Law of large numbers for super-brownian motions with a single point source

We investigate the super-Brownian motion with a single point source in dimensions 2 and 3 as constructed by Fleischmann and Mueller in 2004. Using analytic facts we derive the long time behavior of the mean in dimension 2 and 3 thereby complementing previous work of Fleischmann, Mueller and Vogt. Using spectral theory and martingale arguments we prove a version of the strong law of large numbers for the two dimensional superprocess with a single point source and finite variance.

Assessing L2 task performance: understanding effects of task design

The overarching aim of the research reported here was to investigate the effects of task structure and storyline complexity of oral narrative tasks on second language task performance. Participants were 60 Iranian language learners of English who performed six narrative tasks of varying degree of structure and storyline complexity in an assessment setting. A number of analytic detailed measures were employed to examine whether there were any differences in the participants’ performances elicited by the different tasks in terms of their accuracy, fluency, syntactic complexity and lexical diversity. Results of the data analysis showed that performance in the more structured tasks was more accurate and to a great extent more fluent than that in the less structured tasks. The results further revealed that syntactic complexity of L2 performance was related to the storyline complexity, i.e. more syntactic complexity was associated with narratives that had both foreground and background storylines. These findings strongly suggest that there is some unsystematic variance in the participants’ performance triggered by the different aspects of task design.

Axonal velocity distributions in neural feld equations

By modelling the average activity of large neuronal populations, continuum mean field models (MFMs) have become an increasingly important theoretical tool for understanding the emergent activity of cortical tissue. In order to be computationally tractable, long-range propagation of activity in MFMs is often approximated with partial differential equations (PDEs). However, PDE approximations in current use correspond to underlying axonal velocity distributions incompatible with experimental measurements. In order to rectify this deficiency, we here introduce novel propagation PDEs that give rise to smooth unimodal distributions of axonal conduction velocities. We also argue that velocities estimated from fibre diameters in slice and from latency measurements, respectively, relate quite differently to such distributions, a significant point for any phenomenological description. Our PDEs are then successfully fit to fibre diameter data from human corpus callosum and rat subcortical white matter. This allows for the first time to simulate long-range conduction in the mammalian brain with realistic, convenient PDEs. Furthermore, the obtained results suggest that the propagation of activity in rat and human differs significantly beyond mere scaling. The dynamical consequences of our new formulation are investigated in the context of a well known neural field model. On the basis of Turing instability analyses, we conclude that pattern formation is more easily initiated using our more realistic propagator. By increasing characteristic conduction velocities, a smooth transition can occur from self-sustaining bulk oscillations to travelling waves of various wavelengths, which may influence axonal growth during development. Our analytic results are also corroborated numerically using simulations on a large spatial grid. Thus we provide here a comprehensive analysis of empirically constrained activity propagation in the context of MFMs, which will allow more realistic studies of mammalian brain activity in the future.

How Twitter is studied in the medical professions: a classification of Twitter papers indexed in PubMed

Background: Since their inception, Twitter and related microblogging systems have provided a rich source of information for researchers and have attracted interest in their affordances and use. Since 2009 PubMed has included 123 journal articles on medicine and Twitter, but no overview exists as to how the field uses Twitter in research. // Objective: This paper aims to identify published work relating to Twitter indexed by PubMed, and then to classify it. This classification will provide a framework in which future researchers will be able to position their work, and to provide an understanding of the current reach of research using Twitter in medical disciplines. Limiting the study to papers indexed by PubMed ensures the work provides a reproducible benchmark. // Methods: Papers, indexed by PubMed, on Twitter and related topics were identified and reviewed. The papers were then qualitatively classified based on the paper’s title and abstract to determine their focus. The work that was Twitter focused was studied in detail to determine what data, if any, it was based on, and from this a categorization of the data set size used in the studies was developed. Using open coded content analysis additional important categories were also identified, relating to the primary methodology, domain and aspect. // Results: As of 2012, PubMed comprises more than 21 million citations from biomedical literature, and from these a corpus of 134 potentially Twitter related papers were identified, eleven of which were subsequently found not to be relevant. There were no papers prior to 2009 relating to microblogging, a term first used in 2006. Of the remaining 123 papers which mentioned Twitter, thirty were focussed on Twitter (the others referring to it tangentially). The early Twitter focussed papers introduced the topic and highlighted the potential, not carrying out any form of data analysis. The majority of published papers used analytic techniques to sort through thousands, if not millions, of individual tweets, often depending on automated tools to do so. Our analysis demonstrates that researchers are starting to use knowledge discovery methods and data mining techniques to understand vast quantities of tweets: the study of Twitter is becoming quantitative research. // Conclusions: This work is to the best of our knowledge the first overview study of medical related research based on Twitter and related microblogging. We have used five dimensions to categorise published medical related research on Twitter. This classification provides a framework within which researchers studying development and use of Twitter within medical related research, and those undertaking comparative studies of research relating to Twitter in the area of medicine and beyond, can position and ground their work.

Classification of cortical microcircuits based on micro-electrode-array data from slices of rat barrel cortex

The bewildering complexity of cortical microcircuits at the single cell level gives rise to surprisingly robust emergent activity patterns at the level of laminar and columnar local field potentials (LFPs) in response to targeted local stimuli. Here we report the results of our multivariate data-analytic approach based on simultaneous multi-site recordings using micro-electrode-array chips for investigation of the microcircuitary of rat somatosensory (barrel) cortex. We find high repeatability of stimulus-induced responses, and typical spatial distributions of LFP responses to stimuli in supragranular, granular, and infragranular layers, where the last form a particularly distinct class. Population spikes appear to travel with about 33 cm/s from granular to infragranular layers. Responses within barrel related columns have different profiles than those in neighbouring columns to the left or interchangeably to the right. Variations between slices occur, but can be minimized by strictly obeying controlled experimental protocols. Cluster analysis on normalized recordings indicates specific spatial distributions of time series reflecting the location of sources and sinks independent of the stimulus layer. Although the precise correspondences between single cell activity and LFPs are still far from clear, a sophisticated neuroinformatics approach in combination with multi-site LFP recordings in the standardized slice preparation is suitable for comparing normal conditions to genetically or pharmacologically altered situations based on real cortical microcircuitry.

Numerical conformal mapping and mesh generation for polygonal and multiply-connected regions

Details are given of a boundary-fitted mesh generation method for use in modelling free surface flow and water quality. A numerical method has been developed for generating conformal meshes for curvilinear polygonal and multiply-connected regions. The method is based on the Cauchy-Riemann conditions for the analytic function and is able to map a curvilinear polygonal region directly onto a regular polygonal region, with horizontal and vertical sides. A set of equations have been derived for determining the lengths of these sides and the least-squares method has been used in solving the equations. Several numerical examples are presented to illustrate the method.

Complex-valued b-spline neural networks for modelling and inverse of wiener systems

Communication signal processing applications often involve complex-valued (CV) functional representations for signals and systems. CV artificial neural networks have been studied theoretically and applied widely in nonlinear signal and data processing [1–11]. Note that most artificial neural networks cannot be automatically extended from the real-valued (RV) domain to the CV domain because the resulting model would in general violate Cauchy-Riemann conditions, and this means that the training algorithms become unusable. A number of analytic functions were introduced for the fully CV multilayer perceptrons (MLP) [4]. A fully CV radial basis function (RBF) nework was introduced in [8] for regression and classification applications. Alternatively, the problem can be avoided by using two RV artificial neural networks, one processing the real part and the other processing the imaginary part of the CV signal/system. A even more challenging problem is the inverse of a CV

The Brownian traveller on manifolds

We study the inuence of the intrinsic curvature on the large time behaviour of the heat equation in a tubular neighbourhood of an unbounded geodesic in a two-dimensional Riemannian manifold. Since we consider killing boundary conditions, there is always an exponential-type decay for the heat semigroup. We show that this exponential-type decay is slower for positively curved manifolds comparing to the at case. As the main result, we establish a sharp extra polynomial-type decay for the heat semigroup on negatively curved manifolds comparing to the at case. The proof employs the existence of Hardy-type inequalities for the Dirichlet Laplacian in the tubular neighbourhoods on negatively curved manifolds and the method of self-similar variables and weighted Sobolev spaces for the heat equation.

Superhumps: confronting theory with observation

We review the theory and observations related to the "superhump" precession of eccentric accretion discs in close binary systems. We agree with earlier work, although for different reasons, that the discrepancy between observation and dynamical theory implies that the effect of pressure in the disc cannot be neglected. We extend earlier work that investigates this effect to include the correct expression for the radius at which resonant orbits occur. Using analytic expressions for the accretion disc structure, we derive a relationship between the period excess and mass ratio with the pressure effects included. This is compared to the observed data, recently derived results for detailed integration of the disc equations and the equivalent empirically derived relations and used to predict values for the mass ratio based on measured values of the period excess for 88 systems.

Fireballs, flares, and flickering: A semianalytic, LTE, explosive model from accretion disks to supernovae

We derive simple analytic expressions for the continuum light curves and spectra of flaring and flickering events that occur over a wide range of astrophysical systems. We compare these results to data taken from the cataclysmic variable SS Cygni and also from SN 1987A, deriving physical parameters for the material involved. Fits to the data indicate a nearly time-independent photospheric temperature arising from the strong temperature dependence of opacity when hydrogen is partially ionized.

The joint influence of personal achievement goals and classroom goal structures on achievement-relevant outcomes

The authors provide an analytic framework for studying the joint influence of personal achievement goals and classroom goal structures on achievement-relevant outcomes. This framework encompasses 3 models (the direct effect model, indirect effect model, and interaction effect model), each of which addresses a different aspect of the joint influence of the 2 goal levels. These 3 models were examined together with a sample of 1,578 Japanese junior high and high school students from 47 classrooms. Results provided support for each of the 3 models: Classroom goal structures were not only direct, but also indirect predictors of intrinsic motivation and academic self-concept, and some cross-level interactions between personal achievement goals and classroom goal structures were observed (indicating both goal match and goal mismatch effects). A call is made for more research that takes into consideration achievement goals at both personal and structural levels of representation. (PsycINFO Database Record (c) 2012 APA, all rights reserved)(journal abstract)

Separation of performance-approach and performance-avoidance achievement goals: A broader analysis

In the literature on achievement goals, performance-approach goals (striving to do better than others) and performance-avoidance goals (striving to avoid doing worse than others) tend to exhibit a moderate to high correlation, raising questions about whether the 2 goals represent distinct constructs. In the current article, we sought to examine the separability of these 2 goals using a broad factor-analytic approach that attended to issues that have been overlooked or underexamined in prior research. Five studies provided strong evidence for the separation of these 2 goal constructs: Separation was observed not only with exploratory factor analysis across different age groups and countries (Studies 1a and 1b) but also with change analysis (Study 2), ipsative factor analysis (Study 3), within-person analysis (Study 4), and behavioral genetics analysis (Study 5). We conclude by discussing the implications of the present research for the achievement goal literature, as well as the psychological literature in general.

A cross-cultural examination of the psychometric properties of responses to the Achievement Goal Questionnaire

The psychometric properties of scores from the Achievement Goal Questionnaire were examined in samples of Japanese (N = 326) and Canadian (N = 307) post secondary students. Previous research found evidence of a four-factor structure of achievement goals in U.S. samples. Using confirmatory factor-analytic techniques, the authors found strong evidence for the four-factor structure of achievement goals in both the Canadian and Japanese populations. Subsequent multi group structural equation modeling indicated the metric invariance of this four-factor structure across the two populations.

Digital code-switching between Cypriot and Standard Greek: performance and identity play online

Studies of code-switching in writing are very limited in comparison with the numerous investigations of this phenomenon in oral communication. Recent research has revealed that in text-based computer-mediated communication internet users bring into play the various languages available in their linguistic repertoire and, consequently, switch between them. In this case study, I investigate digital code-switching between Cypriot and Standard Greek, the two varieties of Greek spoken on the island of Cyprus. Following Auer’s conversation analytic approach and Gafaranga’s view that conversational structure coexists with social structure, I investigate code-switching in online interactions. The data to be analysed here, unlike those considered in most studies of code-switching, are written data, obtained from channel #Cyprus of Internet Relay Chat. The results suggest that code-switching in writing is influenced not only by macro-sociolinguistic factors, but they are also shaped by the medium- and social-specific characteristics of Internet Relay Chat. This, in turn, allows internet users to gain access to different roles and perform various identities within this online context.

Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-dGFEM

We study the approximation of harmonic functions by means of harmonic polynomials in two-dimensional, bounded, star-shaped domains. Assuming that the functions possess analytic extensions to a delta-neighbourhood of the domain, we prove exponential convergence of the approximation error with respect to the degree of the approximating harmonic polynomial. All the constants appearing in the bounds are explicit and depend only on the shape-regularity of the domain and on delta. We apply the obtained estimates to show exponential convergence with rate O(exp(−b square root N)), N being the number of degrees of freedom and b>0, of a hp-dGFEM discretisation of the Laplace equation based on piecewise harmonic polynomials. This result is an improvement over the classical rate O(exp(−b cubic root N )), and is due to the use of harmonic polynomial spaces, as opposed to complete polynomial spaces.