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PubMedDate not supplied

[A method for teaching mathematics].

This paper reports on an experience in teaching mathematics in a graduate course in public health, intermingled with reflections and concepts. Students enrolled in such courses generally feel uneasy about learning mathematics. Without underrating the usual obstacles and even affinities in developing abstractions, the results suggest that a major portion of the difficulties derives not from mathematics itself, but from an oppressive experience in the past. Difficulties also relate to the construction of space in the classroom. Such a perspective involves understanding experiments and life experiences in which the subjects are involved. In short, the work focuses on how to transmit mathematics in the development of a pedagogical approach.

Education, Graduate↗
PubMed2004

Self-concept and self-efficacy: a test of the internal/external frame of reference model and predictions of subsequent motivation and achievement.

We examined how final grades in mathematics and verbal arts in the first year of high school (Grade 11) were predicted in a Norwegian population by sex, previous grades in middle school (Grade 10), self-concept, self-efficacy at a domain-specific level, and intrinsic motivation. Direct and indirect relations were examined by means of a series of regression analyses. Participants were 483 students from six Norwegian high schools. End of term grades in high school correlated positively with grades in middle school in both mathematics (r = .62) and verbal arts (r = .55). The relation between grades at the two points of time was to a large extent mediated through mathematics, verbal self-concept, and self-efficacy. Intrinsic motivation also correlated positively with subsequent achievement (r = .63 and .42 in mathematics and verbal arts, respectively). However, intrinsic motivation had little predictive value for subsequent grades over and above the prediction made by self-concept and self-efficacy. Thus, self-concept and self-efficacy were the strongest predictors of subsequent grades. Predictions from the Internal/External frame of reference model were supported for self-concept but not for domain-specific self-efficacy.

Adolescent↗
PubMed1985

Clinical evaluation of left ventricular function using the cardiac helical fiber model: an echocardiographic study.

The cardiac helical fiber concept was introduced in 1969 and was shown mathematically to provide better approximations of normal ejection fractions compared with the conventional circumferential fiber model. The clinical applicability of this concept was evaluated noninvasively by M-mode and two-dimensional echocardiography in 55 subjects: 10 with aortic insufficiency, 10 with congestive cardiomyopathy, eight with hypertension, eight who were long-distance runners, 12 who were active and seven who were sedentary normals. Comparison of myocardial shortening by the circumferential and helical fiber models showed that the former discriminated only two groups of subjects, while endocardial and epicardial helical shortening discriminated three and four groups, respectively. Regression analyses suggest that more than 90% (r2 = 0.92) of variation in ejection fraction may be accounted for by variation in endocardial shortening, and that more than 75% (r2 = 0.77) of variation in observed endocardial shortening may be accounted for by variation in epicardial contraction. The study demonstrates that the helical fiber length concept may be useful for the noninvasive evaluation of left ventricular function in man.

Adult↗
PubMed2002

Entropy production and excess entropy in a nonequilibrium steady-state of single macromolecules.

Based on a recently developed formalism for mesoscopic stochastic dynamics of single macromolecules, such as motor proteins, in aqueous solution, we demonstrate mathematically the principle of the nonequilibrium thermodynamics originated by the Brussels group. The key concepts of excess entropy and excess entropy production, and their mathematical properties as well as physical interpretations, are discussed. The newly developed stochastic macromolecular mechanics is consistent with the general theory of nonequilibrium thermodynamics far from equilibrium, and more importantly, it bridges the abstract theory with the current experimental and modeling work on molecular motors and other biological systems in nonequilibrium steady state.

Journal Article↗
PubMed1976

An analysis of the interaction of a platinum complex and radiation with CHO cells using the molecular theory of cell survival.

A mathematical analysis is developed from the concepts of the molecular theory of cell survival to explain the cytotoxic action of a platinum complex on CHO cells and its synergistic interaction with radiation. In the analysis, it is assumed that both inter- and intra-strand cross-links induced by the Pt complex in the DNA contribute to cell killing and that the synergistic effect arises from the interaction between an intra-strand cross-link and a radiation-induced single-strand break on complementary strands of the DNA. The analysis is shown to be compatible with experimental results. Further, a mechanistic model is developed in an attempt to explain in more detail the processes which appear to be involved in the expression of the cytological damage.

Antineoplastic Agents↗
PubMed1991

The mathematical description of structures.

Any mathematical description of structures should start from a precisely stated definition of the concept of "structure". Unfortunately no universally accepted definition of this type exists. All that can be said is that the concept of "structure" is changing together with the modern physico-mathematical thought, so that different 'points of view' on the problem of the mathematical description of structures can be distinguished. The aim of this paper is to compare the explicative and predictive power of these different 'viewpoints' without entering into historical detail, in order to critically examine the limits and powers of the mathematical tools available today.

Classification↗
PubMedDate not supplied

[Mathematical model of two pathways of light perception by the photoreceptor cell].

On the basis of the concept postulating polyfunctional role of rhodopsin in the photoreceptor cell excitation a mathematical model of two pathways of excitation was formulated. One pathway involves the appearance of Ca2+ ions in the cell, which block the sodium channels. The second one results in cGMP splitting which also brings about the blocking of sodium channels. A change in the concentration of acting agents and development of cell excitation under illumination was calculated. The calcium branch is shown to be rapid and direct, but of a low sensitivity. The cGMP branch is a slow one but has a high intensification coefficient. The action time of the calcium branch does not depend on illumination, while the time of cGMP branch decreases with the illumination rise and is in an inverse proportion to the square root of the flash intensity. Under repeated illumination the amplitude of calcium response decreases, and its time remains constant. In cGMP branch the time of the response to the second flash decreases. The amplitude of the second response depends on the intensity of the first flash, it can be smaller or larger than the amplitude of the first response.

Cyclic GMP↗
PubMed1992

Cognitive arithmetic: a review of data and theory.

The area of cognitive arithmetic is concerned with the mental representation of number and arithmetic, and the processes and procedures that access and use this knowledge. In this article, I provide a tutorial review of the area, first discussing the four basic empirical effects that characterize the evidence on cognitive arithmetic: the effects of problem size or difficulty, errors, relatedness, and strategies of processing. I then review three current models of simple arithmetic processing and the empirical reports that support or challenge their explanations. The third section of the review discusses the relationship between basic fact retrieval and a rule-based component or system, and considers current evidence and proposals on the overall architecture of the cognitive arithmetic system. The review concludes with a final set of speculations about the all-pervasive problem difficulty effect, still a central puzzle in the field.

Attention↗
PubMed1982

Toward a better understanding of radiographic contrast.

Contrast is a familiar term that relates directly to the ability of human observers to detect differences in optical density. It also has been used to describe changes in x-ray fluence determined by attenuation differences in tissues of diagnostic interest. Ambiguous conclusions in the literature can be often traced to a lack of specificity in what is being measured and the validity of the implicit assumptions involved. Particularly troublesome are nonspecific bases for normalization and the assumption that a finite change in fluence can be accurately represented as a differential. These practices also tend to obscure consideration of system nonlinearities which can result in contrast enhancement produced by exposure to fogging radiation. Precisely defined components of contrast are symmetrically determined by the concept of modulation. This concept provides a powerful basis for mathematical description of linear systems. Bases for linearization of radiographic systems are also confusing unless thay are explicitly stated. This is particularly true for transfer functions as defined in many radiographic applications. Special functions which account for nonlinearity commonly associated with contrast gain in the detector simplify description and provide a quantitatively meaningful basis for specifying system performance in terms of information theory.

Mathematics↗
PubMed1988

The aperture problem--I. Perception of nonrigidity and motion direction in translating sinusoidal lines.

To examine how local velocities from different regions of the visual field combine to form a coherent motion percept, we subjected a sinusoidal line stimulus to translational motion. Horizontal movement of a sinewave line along its axial direction is perceived as nonrigid if the angle at the zero crossing is smaller than a critical angle of about 15 deg. This angle is independent of spatial scale and the number of sinusoidal cycles. To extend the applicability of this concept of angle, we developed a mathematical model to predict an observer's sensitivity to small changes in motion direction based on two assumptions: (1) the computed velocity signal is obtained from the intersection of constraint lines defined by local velocity components, (2) local velocity components are contaminated by noise. Measurement of directional discrimination thresholds of moving targets confirmed our expectations. Thresholds varied as a function of the angle of the local contour independent of spatial scale and in quantitative accord with our assumptions.

Discrimination, Psychological↗
PubMed2006

Synergetics of brain function.

Several brain functions such as movement coordination and visual perception are analysed in terms of synergetics, an interdisciplinary field of research dealing with spontaneous pattern formation. Accordingly, the brain is conceived as a self-organizing system operating close to instabilities where its activities are governed by collective variables, the order parameters, that enslave the individual parts, i.e., the neurons. In this approach, emphasis is laid on qualitative changes of behavioral and neuronal activities. These concepts are substantiated by detailed experimental and theoretical studies of the coordination of finger movements by direct observation of their changes and MEG measurements. In its main part, this paper deals with visual pattern recognition. Using general properties of order parameters, at the phenomenological level bistability, hysteresis and oscillations of visual perception can be modelled. Then, at the microscopic level, a network of pulse-coupled neurons is treated, where the dynamics of the dendritic currents as well as the axonic pulses (spikes) are taken into account. Both pulse-synchronization as well as pattern recognition are treated. In the high pulse frequency limit the attractor network of the synergetic computer is recovered. In the next step, the concept of quasi-attractors is mathematically formulated where due to saturation of attention attractors are closed. Depending on incoming signals, the visual system thus wanders from quasi-attractor to quasi-attractor. The paper includes an interpretation of consciousness in terms of order parameters as well as a discussion on linearity versus nonlinearity, the binding problem, and the psychological "present".

Animals↗
PubMed2004

An error catastrophe in cancer?

A comparison between the evolution of cancer cell populations and RNA viruses reveals a number of remarkable similarities. Both display high levels of plasticity and adaptability as a consequence of high degrees of genetic variation. It has been suggested that, as it occurs with RNA viruses, there is a threshold in the levels of genetic instability affordable by cancer cells in order to be able to overcome selection barriers (Trends Genet. 15 (1999) M57). Here we explore this concept by means of a simple mathematical model. It is shown that an error threshold exists in this model, which investigates both competition between cancer cell populations and its impact on overall tumor growth dynamics. Once the threshold is reached, the highly unstable tumor cell populations, which were sustaining malignant growth, become unable to maintain their genetic information, which in turn triggers a slowed down overall tumor growth regime.

Animals↗
PubMed2003

Super-resolution in computational imaging.

Super-resolution is a word used in different contexts but mainly in the case of methods aimed at improving the resolution of an optical instrument beyond the diffraction limit. Such a result may be achieved by means of specific instrumental techniques (such as, for instance, interferometry) or by means of a suitable processing of a digital image; in the latter case we will use the expression computational super-resolution (CSR). In this paper we describe the basic concepts underlying CSR without using the mathematics required for establishing its theoretical validity. The aim is to introduce a wide audience to this topic, to specify the situations where CSR is feasible and to emphasize the point that unlimited CSR is not possible.

Algorithms↗
PubMed2000

Does osteocyte formation cause the nonlinear refilling of osteons?

Marotti (Ital J Anat Embryol 1 01:25-79, 1996) described a theory of osteocyte differentiation from osteoblasts during bone formation. This theory postulates that, when a previously formed osteocyte is sufficiently covered by new bone and osteoid, it sends an inhibitory signal through its dendritic processes to the neighboring osteoblasts that reduces their individual apposition rates. The osteoblast most affected by this inhibition becomes buried by its neighbors, and becomes one of the next layer of osteocytes. By pursuing this concept, the present study develops a mathematical theory that predicts another observation about bone remodeling: the diminishment of the apposition rate during the refilling of basic multicellular units (BMUs). This decrease in apposition rate is different in osteonal and surface (e.g., trabecular) BMUs, and the theory shows that this result is consistent with the accrual of osteocyte inhibition throughout the refilling period, with the different ratios of bone volume to surface area in these two types of BMUs.

Bone Remodeling↗
PubMed2005

Two-digit comparison: decomposed, holistic, or hybrid?

We investigate whether two-digit numbers are decomposed for purposes of numerical comparison (e.g., choosing the larger one). Earlier theorists concluded that numbers are processed holistically (Brysbaert, 1995; Dehaene, Dupoux, & Mehler, 1990), or that holistic and decomposed processes operate in parallel (Nuerk, Weger, & Willmes, 2001). In the present experiment, we presented pairs of two-digit numbers with a decade distance of either zero (e.g., 54-57) or one (54-61). If a holistic process contributes to two-digit comparison, there should be an overall distance effect for number pairs with a decade distance of one. On the other hand, if numbers are decomposed and a holistic comparison does not contribute, this overall distance effect should be absent for these number pairs. Evidence is found that, at least in the present task settings, numbers are not compared holistically. The results are interpreted in terms of a recently proposed theory of numerical cognition (Verguts & Fias, 2004; Verguts, Fias, & Stevens, in press).

Association Learning↗
PubMed1988

Analogical transfer, problem similarity, and expertise.

When we encounter a new problem, we are often reminded of similar problems solved earlier and may use the solution procedure from an old problem to solve a new one. Such analogical transfer, however, has been difficult to demonstrate empirically, even within a single experimental session. This article proposes a framework for conceptualizing analogical problem solving that can account for the conflicting findings in the literature. In addition, the framework leads to two predictions concerning the transfer behavior of experts and novices. These predictions concern both positive and negative transfer and are based on the different types of features included in the problem representations of experts and novices. First, when two problems share structural features but not surface features, spontaneous positive transfer should be more likely in experts than in novices. Second, when two problems share surface but not structural features, spontaneous negative transfer should be stronger for novices than for experts. These predictions were supported by the results of three experiments involving college students solving a complex arithmetic word problem.

Achievement↗