Indice de Point Fixe pour les Morphismes de Chaînes

2000 Mathematics Subject Classification: 54H25, 55M20.

Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type

MSC 2010: 33C47, 42C05, 41A55, 65D30, 65D32

A Note on the L2-norm of the Second Fundamental Form of Algebraic Manifolds

2000 Mathematics Subject Classification: 53C42, 53C55.

Polynomial automorphisms over finite fields: Mimicking tame maps by the Derksen group

2010 Mathematics Subject Classification: 14L99, 14R10, 20B27.

The relationship between spoken language and speech and nonspeech processing in children with autism:a magnetic event-related field study

It has been proposed that language impairments in children with Autism Spectrum Disorders (ASD) stem from atypical neural processing of speech and/or nonspeech sounds. However, the strength of this proposal is compromised by the unreliable outcomes of previous studies of speech and nonspeech processing in ASD. The aim of this study was to determine whether there was an association between poor spoken language and atypical event-related field (ERF) responses to speech and nonspeech sounds in children with ASD (n = 14) and controls (n = 18). Data from this developmental population (ages 6-14) were analysed using a novel combination of methods to maximize the reliability of our findings while taking into consideration the heterogeneity of the ASD population. The results showed that poor spoken language scores were associated with atypical left hemisphere brain responses (200 to 400 ms) to both speech and nonspeech in the ASD group. These data support the idea that some children with ASD may have an immature auditory cortex that affects their ability to process both speech and nonspeech sounds. Their poor speech processing may impair their ability to process the speech of other people, and hence reduce their ability to learn the phonology, syntax, and semantics of their native language.

Deconvolution of magnetic acoustic change complex (mACC)

Objective: The aim of this study was to design a novel experimental approach to investigate the morphological characteristics of auditory cortical responses elicited by rapidly changing synthesized speech sounds. Methods: Six sound-evoked magnetoencephalographic (MEG) responses were measured to a synthesized train of speech sounds using the vowels /e/ and /u/ in 17 normal hearing young adults. Responses were measured to: (i) the onset of the speech train, (ii) an F0 increment; (iii) an F0 decrement; (iv) an F2 decrement; (v) an F2 increment; and (vi) the offset of the speech train using short (jittered around 135. ms) and long (1500. ms) stimulus onset asynchronies (SOAs). The least squares (LS) deconvolution technique was used to disentangle the overlapping MEG responses in the short SOA condition only. Results: Comparison between the morphology of the recovered cortical responses in the short and long SOAs conditions showed high similarity, suggesting that the LS deconvolution technique was successful in disentangling the MEG waveforms. Waveform latencies and amplitudes were different for the two SOAs conditions and were influenced by the spectro-temporal properties of the sound sequence. The magnetic acoustic change complex (mACC) for the short SOA condition showed significantly lower amplitudes and shorter latencies compared to the long SOA condition. The F0 transition showed a larger reduction in amplitude from long to short SOA compared to the F2 transition. Lateralization of the cortical responses were observed under some stimulus conditions and appeared to be associated with the spectro-temporal properties of the acoustic stimulus. Conclusions: The LS deconvolution technique provides a new tool to study the properties of the auditory cortical response to rapidly changing sound stimuli. The presence of the cortical auditory evoked responses for rapid transition of synthesized speech stimuli suggests that the temporal code is preserved at the level of the auditory cortex. Further, the reduced amplitudes and shorter latencies might reflect intrinsic properties of the cortical neurons to rapidly presented sounds. Significance: This is the first demonstration of the separation of overlapping cortical responses to rapidly changing speech sounds and offers a potential new biomarker of discrimination of rapid transition of sound.

Heterogeneous labour and the determination of value

Heterogeneity of labour and its implications for the Marxian theory of value has been one of the most controversial issues in the literature of the Marxist political economy. The adoption of Marx's conjecture about a uniform rate of surplus value leads to a simultaneous determination of the values of common and labour commodities of different types and the uniform rate of surplus value. Determination of these variables can be formally represented as a parametric cigenvalue problem. Morishima's and Bródy's earlier results are analysed and given new interpretations in the light of the suggested procedure. The main questions are addressed in a more general context too. The analysis is extended to the problem of segmented labour market, as well.

Thinking in three dimensions: Exploring students' geometric thinking and spatial ability with the Geometer's Sketchpad

Current reform initiatives recommend that geometry instruction include the study of three-dimensional geometric objects and provide students with opportunities to use spatial skills in problem-solving tasks. Geometer's Sketchpad (GSP) is a dynamic and interactive computer program that enables the user to investigate and explore geometric concepts and manipulate geometric structures. Research using GSP as an instructional tool has focused primarily on teaching and learning two-dimensional geometry. This study explored the effect of a GSP based instructional environment on students' geometric thinking and three-dimensional spatial ability as they used GSP to learn three-dimensional geometry. For 10 weeks, 18 tenth-grade students from an urban school district used GSP to construct and analyze dynamic, two-dimensional representations of three-dimensional objects in a classroom environment that encouraged exploration, discussion, conjecture, and verification. The data were collected primarily from participant observations and clinical interviews and analyzed using qualitative methods of analysis. In addition, pretest and posttest measures of three-dimensional spatial ability and van Hiele level of geometric thinking were obtained. Spatial ability measures were analyzed using standard t-test analysis. ^ The data from this study indicate that GSP is a viable tool to teach students about three-dimensional geometric objects. A comparison of students' pretest and posttest van Hiele levels showed an improvement in geometric thinking, especially for students on lower levels of the van Hiele theory. Evidence at the p < .05 level indicated that students' spatial ability improved significantly. Specifically, the GSP dynamic, visual environment supported students' visualization and reasoning processes as students attempted to solve challenging tasks about three-dimensional geometric objects. The GSP instructional activities also provided students with an experiential base and an intuitive understanding about three-dimensional objects from which more formal work in geometry could be pursued. This study demonstrates that by designing appropriate GSP based instructional environments, it is possible to help students improve their spatial skills, develop more coherent and accurate intuitions about three-dimensional geometric objects, and progress through the levels of geometric thinking proposed by van Hiele. ^

Rank and k-nullity of contact manifolds

We prove that the dimension of the 1-nullity distribution N(1) on a closed Sasakian manifold M of rankl is at least equal to 2l−1 provided that M has an isolated closed characteristic. The result is then used to provide some examples of k-contact manifolds which are not Sasakian. On a closed, 2n+1-dimensional Sasakian manifold of positive bisectional curvature, we show that either the dimension of N(1) is less than or equal to n+1 or N(1) is the entire tangent bundle TM. In the latter case, the Sasakian manifold Mis isometric to a quotient of the Euclidean sphere under a finite group of isometries. We also point out some interactions between k-nullity, Weinstein conjecture, and minimal unit vector fields.

Economia criativa e estratégia como prática social: uma abordagem teórico-empírico-conceitual a partir de ambientes criativos de grupos musicais

This study seeks to identify how creative environments of musical groups are configured in the Strategy as Practice perspective as theoretical, empirical and conceptual models. It develops within the theoretical framework, discussions on the context of the Creative Economy, Creative Industries, creative environment, organizational paradigm of Creative Economy, music as a creative environment and business, design and dynamics of Strategy as Practice and conjecture about the contextualism and other epistemological currents. The study is shaped as an exploratory and descriptive research, utilizing the qualitative method and being characterized as a Grounded Theory. A total of four musical groups of different styles, markets and areas of operation with over ten years of activity were surveyed. The Grounded Theory and simple observation methods were used for both data collection and analysis. The software ATLAS.ti. was used to help with the analysis. The research shows that the bands perceive the specialized expertise in the virtual social media as a strategic differentiator. It also shows that the groups nourish individuation and the differentiation in their relationship with the individual. Finally, it validates that these organizations get teams involved and value the dynamic design of their routines in strategic decision making, paying attention to a strategic social bias. Strategy and Creative Practice is the main category that emerged from the data. This category is explained through the three aforementioned results. It shows that organizations that are part of the Creative Economy perform simultaneously and dynamically creative and strategic making at both artistic and managerial levels.The theory created is validated by the principles of degree of coherence, functionality, relevance, flexibility, density and integration, and it is inserted in the contextualism principle, which points the knowledge as related to the context in which it is placed and discussed.

Some examples of special Lagrangian tori

A short paper giving some examples of smooth hypersurfaces M of degree n+1 in complex projective n-space that are defined by real polynomial equations and whose real slice contains a component diffeomorphic to an n-1 torus, which is then special Lagrangian with respect to the Calabi-Yau metric on M.

Calibrated embeddings in the special Lagrangian and coassociative cases

Every closed, oriented, real analytic Riemannian 3-manifold can be isometrically embedded as a special Lagrangian submanifold of a Calabi-Yau 3-fold, even as the real locus of an antiholomorphic, isometric involution. Every closed, oriented, real analytic Riemannian 4-manifold whose bundle of self-dual 2-forms is trivial can be isometrically embedded as a coassociative submanifold in a G_2-manifold, even as the fixed locus of an anti-G_2 involution. These results, when coupled with McLean's analysis of the moduli spaces of such calibrated submanifolds, yield a plentiful supply of examples of compact calibrated submanifolds with nontrivial deformation spaces.

Moduli Space of (0,2) Conformal Field Theories

In this thesis we study aspects of (0,2) superconformal field theories (SCFTs), which are suitable for compactification of the heterotic string. In the first part, we study a class of (2,2) SCFTs obtained by fibering a Landau-Ginzburg (LG) orbifold CFT over a compact K\"ahler base manifold. While such models are naturally obtained as phases in a gauged linear sigma model (GLSM), our construction is independent of such an embedding. We discuss the general properties of such theories and present a technique to study the massless spectrum of the associated heterotic compactification. We test the validity of our method by applying it to hybrid phases of GLSMs and comparing spectra among the phases. In the second part, we turn to the study of the role of accidental symmetries in two-dimensional (0,2) SCFTs obtained by RG flow from (0,2) LG theories. These accidental symmetries are ubiquitous, and, unlike in the case of (2,2) theories, their identification is key to correctly identifying the IR fixed point and its properties. We develop a number of tools that help to identify such accidental symmetries in the context of (0,2) LG models and provide a conjecture for a toric structure of the SCFT moduli space in a large class of models. In the final part, we study the stability of heterotic compactifications described by (0,2) GLSMs with respect to worldsheet instanton corrections to the space-time superpotential following the work of Beasley and Witten. We show that generic models elude the vanishing theorem proved there, and may not determine supersymmetric heterotic vacua. We then construct a subclass of GLSMs for which a vanishing theorem holds.

Optimal 5-step nilpotent quadratic algebras

By the Golod–Shafarevich theorem, an associative algebra $R$ given by $n$ generators and $<n^2/3$ homogeneous quadratic relations is not 5-step nilpotent. We prove that this estimate is optimal. Namely, we show that for every positive integer $n$, there is an algebra $R$ given by $n$ generators and $\lceil n^2/3\rceil$ homogeneous quadratic relations such that $R$ is 5-step nilpotent.