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PubMed2005

Experimental study and simplified mathematical description of preferential crystallization.

The purpose of this paper is to investigate the concept of preferential crystallization, with a focus on aspects of quantification and application from an engineering point of view. The amino acid threonine was used as a model system in the experiments performed. Application of on-line polarimetry in combination with measurements of an on-line density meter proved the general applicability of this method in order to monitor directly the resolution progress, to recognize the region of "safe" resolution, and to gain information about the crystallization kinetics. For evaluation of the crystal growth kinetics of the desired enantiomers, the method of moments was applied to analyze isothermal single-step crystallization experiments. A population balance model is used in order to simulate the time changes of liquid-phase composition during the preferential crystallization process. Finally, preliminary experimental results regarding the cyclic operation mode are presented.

Journal Article↗
PubMed1981

[Compartment analysis of potassium metabolism--mathematical modelling of 42-K tracer kinetics].

The possibility of application of the theoretical concept of the compartment analysis in the modelling of the potassium balance was demonstrated. A use of the compartment analysis of the potassium balance in the clinical routine diagnostics in the sense of a highly specialised functional diagnostics seems according to recent experiences reasonable only in closest cooperation with clinicians. The diagnostics and the control of therapy of the chronic syndrome of potassium deficit as well as metabolically conditioned disturbances of the distribution of potassium were to be seen as possible indication. At the same time the establishment of reference values for the demarcation of relative disturbances of distribution as well as for the establishment of the normal region of the turnover rates were necessary.

Body Fluid Compartments↗
PubMed1998

Standardized structure and modular design of a pharmacokinetic database.

BACKGROUND: The accumulated knowledge on drugs can be used for an individual drug dosage adjustment if it is placed at our disposal in an informatically structured form. THEORY AND METHODS: We have started building up a pharmacokinetic database aimed at adjusting drug dosages, in exemplary form, to patients with renal impairment. Parameters needed for the three dosage adjustment rules (Dettli, Kunin, Holford) and the most general concept of pharmacokinetics constituted the theoretical basis. TWO PROCESSES PERTAIN TO ALL DRUGS: Distribution and elimination. Total drug clearance and at least two parameters representing distribution and elimination processes are closely interdependent in mathematical terms (clearance = volume of distribution*rate of elimination). This relation yields the unifying concept that serves as a prerequisite for a structured recording of 30 assigned pharmacokinetic and pharmacodynamic parameters within an informatic database. SOLUTIONS AND RESULTS: The information is retrieved and referenced from 2383 original publications by means of a standardized input module. The complete database at present contains 15,397 records for 1573 drugs. A programmed meta-analytic algorithm is used to calculate the statistical measures for the central value and variance--as available--from the pooled values of primary records. The statistically standardized parameters are extracted for 6601 pharmacokinetic parameters, and placed at the users disposal with the output module. PRACTICAL UTILITY: Following meta-analysis, published pharmacokinetics can be used as statistical estimates of population parameters. The statistical estimates with variances permit an individual drug dosage adjustment by applying the Bayesian approach or neural networks.

Algorithms↗
PubMed2005

What counts as knowing? The development of conceptual and procedural knowledge of counting from kindergarten through Grade 2.

The development of conceptual and procedural knowledge about counting was explored for children in kindergarten, Grade 1, and Grade 2 (N = 255). Conceptual knowledge was assessed by asking children to make judgments about three types of counts modeled by an animated frog: standard (correct) left-to-right counts, incorrect counts, and unusual counts. On incorrect counts, the frog violated the word-object correspondence principle. On unusual counts, the frog violated a conventional but inessential feature of counting, for example, starting in the middle of the array of objects. Procedural knowledge was assessed using speed and accuracy in counting objects. The patterns of change for procedural knowledge and conceptual knowledge were different. Counting speed and accuracy (procedural knowledge) improved with grade. In contrast, there was a curvilinear relation between conceptual knowledge and grade that was further moderated by children's numeration skills (as measured by a standardized test); the most skilled children gradually increased their acceptance of unusual counts over grade, whereas the least skilled children decreased their acceptance of these counts. These results have implications for studying conceptual and procedural knowledge about mathematics.

Child↗
PubMed1975

Biological effects evaluated as a function of patient thickness, beam quality, SSD,and treatment schedule.

Continuing efforts are being made by clinical radiotherapists to evaluate radiationcomplications to normal tissue and organs by specific time-dose parameters. Currently,the NSD concept of Ellis is receiving wide application in the literature in the reporting of radiation complications and normal tissue tolerances. To afford an easy and broad application of the NSD concept to the evaluation of physiological, functional, or structural changes, the authors have evolved mathematical expressions for the calculations of NSD as a function of patient thickness, beam energy, SSD, and treatment schedule involving coplanar field arrangements whether the fields are treated alternately or simultaneously. Several interesting aspects evolving form the concepts of treatment planning interms of the NSD or biological effects indicate that 1) for beam energies above 22 MeV, treatment is more ideally performed by treating only one field per day, since the depth of electronic equiliberium provides more effective sparing of superficial organs andtissues; 2) large-field therapy, such as the total nodal irradiation of Hodgkin'sdisease, can be more effectively treated in terms of tissue sparing by higher energy beamsthan cobalt-60 or 4-MeV for practically all patient dimensions; 3) a new concept ofintegral biological dose,the "gram-ret", is proposed, which represents the quantitation of total biological effect; 4) a series of tables with multiplication factors programmed on a digital computeris presented, which very quickly make available the NSD in any fractionated radiation treatment cycle to any plane of the body as a fuction of the beam energy, SSD, patient thickness, and continuous or split-course therapy schedule.

Dose-Response Relationship, Radiation↗
PubMed2006

A model of the chemical bond must be rooted in quantum mechanics, provide insight, and possess predictive power.

In this response to the preceding paper by Bader, we show that the core arguments and statements presented in the latter are flawed. We argue that it is insufficient for a model of the chemical bond to be rooted in quantum mechanics. A good model must in addition provide insight and possess predictive power. Our molecular orbital (MO) model of the chemical bond, in particular, the associated energy-decomposition approach satisfies all these conditions. On the other hand, Atoms-in-Molecules (AIM) theory is only rooted in quantum mechanics as far as its mathematical framework is concerned. The physical status of its central concepts is not so clear. In particular, "bond paths" and "bond critical points" are once more confirmed not to be indicators of a stabilizing interaction. Moreover, AIM theory lacks any predictive power. We also address specific questions raised in the preceding paper. Finally, interpreting chemical bonding implies choosing a perspective on this phenomenon. That there are many perspectives is a matter of fact and this is in no way unphysical. What is unscientific is to claim uniqueness and truth for one of these choices, namely AIM, and to dismiss on this ground all other approaches.

Comment↗
PubMed2003

Eigenmobilities in background electrolytes for capillary zone electrophoresis: II. Eigenpeaks in univalent weak electrolytes.

We analyze in detail a mathematical model of capillary zone electrophoresis (CZE) based on the conception of eigenmobilities, which are eigenvalues of the matrix tied to the linearized continuity equations. Our model considers CZE systems, where constituents are weak electrolytes and where pH of the background electrolyte may reach the full range from 0 to 14. Both hydrogen and hydroxide ions are taken into account in relations for conductivity and electroneutrality. An electrophoretic system with N constituents has N eigenmobilities. We reveal that two of the eigenmobilities have a special meaning as they exist due to the presence of hydrogen ions and hydroxide ions (in water solutions). These two eigenmobilities are responsible for the existence of two corresponding system zones (system peaks). We show that the stationary zone (injection zone, water zone, gap, peak, dip) is in many common background electrolytes composed of these two eigenzones which overlap, due to their very low electrophoretic mobility, into one zone. Other eigenmobilities give rise to system zones originating due to a possible existence of double (or multiple) coconstituents in the background electrolyte. The last group of eigenmobilities is connected with the movement of eigenzones accompanying analytes and enabling their indirect UV or conductivity detection. The model allows assessing experimentally available quantities such as effective mobility of the analyte, molar conductivity detection response, transfer ratio, and relative velocity slope and gives a picture about migration of analytes, their electromigration dispersion and signals obtained in detectors. It allows computer simulation of electropherograms and enables optimization of background electrolytes.

Electric Conductivity↗
PubMed2001

Does the coordination of verbal and motor information explain the development of counting in children?

Counting is often considered to be the coordination of two actions: saying the number-words and pointing to each object. We report three experiments to test the hypothesis that this coordination requires the use of the central executive (A. D. Baddeley, 1990), and that the cost of coordination decreases with age. Participants were 5- and 9-year-old children and adults. At all ages tested, the manipulation of the difficulty of each component affected counting performance but did not make coordination more difficult. These results suggest that, at least from the age 5, counting is a procedure in which the control of coordination is not attention demanding.

Adult↗
PubMed2001

Kindergartners' understanding of additive commutativity within the context of word problems.

Baroody and Gannon (1984) proposed that children's understanding of additive commutativity progresses through several levels of understanding based on a unary view of addition (change meaning) before developing a "true" level of understanding based on a binary conception (part-whole meaning). Resnick (1992) implied that children have both a unary and a binary conception of additive commutativity from the earliest stages of development. Fifty-three 5- and 6-year-old (M = 6-0) kindergartners' unary and binary understanding of additive commutativity was investigated using performance on tasks involving change-add-to and part-part-whole word problems, respectively. The data were inconsistent with the predictions of both models and suggest three alternate theoretical explanations. Moreover, the data indicate that success on a task involving change-add-to problems may be a more rigorous test of understanding of additive commutativity than that involving part-part-whole problems.

Analysis of Variance↗
PubMed1994

Transport of calcium by mitochondria.

The identification of intramitochondrial free calcium ([Ca2+]m) as a primary metabolic mediator [see Hansford (this volume) and Gunter, T. E., Gunter, K. K., Sheu, S.-S., and Gavin, C. E. (1994) Am. J. Physiol. 267, C313-C339, for reviews] has emphasized the importance of understanding the characteristics of those mechanisms that control [Ca2+]m. In this review, we attempt to update the descriptions of the mechanisms that mediate the transport of Ca2+ across the mitochondrial inner membrane, emphasizing the energetics of each mechanism. New concepts within this field are reviewed and some older concepts are discussed more completely than in earlier reviews. The mathematical forms of the membrane potential dependence and concentration dependence of the uniporter are interpolated in such a way as to display the convenience of considering Vmax to be an explicit function of the membrane potential. Recent evidence for a transient rapid conductance state of the uniporter is discussed. New evidence concerning the energetics and stoichiometries of both Na(+)-dependent and Na(+)-independent efflux mechanisms is reviewed. Explicit mathematical expressions are used to describe the energetics of the system and the kinetics of transport via each Ca2+ transport mechanism.

Animals↗
PubMed1983

The effects of EMG-assisted relaxation training on the academic performance, locus of control, and self-esteem of hyperactive boys.

This study investigated effects of EMG-assisted relaxation training on the academic performance, locus of control, and self-esteem of hyperactive junior high school-age boys. Twenty-four subjects each were randomly assigned to the treatment and control condition. Treatment consisted of six 20 to 25-minute sessions conducted biweekly. Pretreatment frontalis EMG, math, reading, and language performance, locus of control, and self-esteem were assessed for both groups. Outcome measures were again obtained on these dependent variables 2 weeks after the last treatment session. Experimental subjects demonstrated significantly higher posttreatment reading and language performance. Math performance gain did not reach statistical significance. A significant internal shift in locus of control was observed; however, self-esteem did not improve to that level. These outcomes correlated with significantly lower posttreatment frontalis EMG in the experimental group. EMG level did not change during the course of this study for control subjects. Implications of these findings are discussed in terms of existent research.

Achievement↗
PubMed1990

Children's understanding of counting.

This study examines the abstractness of children's mental representation of counting, and their understanding that the last number word used in a count tells how many items there are (the cardinal word principle). In the first experiment, twenty-four 2- and 3-year-olds counted objects, actions, and sounds. Children counted objects best, but most showed some ability to generalize their counting to actions and sounds, suggesting that at a very young age, children begin to develop an abstract, generalizable mental representation of the counting routine. However, when asked "how many" following counting, only older children (mean age 3.6) gave the last number word used in the count a majority of the time, suggesting that the younger children did not understand the cardinal word principle. In the second experiment (the "give-a-number" task), the same children were asked to give a puppet one, two, three, five, and six items from a pile. The older children counted the items, showing a clear understanding of the cardinal word principle. The younger children succeeded only at giving one and sometimes two items, and never used counting to solve the task. A comparison of individual children's performance across the "how-many" and "give-a-number" tasks shows strong within-child consistency, indicating that children learn the cardinal word principle at roughly 3 1/2 years of age. In the third experiment, 18 2- and 3-year-olds were asked several times for one, two, three, five, and six items, to determine the largest numerosity at which each child could succeed consistently. Results indicate that children learn the meanings of smaller number words before larger ones within their counting range, up to the number three or four. They then learn the cardinal word principle at roughly 3 1/2 years of age, and perform a general induction over this knowledge to acquire the meanings of all the number words within their counting range.

Attention↗
PubMed1990

Starting to add worse: effects of learning to multiply on children's addition.

A major stumbling block in acquiring a new skill can be integrating it with old but related knowledge. Learning multiplication is a case in point, because it involves integrating new relations with previously acquired arithmetic knowledge (in particular, addition). Two studies explored developmental changes in the relations between single-digit addition and multiplication. In the first study, third-graders, fifth-graders, and adults performed simple addition or multiplication in mixed- and blocked-operations formats. Substantial interfering effects from related knowledge were found at all age levels, but were more pronounced for younger subjects. Thus in the early stages of learning multiplication, one consequence of learning a new operation is interference in performance of an earlier, related, but less recently studied skill. Consideration of error patterns supported the view that the problem of integrating operations is a prominent one even in the early stages of mastering multiplication. Patterns of errors were generally consistent across all age groups, and all groups were much more likely to give a correct multiplication response to an addition problem than the reverse. A second, longitudinal study confirmed this finding, showing evidence for impaired performance of addition over time within individual children (second-, third-, and fourth-graders) tested on simple addition and multiplication over a 5-month period. Analysis of reaction times for addition indicated that second-graders in advanced math classes and third-graders in regular math classes tended to slow down over the year in responses to addition problems. Fourth-graders, on the other hand, tended to increase their speed of addition over the course of the year. Multiplication showed a different pattern during this period, with no evidence for slowing among children who were able to perform this task. Disruption of previously learned knowledge in the course of acquiring new skills provides evidence that new knowledge and old knowledge are being integrated. This kind of non-monotonic development may provide an empirical method for determining the functional limits of a domain of knowledge.

Adult↗
PubMed1992

Cognitive mechanisms in numerical processing: evidence from acquired dyscalculia.

This article discusses cognitive neuropsychological research on acquired dyscalculia (i.e., impaired numerical processing resulting from brain damage), surveying issues of current interest, and illustrating the ways in which analyses of acquired deficits can contribute to an understanding of normal processing. I first review the logic whereby inferences concerning normal cognition are drawn from patterns of impaired performance. I then consider research exploring the general functional architecture of the cognitive numerical processing mechanisms, and finally turn to studies aimed at probing the internal structure and functioning of individual processing components.

Brain Damage, Chronic↗
PubMed2005

Never getting to zero: Elementary school students' understanding of the infinite divisibility of number and matter.

Clinical interviews administered to third- to sixth-graders explored children's conceptualizations of rational number and of certain extensive physical quantities. We found within child consistency in reasoning about diverse aspects of rational number. Children's spontaneous acknowledgement of the existence of numbers between 0 and 1 was strongly related to their induction that numbers are infinitely divisible in the sense that they can be repeatedly divided without ever getting to zero. Their conceptualizing number as infinitely divisible was strongly related to their having a model of fraction notation based on division and to their successful judgment of the relative magnitudes of fractions and decimals. In addition, their understanding number as infinitely divisible was strongly related to their understanding physical quantities as infinitely divisible. These results support a conceptual change account of knowledge acquisition, involving two-way mappings between the domains of number and physical quantity.

Boston↗
PubMed2005

Stability and change in children's division strategies.

Age-related changes in children's performance on simple division problems (e.g., 6/2, 72/9) were investigated by asking children in Grades 4 through 7 to solve 32 simple division problems. Differences in performance were found across grade, with younger children performing more slowly and less accurately than older children. Problem size effects were also found in that children were faster and more accurate on small problems than on large problems. Two strategies changed across age, with children in Grade 4 relying heavily on the strategy of "addition" (adding the divisor until the dividend was reached) to solve the problems and children in Grades 5 through 7 relying primarily on the strategy of "multiplication" (recasting the division problem as a multiplication problem) to solve the problems. Surprisingly, the frequency of direct retrieval (retrieving the answer directly from memory) did not increase across grade and never became the dominant strategy of choice. Reasons for why retrieval use remains infrequent and age invariant are discussed. Overall, the results suggest that division is a unique operation and that the continued study of division may have implications for further understanding of how procedural and conceptual knowledge of arithmetic develops.

Age Factors↗
PubMed2006

Children's understanding of the arithmetic concepts of inversion and associativity.

Previous studies have shown that even preschoolers can solve inversion problems of the form a+b-b by using the knowledge that addition and subtraction are inverse operations. In this study, a new type of inversion problem of the form d x e/e was also examined. Grade 6 and 8 students solved inversion problems of both types as well as standard problems of the form a+b-c and d x e/f. Students in both grades used the inversion concept on both types of inversion problems, although older students used inversion more frequently and inversion was used most frequently on the addition/subtraction problems. No transfer effects were found from one type of inversion problem to the other. Students who used the concept of associativity on the addition/subtraction standard problems (e.g., a+b-c=[b-c]+a) were more likely to use the concept of inversion on the inversion problems, although overall implementation of the associativity concept was infrequent. The findings suggest that further study of inversion and associativity is important for understanding conceptual development in arithmetic.

Adolescent↗