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Results for “Mathematical Concepts”

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PubMed1998

Self-concept of academic ability as a function of sex, age, and academic achievement among African adolescents.

This study examined (a) sex and age variations for scores on Self-concept of Academic Ability and academic achievement among 244 African adolescents attending a coeducational high school and (b) correlations between scores on Self-concept of Academic Ability and academic achievement by sex and age. No significant sex differences were found, but there were significant age differences on the Self-concept scores and measures of English, science, and history but not in mathematics. A significant positive correlation was found between Self-concept scores and academic achievement for boys and girls and in all age groups, but the magnitude of the correlations with achievement in mathematics was stronger among boys than among girls.

Achievement↗

PubMed2001

Highly efficient synthesis of ampicillin in an "aqueous solution-precipitate" system: repetitive addition of substrates in a semicontinuous process.

The synthesis of ampicillin catalyzed by Escherichia coli penicillin acylase was optimized in an aqueous system with partially dissolved antibiotic nucleus 6-aminopenicillanic acid (6-APA). The yields of both 6-APA and acyl donor could be improved by repetitively adding substrates to the reaction, allowing the concentration of 6-APA to remain saturated throughout. In this reaction concept, with four subsequent additions of substrates, 97% conversion of 6-APA and 72% of D-(-)-phenylglycine methyl ester (D-PGM) to ampicillin was achieved. The synthetic potential of this concept was estimated using a mathematical model which showed that by increasing the amount of added substrates a nearly quantitative conversion of 6-APA and 85% conversion of acyl donor into ampicillin could be achieved.

Ampicillin↗

PubMed1992

The chaotic behaviour of resting human respiration.

The study of non-linear mathematics has led to the concept of an attractor that can confine to within certain boundaries the path traced out in multidimensional space when a variable is plotted against itself delayed by various lag times. The type of attractor present can be determined by monitoring the exponential rate (called a Lyapunov exponent) at which almost identical values within a time series become dissimilar. Lyapunov exponents estimated from data collected during the normal resting breathing of eight adults were all positive, end-tidal PCO2 had the lowest Lyapunov exponent (0.06 +/- 0.01 bits/s; Mean +/- SE), breath and expiratory duration had the highest exponents (0.23 bits/s). The results indicate that resting respiration is chaotic. This chaotic behaviour may allow fast and flexible responses to sudden changes, allow if necessary complete readjustment of the control parameters, and may be involved in the phase locking of respiration to external stimuli.

Adolescent↗

PubMed1993

An echocardiographic study of the fluid mechanics of obstruction in hypertrophic cardiomyopathy.

OBJECTIVES: The goal of this study was to investigate the hydrodynamic cause of mitral-septal contact and obstruction in patients with hypertrophic cardiomyopathy. BACKGROUND: Mitral-septal apposition has been shown to be the cause of obstruction in patients with hypertrophic cardiomyopathy. With obstruction, characteristic continuous wave Doppler tracings show an increasing acceleration of flow. (Tracing is concave to the left.) METHODS: We studied 24 consecutive patients who had a Doppler echocardiographic pressure gradient > or = 36 mm Hg. We pursued two lines of inquiry. 1) Before the onset of obstruction, we systematically measured the angle between the direction of left ventricular Doppler color flow and the protruding mitral leaflet in early systole. 2) After the onset of obstruction, we qualitatively analyzed the concave contour of the continuous wave Doppler tracings in our patients and developed a hydrodynamic theory of the obstruction phase to explain the characteristic tracings. We present a mathematic model to support this concept. RESULTS: We measured 129 angles. Just before mitral-septal contact, the protruding mitral leaflet projects at a mean 40 degrees and 45 degrees relative to flow in the apical long-axis and apical five-chamber views, respectively. At mitral-septal contact, the obstructing leaflet projects at a mean 52 degrees and 58 degrees relative to flow in the same respective views. Even very early in systole, at leaflet coaptation, 11 of 23 patients had angles > 15 degrees relative to flow. After mitral-septal apposition, obstruction across a cowl-shaped orifice begins. During this stage, the obstructing leaflet projects at a mean 55 degrees and 63 degrees relative to flow. In 22 patients, the continuous wave Doppler tracing of the left ventricular outflow jet showed an increasing acceleration of flow. CONCLUSIONS: Just before mitral-septal contact, the protruding leaflets project at high angles relative to flow. At these high angles, flow drag, the pushing force of flow, is the dominant hydrodynamic force on the protruding leaflet and appears to be the immediate cause of obstruction. The high angle between flow direction and the protruding leaflet precludes significant Venturi effects. Even earlier in systole, at leaflet coaptation, flow drag is dominant in half of the patients, with angles relative to flow > 15 degrees. After obstruction is triggered, it appears from our data and model that the leaflet is forced against the septum by the pressure difference across the orifice. The increasing acceleration of Doppler flow is explained by a time-dependent amplifying feedback loop in which the rising pressure difference across the orifice leads to a smaller orifice and a higher pressure difference.

Adult↗

PubMedDate not supplied

Radiological laser film scanner sampling artifact.

Artifacts seen on laser digitized radiographs are analyzed and mathematically explained based on the concept of image contrast. Our investigation considered the following determinants: (a) laser spot size, (b) signal processing components, (c) image characteristics, and (d) observer performance. A functional relationship between the sampling interval, laser spot size, and the contrast of the artifact seen on the digitized image is derived. This relationship is verified experimentally using a variable spot size laser source and sampling at interval of 175.0 microns. The problem of digitizing artifact seen on film images obtained with anti-scatter grids is discussed.

Analog-Digital Conversion↗

PubMed2006

GINsim: a software suite for the qualitative modelling, simulation and analysis of regulatory networks.

This paper presents GINsim, a Java software suite devoted to the qualitative modelling, analysis and simulation of genetic regulatory networks. Formally, our approach leans on discrete mathematical and graph-theoretical concepts. GINsim encompasses an intuitive graph editor, enabling the definition and the parameterisation of a regulatory graph, as well as a simulation engine to compute the corresponding qualitative dynamical behaviour. Our computational approach is illustrated by a preliminary model analysis of the inter-cellular regulatory network activating Notch at the dorsal-ventral boundary in the wing imaginal disc of Drosophila. We focus on the cross-regulations between five genes (within and between two cells), which implements the dorsal-ventral border in the developing imaginal disc. Our simulations qualitatively reproduce the wild-type developmental pathway, as well as the outcome of various types of experimental perturbations, such as loss-of-function mutations or ectopically induced gene expression.

Animals↗

PubMed2003

Measurement of heart rate variability by methods based on nonlinear dynamics.

Heart rate (HR) variability has been conventionally analyzed with time and frequency domain methods, which measure the overall magnitude of R-R interval fluctuations around its mean value or the magnitude of fluctuations in some predetermined frequencies. Analysis of HR 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 HR dynamics, such as fractal scaling exponents, may provide more powerful prognostic information than the traditional HR variability indexes. In particular, short-term fractal scaling exponent measured by detrended fluctuation analysis method has been shown to predict fatal cardiovascular events in various populations. Approximate entropy, a nonlinear index of HR dynamics, which describes the complexity of R-R interval behavior, has provided information on the vulnerability to atrial fibrillation. There are many other nonlinear indexes, eg, Lyapunov exponent and correlation dimensions, which also give information on the characteristics of HR dynamics, but their clinical utility is not well established. Although concepts of chaos theory, fractal mathematics, and complexity measures of HR 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.

Atrial Fibrillation↗

PubMed2006

Combinatorial decomposition of an outbreak signature.

We use mathematically rigorous definitions of epidemiological concepts in order to derive a sequential combinatorial model of disease outbreak decomposition. We define the idea of a population specific 'disease signature' and use this in order to decompose and further understand outbreaks as incidents of spatial and temporal spread of disease exposure both in, and across, populations. This allows us to differentiate between different disease spread scenarios with a level of sensitivity that previous models were unable to provide. This perspective leads us to propose a new practical definition for 'outbreak'. In addition, we are able to use this model to understand, estimate, and, in some cases, correct for, the likely instances of reporting error inherent in disease surveillance. We demonstrate our model first with a hypothetical outbreak scenario and then in an analysis of suspected outbreaks of waterborne diseases in Massachusetts (MA) in 1995.

Adult↗

PubMed2003

Fratricide: a mechanism for T memory-cell homeostasis.

Immunological memory depends on a self-renewing pool of antigen-specific T memory (Tm) cells but the homeostatic mechanisms that maintain the size and diversity of the pool are largely unknown. Competition for space or growth factors has been suggested as a mechanism but how these factors themselves are regulated is unclear. We suggest that Tm-cell fratricide by Fas-mediated apoptosis results in a density-dependent death rate that controls the size of the pool without requiring competition for resources or an external quorum-sensing mechanism. A mathematical model based on this concept predicts the known behaviour of the Tm pool, including observed differences in heterogeneity of the CD4 and CD8 compartments and might provide a paradigm for homeostasis of other haematopoietic-cell populations.

Animals↗

PubMedDate not supplied

Covalent coupling method for lipase immobilization on controlled pore silica in the presence of nonenzymatic proteins.

Candida rugosa lipase was covalently immobilized on silanized controlled pore silica previously activated with glutaraldehyde in the presence of nonenzymatic proteins. This strategy is suggested to protect the enzyme from aggregation effects or denaturation that occurs as a result of the presence of silane precursors used in the formation of the silica matrix. The immobilization yield was evaluated as a function of the lipase loading and the additive type (albumin and lecithin) using statistical concepts. In agreement with the mathematical model, the maximum coupling yield (32.2%) can be achieved working at high lipase loading (450 units x g(-1) support) using albumin as an additive. In these conditions, the resulting immobilized lipase exhibits high hydrolytic (153.2 U x mg(-1)) and esterification (337.6 mmol x g(-1) x min) activities. The enhanced activity of the final lipase derivative is the sum of the benefits of the immobilization (that prevents enzyme aggregation) and the lipase coating by additives that increases the accessibility of active sites to the substrate.

Butanols↗

PubMed1997

Age and gender differences in the self-esteem of Chinese children.

A Chinese version of the Self-Description Questionnaire 1 (SDQ-1; Marsh, 1988) was used to investigate age and gender differences in a sample of 303 male and 296 female 10-year-old children and 116 male and 116 female 13-year-old children attending typical Beijing public schools. Significant Age x Gender interaction effects were found on all 8 SDQ-1 scales. Main effects for age were found on the Physical Abilities, Reading, and School subscales and for gender on the same three subscales plus Peer Relations. Further analysis indicated that the older girls tended to report significantly lower self-esteem than both the younger girls and older boys in the areas of physical abilities, reading, mathematics, and general self-concept. The boys reported more positive self-perceptions on most nonacademic self-scales, but both the older boys and older girls reported less favorable self-esteem than their younger peers on the scales for reading and school in general.

Adolescent↗

PubMed2006

Systems-based medicine approaches to understand and treat complex diseases. The example of multiple sclerosis.

Systems medicine is an emerging concept that acknowledges the complexity of a multitude of non-linear interactions among molecular and physiological variables. Under this new paradigm, rather than a collection of symptoms, diseases are seen as the product of deviations from a robust steady state compatible with life. This concept requires the incorporation of mathematics and physics to the more classical arsenal of physiology and molecular biology with which physicians are trained today. This review explores the diverse types of information that can be accumulated towards the understanding of multiple sclerosis (MS), a complex autoimmune disease that targets the central nervous system (CNS). The challenge of data integration and modeling of dynamical systems is discussed in the context of disease susceptibility and response to treatment. A theoretical framework that supports the use of combination therapy is also presented.

Animals↗

PubMed2006

Pairwise alignment of protein interaction networks.

With an ever-increasing amount of available data on protein-protein interaction (PPI) networks and research revealing that these networks evolve at a modular level, discovery of conserved patterns in these networks becomes an important problem. Although available data on protein-protein interactions is currently limited, recently developed algorithms have been shown to convey novel biological insights through employment of elegant mathematical models. The main challenge in aligning PPI networks is to define a graph theoretical measure of similarity between graph structures that captures underlying biological phenomena accurately. In this respect, modeling of conservation and divergence of interactions, as well as the interpretation of resulting alignments, are important design parameters. In this paper, we develop a framework for comprehensive alignment of PPI networks, which is inspired by duplication/divergence models that focus on understanding the evolution of protein interactions. We propose a mathematical model that extends the concepts of match, mismatch, and gap in sequence alignment to that of match, mismatch, and duplication in network alignment and evaluates similarity between graph structures through a scoring function that accounts for evolutionary events. By relying on evolutionary models, the proposed framework facilitates interpretation of resulting alignments in terms of not only conservation but also divergence of modularity in PPI networks. Furthermore, as in the case of sequence alignment, our model allows flexibility in adjusting parameters to quantify underlying evolutionary relationships. Based on the proposed model, we formulate PPI network alignment as an optimization problem and present fast algorithms to solve this problem. Detailed experimental results from an implementation of the proposed framework show that our algorithm is able to discover conserved interaction patterns very effectively, in terms of both accuracies and computational cost.

Algorithms↗

PubMed2005

A reliable index for the prognostic significance of blood pressure variability.

OBJECTIVES: This study presents a reliable index inspired by the total variability concept of real analysis in mathematics, called average real variability (ARV), for the prognostic significance of blood pressure variability (BPV) overcoming the pitfalls of the commonly used standard deviation (SD). BACKGROUND: Recent studies have suggested that an increase in BPV is associated with an increase in subsequent cardiovascular events/complications. However, there are other studies where the cited association was not found or was lost in the presence of other well-known risk factors. An explanation for these apparently contradictory results may be the selection of the variability index used (SD). METHODS: Ambulatory blood pressure monitoring in 312 subjects aged > or = 55 years. Logistic regression models and survival methods were used to establish the prognostic significance of awake systolic BPV: in particular, (i) the performance of ARV versus SD, and (ii) the value of BPV relative to other well-known risk factors. RESULTS: The analyses using the ARV index show a statistically significant relative risk equal to 4.548 (P = 0.006) for the group with high BPV with respect to the low BPV group (reference level); in contrast, the corresponding relative risk associated to the SD index was not statistically significant. Furthermore, ARV exhibited a similar predictive value to systolic blood pressure. CONCLUSIONS: The proposed ARV index is a more reliable representation of time series variability than SD and may be less sensitive to the relative low sampling frequency of the ambulatory blood pressure monitoring devices. The results suggest that ARV adds prognostic value to the ABPM and could prompt the use of therapeutic measures to control BPV.

Aged↗

PubMed1999

A computer-assisted training/monitoring system for TURP structure and design.

A generic framework for a computer-assisted system for both soft tissue endoscopic surgery and surgical training is being researched and developed. The concept demonstrator is a specific system for transurethral prostatic resection (TURP). The main novelty of the research is that it is not confined to an in vitro trainer system. An in vivo monitoring version of the system, for use in the operating theater, is also being researched. This paper presents the framework's structure and design using the United Modeling Language. It also discusses and justifies the underlying information technologies chosen to implement this approach. Object-oriented concepts and well-proven mathematical tools have been adopted as the foundation of this research and development. The rationale for having chosen such tools is presented. The objectives are to arrive at a system which is modular, general, and reusable.

Computer Simulation↗

PubMed2005

Evolution of genetic potential.

Organisms employ a multitude of strategies to cope with the dynamical environments in which they live. Homeostasis and physiological plasticity buffer changes within the lifetime of an organism, while stochastic developmental programs and hypermutability track changes on longer time-scales. An alternative long-term mechanism is "genetic potential"--a heightened sensitivity to the effects of mutation that facilitates rapid evolution to novel states. Using a transparent mathematical model, we illustrate the concept of genetic potential and show that as environmental variability decreases, the evolving population reaches three distinct steady state conditions: (1) organismal flexibility, (2) genetic potential, and (3) genetic robustness. As a specific example of this concept we examine fluctuating selection for hydrophobicity in a single amino acid. We see the same three stages, suggesting that environmental fluctuations can produce allele distributions that are distinct not only from those found under constant conditions, but also from the transient allele distributions that arise under isolated selective sweeps.

Journal Article↗

PubMed2002

Applications of artificial neural network in AIDS research and therapy.

In recent years considerable effort has been devoted to applying pattern recognition techniques to the complex task of data analysis in drug research. Artificial neural networks (ANN) methodology is a modeling method with great ability to adapt to a new situation, or control an unknown system, using data acquired in previous experiments. In this paper, a brief history of ANN and the basic concepts behind the computing, the mathematical and algorithmic formulation of each of the techniques, and their developmental background is presented. Based on the abilities of ANNs in pattern recognition and estimation of system outputs from the known inputs, the neural network can be considered as a tool for molecular data analysis and interpretation. Analysis by neural networks improves the classification accuracy, data quantification and reduces the number of analogues necessary for correct classification of biologically active compounds. Conformational analysis and quantifying the components in mixtures using NMR spectra, aqueous solubility prediction and structure-activity correlation are among the reported applications of ANN as a new modeling method. Ranging from drug design and discovery to structure and dosage form design, the potential pharmaceutical applications of the ANN methodology are significant. In the areas of clinical monitoring, utilization of molecular simulation and design of bioactive structures, ANN would make the study of the status of the health and disease possible and brings their predicted chemotherapeutic response closer to reality.

Acquired Immunodeficiency Syndrome↗

PubMedDate not supplied

[Regulation of nitrate metabolism through anion polycompartmentation in plant roots].

A new concept illustrated by a corresponding mathematical model of nitrate metabolism regulation is proposed. The model is based on root nitrate compartmentation in several functional pools: storage, metabolic and a mobile pool which is intended for translocation to shoots. Data on nitrate uptake, compartmentation, reduction in intact roots and translocation to shoots were obtained on steady-state wheat seedlings grown at 25 and 12 degrees C in the root zone. The net uptake, influx/efflux ratio, mobile pool size and translocation changed depending on the medium temperature. The oscillations of the net uptake rate, nitrate tissue concentration were revealed and the effect of temperature on these changes was demonstrated. The scheme of regulation is based on the idea that net uptake through nitrate influx/efflux is under the control of the nitrate the mobile pool whose size was dependent on the nitrate translocation into shoots. The mathematical model is represented by a system of ordinary differential equations simplified according to the time hierarchy of reactions. It has a limit cycle at definite values of the parameters. The model postulates the mechanism of a positive feed-back regulation of the transfer of newly absorbed nitrate into translocated pool formed in the root cortex. Theoretical results are verified experimentally.

Anions↗