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PubMed1991

The height + width = area of a rectangle rule in five-year-olds: effects of stimulus distribution and graduation of the response scale.

This study attempts to account for disparities between the Anderson and Cuneo (1978), Leon (1982), and Lautrey, Mullet, and Paques (1989) studies in regard to children's area judgment. Two task variables were manipulated: stimulus distribution (biased/unbiased) and the type of response scale (graduated/ungraduated). Three age groups (5, 6, and 7 year olds) were tested. The mean integration pattern for 5-year-olds presented a negatively biased stimulus distribution, and an ungraduated response scale was highly convergent and suggested the use of a centration rule (replication of the Lautrey et al. results). When 5-year-olds were presented with an unbiased stimulus distribution and a graduated scale, the integration pattern was only slightly convergent (as in Leon). The effects of two factors (age and graduation) were significant and combined additively: The older the child, the more graduated the response scale and the more the integration pattern tended to form three ascending parallel lines (the Anderson & Cuneo results).

Child Development↗
PubMed2005

Preschool children master the logic of number word meanings.

Although children take over a year to learn the meanings of the first three number words, they eventually master the logic of counting and the meanings of all the words in their count list. Here, we ask whether children's knowledge applies to number words beyond those they have mastered: Does a child who can only count to 20 infer that number words above 'twenty' refer to exact cardinal values? Three experiments provide evidence for this understanding in preschool children. Before beginning formal education or gaining counting skill, children possess a productive symbolic system for representing number.

Analysis of Variance↗
PubMed2007

One, two, three, four, nothing more: an investigation of the conceptual sources of the verbal counting principles.

Since the publication of [Gelman, R., & Gallistel, C. R. (1978). The child's understanding of number. Cambridge, MA: Harvard University Press.] seminal work on the development of verbal counting as a representation of number, the nature of the ontogenetic sources of the verbal counting principles has been intensely debated. The present experiments explore proposals according to which the verbal counting principles are acquired by mapping numerals in the count list onto systems of numerical representation for which there is evidence in infancy, namely, analog magnitudes, parallel individuation, and set-based quantification. By asking 3- and 4-year-olds to estimate the number of elements in sets without counting, we investigate whether the numerals that are assigned cardinal meaning as part of the acquisition process display the signatures of what we call "enriched parallel individuation" (which combines properties of parallel individuation and of set-based quantification) or analog magnitudes. Two experiments demonstrate that while "one" to "four" are mapped onto core representations of small sets prior to the acquisition of the counting principles, numerals beyond "four" are only mapped onto analog magnitudes about six months after the acquisition of the counting principles. Moreover, we show that children's numerical estimates of sets from 1 to 4 elements fail to show the signature of numeral use based on analog magnitudes - namely, scalar variability. We conclude that, while representations of small sets provided by parallel individuation, enriched by the resources of set-based quantification are recruited in the acquisition process to provide the first numerical meanings for "one" to "four", analog magnitudes play no role in this process.

Awareness↗
PubMed2005

Monkeys match the number of voices they hear to the number of faces they see.

Convergent evidence demonstrates that adult humans possess numerical representations that are independent of language [1, 2, 3, 4, 5 and 6]. Human infants and nonhuman animals can also make purely numerical discriminations, implicating both developmental and evolutionary bases for adult humans' language-independent representations of number [7 and 8]. Recent evidence suggests that the nonverbal representations of number held by human adults are not constrained by the sensory modality in which they were perceived [9]. Previous studies, however, have yielded conflicting results concerning whether the number representations held by nonhuman animals and human infants are tied to the modality in which they were established [10, 11, 12, 13, 14 and 15]. Here, we report that untrained monkeys preferentially looked at a dynamic video display depicting the number of conspecifics that matched the number of vocalizations they heard. These findings suggest that number representations held by monkeys, like those held by adult humans, are unfettered by stimulus modality.

Acoustic Stimulation↗
PubMed2005

Children's profiles of addition and subtraction understanding.

The current research explored children's ability to recognize and explain different concepts both with and without reference to physical objects so as to provide insight into the development of children's addition and subtraction understanding. In Study 1, 72 7- to 9-year-olds judged and explained a puppet's activities involving three conceptual relations: (a) a+b=c, b+a=c; (b) a-b=c, a-c=b; and (c) a+b=c, c-b=a. In Study 2, the self-reports and problem-solving accuracy of 60 5- to 7-year-olds were recorded for three-term inverse problems (i.e., a+b-b=?), pairs of complementary addition and subtraction problems (i.e., a+b=c, c-b=?), and unrelated addition and subtraction problems (e.g., 3-2). Both studies highlighted individual differences in the concepts that children understand and the role of concrete referents in their understanding. These differences were related to using efficient procedures to solve unrelated addition and subtraction problems in Study 2. The results suggest that a key advance in children's conceptual understanding is incorporating subtractive relations into their mental representations of how parts are added to form a whole.

Aptitude↗
PubMed2006

On the gestalt concept.

We define a gestalt as the invariants of a collection of patterns that can mutually be transformed into each other through a class of transformations encoded by, or conversely, determining that gestalt. The class of these transformations needs to satisfy structural regularities like the ones of the mathematical structure of a group. This makes an analysis of a gestalt possible in terms of relations between its representing patterns. While the gestalt concept has its origins in cognitive psychology, it has also important implications for morphology.

Cognition↗
PubMed2006

What do semi-illiterate adults know about 2-digit Arabic numbers?

Brazilian semi-illiterates (n=19) with 1 to 4 years of academic training compared 2-digit Arabic numbers. Like competent readers, semi-illiterates responded faster and more accurately when the larger number also had the larger unit digit (unit-decade compatibility). Even semi-illiterates with minimal academic training were sensitive to the unit-decade compatibility on number comparison. Probably semi-illiterates derive their ability to automatically activate unit-decade segmentation directly from the oral/verbal number representation. Interestingly, processing speed had an effect on two-digit number comparison. Faster participants showed a smaller or even inverted unit-decade compatibility. Processing speed reflects increased automatization of number segmentation and better selection of the decade-digits for comparison, what eliminates the semantic interference of units. In line with previous research, our data suggest that unit-decade segmentation plays a pervasive role in Arabic number comparison.

Adolescent↗
PubMed2005

Linear mass balance equilibration: a new approach for an old problem.

Interval analyses are well known in the mathematics literature but have found few applications in control engineering. Based on the interval concept, we present here a methodology for data reconciliation and mass balance equilibration which is a very classical problem in mineral and chemical engineering. Indeed, this problem is solved with the view of inequality constraints which allows us to represent measurements by interval without particular knowledge and hypothesis about the density probability function of the measurement errors. As a main result, the paper gives a set of solutions for the reconciled data under an interval form and not only one solution as is the case with classical approaches.

Algorithms↗
PubMed2000

Respiratory rhythm generation in neonatal and adult mammals: the hybrid pacemaker-network model.

We review a new unified model of respiratory rhythm generation - the hybrid pacemaker-network model. This model represents a comprehensive synthesis of cellular and network mechanisms that can theoretically account for rhythm generation in different functional states, from the most reduced states in the neonatal nervous system in vitro to the intact adult system in vivo. The model incorporates a critical neuronal kernel consisting of a network of excitatory neurons with state-dependent, oscillatory bursting or pacemaker properties. This kernel, located in the pre-Bötzinger complex of the ventrolateral medulla, provides a rudimentary pacemaker network mechanism for generating an inspiratory rhythm, revealed predominately in functionally reduced states in vitro. In vivo the kernel is embedded in a larger network that interacts with the kernel via inhibitory synaptic connections that provide the dynamic control required for the evolution of the complete pattern of inspiratory and expiratory network activity. The resulting hybrid of cellular pacemaker and network properties functionally endows the system with multiple mechanisms of rhythm generation. New biophysically realistic mathematical models of the hybrid pacemaker-network have been developed that illustrate these concepts and provide a computational framework for investigating interactions of cellular and network processes that must be analyzed to understand rhythm generation.

Animals↗
PubMed1997

The Stability of the Generalized Hopfield Networks in Randomly Asynchronous Mode.

We present a study on the stability of the generalized Hopfield network in randomly asynchronous mode. First, the stability is investigated from the state space of the network. We introduce a concept of hole and define two kinds of stability in randomly asynchronous mode. By mathematical inductive method, we have proved that a generalized Hopfield network with non negative weights is strictly stable, that is, the network evolves to a simple hole-stable state with probability one when it starts at any initial state. For the general case, we made the simulation experiments on the networks with the number of neurons from 5 to 10. The empirical results have shown that almost any generalized Hopfield network with simple holes is strictly stable. Copyright 1997 Elsevier Science Ltd.

Journal Article↗
PubMed1982

Representations of qualitative and quantitative dimensions.

Geometric representations of psychological dimensions are analyzed and compared to an alternative set-theoretical approach. Judgments of similarity between forms and figures reveal the following effects: (a) qualitative attributes are curved relative to quantitative attributes, contrary to intradimensional subtractivity; (b) quantitative attributes augment differences in qualitative attributes, contrary to interdimensional additivity; (c) adding a new dimension with a fixed value increases similarity, contrary to translation invariance. The implications of these results to multidimensional representations of proximity data are discussed.

Adolescent↗
PubMed2005

The role of salience in the extraction of algebraic rules.

Recent research suggests that humans and other animals have sophisticated abilities to extract both statistical dependencies and rule-based regularities from sequences. Most of this research stresses the flexibility and generality of such processes. Here the authors take up an equally important project, namely, to explore the limits of such processes. As a case study for rule-based generalizations, the authors demonstrate that only repetition-based structures with repetitions at the edges of sequences (e.g., ABCDEFF but not ABCDDEF) can be reliably generalized, although token repetitions can easily be discriminated at both sequence edges and middles. This finding suggests limits on rule-based sequence learning and new interpretations of earlier work alleging rule learning in infants. Rather than implementing a computerlike, formal process that operates over all patterns equally well, rule-based learning may be a highly constrained and piecemeal process driven by perceptual primitives--specialized type operations that are highly sensitive to perceptual factors.

Adult↗
PubMed1993

Referential set presentation effects on complementation by 6-year-olds.

What difficulties do children encounter when responding to complementation instructions? The responses of 50 children to six complementation requests were examined. For half of the children, the objects in the referential set were pooled, and for the other half, they were physically separated by category (pencils were presented in a pencil box, buttons in a sewing kit, and balls of yarn in a knitting basket). Reinforcing the identifying status of the semantic property by separating the objects into categories led to an increase in the number of responses bearing on the subset designated in the instructions (e.g., in response to "Give me everything that is not a black button," the children handed over only the nonblack buttons). In contrast, older children gave responses based on the entire set. The meaning attributed by children to object properties and the effects of that attribution on processing mode merit further study.

Adolescent↗
PubMed2000

Efficient identification and analysis of substructures in proteins using the kappa-tau framework: left turns and helix c-cap motifs.

We have recently (1) introduced an exact mathematical description of chain molecules based on discrete analogues of the curvature and torsion concepts in differential geometry called the kappa-tau framework, and applied it to the analysis of all known protein structures. We here use it to extract and analyze defined structural motifs from the Protein Data Bank. We find a class of left handed 4 residues long, open turns, tentatively called left alpha-tums, which do not exhibit internal backbone H-bonding and join both alpha and beta1 strands at the surface of many different proteins. Further, we discuss results on helix capping substructures such as the Schellman and alpha(L) motifs. The kappa-tau methodology proves to be the most efficient methodology to handle such problems available to date, and will greatly expand our capability to decipher the information hidden in the known structures and understand the fundamental relation between sequence and structure.

Amino Acid Motifs↗
PubMed1993

Hierarchical functional organization of formal biological systems: a dynamical approach. I. The increase of complexity by self-association increases the domain of stability of a biological system.

In this series of papers, a theory of functional organization is proposed for biological systems (formal biological system, FBS), which is based on the concept of 'functional interaction', and on a 'functional self-association hypothesis'. From the specific properties of functional interactions, i.e. non-symmetry, non-locality, and non-instantaneity, it is shown that a biological system can be considered as constituted by two hierarchical systems: (i) the (O-FBS) that describes the topology of the FBS, i.e. the functional organization, with a hierarchical directed graph; (ii) the (D-FBS) that describes the continuous non-linear dynamics of the FBS with a field. In the framework of this theory, the problem of the relation between structure and function is considered to be due to the distinction between structural organization and functional organization. Some advantages of this approach are: (i) the description of the time evolution, during development, of the organization of an FBS with an optimum principle, which leads to a clear comparison with a physical system (paper II); (ii) the description of the space-time dynamics as the variation in space and time of field variables in a hierarchical 'space of structural units'; and, consequently, the relation between topology and geometry, and the existence of non-locality in these hierarchical spaces (paper III). In this paper, the basic concepts of functional interaction, hierarchical functional organization, and physiological function are discussed from a mathematical viewpoint, and arguments for the validity of the self-association hypothesis are given. Specifically, it is shown that, for a particular class of biological systems that are taken as an example, the domain of stability of the (D-FBS) is increased after functional association. This property, which is specifically due to the nature of the biological system, corresponds to an increase in complexity. It will be shown in the second paper that such a self-organization corresponds also to an optimal principle for the (O-FBS). The case of real biological systems (RBSS) is considered in relation with the present theory, which leads to a new hierarchical representation in terms of fields. Such representation could be a base for integrative physiology. As an example, some physiological functions, respiratory and cardio-vascular, are considered and it is shown that the heart shock emerges from the formulation as a cyclic sub-graph.

Animals↗
PubMed2002

Broken quantum symmetry and confinement phases in planar physics.

Many two-dimensional physical systems have symmetries which are mathematically described by quantum groups (quasitriangular Hopf algebras). In this Letter we introduce the concept of a spontaneously broken Hopf symmetry and show that it provides an effective tool for analyzing a wide variety of phases exhibiting many distinct confinement phenomena.

Journal Article↗
PubMedDate not supplied

Young children's reasoning about many-to-one correspondences.

Young children's understanding of many-to-one correspondence problems was studied to illuminate the developmental transition from additive to multiplicative numerical knowledge. A many-to-one correspondence exists when a fixed number of target objects (greater than 1) is associated with each of a set of referents, as in putting 3 flowers in each of several vases. Two experiments examined effects of a brief training procedure that highlighted the iterative nature of many-to-one mappings. In Experiment 1, 5- and 6-year-old children did not benefit from the training, but a subset of 7-year-olds did. In Experiment 2, 7-year-olds showed training effects that extended to generalization problems. Patterns of performance across experimental and generalization problems suggested that some children had difficulty applying what they learned from training to the experimental problems.

Age Factors↗
PubMed2003

The development of numerical estimation: evidence for multiple representations of numerical quantity.

We examined children's and adults' numerical estimation and the representations that gave rise to their estimates. The results were inconsistent with two prominent models of numerical representation: the logarithmic-ruler model, which proposes that people of all ages possess a single, logarithmically spaced representation of numbers, and the accumulator model, which proposes that people of all ages represent numbers as linearly increasing magnitudes with scalar variability. Instead, the data indicated that individual children possess multiple numerical representations; that with increasing age and numerical experience, they rely on appropriate representations increasingly often; and that the numerical context influences their choice of representation. The results, obtained with second graders, fourth graders, sixth graders, and adults who performed two estimation tasks in two numerical contexts, strongly suggest that one cause of children's difficulties with estimation is reliance on logarithmic representations of numerical magnitudes in situations in which accurate estimation requires reliance on linear representations.

Adult↗