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PubMed1994

The effect of mathematics and coordinate system on comparability and "dependencies" of nucleic acid structure parameters.

This paper critically examines the methodologies used to analyze nucleic acid three-dimensional structure based on guidelines set at a 1988 EMBO workshop. The implications of these analyses cannot be fully understood without a thorough knowledge of how the numbers are calculated. This paper addresses one aspect of the calculations, namely the observed correlations between various parameters. These correlations are addressed in the mathematics by explicitly incorporating the concept of a pivot point, which is the point about which a base rotates as it buckles, propeller twists and opens. Pivot points enable one to model the physical motion of bases more accurately. As a result, they greatly reduce and/or eliminate the statistical correlations between rotational and translational parameters found in other approaches. The correlations that are reduced or eliminated are actually artifacts of the mathematics employed and do not reflect true structural properties of nucleic acids. The mathematics we have developed, including the mathematics of pivot points, are presented in the companion paper. Here, we explain how some of the observed correlations occur as a by-product of the method of calculation, while others are truly structural, and we show how optimum pivot points can be determined to minimize artifactual correlations. The observation that experimental bases often rotate about the long axis in a "propeller" motion as well as rotate about the Z-axis of each base, "opening" into the major groove, is evident in the location of the optimum region for the pivot point as determined in this study. We consider locating a pivot point as a calibration step to increase the agreement between physical intuition and the mathematics of our program.

Base Sequence↗
PubMed2004

Mathematical comparison between volume of distribution (V) and volume of distribution at steady-state (Vss) utilizing model-independent approach.

Pharmacokinetic textbooks state that the (apparent) volume of distribution based on drug concentration in plasma (V or Vbeta) is always greater than the volume of distribution (apparent) under steady state conditions (Vss), but do not provide a general model-independent mathematical proof. Wagner's mathematical comparison between Vbeta and Vss is based on microscopic rate constants of either specific models and is restricted solely to the two-compartment open body model. Nakashima and Benet utilizing a model-dependent approach showed a mathematical relationship between Vbeta and Vss for a multicompartment model, but again by using microscopic model constants. The limitation of these two above mentioned mathematical comparisons is the necessity of knowledge of the model's structure and its microscopic rate constants. The present article describes a new non-compartmental, model-independent, general mathematical proof for Vbeta to be always greater than Vss. This new method does not require any knowledge of microscopical rate constants and is based solely on an exponentially decreasing function, which is the common way to describe drug disposition following i.v. bolus.

Algorithms↗
PubMed1994

Nucleic acid structure analysis. Mathematics for local Cartesian and helical structure parameters that are truly comparable between structures.

Analyzing nucleic acid structures in a comparable manner has become increasingly important as the number of solved structures has increased. This paper presents the concepts, mathematics, theorems, and proofs that form the basis of a new program to analyze three-dimensional DNA and RNA structures. The approach taken here provides numerical data in accordance with guidelines set at a 1988 EMBO workshop. Mathematical definitions are provided for all local structural parameters described in the guidelines. The definitions satisfy the guideline requirements while preserving the original physical intuition of the parameters. In particular, the rotational parameters are true rotations based on a simple physical model (net rotation at constant angular velocity), not Euler angles or angles between vectors and planes as is the case with other approaches. As a result, the mathematical definitions are symmetrical with the property that a 5 degrees tilt is the same as a 5 degrees roll and a 5 degrees twist, except that the rotations take place about different axes. In other approaches, a 5 degrees tilt can mean a different amount of net rotation than a 5 degrees roll or a 5 degrees twist. A second unique feature of the mathematics is that it explicitly incorporates the concept of a pivot point, which is the point about which a base in a base-pair rotates as it buckles, propeller twists, and opens. Pivot points enable one to model the physical motion of bases more accurately. As a result, they greatly reduce and/or eliminate the statistical correlations between rotational and translational parameters that arise as mathematically induced artifacts in other approaches. This paper, together with the statistical analysis in the companion paper for determining the locations of the pivot points, provides everything needed to understand the output of the program as it relates to individual structures.

Base Composition↗
PubMed1997

The S factor--a new derived hemodynamic oxygenation parameter--a useful tool for simplified mathematical modeling of global problems of oxygen transport.

We describe a new derived hemodynamic oxygenation parameter, the S factor (S). The factor is based on oxygen delivery and oxygen consumption and can range from -3 to 1. It allows simplified mathematical modeling of clinical problems of oxygen transport and can be applied to many clinical situations. A new hemodynamic oxygenation parameter, the S factor (S), is introduced as an aid to mathematical modeling. It is defined as follows: [formula: see text] (DO2 = oxygen delivery, VO2 = oxygen consumption) S can theoretically vary from -3 (DO2 = VO2) to +1 (VO2 = 0). When DO2/VO2 = 4 (ie. OER = 0.25), S = 0. An S < 0 implies utilization of reserve oxygen transport capacity. An S > 0 implies increased oxygen delivery in relation to oxygen consumption (ie. "shunted oxygen delivery"). By algebraic manipulation and substitution of the components of DO2 into Equation 1: DO2 = Q x Ca x 10 DO2 = Q [(Hb)(Sat)(1.36) + PaO2(.0031)] 10 (2) the following equations can be derived: [formula: see text] [formula: see text] Ca - Cv (Ca = arterial content, Cv = venous content) can be determined by substituting components of oxygen consumption: VO2 = Q (Ca - Cv) x 10 (5) into equation 1 and solving for Ca - Cv. [formula: see text] Equation 6 can be simplified to: [formula: see text] A previously defined relationship between mixed venous PO2 (PvO2) and DO2/VO2 (where calculated P50 is 26.6 +/- 1.0) can be used to modify S in a clinically relevant manner. PvO2 = 5.44D O2/VO2 + 18.16 (8) The relationship between S and PvO2 can be defined by substituting Equation 4 into Equation 1 and solving for PvO2 PvO2 = [21.76/(1-S)] + 18.16 (9) As an example, at a PvO2 of 28 torr (anaerobic threshold), S = -1.2. The relationship between PvO2 and S is shown in Figure 1. S, which can also be defined as 1-4(VO2/DO2) or 1-4(OER), is a useful tool for mathematical modeling of global problems of oxygen transport because the previously derived equations with the S value allow the components of oxygen transport to be interrelated in a clinically relevant manner. Additional advantages of using S in mathematical modeling are: 1. Conceptually it 'fits' in that in regards to the sign (+ or -), as a -S implies utilization of reserve oxygen transport capacity and a +S implies wasted or excess oxygen delivery (shunted). 2. These concepts are easily quantified using the S factor. 3. It 'spreads out' the difference between values for parameters (OER or S) integrating components of oxygen transport, ie. in the 'normal state' regarding oxygen transport, OER = 0.25 and S = 0. At the anaerobic threshold (PvO2 = 28 torr), OER = 0.55 and S = -1.2. Thus, the change in OER from 'normal state' to anaerobic threshold is 0.3 (0.55-0.25) and the change in S is 1.2. This represents a four-fold increase. Four examples of mathematical modeling of global problems of oxygen transport using the S factor are described below.

Anaerobiosis↗
PubMed2000

Success and failure in school mathematics: effects of instruction and school environment.

Given the stubborn phenomenon of many children's serious difficulties and failure in mathematical learning, the hypothesis of developmental delay, or neurocognitively based deficiency should be complemented by further explanantions of children's weaknesses and substandard performance in mathematics. One obvious explanantion is that schooling and instruction for low ability children and for children with special needs is often inadequate. The present contribution examines selected research on mathematics learning under a cognitive instructional (didactical) perspective. Constructivist learning theory, the rooting of meaningful learning in concrete modeling activities, the balancing of understanding and practice in mathematics instruction, diagnostic and adaptive teaching, computer-assisted instruction, and the role of nonmathematical stumbling-blocks are discussed as principles and factors of effective mathematics learning and teaching.

Adolescent↗
PubMed2005

Validation the use of refractometer and mathematic equations to measure dietary formula contents for clinical application.

BACKGROUND AND AIMS: Gastric residual volumes are widely used to evaluate gastric emptying for patients receiving enteral feeding, but controversy exists about what constitutes gastric residual volume. We have developed a method by using refractometer and derived mathematical equations to calculate the formula concentration, total residual volume (TRV), and formula volume. In this study, we like to validate these mathematical equations before they can be implemented for clinical patient care. METHODS: Four dietary formulas were evaluated in two consecutive validation experiments. Firstly, dietary formula volume of 50, 100, 200, and 400 ml were diluted with 50 ml water, and then the Brix value (BV) was measured by the refractometer. Secondly, 50 ml of water, then 100 ml of dietary formula were infused into a beaker, and followed by the BV measurement. After this, 50 ml of water was infused and followed by the second BV measurement. The entire procedure of infusing of dietary formula (100 ml) and waster (50 ml) was repeated twice and followed by the BV measurement. RESULTS: The formula contents (formula concentration, TRV, and formula volume) were calculated by mathematical equations. The calculated formula concentrations, TRVs, and formula volumes measured from mathematic equations were strongly close to the true values in the first and second validation experiments (R2>0.98, P<0.001). CONCLUSIONS: Refractometer and the derived mathematical equations may be used to accurately measure the formula concentration, TRV, and formula volume and served as a tool to monitor gastric emptying for patients receiving enteral feeding.

Enteral Nutrition↗
PubMed2004

Mathematical coupling can undermine the statistical assessment of clinical research: illustration from the treatment of guided tissue regeneration.

OBJECTIVES: Previous periodontal literature has shown that there is a strong relationship between treatment effects, such as guided tissue regeneration (GTR), and baseline disease severity. However, relating change to baseline values using correlation or regression is methodologically flawed due to mathematical coupling, where the statistical procedure of testing the null hypothesis-that the coefficient of correlation or slope of regression is equal to zero-becomes erroneous. The aim of this study is to investigate if baseline disease severity is genuinely associated with the treatment outcome of intrabony defects using GTR after adjustment for mathematical coupling. In particular, we seek to demonstrate the potential effect that mathematical coupling has in distorting the results from the statistical analyses of trials of dental treatment, using data from the periodontal literature on GTR. The erroneous results arising from the use of simple correlation and regression techniques to analyse this association will be demonstrated, also the methodological flaw where the statistical procedure tests the null hypothesis-that the coefficient of correlation or the slope of regression is equal to zero. METHODS: Three main periodontal journals were electronically and manually searched to extract the data for the clinical outcomes of pocket probing depth (PPD) and lifetime cumulative attachment loss (LCAL) in the studies using GTR. The relationship between clinical outcomes and baseline measurements were reanalysed using Oldham's method and the variance ratio test. RESULTS: The results of these analyses were compared with those from the papers where the authors used the standard approach of correlation or regression. This shows that mathematical coupling caused spurious correlations between baseline disease severity and treatment effect. Ten out of 12 studies for PPD and nine out of 14 for LCAL initially claimed a significant positive relationship; after using either of the more appropriate statistical methods of adjustment, only three correlations in each group of studies remained significant. CONCLUSIONS: Previous evidence suggesting an association between baseline disease severity and treatment effect for GTR is challenged and therefore needs to be critically reviewed. All future clinical research should avoid using mathematically coupled data in correlation or regression analysis. In seeking to examine the bivariate association between baseline and subsequent change, Oldham's method is recommended.

Alveolar Bone Loss↗
PubMed2005

Cognitive processes that underlie mathematical precociousness in young children.

The working memory (WM) processes that underlie young children's (ages 6-8 years) mathematical precociousness were examined. A battery of tests that assessed components of WM (phonological loop, visual-spatial sketch pad, and central executive), naming speed, random generation, and fluency was administered to mathematically precocious and average-achieving children. The results showed that (a) precocious children performed better on executive processing, inhibition, and naming speed tasks than did average-achieving children, although the two groups were statistically comparable on measures of the phonological loop and visual-spatial sketch pad, and (b) the executive component of WM predicted mathematical accuracy independent of chronological age, reading, inhibition, and naming speed. The results support the notion that the executive system is an important predictor of children's mathematical precociousness and that this system can operate independent of individual differences in the phonological loop, inhibition, and reading in predicting mathematical accuracy.

Child↗
PubMed2005

Sex differences in intrinsic aptitude for mathematics and science?: a critical review.

This article considers 3 claims that cognitive sex differences account for the differential representation of men and women in high-level careers in mathematics and science: (a) males are more focused on objects from the beginning of life and therefore are predisposed to better learning about mechanical systems; (b) males have a profile of spatial and numerical abilities producing greater aptitude for mathematics; and (c) males are more variable in their cognitive abilities and therefore predominate at the upper reaches of mathematical talent. Research on cognitive development in human infants, preschool children, and students at all levels fails to support these claims. Instead, it provides evidence that mathematical and scientific reasoning develop from a set of biologically based cognitive capacities that males and females share. These capacities lead men and women to develop equal talent for mathematics and science.

Adolescent↗
PubMed1999

Considering academic qualification in mathematics as an entry requirement for a diploma in nursing programme.

A study carried out with first year students on a Diploma in Nursing programme at Nottingham University School of Nursing revealed that some students were struggling with basic arithmetic. A group was subsequently set up to address a range of issues relating to mathematics in nursing and nurse education. One of the areas investigated by the group was minimum entry requirement to the Diploma programme. In particular we wanted to determine the reliability of Mathematics GCSE Grade C as an indicator of arithmetic competence. Academic grades in mathematics (achieved prior to attendance at the School of Nursing) were compared with scores in an arithmetic test administered to students upon commencement on the Diploma in Nursing programme. It was found that the performance of students with Mathematics GCSE Grade C varied widely and some students could not solve basic arithmetic problems without the aid of a calculator. Schools of Nursing which adopt a policy of minimum qualifications in mathematics should not be complacent in assuming that students will be competent at arithmetic. The implementation of a programme of early assessment and tutorial support throughout the Diploma in Nursing programme is also recommended.

Curriculum↗
PubMed1999

Ability and attitudes to mathematics of post-registration health-care professionals.

A small study was conducted to investigate the mathematical abilities and attitudes to mathematics teaching of a sample of students embarking upon post-registration courses in health care. Mathematical ability showed a number of deficiencies of some concern. Expressed attitudes to mathematics teaching led to a discussion of the nature of mathematics teaching and some recommendations for remedial action.

Adult↗
PubMed1993

Achievement-related expectancies, academic self-concept, and mathematics performance of academically underprepared adolescent students.

The relationship between achievement-related expectancies, academic self-concept, and mathematics performance of 191 academically underprepared adolescent students was examined. After the effects of prior academic achievement were controlled for, a significant main effect for academic self-concept was found; as expected, students with higher academic self-concept earned significantly higher mathematics grades. In addition, after the effects of prior achievement were controlled for, female students were found to earn significantly higher mathematics grades than did male students. A significant three-way (Sex x Ethnic Group x Achievement-Related Expectancies) interaction was also noted. Unlike in several previous studies, no significant racial differences in mathematics performance were found. These students had a similar socioeconomic status (SES), and the effects of prior academic achievement were controlled for, suggesting that racial and gender differences in mathematics achievement may be partially explained by prior schooling and SES background, as posited by Reyes and Stanic (1988).

Adolescent↗
PubMed1987

Parasitic contamination cycles and mathematical epidemiology.

Mathematics plays an essential role in epidemiology. Whether simple questions are asked about simple relations, or complicated questions about complicated relations, the best fitting mathematical figures are always searched for. In a holistic approach, it may often be necessary to assess complicated relations by using (real) mathematical models (simulation models). Examples are presented of parasitic contamination cycles which require more or less complicated mathematics to answer epidemiological questions regarding prevalence and incidence of infection in the human population: Trichinella, Toxocara and Toxoplasma. Some general remarks on epidemiological insights which are necessary to understand abstract concepts of the 'real world' ('mathematical modelling'), are discussed.

Animals↗
PubMedDate not supplied

Complementary roles for toxicologic pathology and mathematics in toxicogenomics, with special reference to data interpretation and oscillatory dynamics.

Toxicogenomics is an emerging multidisciplinary science that will profoundly impact the practice of toxicology. New generations of biologists, using evolving toxicogenomics tools, will generate massive data sets in need of interpretation. Mathematical tools are necessary to cluster and otherwise find meaningful structure in such data. The linking of this structure to gene functions and disease processes, and finally the generation of useful data interpretation remains a significant challenge. The training and background of pathologists make them ideally suited to contribute to the field of toxicogenomics, from experimental design to data interpretation. Toxicologic pathology, a discipline based on pattern recognition, requires familiarity with the dynamics of disease processes and interactions between organs, tissues, and cell populations. Optimal involvement of toxicologic pathologists in toxicogenomics requires that they communicate effectively with the many other scientists critical for the effective application of this complex discipline to societal problems. As noted by Petricoin III et al (Nature Genetics 32, 474-479, 2002), cooperation among regulators, sponsors and experts will be essential for realizing the potential of microarrays for public health. Following a brief introduction to the role of mathematics in toxicogenomics, "data interpretation" from the perspective of a pathologist is briefly discussed. Based on oscillatory behavior in the liver, the importance of an understanding of mathematics is addressed, and an approach to learning mathematics "later in life" is provided. An understanding of pathology by mathematicians involved in toxicogenomics is equally critical, as both mathematics and pathology are essential for transforming toxicogenomics data sets into useful knowledge.

Animals↗
PubMed2003

Comprehension of algebraic expressions by experienced users of mathematics.

Little is known about how people comprehend mathematical expressions. In the present study we investigate the internal representations used by experienced users of mathematics to encode algebraic expressions. Initially, a memory recognition task was conducted that examined the role of mathematical syntax in the encoding of algebraic expressions. The results indicate that participants could more readily identify those parts of a previously seen expression that were syntactically well formed than those that were not well formed, suggesting that syntax plays an important role. To determine the level of syntactic structure involved, a second recognition task was conducted. The results indicate that algebraic expressions are encoded into components that represent the phrasal constituents of the expression. However, the results of these experiments did not rule out the possibility that the visual processes of perceptual organization were used to encode the expressions, or that the data were a consequence of a mathematical "lexicon" of common mathematical "phrases". Three further experiments were conducted to examine this, the results of which indicate that the encoding of algebraic expressions is based primarily on processes that occur beyond the level of visual or "lexical" processing. This is consistent with our finding that syntactic structure plays a key role.

Adolescent↗
PubMed2006

A common prefrontal-parietal network for mnemonic and mathematical recoding strategies within working memory.

Previous studies have indicated that the lateral prefrontal cortex (LPFC) is closely involved in strategic recoding, even when such processes lessen task demands. For example, 2 studies presented, in the spatial and verbal domains, sequences of stimuli for participants to retain during a short interval and then retrieve. Stimuli were either randomly arranged or structured (forming symmetries and regular shapes for the spatial task and mathematical patterns for the verbal task). Although participants performed the structured tasks better by reorganizing or "chunking" them into more efficient forms, LPFC activity was greater for the structured compared with the random sequences. However, although these results demonstrate that LPFC is involved in strategic recoding, regardless of the type of modality, it remains to be seen whether such a result generalizes to different types of strategic recoding processes. To test this, we presented digit sequence trials that separately emphasized mnemonic or mathematical recoding strategies. While participants were able to gain a performance benefit from either type of recoding strategy, increased LPFC activity was observed for both mathematical and mnemonic recoding trials, compared with either unstructured sequences or control conditions matched for mathematical or mnemonic processes. However, mathematically structured trials activated the LPFC significantly more than mnemonic recoding trials. In addition, lateral posterior parietal cortex was consistently coactivated with LPFC for strategic recoding trials, both in the current experiments and in previous related studies. We conclude that a prefrontal-parietal network is involved in strategic recoding in working memory, regardless of the type of recoding process.

Adult↗
PubMed2006

Deaf college students' mathematical skills relative to morphological knowledge, reading level, and language proficiency.

This study of deaf college students examined specific relationships between their mathematics performance and their assessed skills in reading, language, and English morphology. Simple regression analyses showed that deaf college students' language proficiency scores, reading grade level, and morphological knowledge regarding word segmentation and meaning were all significantly correlated with both the ACT Mathematics Subtest and National Technical Institute for the Deaf (NTID) Mathematics Placement Test scores. Multiple regression analyses identified the best combination from among these potential independent predictors of students' performance on both the ACT and NTID mathematics tests. Additionally, the participating deaf students' grades in their college mathematics courses were significantly and positively associated with their reading grade level and their knowledge of morphological components of words.

Achievement↗
PubMedDate not supplied

The mathematical analysis of breath alcohol profiles generated during breath exhalation.

The mathematical analysis of time domain data provides a useful tool for evaluating biological and instrumental systems. Breath alcohol profile measurements generated during exhalation constitute biological signals that can be subjected to a variety of mathematical treatments. The present paper discusses the application of a variety of mathematical procedures to breath alcohol profiles. These mathematical procedures include model approximation, data smoothing, integration, differentiation, and fourier transformation. The different mathematical procedures provide insight into the physiology of breath alcohol measurement and suggest forensic as well as instrumental applications.

Breath Tests↗