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At least 775 records · Page 43Linked to original sources
PubMed2006

Preschool children's mathematical knowledge: The effect of teacher "math talk.".

This study examined the relation between the amount of mathematical input in the speech of preschool or day-care teachers and the growth of children's conventional mathematical knowledge over the school year. Three main findings emerged. First, there were marked individual differences in children's conventional mathematical knowledge by 4 years of age that were associated with socioeconomic status. Second, there were dramatic differences in the amount of math-related talk teachers provided. Third, and most important, the amount of teachers' math-related talk was significantly related to the growth of preschoolers' conventional mathematical knowledge over the school year but was unrelated to their math knowledge at the start of the school year.

Achievement↗
PubMed2004

Autopoiesis and cognition.

This article revisits the concept of autopoiesis and examines its relation to cognition and life. We present a mathematical model of a 3D tesselation automaton, considered as a minimal example of autopoiesis. This leads us to a thesis T1: "An autopoietic system can be described as a random dynamical system, which is defined only within its organized autopoietic domain." We propose a modified definition of autopoiesis: "An autopoietic system is a network of processes that produces the components that reproduce the network, and that also regulates the boundary conditions necessary for its ongoing existence as a network." We also propose a definition of cognition: "A system is cognitive if and only if sensory inputs serve to trigger actions in a specific way, so as to satisfy a viability constraint." It follows from these definitions that the concepts of autopoiesis and cognition, although deeply related in their connection with the regulation of the boundary conditions of the system, are not immediately identical: a system can be autopoietic without being cognitive, and cognitive without being autopoietic. Finally, we propose a thesis T2: "A system that is both autopoietic and cognitive is a living system."

Automation↗
PubMedDate not supplied

The maximum lactate clearance: a new concept to approach the endurance level of an athlete.

The purpose of this study is to present a mathematical model based on physiological observations which describes the evolution of the blood lactate concentration ([LA-]) versus the oxygen uptake (VO2) during a continuous graded exercise test. This model is based on several assumptions: 1) [LA-] reflects the balance between the rates of appearance and disappearance of the lactate in the blood compartment; 2) VO2 measured at the end of each step, is a linear function of the power output and thus of the time; 3) the appearance rate of lactate into the blood is an exponential function of VO2; 4) the rate of disappearance is a saturable process which can be modelized by Michaelis-Menten kinetics; 5) the volume of distribution of lactate in the blood compartment is a constant during exercise. The parameters used in this model correspond to the integration of several biochemical and physiological phenomenons. The originality of this approach is to express the rate of lactate appearance and disappearance versus VO2 rather than time. Whatever the general pattern of the data, the fitted curve gives always very good results. Especially, the theoretical curve fits the decrease in [LA-] usually observed during the first steps of such an exercise. From the computed parameters the evolution of lactate clearance during a continuous graded exercise test may be modelized. A strong relationship exists between the level of endurance training and the maximum lactate clearance (Clmax) reached during the exercise test. The VO2 for Clmax is an indicator of the shift of the relationship [LA-]-VO2. Then, we propose to use the maximum lactate clearance which is individually determined, to characterize the endurance level of an athlete.

Adolescent↗
PubMed2004

Concepts and tools for predictive modeling of microbial dynamics.

Description of microbial cell (population) behavior as influenced by dynamically changing environmental conditions intrinsically needs dynamic mathematical models. In the past, major effort has been put into the modeling of microbial growth and inactivation within a constant environment (static models). In the early 1990s, differential equation models (dynamic models) were introduced in the field of predictive microbiology. Here, we present a general dynamic model-building concept describing microbial evolution under dynamic conditions. Starting from an elementary model building block, the model structure can be gradually complexified to incorporate increasing numbers of influencing factors. Based on two case studies, the fundamentals of both macroscopic (population) and microscopic (individual) modeling approaches are revisited. These illustrations deal with the modeling of (i) microbial lag under variable temperature conditions and (ii) interspecies microbial interactions mediated by lactic acid production (product inhibition). Current and future research trends should address the need for (i) more specific measurements at the cell and/or population level, (ii) measurements under dynamic conditions, and (iii) more comprehensive (mechanistically inspired) model structures. In the context of quantitative microbial risk assessment, complexity of the mathematical model must be kept under control. An important challenge for the future is determination of a satisfactory trade-off between predictive power and manageability of predictive microbiology models.

Bacteria↗
PubMed2001

Popperian falsification of methods of assessing surgically induced astigmatism.

To test several methods of assessing surgically induced astigmatism (SIA). Department of Ophthalmology, Arhus University Hospital, Arhus, Denmark. Assessment methods can be divided into 3 groups. Group 1 includes methods that consider only astigmatic magnitude and disregard astigmatic direction, such as the algebraic and simple subtraction methods. Group 2 can be termed "astigmatic magnitude not considering axis" and includes several almost identical techniques known as the methods of Naylor, Jaffe, Kaye, Holladay, and Olsen. Group 3 includes Naeser polar value analysis and the methods later described by Alpins and Holladay. The methods were tested in situations in which the expected result was known. When this result was not produced, the specific assessment method was considered falsified in a classical Popperian manner. The simple falsification experiments revealed that the methods in Groups 1 and 2 are erroneous. Mathematical analysis disclosed that the methods in Group 3 are similar, although derived from different concepts. The algebraic, simple subtraction, astigmatic magnitude not considering axis, and vector decomposition methods for assessment of SIA are erroneous and should not be used. The Naeser, Alpins, and Holladay methods are identical and in agreement with current research in optometry.

Astigmatism↗
PubMedDate not supplied

Evolution and analysis of model CPGs for walking: I. Dynamical modules.

Can one develop an abstract description of the dynamics of pattern generators that provides quantitative insight into their operation? We explored this question by examining the dynamics of a model central pattern generator that was created using an evolutionary algorithm. We propose an abstract description based on the concept of a dynamical module, a set of neurons that simultaneously make their transitions from one quasistable state to another while the synaptic inputs that they receive from other neurons remain essentially constant, thus temporarily reducing the dimensionality of the circuit dynamics. Using the mathematical tools of dynamical systems theory, we describe a method for identifying dynamical modules and demonstrate that this concept can be used to quantitatively characterize constraints on neural architecture, account for phase durations, and predict the effects of parameter changes. Moreover, this abstract description reveals coordinated parameter changes that leave the overall circuit dynamics essentially unchanged. In a companion article we employ this abstract description to examine the relationship between general principles and individual variability in large populations of evolved model pattern generators.

Gait↗
PubMed2004

[Modern concepts in pharmacokinetics of intravenous anesthetics].

From a pharmacological perspective, anesthesia is concerned with controlling the time course of drug effect. Mathematical models are commonly used to relate the administered drug dose to the measured drug concentration (a pharmacokinetic model) and to relate the measured drug concentrations to the measured drug effects (a pharmacodynamic model). With such models, the time course of the drug effect for different drug regimens can be predicted. Although the conventional pharmacokinetic parameters such as the volume of distribution, clearance, distribution and elimination half-lives can be used to accurately describe the time course of the plasma concentration, the plasma is usually not the site of drug effect. An understanding of the "effect compartment concept" and the "time of the peak effect site concentration," together with the concepts of" context sensitive"half-time and "relevant decrement time,' contribute substantially to the anesthetist's understanding of the principles governing the onset and offset of drug effect. As part of a computer-controlled infusion system, the pharmacokinetic model facilitates optimized and rational dosing. These systems, also called target-controlled infusion systems (TCI), calculate the infusion rates for rapidly achieving and then maintaining a target concentration.

Algorithms↗
PubMed1995

On the mechanical function of tendon.

A mesoscopic approach is followed for mathematical modelling of the specific deformation properties of tendon. The approach starts from our general concept of modelling mechanical behaviour of heterogeneous media and assumes that the structure of tendon is optimized in such a way that it enables its adjacent muscle to work with a constant performance in the course of increasing loading (acting like a gearbox in a car). The model based on this assumption gives results that are in a very good accordance with observed properties of tendons. Clinical experience reveals that if this function of tendon is violated pathological changes appear in the respective muscle. RELEVANCE: Clarification and mathematical modelling of the mechanical function of tendon is of intellectual interest in its own right, but it is important also for cautioning surgeons against unnecessary violation of this function, and for tissue engineering aspects if tendon must be replaced.

Journal Article↗
PubMed2002

The influence of sharing on children's initial concept of division.

We report three studies that investigate young children's ability to solve partitive division problems when presented with a concrete model of a problem. In the studies, 5- to 8-year-olds were given problems about sharing "sweets" between dolls, and the sweets were grouped in one of two different ways. When the sweets were grouped by the divisor, the number of groups coincided with the number of dolls (divisor) and the number in each group was the answer (quotient). When the sweets were grouped by the quotient, the reverse was true. In all three experiments, children found it much easier to solve the problems in the Grouping-by-Divisor condition than in the Grouping-by-Quotient condition (although there was some evidence of a developmental improvement in the tasks). It is suggested that the Grouping-by-Divisor condition is easier because it coincides with the end point of sharing. The findings are discussed with reference to schemas of action in children's mathematical understanding.

Analysis of Variance↗
PubMed2006

[Diagnostic tests: basic concepts for their correct interpretation and use].

The present article aims to disseminate knowledge of a topic that is important in clinical epidemiology: evaluation of diagnostic tests. Mathematical formulae are kept to a minimum. The significance and interpretation of the most important diagnostic indexes characterizing these tests are explained in order to describe their use in daily clinical practice, especially their role in the design of diagnostic protocols. Features related to evidence-based medicine, which represent the next step after mastery of these concepts, are not analyzed.

Clinical Protocols↗
PubMed1993

Urea modeling and Kt/V: a critical appraisal.

Since the origin of chronic hemodialysis, a way to quantify the therapy and define its adequacy has been sought. Currently accepted methods rely on the mathematical description of urea kinetics and the evaluation of an index, Kt/V. The history of this concept, and its validation by the National Cooperative Dialysis Study are described. There are six major methods of calculating Kt/V--"three-point" kinetic modeling, "2-BUN" kinetic modeling, percent reduction of urea, In(post/pre-ratio), empirical estimation, and direct quantification of dialysate urea. The assumptions underlying all of these methods are similar: (1) Urea is a valid marker solute for uremic toxicity; (2) urea behaves as described by the mathematical model; (3) input variables can be measured accurately; (4) outputs from the model are consistent and reproducible; and (5) the clinical significance of Kt/V is established by valid outcome studies. Each of these assumptions is examined in turn, and found to be flawed. In particular, the measurement of dialyzer urea clearance is highly method-dependent and inaccurate; measurements in 101 dialyses by four common methods had an overall 27.5% variation among the results of the various methods. Outputs from the six methods of urea monitoring showed wide variation, especially in values of urea distribution volume and protein catabolic rate. Kt/V results were more reproducible, but the clinical significance of a particular value of Kt/V is very poorly established. Urea kinetic modeling is a remarkable conceptual advance and useful tool for understanding the physiology and quantification of dialysis, but Kt/V cannot be a standard for adequacy, since it is both approximate and unvalidated.

Humans↗
PubMed1993

On the soundness and safety of expert systems.

The problems of developing sound and safe expert systems are discussed, with particular reference to medicine. The concepts, notations, methods, results and technologies which have emerged from the study of mathematical logic as a computational paradigm offer many benefits for improving the quality of expert systems. Logic programming offers a better discipline for design, specification and implementation than ad hoc development methodologies. When logic programming is combined with software engineering methods, such as a software development life-cycle, the probability of routinely developing large-scale yet efficient and sound applications will be increased. However, although soundness is a necessary property of any technology it is not sufficient for assuring safety. Established methods for improved software safety are discussed, and a number of approaches to improving the safety of medical expert systems is identified. The possibility of introducing an appropriately extended life-cycle, and the potential benefits of a formal theory of safety are discussed.

Artificial Intelligence↗
PubMed2006

Sustainable ecosystem management using optimal control theory: part 1 (deterministic systems).

The concept of sustainability, an abstract one by its nature, has been given a mathematical representation through the use of Fisher information as a measure. It is used to propose the sustainability hypotheses for dynamical systems, which has paved the way to achieve sustainable development through externally enforced control schemes. For natural systems, this refers to the task of ecosystem management, which is complicated due the lack of clear objectives. This work attempts to incorporate the idea of sustainability in ecosystem management. The natural regulation of ecosystems suggests two possible control options, top-down control and bottom-up control. A comparison of these two control philosophies is made on generic food chain models using the objectives derived from the sustainability hypotheses. Optimal control theory is used to derive the control profiles to handle the complex nature of the models and the objectives. The results indicate a strong relationship between the hypotheses and the dynamic behavior of the models, supporting the use of Fisher information as a measure. As regards to ecosystem management, it has been observed that top-down control is more aggressive but can result in instability, while bottom-up control is guaranteed to give a stable and improved dynamic response. The results also indicate that bottom-up control is a better option to affect shifts in the dynamic regimes of a system, which may be required to recover the system from a natural disaster like the hurricane Katrina.

Animals↗
PubMed2006

Pseudo amino acid composition and multi-class support vector machines approach for conotoxin superfamily classification.

Conotoxins are disulfide rich small peptides that target a broad spectrum of ion-channels and neuronal receptors. They offer promising avenues in the treatment of chronic pain, epilepsy and cardiovascular diseases. Assignment of newly sequenced mature conotoxins into appropriate superfamilies using a computational approach could provide valuable preliminary information on the biological and pharmacological functions of the toxins. However, creation of protein sequence patterns for the reliable identification and classification of new conotoxin sequences may not be effective due to the hypervariability of mature toxins. With the aim of formulating an in silico approach for the classification of conotoxins into superfamilies, we have incorporated the concept of pseudo-amino acid composition to represent a peptide in a mathematical framework that includes the sequence-order effect along with conventional amino acid composition. The polarity index attribute, which encodes information such as residue surface buriability, polarity, and hydropathy, was used to store the sequence-order effect. Several methods like BLAST, ISort (Intimate Sorting) predictor, least Hamming distance algorithm, least Euclidean distance algorithm and multi-class support vector machines (SVMs), were explored for superfamily identification. The SVMs outperform other methods providing an overall accuracy of 88.1% for all correct predictions with generalized squared correlation of 0.75 using jackknife cross-validation test for A, M, O and T superfamilies and a negative set consisting of short cysteine rich sequences from different eukaryotes having diverse functions. The computed sensitivity and specificity for the superfamilies were found to be in the range of 84.0-94.1% and 80.0-95.5%, respectively, attesting to the efficacy of multi-class SVMs for the successful in silico classification of the conotoxins into their superfamilies.

Algorithms↗
PubMed2004

Risk potentials for humans of original and remediated PAH-contaminated soils: application of biomarkers of effect.

Contaminated soils represent a potential health risk for the human population. Risk assessment for humans requires specific methods, which must reflect the peculiarities of human behaviour, physiology and biochemistry with respect to contaminant uptake and processing. Biomarkers of effect or exposure have become an appropriate tool. Organic pollutants influence the expression profile of cytochromes P450 (CYP), and CYP1A1 has been shown to be a suitable biomarker for polycyclic aromatic hydrocarbons (PAH). The latter are widely distributed in soils and constitute an important soil contamination. Upon intake of PAH-contaminated soils, CYP1A1 is induced in various organs of rats and minipigs. Increased CYP1A1-levels in lung, kidney and spleen, after oral soil intake, indicate that contaminants escape the primary duodenal and hepatic metabolism and reach further organs. Dose-response relationships reveal that induction effects are to be expected in children based on known exposure conditions. Generally, CYP1A1-induction does not correlate with results of toxicity tests with lower organisms, performed with the same soils. The organic carbon content is largely responsible for this discrepancy. It severely affects the toxicity of soil bound PAH for microorganisms, but obviously affects the mobilization efficiency for PAH in the gastro-intestinal tract of mammals to a minor extent. Soil remediation by different methods may result in a significant reduction of the PAH content and of toxicity. Ingestion of remediated soils by rats shows, however, that the induction potential for CYP1A1 is only slightly decreased after remediation. This means that the major inducing components resist biological remediation or soil washing and remain in the soil. Because data obtained with experimental animals form the guiding principle for in vitro tests to be developed, the suitability of the animal model used for extrapolations to humans has to be proven. Upon soil ingestion, minipigs show a tissue-specific response pattern, which substantially differs from that of rats, which are widely used as animal models. It is not known which response pattern resembles that of man. In summary, cytochromes P450, in particular CYP1A1, are suitable biomarkers to assess the bioavailability of soil bound contaminants and their effects on mammalian species. There are, however, a number of questions to be answered in order to develop an in vitro test for human risk assessment. This concerns, for example, the identification of the suitable animal model, the identification of biomarkers for other contaminants and concepts to transpose the in vivo data to in vitro technologies or to mathematical modelling.

Animals↗
PubMed1998

Definition of amide protection factors for early kinetic intermediates in protein folding.

Hydrogen-deuterium exchange experiments have been used previously to investigate the structures of well defined states of a given protein. These include the native state, the unfolded state, and any intermediates that can be stably populated at equilibrium. More recently, the hydrogen-deuterium exchange technique has been applied in kinetic labeling experiments to probe the structures of transiently formed intermediates on the kinetic folding pathway of a given protein. From these equilibrium and nonequilibrium studies, protection factors are usually obtained. These protection factors are defined as the ratio of the rate of exchange of a given backbone amide when it is in a fully solvent-exposed state (usually obtained from model peptides) to the rate of exchange of that amide in some state of the protein or in some intermediate on the folding pathway of the protein. This definition is straightforward for the case of equilibrium studies; however, it is less clear-cut for the case of transient kinetic intermediates. To clarify the concept for the case of burst-phase intermediates, we have introduced and mathematically defined two different types of protection factors: one is P struc, which is more related to the structure of the intermediate, and the other is P app, which is more related to the stability of the intermediate. Kinetic hydrogen-deuterium exchange data from disulfide-intact ribonuclease A and from cytochrome c are discussed to explain the use and implications of these two definitions.

Amides↗
PubMed1984

Biological similitude: statistical and functional relationships in comparative physiology.

A concept of biological similitude based on the distinction between extensive and intensive properties of animals is discussed. This concept provides a theoretical basis for using the power function as a mathematical-physical model whose numerical and dimensional constraints give some insight into the nature of the relationship between body mass and energy metabolism. In particular a theoretically mass-independent expression for energy metabolism is derived that can be used for qualitative intra- and interspecific comparisons of energy metabolism.

Animals↗
PubMed2006

Fractal analysis of Mesoamerican pyramids.

A myth of ancient cultural roots was integrated into Mesoamerican cult, and the reference to architecture denoted a depth religious symbolism. The pyramids form a functional part of this cosmovision that is centered on sacralization. The space architecture works was an expression of the ideological necessities into their conception of harmony. The symbolism of the temple structures seems to reflect the mathematical order of the Universe. We contemplate two models of fractal analysis. The first one includes 16 pyramids. We studied a data set that was treated as a fractal profile to estimate the Df through variography (Dv). The estimated Fractal Dimension Dv = 1.383 +/- 0.211. In the second one we studied a data set to estimate the Dv of 19 pyramids and the estimated Fractal Dimension Dv = 1.229 +/- 0.165.

Archaeology↗