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PubMed2004

Cancer death statistics: analogy between epidemiology and critical systems in physics.

The determination of risk factors in carcinogenesis is said to be an essential step towards the understanding of this disease. Most mathematical models describing the evolution of mortality figures use the concept of death probability (or "force of mortality" or "hazard of death"). When summarizing the death statistics through this unique parameter, one implicitly makes the assumption that the death events are independent from one individual to another. In this paper, we show that this hypothesis has profound consequences as it implies a "gaussian" behavior of the death statistics fluctuations. In order to verify the validity of this assumption, French cancer death statistics between the years 1978-1996 are examined. Their fluctuations, for every age bracket, are computed and then compared to the expected gaussian fluctuations that should emerge from a model of death probability. We show that the observed fluctuations are in close agreement with a gaussian model up to 35-40 years. After 40 years, the fluctuations are much higher and cannot be explained by a model where every individual would have a given "probability of death". These observations may produce a new insight into old-age cancer mortality. It suggests that there could exist a major difference between cancers in young or older organisms: cancer developed in young organisms are the consequence of a specific attack against an organ (essentially originated from a single cause, like a virus or a genetic deficiency). On the other hand, older organism are closer to a "critical state" and, as such, the outcome of a cancer in a given organ could be the consequence of a chain of "malfunctions" (analogous to an avalanche in physical systems) in the entire organism.

Adolescent↗
PubMed2000

Representation of the cardinality principle: early conception of error in a counterfactual test.

There is debate over how the integration of non-verbal quantifying and verbal counting relates to the representation of number principles. A stringent representational test would be one in which a child obeyed a number principle where it ran counter to a characteristic procedure. We devised a test relying on the uniqueness principle for using evidence from a miscount in inferring a counterfactual cardinal number. All the 5-year-olds passed, as did half the preschoolers. Subtests probed associated number-skills. We suggest that a crucial preschool step is to start conceptualising error by categorising relations between counting and miscounting. That step is taken at a similar age to passing a representational theory of mind test but the two were uncorrelated.

Child Development↗
PubMed2002

On the impact of different number representations in the number bisection task.

The number bisection task--in which the numerical middle of two other numbers has to be determined (e.g., 6 is the numerical middle of 4 and 8)--has recently been used in neuropsychological case studies in addition to the number comparison task to assess quantitative capabilities in number processing. While factors determining difficulty in normal participants have often been systematically investigated in the number comparison task, this has not yet been done in the number bisection task. Based on a pilot study by van Herten (1999), we extracted four factors that we hypothesized to modulate difficulty in a verification version of the number bisection task in normal participants: Multiplicativity (whether or not the three numbers are part of a multiplication table), range (distance between the smallest and the largest number) for bisectable number triplets as well as distance of the middle number to the numerical middle, and bisection possibility for non-bisectable triplets. In the current study, we obtained large effects for all four factors on RT and accuracy data and some interesting interactions in normal participants. In a regression analysis, we additionally observed inhibitory effects of decade crossing and of ten inclusion (whether or not one of the three numbers was a decade number). We discuss the impact of these results for the use of the number bisection task as an assessment tool in neuropsychology. Finally, we examine the consequences of these results for models of number processing.

Adult↗
PubMed1997

Arithmetic facts without meaning.

The paper presents a single-case study of patient J.G. showing severe calculation problems (and also agraphia, finger agnosia, right-left disorientation and apraxia) after the surgery of a left parietal tumor. Although the patient completely lost conceptual knowledge of arithmetic, she preserved part of memorised fact knowledge (multiplications and some additions and subtractions). The study indicates that arithmetic facts can be represented at a superficial level without understanding of the operation performed. The study completes a valid double dissociation between two types of knowledge involved in calculation (memorised facts and conceptual knowledge).

Brain Neoplasms↗
PubMed1992

Development of calculation abilities in young children.

This study investigates the development of skills for solving verbally and nonverbally presented calculation problems in children between 4 and 6 years of age. Identical addition and subtraction calculations were presented in three problem-type formats: nonverbal problems, story problems, and number-fact problems. The nonverbal problems involved presenting sets of physical referents that were then transformed either by adding or removing elements. The child saw the initial set and the number of elements that were added or removed, but not the final set. The task was to construct an array that contained the number of elements in the final set. The story problems and number-fact problems were presented orally, without props. Results indicate that children as young as 4 years of age have some success on the nonverbal problems, showing that they can transform sets by adding or subtracting elements. In contrast, children do not achieve comparable levels of success on the story problems or number-fact problems until 5 1/2 to 6 1/2 years of age. Moreover, throughout the age range tested, children performed better on nonverbal problems than on either story problems or number-fact problems. These results suggest that children's earliest ability to add and subtract is based on experiences combining and separating sets of objects in the world and that this ability precedes the development of conventional verbal methods of calculating.

Aptitude↗
PubMed1980

Aspects of cognitive activity in schizophrenia.

The application of Piaget's genetic psychology tests to schizophrenic patients yielded the following findings. The intelligence quotient of schizophrenics, although within the normal range, is slightly lower than that of a control population of similar age. This is due not to a loss of the operations of the intellect, but to a difficulty experienced by the patients in actualizing the operations. The difficulty is seen particularity in operations dealing with specific objects which require a constant maintenance of the equilibrium between assimilation and accommodation. The thought processes of hebephrenic patients oscillate between excessive assimilation, resulting in distortion of observable data, and excessive accommodation which by adhering to the observable data distorts the reasoning processing. The thought processes of paranoid schizophrenics are dominated by excessive assimilation. This predominance explains their tendency to distort observable data and their difficulty in the generalization of reasoning; it also has an impact on the assimilation/accommodation equilibrium of thier logical operations, leading to (a) difficulties in delimiting reflecting abstractions, and therefore the comprehension and extension of concepts, and (b) loss of proof based on logico-mathematical reasoning and, as a result, a propensity to resort to magical thinking and subjective explanations.

Cognition↗
PubMed2002

QSAR of ecotoxicological data on the basis of data-driven if-then-rules.

A rather small data matrix of seven chemicals and 17 different ecotoxicological end points is examined by methods of Discrete Mathematics. Especially, the lattice theory and its variant, the Formal Concept Analysis may be an attractive tool to analyze Quantitative Structure Activity Relationships, when a numerical functional approach is not at hand. The central item is the so called concept, which is a pair of subsets: A subset of molecules and a subset of properties which correspond to each other. The concepts are partially ordered due to a subset relation. From this subset relation, if-then-rules are derived, which aim to relate the structure of molecules with their ecotoxicological properties. For example, the following chemical rule is found: Cl --> (2A,2C,2M). That means, all substances considered here having a "-Cl" as structural code have a medium ecotoxicological effect on Daphnia magna, Orconectes immunisare (Crustacea) and on Photobacterium phosphoreum, at least within the training set.

Animals↗
PubMed1998

The role of conceptual understanding in children's addition problem solving.

The study examined the relationship between children's conceptual understanding and addition problem-solving procedures. Forty-eight 6- to 8-year-olds solved addition problems and, in a 2nd task, were prompted to judge whether a puppet could use the arithmetic properties of one problem to solve the next problem. Relational properties between consecutive problems were manipulated to reflect aspects of additive composition, commutativity, and associativity principles. Conceptual understanding was assessed by the ability to spontaneously use such relational properties in problem solving (Task 1) and to recognize and explain them when prompted (Task 2). Results revealed that conceptual understanding was related to using order-indifferent, decomposition, and retrieval strategies and speed and accuracy in solving unrelated problems. The importance of conceptual understanding for addition development is discussed.

Association Learning↗
PubMed1998

Conscious and unconscious strategy discoveries: a microgenetic analysis.

We examined second graders' strategy discoveries on a task that could be solved either by arithmetic computation or by a simple insight. Strategy use was assessed on each trial through both an implicit measure and an explicit one. The results provided unambiguous evidence that strategies can be discovered without conscious awareness. Almost 90% of children showed the insight at an implicit, unreportable level before they showed it at an explicit, reportable one. When children received the relevant problems on each trial, 80% reported the insight within 5 trials of when their solution times indicated that they first generated it. Implications for understanding the relation between unconscious and conscious discoveries and for the role of competing activations in strategy discovery are discussed.

Awareness↗
PubMed2002

Multiple cues for quantification in infancy: is number one of them?

A review and synthesis of the literature on quantification in infancy and early childhood is provided. In most current conceptualizations, early quantification is assumed to be number based. However, the extant literature provides no clear-cut evidence that infants use number to perform quantitative tasks. Instead, new research suggests that quantification is initially based on nonnumerical cues, such as area and contour length, whether or not a task involves discrete items. The authors discuss the implications of these findings with respect to early quantification and its relation to later numerical development.

Child Development↗
PubMed2004

Forward and backward number translation requires conceptual mediation in both balanced and unbalanced bilinguals.

It is much debated whether translation is semantically mediated or based on word-word associations at the lexical level. In 2 experiments with Dutch (L1)-French (L2) bilinguals, the authors showed that there is a semantic number magnitude effect in both forward and backward translation of number words: It takes longer to translate number words representing large quantities (e.g., acht, huit [eight]) than small quantities (e.g., twee, deux [two]). In a 3rd experiment, the authors replicated these effects with number words that had been acquired only just before the translation task. Finally, it was shown that the findings were not due to the restricted semantic context of the stimuli. These findings strongly suggest that translation processes can be semantically mediated in both directions, even at low levels of L2 proficiency.

Adolescent↗
PubMed2007

Rhesus monkeys (Macaca mulatta) enumerate large and small sequentially presented sets of items using analog numerical representations.

Two rhesus monkeys selected the larger of two sequentially presented sets of items on a computer monitor. In Experiment 1, performance was related to the ratio of set sizes, and the monkeys discriminated between sets with up to 10 items. Performance was not disrupted when 1 set had fewer than 4 items and 1 set had more than 4 items, a critical trial type for differentiating object file and analog models of numerical representation. Experiment 2 controlled the interitem rate of presentation. Experiment 3 included some trials on which number and amount (visual surface area) offered conflicting cues. Experiment 4 varied the total duration of set presentation and the duration of item visibility. In all of the experiments, performance remained high, although total set presentation duration also acted as a partial cue for the monkeys. Overall, the data indicated that rhesus monkeys estimate the approximate number of items in sequentially presented sets and that they are not relying solely on nonnumerical cues such as rate, duration, or cumulative amount.

Animals↗
PubMed2006

Grey Parrot (Psittacus erithacus) numerical abilities: addition and further experiments on a zero-like concept.

A Grey parrot (Psittacus erithacus), able to quantify 6 or fewer item sets (including heterogeneous subsets) by using English labels (I. M. Pepperberg, 1994), was tested on addition of quantities involving 0-6. He was, without explicit training, asked, "How many total X?" for 2 sequentially presented collections (e.g., of variously sized jelly beans or nuts) and required to answer with a vocal English number label. His accuracy suggested (a) that his addition abilities are comparable to those of nonhuman primates and young children, (b) some limits as to his correlation of "none" and the concept of zero, and (c) a possible counting-like strategy for the quantity 5.

Animals↗
PubMed2000

Representing quantity beyond whole numbers: some, none, and part.

Previous research has demonstrated how children develop the ability to use notational representations to indicate simple quantities. These studies have shown a developmental shift from the use of idiosyncratic, to analogical, to conventional, numerical notations. The present paper extends these findings by reporting the results from a study in which children from 3 to 7 years old were asked to write a representation to indicate a quantity presented in a game-like scenario. Three kinds of quantities were included: whole numbers, zeros, and fractions. The children's notations were shown to them shortly after they were produced and then again two weeks later to see if children could interpret them. The results showed the familiar developmental pattern towards increased use of conventional notations for all quantities. The ability to read the notations was greatest for conventional numbers where performance was at ceiling, lower for analogue representations, and very poor for idiosyncratic global recordings. Children's choice of a notational format was influenced almost entirely by their age and not by the quantity being represented. Children were able to solve the zero problems almost as well as they could the whole numbers, but their understanding and use of representations for fractions was very limited.

Child↗
PubMed2000

Children's strategy use in computational estimation.

This study reports an investigation of ten-year-old children's strategy use in computational estimation (i.e., give an approximate answer like 400 to an arithmetic problem like 224 + 213). Children used four strategies: rounding with decomposition, rounding without decomposition, truncation, and compensation. Strategies appeared to differ in frequency and effectiveness. Finally, children chose strategies in an adaptive way so as to obtain fast and accurate performance. Implications of these findings for understanding children's computational estimation performance and strategies in numerical cognition in general are discussed.

Child↗