship corresponds to a Michaelis-Menten reaction. Ca2+ influx increases with the Ca2+ permeable coefficient of cell membrane. These results are consistent with the experimental results is a qualitative way and indicate that the model is suitable to elucidate the regulation mechanism of intracellular Ca2+ concentration. From the theoretical point of view, therefore, it is suggested that intracellular Ca2+ concentration may depend on two factors: one is the Ca2+ dependence of the Ca2+ active transport system, the other the Ca2+ permeability of the cell membrane.

Calcium↗

PubMed1990

Mathematical modelling of metabolic pathways affected by an enzyme deficiency.

The regulation of metabolic pathways of the red cell affected by an enzyme deficiency is studied on the basis of comprehensive mathematical models. The main steps of such a theoretical approach are outlined considering individual alterations in the kinetic properties of two regulatory enzymes: pyruvate kinase and glucose-6-phosphate dehydrogenase. It is demonstrated that mathematical modelling helps to relate the observed changes of cellular quantities as shortened life-span, or as resistance against oxidative stress to alterations in the metabolic regulation.

Animals↗

PubMed1990

The game of the pentose phosphate cycle: a mathematical approach to study the optimization in design of metabolic pathways during evolution.

The optimization of the pathway structure of the pentose phosphate cycle is studied by means of abstraction to a model designed as a mathematical game of combinatorial optimization. The objective of the game is to convert pentoses into hexoses, which is the aim of the non-oxidative phase of the metabolic cycle, and it includes two kinds of hypotheses: (a) the hypothesis of the mechanisms based on the enzyme mechanisms available to cells, and (b) the hypothesis of simplicity which establishes that the optimal solution must have the least number of steps and the least number of carbons in every intermediate. A mathematical proof of the optimal solution of this problem is given, and it is demonstrated that such a solution is the same as occurs in cells. The Calvin cycle and the "L-type" of the pentose cycle are also studied by a similar method, and equivalent results are obtained. These results point out the role which the hypothesis of simplicity may have played in the evolution of metabolic pathways.

Biological Evolution↗

PubMedDate not supplied

[The mathematical modelling of the displacement of the hard palate tissues in conservative uranoplasty].

Presents a mathematical model of sparing uranoplasty techniques developed by the authors; using this model, a physician may assess before surgery the volume of tissues needed to close the palatal defect. Experience gained with 72 surgeries carried out in children with unilateral cleft palate confirms the desirability of preliminary computations. Mathematical models for the most prevalent sparing uranoplasty methods are offered.

Child↗

PubMed1990

[A mathematical model of membrane ion transport in psoriasis].

The authors discuss the problems related to mathematical simulation of ionic transport via cellular membrane and to identification of such models as exemplified by calcium metabolism. The examined model adequately reflects the characteristic features of the time course of ion transport in various stages of psoriasis, this permitting the use of this model in mathematical solving of the problem of optimal treatment of psoriasis patients. Graphs and results of estimations made with personal IBM-compatible computer are presented.

Biological Transport↗

PubMed1990

Journal deselection in a biomedical research library: a mediated mathematical approach.

A unique mathematical formula was developed to use for journal deselection decisions. The formula factors in subscription cost, shelving and storage cost, interlibrary loan cost, staffing cost, and use level to determine the institutional cost ratio; this ratio serves as an indicator of the cost-effectiveness of each subscription title. Once the institutional cost ratio was calculated for each of 537 titles, a committee of library staff and senior library customers reviewed the ranked list to decide which subscriptions should be canceled. The committee also considered possible exceptions based on subjective criteria such as availability at local libraries, unrecorded use, and relative importance of the journal. The preliminary cancellation list was then reviewed by the library's research users. They were able to justify library subscriptions to a few additional titles. This method enabled the library to cut its subscription costs by 46%, while cutting only 8% of the total use. In addition, by mediating the mathematical approach with human intervention, the library made these severe cuts without unduly distressing its patrons.

Book Selection↗

PubMed1990

Mathematical models of sow reproduction.

Nutrition affects reproduction, but the physiological mechanisms are not known. Defining those mechanisms is a high priority for animal scientists. This paper briefly describes mathematical models developed to aid in elucidating those mechanisms and which may be applied to predict animal performance. Two types of mechanistic mathematical models of sows are described, based respectively on nutrient partitioning and on metabolic and physiological principles. The nutrient partitioning model is relatively mature but the metabolic/physiological model is still at an early stage of development. The use of such models in the design and evaluation of feeding programmes, in understanding the biological system and in improving research efficiency are outlined. These two models are now being used as described, and it is anticipated that they, and other models, will make important contributions to the marked improvements in reproductive performance in commercial pig production that is anticipated during the next few years.

Animals↗

PubMed1990

[Woronoff rings in a mathematical model].

The width of a Woronoff ring is thought to be constant and independent of the diameter of the lesion. Clinical observations have allowed us to demonstrate that this is true only for lesions of a certain minimum size or greater. It is suggested that the paleness within the ring is caused by diffusion of a mediator from the psoriatic plaque into its environment. A mathematical model is formulated, and it is shown that clinical observations are consistent with the pathogenetic hypothesis. In addition, the mathematical model is used to derive some properties of the hypothetical mediator.

Diffusion↗