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The paper analyzes trends in development of advanced thermal irradiation technology which increases the three-dimensional selectivity of radiation and elevates the level of automatic targeted radiation source control through mathematical simulation of technology and irradiation objects. It also presents concepts of adaptive irradiation and problems in the construction of mathematical models.
Heart rate variability has been analyzed conventionally with time and frequency domain methods, which measure the overall magnitude of RR interval fluctuations around its mean value or the magnitude of fluctuations in some predetermined frequencies. Analysis of heart rate dynamics by methods based on chaos theory and nonlinear system theory has gained recent interest. This interest is based on observations suggesting that the mechanisms involved in cardiovascular regulation likely interact with each other in a nonlinear way. Furthermore, recent observational studies suggest that some indexes describing nonlinear heart rate dynamics, such as fractal scaling exponents, may provide more powerful prognostic information than the traditional heart rate variability indexes. In particular, the short-term fractal scaling exponent measured by the detrended fluctuation analysis method has predicted fatal cardiovascular events in various populations. Approximate entropy, a nonlinear index of heart rate dynamics, that describes the complexity of RR interval behavior, has provided information on the vulnerability to atrial fibrillation. Many other nonlinear indexes, e.g., Lyapunov exponent and correlation dimensions, also give information on the characteristics of heart rate dynamics, but their clinical utility is not well established. Although concepts of chaos theory, fractal mathematics, and complexity measures of heart rate behavior in relation to cardiovascular physiology or various cardiovascular events are still far away from clinical medicine, they are a fruitful area for future research to expand our knowledge concerning the behavior of cardiovascular oscillations in normal healthy conditions as well as in disease states.
Due to noise and irregularity of the gradient image, watershed algorithm used to segment images generally leads to over-segmentation, which is unacceptable. A novel watershed algorithm, which combines with some concepts of wavelet analysis and mathematic morphology, is proposed in this paper. The test shows that this method can solve the problem of over-segmentation and achieve the anticipative goal.
BACKGROUND: Current pressure on secondary schools to increase ability grouping has raised concerns about the impact of setting on pupils' self-concepts. Evidence from previous research is conflicting. A multidimensional measure and multilevel modelling promise to clarify the effects. AIMS: This paper aims to examine the effects of structured ability grouping on year 9 pupils' self-concepts. SAMPLES: The sample comprises over 3000 year 9 pupils (aged 13-14 years) in 45 mixed secondary comprehensive schools in England. The schools represent three levels of ability grouping in the lower school (years 7 to 9). METHODS: Pupils responded to a multidimensional self-concept scale measuring academic and general facets of the self-concept. Measures of attainment were collected in English, mathematics and science. Multilevel modelling was used to examine the effect of the type of school on the general facets of the pupils' self-concept and the effects of setting in each curriculum subject on the academic facets of the self-concept. RESULTS: Pupils' general self-concept was higher in the group of schools with moderate levels of setting. The degree of setting in mathematics and science had no effect on the corresponding academic self-concepts but setting in English tended to lower the self-concepts of the higher attaining pupils and raise the self-concepts of lower attaining pupils. Gender differences were consistent with previous research, with boys having significantly higher self-concept scores than girls, except in English. These findings indicate that the degree of stratification in schools can have an impact on adolescents' self-esteem and views of themselves in school.
A general mathematical model for population dispersal featuring long range taxis is presented and exemplified by the dispersal episode of the Africanized honey bees (Apis mellifera adansonii) throughout the American Continent. The mathematical model is a discrete-time and nonlocal model represented by an integrodifference recursion. A new taxis concept is defined and introduced into the mathematical model by an appropriate modification of the redistribution kernel. The model is capable of predicting the natural barrier for the expansion of the Africanized honey bees in the southern part of the Continent due to low winter temperatures. It also describes a sensitive expansion velocity with respect to the quality of resources, which can explain the AHB's astounding spread rate, by using two different kinds of population dynamics strategies, one for a resourceful environment and the other for poor regions.
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This work proposes a mathematical model for the electrochemical remediation of clayey soils based on the total volume concept for a two-phase system. The mathematical formulation was done including contributions from theories for: groundwater, membranes, porous electrodes and environmental soil chemistry. The resulting model accounts for: free and complexed species in the soil matrix and the pore solution; chemical reactions taking place on either phase and/or between phases; a dynamic soil surface charge affected by the ion content of the pore solution; and electroneutrality of the total volume. Soil surface charge was included in a modified Ohm's law (voltage gradient) and in a modified Schlög's law (convective movement). Numerical implementation was done using orthogonal collocation on finite elements for spatial derivatives, and forward finite differences for time derivatives. Visual Fortran supported by IMSL subroutines was used for computer simulation. Model predictions were successfully compared with reported experimental data. Also, an analysis of pH profiles through the soil is provided for conditions when parameters including hydrostatic head, applied current density and initial pH are modified.
This paper assembles current concepts about bone fatigue and osteonal remodeling into a mathematical theory of the repair of fatigue damage and the etiology of stress fracture. The model was used to address three questions. (a) How does the half-life of fatigue damage compare with the duration of the remodeling cycle? (b) Does the porosity associated with the remodeling response contribute to stress fracture? (c) To what extent is a periosteal callus response necessary to augment repair by remodeling? To develop the theory, existing experimental data were used to formulate mathematical relationships between loading, damage, periosteal bone formation, osteonal remodeling, porosity, and elastic modulus. The resulting nonlinear relationships were numerically solved in an iterative fashion using a computer, and the behavior of the model was studied for various loading conditions and values of system parameters. The model adapted to increased loading by increasing remodeling to repair the additional damage and by adding new bone periosteally to reduce strain. However, if too much loading was encountered, the porosity associated with increased remodeling caused the system to become unstable; i.e., damage, porosity, and strain increased at a very high rate and without limit. It is proposed that this phenomenon is the equivalent of a stress fracture and that its biological and mechanical elements are significant in the etiology of stress fractures. Additional experiments must be done to test the model and provide better values for its parameters. However, the instability characteristic is relatively insensitive to changes in model parameters.
Between 5% and 8% of school-age children have some form of memory or cognitive deficit that interferes with their ability to learn concepts or procedures in one or more mathematical domains. A review of the arithmetical competencies of these children is provided, along with discussion of underlying memory and cognitive deficits and potential neural correlates. The deficits are discussed in terms of three subtypes of mathematics learning disability and in terms of a more general framework for linking research in mathematical cognition to research in learning disabilities.
Although there is general agreement that cell growth and division are functionally coordinated, the mechanisms that link the two processes are poorly understood. In this study, we have developed a mathematical model based on current biological concepts of the signaling transduction pathways involved in cell growth, which predicts that cell growth rate is proportional to cell surface area at birth. To investigate the relationship between growth control and cell division, we then applied our mathematical model to three classic experiments measuring cycle time versus cell birth size in fission yeast and Xenopus laevis, and the cell cycle delay in mammalian cells after serum withdrawal. When coupled to a cell cycle exhibiting 'sizer' and 'timer' phases, we show that a simple model in which growth rate is proportional to the cell surface area immediately after division reproduces the experimental observations including the relationship between cycle time and birth size in fission yeast and Xenopus laevis. The model also accounts for the cell cycle delay seen in restriction point experiments performed in HeLa cells.
Reciprocal effects models of longitudinal data show that academic self-concept is both a cause and an effect of achievement. In this study this model was extended to juxtapose self-concept with academic interest. Based on longitudinal data from 2 nationally representative samples of German 7th-grade students (Study 1: N = 5,649, M age = 13.4; Study 2: N = 2,264, M age = 13.7 years), prior self-concept significantly affected subsequent math interest, school grades, and standardized test scores, whereas prior math interest had only a small effect on subsequent math self-concept. Despite stereotypic gender differences in means, linkages relating these constructs were invariant over gender. These results demonstrate the positive effects of academic self-concept on a variety of academic outcomes and integrate self-concept with the developmental motivation literature.
Medical image compression can significantly enhance the performance of picture archiving and communication systems and may be considered an enabling technology for telemedicine. The wavelet transform is a powerful mathematical tool with many unique qualities that are useful for image compression and processing applications. Although wavelet concepts can be traced back to 1910, the mathematics of wavelets have only recently been formalized. By exploiting spatial and spectral information redundancy in images, wavelet-based methods offer significantly better results for compressing medical images than do compression algorithms based on Fourier methods, such as the discrete cosine transform used by the Joint Photographic Experts Group. Furthermore, wavelet-based compression does not suffer from blocking artifacts, and the restored image quality is generally superior at higher compression rates.
Students were asked to select one of two analogous problems in order to solve algebra word problems. In Experiment 1, one problem was less inclusive and the other was more inclusive than a test problem. The students judged the complexity and similarity of problems, selected analogous problems, and used the solutions to solve test problems. They performed significantly better on the test problems when given the more inclusive solutions, but used perceived similarity rather than inclusiveness to select analogous problems. The same pattern of results occurred in Experiment 2, in which isomorphic problems replaced the more inclusive problems. The results show that students are deficient in selecting good analogies, both from the same category (Experiment 1) and from a different category (Experiment 2). Students who saw the analogous solutions (Experiment 3) or were majoring in mathematics (Experiment 4) were more likely to select an isomorphic problem over a less inclusive problem, but were not more likely to select a more inclusive over a less inclusive problem.
A new concept in reaction-based chemical analysis is introduced and theoretically described. By utilization of the variability in electrophoretic mobilities among charged species, spatially distinct zones of chemical reagents can be electrophoretically merged under the influence of an applied electric field. Electrophoretically mediated microanalysis (EMMA) exploits this phenomenon as a basis for chemical analysis utilizing capillary electrophoretic systems. EMMA is described in terms of the four stages required for reaction-based analysis: (1) analyte and analytical reagent metering; (2) initiation of reaction; (3) control of reaction conditions and product formation; (4) detection of species whose production or depletion is indicative of the concentration or quantity of the analyte of interest. The method is illustrated by the enzymatic oxidation of ethanol to acetaldehyde by alcohol dehydrogenase with the concurrent reduction of NAD+ to NADH monitored at 340 nm. Experimental results for both substrate and enzyme determinations are shown to agree with the presented theory.
This is a personal commentary on the history and future prospects of mathematical modeling and analysis in biochemical engineering. Major transitions in these fields were driven by the appearance of the Aiba, Humphrey, and Millis text, Fredrickson's guidance on conceptualizing mathematical representations of cell populations, and Ramkrishna's development of the cybernetic modeling approach. The value of mathematical models to organize data, to consider interactions in complex systems in a rational way, to correct the conventional wisdom, and to understand essential qualitative features of biological systems has been clearly documented in prior research. The impact of this research in biotechnology discovery has so far been limited, but this will change in the future if we are adept in recognizing emerging opportunities and in integrating new concepts and tools into our research. Mathematical structures and methods, allied with extraordinary contemporary computing power, are essential to the emerging field of functional genomics. Important in this quest is a hierarchy of powerful modeling, analysis, and computational tools which can capture essential quantitative features of available experimental data and use these effectively for analysis and design of metabolism.
A set of linear pathways often does not capture the full range of behaviors of a metabolic network. The concept of 'elementary flux modes' provides a mathematical tool to define and comprehensively describe all metabolic routes that are both stoichiometrically and thermodynamically feasible for a group of enzymes. We have used this concept to analyze the interplay between the pentose phosphate pathway (PPP) and glycolysis. The set of elementary modes for this system involves conventional glycolysis, a futile cycle, all the modes of PPP function described in biochemistry textbooks, and additional modes that are a priori equally entitled to pathway status. Applications include maximizing product yield in amino acid and antibiotic synthesis, reconstruction and consistency checks of metabolism from genome data, analysis of enzyme deficiencies, and drug target identification in metabolic networks.
A small proportion of people experiencing a sexually transmitted disease (STD), who are frequently infected or often transmit the infection, has been referred to as the "core." Though a prominent paradigm in the epidemiology of STDs, there is confusion about the meaning of the core. The term has been used to refer variously to people who are infected a large proportion of the time, infect more than one other person, are repeatedly infected, or are prostitutes or their clients and to geographic areas with large numbers of cases. Three perspectives that have contributed to the development of the concept of an STD core were identified: mathematical, clinical-epidemiologic, and sociocultural. These different perspectives share the common aim of identifying strategic points of intervention to reduce STDs. The value of the concept of an STD core will ultimately derive from its utility in lowering STD rates.
This manuscript is concerned with concepts rather than abstruse details or mathematics. Discussed are: competition; extended competition, proposed for competition in the strict sense, extended and modified by all related interactions including predation, parasitism, disease, and even cooperation, all of which can be "weapons of competition"; competitive repulsion, proposed for the sum of forces that determine spacings, including ecologic spacings, of individuals and populations; Darwin (biotic) equilibriums; competitive extinction, Gause's principle, limited and limiting resources, and single-resource competition; de facto coexistence of competing species, exemplified by green plants competing for sunlight; niche competition; the two concepts of competitive exclusion; devision of resources and of their utilizers; cause and effect in real situations; and niches, niche overlap, and coexistence. Stressed is the complexity of the real world, and the confusion that can and does arise from modeling it too simply.