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PubMed2001

Non-local concepts and models in biology.

In this paper, we consider local and non-local spatially explicit mathematical models for biological phenomena. We show that, when rate differences between fast and slow local dynamics are great enough, non-local models are adequate simplifications of local models. Non-local models thus avoid describing fast processes in mechanistic detail, instead describing the effects of fast processes on slower ones. As a consequence, non-local models are helpful to biologists because they describe biological systems on scales that are convenient to observation, data collection, and insight. We illustrate these arguments by comparing local and non-local models for the aggregation of hypothetical organisms, and we support theoretical ideas with concrete examples from cell biology and animal behavior.

Animal Communication↗
PubMed2002

Mathematical modelling of biofilm structures.

The morphology of biofilms received much attention in the last years. Several concepts to explain the development of biofilm structures have been proposed. We believe that biofilm structure formation depends on physical as well as general and specific biological factors. The physical factors (e.g. governing substrate transport) as well as general biological factors such as growth yield and substrate conversion rates are the basic factors governing structure formation. Specific strain dependent factors will modify these, giving a further variation between different biofilm systems. Biofilm formation seems to be primarily dependent on the interaction between mass transport and conversion processes. When a biofilm is strongly diffusion limited it will tend to become a heterogeneous and porous structure. When the conversion is the rate-limiting step, the biofilm will tend to become homogenous and compact. On top of these two processes, detachment processes play a significant role. In systems with a high detachment (or shear) force, detachment will be in the form of erosion, giving smoother biofilms. Systems with a low detachment force tend to give a more porous biofilm and detachment occurs mainly by sloughing. Biofilm structure results from the interplay between these interactions (mass transfer, conversion rates, detachment forces) making it difficult to study systems taking only one of these factors into account.

Bacteria↗
PubMed2003

Modern concepts of beauty.

Since the beginning of humanity, man has sought to define beauty. Whether by philosophy, mathematical constructs, social studies, or biology, the fascination with and the study of beauty has consumed our emotions and intellect. Many myths about this powerful force in our daily lives have been created, and some continue to be believed. Recent studies are shaping a new reality of beauty, one founded on evolutionary and biologic findings that link our fascination with beauty to our reproductive success. Cosmetic surgery, itself, may be an ongoing part of our biologic adaptation.

Adaptation, Biological↗
PubMed1996

New perspectives on the theory of permeability and resistance in the study of drug transport and absorption.

Permeability coefficient (P) expressed as distance per unit time has been commonly interpreted to represent the velocity of drug movement across a heterogeneous medium such as skin and intestinal epithelium. The basis of such an interpretation is questioned on several grounds. For example, the basic assumption for calculating P (as defined conventionally) according to the Fick's law of diffusion requires the entire medium to be homogeneous and rate-limiting in transport. The theoretical basis of the widely used total resistance or resistance additivity concept is reviewed. Such a concept is shown to be applicable to the study of total transit time across the medium but may not be applicable to the study of steady-state flux or absorption across the medium under normal conditions. Based on the diffusional, compartmental, absorptive clearance or carrier-mediated-transport analysis it is shown that only the first transport resistance from the bulk medium across the surface (such as cellular membranes) of the permeation medium (such as a cell or a tissue) is usually the deciding factor in drug transport or absorption. Resistances on the other side of the surface barrier usually only affect the drug accumulation vs. time profile in the medium, but not the steady-state flux or absorption. The role of unstirred water layer adjacent to the internal capillary wall is postulated to play an important role in causing the blood-flow dependency in absorption, a phenomenon that cannot be rationalized by the conventional effective permeability concept. The conventional concept of sink conditions on the serosal side is questioned. The present analysis further supports the use of the absorptive or transport clearance concept in absorption or transport study. Effective permeability is regarded as a mathematical operator for transport across a barrier or a tissue, and may be unrelated to the Fick's law of diffusion under most conditions. The velocity unit for P is regarded simply as a "collapsed" unit based on the absorptive or transport clearance per unit gross surface area. It is hoped that this commentary will stimulate further research and discussions in this general area of drug transport and absorption. It appears that there is a need to experimentally confirm the total resistance theory in biological systems.

Cell Membrane Permeability↗
PubMed1990

Numerical abstraction by human infants.

Across several experiments, 6- to 8-month-old human infants were found to detect numerical correspondences between sets of entities presented in different sensory modalities and bearing no natural relation to one another. At the basis of this ability, we argue, is a sensitivity to numerosity, an abstract property of collections of objects and events. Our findings provide evidence that the emergence of the earliest numerical abilities does not depend upon the development of language or complex actions, or upon cultural experience with number.

Attention↗
PubMed1992

Preverbal and verbal counting and computation.

We describe the preverbal system of counting and arithmetic reasoning revealed by experiments on numerical representations in animals. In this system, numerosities are represented by magnitudes, which are rapidly but inaccurately generated by the Meck and Church (1983) preverbal counting mechanism. We suggest the following. (1) The preverbal counting mechanism is the source of the implicit principles that guide the acquisition of verbal counting. (2) The preverbal system of arithmetic computation provides the framework for the assimilation of the verbal system. (3) Learning to count involves, in part, learning a mapping from the preverbal numerical magnitudes to the verbal and written number symbols and the inverse mappings from these symbols to the preverbal magnitudes. (4) Subitizing is the use of the preverbal counting process and the mapping from the resulting magnitudes to number words in order to generate rapidly the number words for small numerosities. (5) The retrieval of the number facts, which plays a central role in verbal computation, is mediated via the inverse mappings from verbal and written numbers to the preverbal magnitudes and the use of these magnitudes to find the appropriate cells in tabular arrangements of the answers. (6) This model of the fact retrieval process accounts for the salient features of the reaction time differences and error patterns revealed by experiments on mental arithmetic. (7) The application of verbal and written computational algorithms goes on in parallel with, and is to some extent guided by, preverbal computations, both in the child and in the adult.

Animals↗
PubMed1989

Judgments of quantity and conservation of quantity: the area of a rectangle.

This study examines the relationships between perceptive judgment of quantity and conservation judgment of quantity with regard to the concept of area. Twenty children who passed an area conservation task (mean age = 8) and 20 children who failed it (mean age = 6, 7) were administered an area judgment task. This task was a replication of Anderson and Cuneo's study (1978, Journal of Experimental Psychology: General, 107, 335-378). The conserving children generally appeared to apply an additive rule (the height and width rule) observed by Anderson and Cuneo in 5 year olds. The nonconserving children in contrast generally presented patterns suggesting centration on one of the two dimensions. The implications for Anderson's and Piaget's conceptions of conservation development are discussed.

Age Factors↗
PubMed1992

The organization of arithmetic facts in memory: evidence from a brain-damaged patient.

We report a single case study of a brain-damaged patient with impaired arithmetic performance. Three principal findings are presented: First, in a task involving production of answers to simple arithmetic problems, the patient's performance was far better for subtraction than for addition or multiplication. Second, in all arithmetic operations performance was generally much better for problems potentially solvable by rule (e.g., 5 + 0) than for problems requiring retrieval of specific facts (e.g., 5 + 3). Third, the dissociation between subtraction and the other arithmetic operations obtained in the production task was not observed in a verification task. The implications of these findings for claims concerning the organization of stored arithmetic facts are discussed.

Aged↗
PubMed2006

Simple arithmetic processing: surface form effects in a priming task.

Models of numerical processing vary on whether they assume common or separate processing pathways for problems represented in different surface forms. The present study employed a priming procedure, with target naming task, in an investigation of surface form effects in simple addition and multiplication operations. Participants were presented with Arabic digit and number word problems in one of three prime-target relationships, including congruent (e.g., '2+3' and '5'), incongruent (e.g., '9+7' and '5') and neutral (e.g., 'X+Y' and '5') conditions. The results revealed significant facilitatory effects in response to congruent digit stimuli at SOAs of 300 and 1000ms, in both operations. In contrast, inhibitory effects were observed in response to incongruent word stimuli in both the addition and multiplication operations at 300ms, and in the addition operation at 1000ms. The overall priming effects observed in the digit condition were significantly greater than in the word condition at 1000ms in the multiplication operation and at 300ms in the addition operation. The results provide support to separate pathway accounts of simple arithmetic processing for problems represented in different surface forms. An explanation for variation in processing due to differences in access to visual and phonological representations is provided.

Adolescent↗
PubMed2004

Verbal mediation of number knowledge: evidence from semantic dementia and corticobasal degeneration.

Patients with corticobasal degeneration (CBD) appear to have impaired number knowledge. We examined the nature of their number deficit while we tested the hypothesis that comprehension of larger numbers depends in part on verbal mediation. We evaluated magnitude judgments and performance on number conservation measures rooted in Piagetian theory in nonaphasic patients with CBD (n=13) and patients with a fluent form of progressive aphasia known as semantic dementia (SD; n=15). We manipulated the numbers of the arrays and the visual-spatial properties of the stimuli being compared during magnitude judgments and Piagetian conservation measures. CBD patients were consistently impaired judging the magnitudes of larger numbers (4-9), while they had minimal difficulty with smaller numbers (magnitudes < or = 3). By comparison, SD patients performed all measures of number knowledge at a ceiling level regardless of number magnitude. Neither patient group was significantly impacted by manipulations of the spatial properties of the stimuli. CBD patients' impairment with larger numbers despite minimal aphasia, and SD patients' intact performance despite an aphasia, challenge the proposal that understanding larger numbers depends on verbal mediation.

Aged↗
PubMed2004

Magnitude comparison in preschoolers: what counts? Influence of perceptual variables.

This study examined numerosity comparison in 3-year-old children. Predictions derived from the analog numerical model and the object-file model were contrasted by testing the effects of size and ratio between numerosities to be compared. Different perceptual controls were also introduced to evaluate the hypothesis that comparison by preschoolers is based on correlated perceptual variables rather than on number per se. Finally, the relation between comparison performance and verbal counting knowledge was investigated. Results showed no evidence that preschoolers use an analog number magnitude or an object-file mechanism to compare numerosities. Rather, their inability to compare sets controlled for surface area suggests that they rely on perceptual cues. Furthermore, the development of numerosity-based representations seems to be related to some understanding of the cardinality concept.

Child, Preschool↗
PubMed2005

Demystifying biomedical signals: a student centred approach to learning signal processing.

The processing and analysis of physiological signals has become firmly established in clinical medicine and biomedical research. Many of the users of this technology however do not come from an engineering or science background, and traditional approaches in teaching signal processing are thus not appropriate for them. We have therefore developed a series of modular courses that are aimed specifically at an audience with a background in medicine, health-care or the life-sciences. In these courses, we focus on the concepts, principles and rationale of applying signal processing methods, rather than the mathematical foundations of the techniques. Thus, we aim to remove some of the perceived 'mystery' often surrounding this subject. The very practical approach, with hands-on experience using the MATLAB software, has been well received, with strong evidence that students have learnt to apply their knowledge. This paper describes the learning and teaching approach taken, and some of the experience acquired.

Algorithms↗
PubMed2004

Core systems of number.

What representations underlie the ability to think and reason about number? Whereas certain numerical concepts, such as the real numbers, are only ever represented by a subset of human adults, other numerical abilities are widespread and can be observed in adults, infants and other animal species. We review recent behavioral and neuropsychological evidence that these ontogenetically and phylogenetically shared abilities rest on two core systems for representing number. Performance signatures common across development and across species implicate one system for representing large, approximate numerical magnitudes, and a second system for the precise representation of small numbers of individual objects. These systems account for our basic numerical intuitions, and serve as the foundation for the more sophisticated numerical concepts that are uniquely human.

Animals↗
PubMed2003

The mental representation of ordinal sequences is spatially organized.

In the domain of numbers the existence of spatial components in the representation of numerical magnitude has been convincingly demonstrated by an association between number magnitude and response preference with faster left- than right-hand responses for small numbers and faster right- than left-hand responses for large numbers (Dehaene, S., Bossini, S., & Giraux, P. (1993) The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122, 371-396). Because numbers convey not only real or integer meaning but also ordinal meaning, the question of whether non-numerical ordinal information is spatially coded naturally follows. While previous research failed to show an association between ordinal position and spatial response preference, we present two experiments involving months (Experiment 1) and letters (Experiment 2) in which spatial coding is demonstrated. Furthermore, the response-side effect was obtained with two different stimulus-response mappings. The association occurred both when ordinal information was relevant and when it was irrelevant to the task, showing that the spatial component of the ordinal representation can be automatically activated.

Adult↗
PubMed2000

Large number discrimination in 6-month-old infants.

Six-month-old infants discriminate between large sets of objects on the basis of numerosity when other extraneous variables are controlled, provided that the sets to be discriminated differ by a large ratio (8 vs. 16 but not 8 vs. 12). The capacities to represent approximate numerosity found in adult animals and humans evidently develop in human infants prior to language and symbolic counting.

Child Development↗
PubMed1995

Impaired arithmetic facts but intact conceptual knowledge--a single-case study of dyscalculia.

We present the case of a young, highly educated patient who showed severe problems in basic arithmetic after a bone marrow transplant followed by extensive irradiation and chemotherapy. Despite his inability to resolve arithmetical fact problems (as 2 + 3), he showed intact processing of algebraic expressions and excellent understanding of complex arithmetic text problems. He perfectly knew arithmetic principles and applied them in various tasks. The performance of the patient suggests that conceptual knowledge (in addition to arithmetical fact knowledge and arithmetic procedures) is a functionally independent component of the calculation system.

Adult↗