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The productivity of lexical categories was studied longitudinally in a sample of 17 young hearing-impaired French-speaking children with cochlear implants. Age of implantation ranged from 22 months to 76 months. Spontaneous speech samples were collected at six-month intervals over a period of 36 months, starting at the one-word stage. Four general measures of their linguistic production (number of utterances, verbal fluency, vocabulary, and grammatical production) as well as 36 specific lexical categories, according to the CHILDES codes, were computed in terms of tokens, i.e., total number of words. Cochlear-implanted children (CI) were compared to a French database of normally hearing children aged 2–4 compiled by the first author. Follow-up results indicate that, at the two-year post-implantation follow-up, noun, and verb morphology was significantly impaired. At the three-year follow-up, the cochlear-implanted group had recovered on adjectives, determiners and nouns, main verbs, and auxiliaries. The two groups differed significantly in processing locative adverbs, prepositions, pronouns, and verbs (infinitive verb, modal, and modal lexical), but individual variability within the cochlear-implanted group was substantial. Results are discussed in terms of recovery and developmental trends and variability in the acquisition of lexical categories by French children two years and three years post-implantation.

The well established effect of word frequency on adult's picture naming performance is now called into question. This is particularly true for variables which are correlated with frequency, as is the case of age of word acquisition. Since the work of [Carrol and White, 1973] there is growing agreement among researchers to confer an important role in lexical access to this variable. Indeed, it has been shown ( [Hodgson and Ellis, 1998]) that for normal English-speaking adults only the variables 'age-of-acquisition' and 'name agreement' are independent predictors of naming success among the various variables considered. However, when brain-damaged subjects with and without degenerative pathologies are studied, word frequency and word length as well as concept familiarity all give significant effects ( [Hirsh and Funnell, 1995]; [Lambon Ralph et al., 1998]; [Nickels and Howard, 1995]). Finally, it has been suggested that the production of specific error types may be related to such variables. According to [Nickels and Howard, 1994] the production of semantic errors is specifically affected by 'imageability' and in the recent study by [Kremin et al., 2001] 'age of acquisition' predicts (frank) word finding difficulties.

This paper focuses on the relationships among language processing (word- and sentence-level), working memory, and verbal/nonverbal linguistic output. The study examined oral language abilities in a group of 26 French-speaking dyslexic children, compared to two control groups (26 normally developing age-matched children and 26 normally developing younger children). The experimental procedure consisted of tasks involving auditory memory skills (digit span, unfamiliar word repetition, sentence repetition), word retrieval (with semantic, phonological and grammatical criteria), and sentence processing (with verbal and act-out production). The major findings reveal that (a) compared with their age-mates, the dyslexic children exhibited a significant deficit affecting all tasks; and (b) the dyslexic children and the younger controls performed similarly on several tasks. The results are consistent with the processing limitation hypothesis and suggest that the core deficit is the formulation of cognitive plans from auditory input to verbal output.

International audience; The SOC framework does not take into account the fact that the oral modality consists of purely transient data, which is not the case for the other modalities. This, however, has important consequences on the nature of oral and written language, on language consciousness, on child language development and on the history of linguistics.

We give a survey of known results on the asymptotic and exact enumeration of discriminants of number fields, both in the absolute and relative case. We give no proofs, and refer instead to the bibliography.

The influence of prosody and its visual analog, punctuation, in text comprehension was investigated in two experiments. In the first experiment 20 subjects listened to three taped passages of equal length and difficulty varying in intonation (normal, monotonous, or altered) and were tested on tasks of text comprehension and word recognition. In the second experiment 20 new subjects read the same passages but with varying punctuation (appropriate, no punctuation, or altered) and were also tested on text comprehension and word recognition. Subjects' reading time was also recorded. ANOVA results revealed that altered prosody and punctuation affect performance in a similar fashion and seriously impair text comprehension and word recognition. This sensitivity to altered intonation suggests that linguistic prosody not only supplies redundant cues for judging sentence structure but that it also manages attentional resources to help with semantic encoding of lexical units and with the organization of linguistic information in long term memory.

The capacity to incorporate significant words into the existing vocabulary and to use these words to form sentences with more mature syntactic structures emerges over a considerable time course in young deaf children who have undergone a cochlear implantation. The purpose of this follow-up study is to document the nature and time span of language production--in morphosyntactic and lexical skills--when a child's first experience with language sounds is provided artificially through electrical stimulation. To examine the development of these two aspects of linguistic processing, five deaf French children, all enrolled in similar postimplantation educational settings, were individually assessed at 6-month intervals over a period of 18 months. Computerized analyses were derived from their spontaneous speech in a 20-min standardized play session. Results for mean length of utterance and vocabulary revealed gradually improving performance for most children, in spite of the generally low starting point. Both measures of production nevertheless remained well below the norms established for normally hearing children. Although the achievement of higher production scores, which underlies more effective interpersonal exchanges, is evident after only 1 year of device use, it is clear that improvement does not always occur at the same pace, as shown by two of the children. This emphasizes the importance of longitudinal studies in documenting intersubject variability and intrasubject stability throughout the experience with an implant.

In the study of language acquisition following early brain damage, results have been divergent. On one hand, some studies claim that language eventually resumes to normal, whereas, on the other hand, studies show lasting deficits throughout development. Discrepancies in the results could arise from different etiologies and tests used. This study attempts to determine the extent to which the development of verb production is affected in later development in children who had simple partial epilepsy (SPE). Measures of diversity and fluency of three verb types, namely main verbs, auxiliary and copula verbs, and nonfinite verbs were used on three children diagnosed as SPE and compared to control groups. Our main results show a limited production of auxiliary verbs. Further analysis of their productions suggest a telegraphic style of speech, as reflected by a superior production of nonfinite verb type compared with normal children. These findings are interpreted as reflecting long-lasting consequences of early brain damage with respect to language development.

Number theory is one of the oldest branches of mathematics, and numbertheoretical results can be found in most ancient cultures. Like many other subjects, it has flourished into a major mathematical discipline. However, it has properties that make it almost unique compared to other mathematical subjects.

A longitudinal study of a child (MV) with developmental verbal dyspraxia was conducted to determine to what extent language development and motor performance in this clinical diagnosis followed a similar course of maturation. Patient MV was observed for two years from the age of 5 years and 6 months. Initially, this young patient exhibited unintelligible and atypical speech production (multiword utterances without consonants), delay in balance and coordination, and impairments in rhythmic tasks; but she was otherwise developing normally with no intellectual impairment or behavioral disorder. MRI scans showed moderately enlarged ventricles, a thin, incompletely myelinated corpus callosum and intact basal ganglia. Two years later, MV's performance was nearly normal only in comprehension aspects of language. In contrast, production aspects of language and speech and neuromotor development showed very little improvement after two years. These observations first suggest that development of receptive and expressive domains within language may be asynchronous, and that the progression of motor control of language appears to follow a parallel course to neuromotor development.

Chronic exposure to elevated glucocorticoid levels in Cushing's syndrome (CS), is associated with deficits in cognitive function and in emotion. The hippocampus plays a crucial role in the behavioral manifestations of the syndrome as it is richest in glucocorticoid receptors and is thus particularly vulnerable to glucocorticoid excess. The wide distribution of glucocorticoid receptors throughout the cerebral cortex, however, suggests that several cognitive functions can also be affected by the dysregulation of glucocorticoids. In this study, we investigated how an excess of glucocorticoid hormones affects cognitive processes. Nineteen patients with chronic hypercortisolemia due to CS were compared to healthy controls matched for age, sex, education, and occupation in tests of processing of visual and spatial information, memory, reasoning and concept formation, language and verbal functions, and attention. Multivariate and univariate analyses revealed overall differences in tests of treatment of visual and spatial information, reasoning and concept formation as well as in verbal and language performance, with poorer performance from CS patients. Differences were also observed in nonverbal aspects of memory and in attention tasks. The results suggest that chronic exposure to elevated levels of cortisol is associated with deficits in several areas of cognition, particularly those involving processing of selective attention and visual components. This study also shows that hormones play an important role in the modulation of cognitive function and that their influence on cerebral structure and function merits closer scrutiny. (JINS, 2000, 6, 20–29.)

The easiest way to start studying number fields is to consider them per se, as absolute extensions of √; this is, for example, what we have done in [Coh0]. In practice, however, number fields are frequently not given in this way. One of the most common other ways is to give a number field as a relative extension, in other words as an algebra L/K over some base field K that is not necessarily equal to √. necessarily equal to ℚ. In this case, the basic algebraic objects such as the ring of integers ℤ L and the ideals of ℤ L , are not only ℤ-modules, but also ℤ K- modules. The ℤ K -module structure is much richer and must be preserved. No matter what means are chosen to compute ℤ L , we have the problem of representing the result. Indeed, here we have a basic stumbling block: considered as ℤ-modules, ℤ L or ideals of ℤ L are free and hence may be represented by ℤ-bases, for instance using the Hermite normal form (HNF); see, for example, [Coh0, Chapter 2]. This theory can easily be generalized by replacing ℤ with any other explicitly computable Euclidean domain and, under certain additional conditions, to a principal ideal domain (PID). In general, ℤ K is not a PID, however, and hence there is no reason for ℤ L to be a free module over ℤ K- A simple example is given by K = ℚ(√-10) and L = K(√1) (see Exercise 22 of Chapter 2).

Class field theory deals with Abelian extensions of base fields. It gives complete answers to the existence of Abelian extensions with given relative or absolute discriminants. However, the algorithmic construction of these extensions is not completely straightforward. There are several ways to do this, but at present the most efficient general method is the use of Kummer extensions. In the next chapter, we will describe two other methods using analytic techniques, one using Stark units and Stark’s conjecture, the other using complex multiplication. Both of these methods impose restrictions on the base field, but when they are applicable they are much more efficient.

Having the necessary tools for dealing theoretically and algorithmically with modules over Dedekind domains, we are now going to study in detail relative extensions of number fields. In the first section, we emphasize the field-theoretic properties, while in the rest of this chapter we study the ring-theoretic properties.

In this chapter, we give the main results of global class field theory for the case of number fields. We refer the reader to [Art-Tat], [Gras], [Has1], [Jan], or [Mart4] for more detailed statements and proofs. We present the results “a la Hasse”, without using ideles. This is more suitable for algorithmic treatment. For an idelic treatment, we refer to [Neu]. I have largely benefited from the notes of J. Martinet [Mart4] in writing this chapter.

In Chapter 3 we studied variants of class and unit groups, the ray class groups Clm(K), as well as the associated unit groups Um(K) of units multiplicatively congruent to 1 modulo m. The fundamental application of these notions through the deep theorems of class field theory is the construction of Abelian extensions.

In this chapter, we will describe in detail the known methods for computing tables of number fields with small discriminant. We can try to pursue two different goals.

In Chapter 3 we gave the main theoretical results concerning global class field theory over number fields. We are now going to study this subject from the algorithmic point of view. In the present chapter, we give efficient algorithms for computing ray class groups of number fields and for computing the conductor and norm group of the Abelian extensions corresponding to congruence subgroups of these ray class groups by Takagi’s Theorem 3.5.1. Thanks to Proposition 3.5.8 and Theorem 3.5.11, this allows us to compute their signature and discriminant.

In [Coh0], I have given a rather extensive list of packages more or less related to number theory. While that list is not out of date, it is perhaps worthwhile to insist here on the really useful packages and also on other types of electronically available information. I also mention programs or data not related to the subject matter of this book but important for number theory and for related subjects. Since pricing policies change very rapidly (and free packages sometimes become not free), I have decided to include no pricing information, but only pointers to the relevant web pages or e-mail addresses.

We discuss some linear acceleration methods for alternating series which are in theory and in practice much better than that of Euler--Van Wijngaarden. One of the algorithms, for instance, allows one to calculate $\sum(-1)^ka_k$ with an error of about $17$.$93^{-n}$ from the first $n$ terms for a wide class of sequences $\{a_k\}$. Such methods are useful for high precision calculations frequently appearing in number theory.

In the preceding chapter we saw how to construct Abelian extensions of a number field K corresponding to a given congruence subgroup (m, C) by using Kummer theory. The main advantage of this method is that it is completely general (and hence is the only method used for the proofs of the existence results in class field theory), but its main drawback is the necessity of working over a larger field K z = K(ζn).

In [Coh0, Chapter 5], we studied quadratic fields in great detail. The goal of the present chapter is to do the same for cubic fields. We have already studied them in some detail in [Coh0, Chapter 6], but in the present chapter we will deal with deeper subjects and also show how to generate tables of cubic fields almost as efficiently as tables of quadratic fields. The spirit of this chapter is slightly different from that of the preceding chapters, which essentially deal with relative extensions, but the results are sufficiently important to be included in a textbook. Had they been known when [Coh0] was first published, they would, of course, have been included there.

The nature of cerebral involvement in the acquisition of language was addressed in this longitudinal study of children with an early diagnosis of epilepsy with simple-partial seizures (SPE) and with epileptogenic foci localized in the left frontal (LF) lobe. Yearly evaluations of six SPE-LF children on tests of linguistic comprehension (pointing, understanding of narrative, and understanding of prepositions) and production (repetition, lexical diversity, and grammatical production) were carried out between the ages of 3 and 8 years and compared to those of large samples of control children on the same tasks and at each age level. Linguistic production of all children were transcribed, coded, and analyzed using the Child Language Data Exchange System (MacWhinney & Snow, 1991). Individual evolution trajectories revealed that SPE-LF children showed a clear dissociation in linguistic performance between comprehension and production. Linguistic comprehension gradually improved to reach normal performance levels by age 7 while linguistic production, even at later stages, remained quite poor. This dissociation in the development of linguistic performance in SPE-LF children suggests a complex interplay between brain maturation dynamics and dysfunction modulating the succession of stages in language development. The observed persistent deficits in specific aspects of linguistic performance argue for an early involvement of the anterior areas of the left cerebral hemisphere in the production of language.

Using the explicit class field theory developed in [3] and tables of number fields in low degree, we construct totally complex number fields having a degree smaller than 80 and a root discriminant near from Odlyzko's bounds. For some degrees, we extend and improve the table of totally complex number fields of small discriminants given by Martinet

Elliptic curve cryptosystems, proposed by Koblitz ([12]) and Miller ([16]), can be constructed over a smaller field of definition than the ElGamal cryptosystems ([6]) or the RSA cryptosystems ([20]). This is why elliptic curve cryptosystems have begun to attract notice. In this paper, we investigate efficient elliptic curve exponentiation. We propose a new coordinate system and a new mixed coordinates strategy, which significantly improves on the number of basic operations needed for elliptic curve exponentiation.

Deficits in verbal fluency and naming, memory and comprehension of verbal information, as well impairment in verbal and logical reasoning are frequently associated with linguistic performance in Parkinson's disease, a neurodegenerative disorder primarily involving subcortical structures and the depletion of dopaminergic neurons in the substantia nigra. Impairment is more pronounced in more complex aspects of language processing as in sentence comprehension, understanding of relational terms and relative clauses, and in aspects of logical reasoning. It is believed that constraints in accessing the cognitive resources needed to implement the processing of syntactic and semantic information, as well as the disruption of reciprocating neural connections between the basal ganglia with the prefrontal cortex, may explain these observed deficits.

We give here the complete table of octic fields with a quartic subfield with minimum discriminants for all signatures and for all the possible Galois groups. Moreover we give some pairs of octic fields arithmetically equivalent (i.e. with the same Dedekind zeta function).

Using the theory of binary pseudo-quadratic forms over Z developed in [5], we sketch an algorithm for computing the relative class group of quadratic extensions. We end by a striking example which can be treated orders of magnitude faster using the relative method than using the absolute one.

Elliptic curve cryptosystems, proposed by Koblitz([8]) and Miller([11]), can be constructed over a smaller definition field than the ElGamal cryptosystems([5]) or the RSA cryptosystems( [16]). This is why elliptic curve cryptosystems have begun to attract notice. There are mainly two types in elliptic curve cryptosystems, elliptic curves E over IF2r and E over IFp. Some current systems based on ElGamal or RSA may often use modulo arithmetic over IFp. Therefore it is convenient to construct fast elliptic curve cryptosystems over IFp. In this paper, we investigate how to implement elliptic curve cryptosystems on E/IFp.

This document is an adapted selection of excerpts from two newly published books, Mathematics by Experiment: Plausible Reasoning in the 21st Century, and Experimentation in Mathematics: Computational Paths to Discovery, published by AK Peters, Natick, Massachussetts. We have gleaned from these two volumes material that explains what experimental mathematics is all about, as well as some of the more engaging examples of experimental mathematics in action. The experimental methodology that we describe in these books provides a compelling way to generate understanding and insight; to generate and confirm or confront conjectures; and generally to make mathematics more tangible, lively and fun for both the professional researcher and the novice. We have concentrated primarily on examples from analysis and number theory, but there are numerous excursions into other areas of mathematics as well. Much of this material is gleaned from existing sources, but there is a signicant amount of material that, as far as we are aware, has not yet appeared in the literature.

Age differences in the representation of semantic information may underlie the cognitive decline observed in aging. The objective of the present study was to determine to what extent elderly and young subjects agreed in the representations of semantic categories. Ninety elderly (77 women, 13 men) and 90 young (74 women, 16 men) participants wrote down the first four associations evoked by each of 30 semantic category names. Results showed differences between the two groups in items selected as most common responses (MCRs); frequency of occurrence of the MCRs differed between the two groups in 21 semantic categories. Results suggest that young and elderly subjects hold different representations of semantic categories and also highlight the importance of using age-appropriate norms in the evaluation of cognitive functions in aging.

We describe the computation of ray class groups of number fields, conductors and discriminants of the corresponding Abelian extensions. As an application we give several number fields with discriminants less than previously known ones.

In this study, 10 men, 10 women, and 13 genetic male transsexuals, all of them righthanded, were tested on two verbal (CV and nonsense polysyllables) and two nonverbal (melodies and triple tone [3T]) dichotic tasks to investigate relations between hormone therapy and auditory cerebral specialization for speech and non speech stimuli in adults. At time of testing, all transsexuals had been under hormonal treatment for at least one year and eight had had corrective surgery. ANOVA results showed a right ear advantage and similar pattern of performance for the three groups in the treatment of speech. In nonverbal tasks, interactions revealed a left ear advantage in the processing of melodies and 3T for men only; women and transsexuals exhibited similar performance in both nonverbal tasks. In accord with generalization from the animal literature, cautious interpretation of the data is some possible hormonal involvement, in adults, in the modulation of right hemispheric cognitive processing.