Gradient competence at the syntax-discourse interface

In this article, we present additional support of Duffield's (2003, 2005) distinction between Underlying Competence and Surface Competence. Duffield argues that a more fine-grained distinction between levels of competence and performance is warranted and necessary. While underlying competence is categorical, surface competence is more probabilistic and gradient, being sensitive to lexical and constructional contingencies, including the contextual appropriateness of a given construction. We examine a subset of results from a study comparing native and learner competence of properties at the syntax-discourse interface. Specifically, we look at the acceptability of Clitic Right Dislocation in native and L2 Spanish, in discourse-appropriate context. We argue that Duffield's distinction is a possible explanation of our results.

Pragmatic deficits with syntactic consequences?: L2 pronominal subjects and the syntax–pragmatics interface

Contemporary acquisition theorizing has placed a considerable amount of attention on interfaces, points at which different linguistic modules interact. The claim is that vulnerable interfaces cause particular difficulties in L1, bilingual and adult L2 acquisition (e.g. Platzack, 2001; Montrul, 2004; Müller and Hulk, 2001; Sorace, 2000, 2003, 2004, 2005). Accordingly, it is possible that deficits at the syntax–pragmatics interface cause what appears to be particular non-target-like syntactic behavior in L2 performance. This syntax-before-discourse hypothesis is examined in the present study by analyzing null vs. overt subject pronoun distribution in L2 Spanish of English L1 learners. As ultimately determined by L2 knowledge of the Overt Pronoun Constraint (OPC) (Montalbetti, 1984), the data indicate that L2 learners at the intermediate and advanced levels reset the Null Subject Parameter (NSP), but only advanced learners have acquired a more or less target null/overt subject distribution. Against the predictions of Sorace (2004) and in line with Montrul and Rodríguez-Louro (2006), the data indicate an overuse of both overt and null subject pronouns. As a result, this behavior cannot be from L1 interference alone, suggesting that interface-conditioned properties are simply more complex and therefore, harder to acquire. Furthermore, the data from the advanced learners demonstrate that the syntax–pragmatics interface is not a predetermined locus for fossilization (in contra e.g. Valenzuela, 2006).

Interface vulnerability and knowledge of the subjunctive/indicative distinction with negated epistemic predicates in L2 Spanish.

Much recent research in SLA is guided by the hypothesis of L2 interface vulnerability (see Sorace 2005). This study contributes to this general project by examining the acquisition of two classes of subjunctive complement clauses in L2 Spanish: subjunctive complements of volitional predicates (purely syntactic) and subjunctive vs. indicative complements with negated epistemic matrix predicates, where the mood distinction is discourse dependent (thus involving the syntax-discourse interface). We provide an analysis of the volitional subjunctive in English and Spanish, suggesting that English learners of L2 Spanish need to access the functional projection Mood P and an uninterpretable modal feature on the Force head available to them from their formal English register grammar, and simultaneously must unacquire the structure of English for-to clauses. For negated epistemic predicates, our analysis maintains that they need to revalue the modal feature on the Force head from uninterpretable to interpretable, within the L2 grammar.With others (e.g. Borgonovo & Prévost 2003; Borgonovo, Bruhn de Garavito & Prévost 2005) and in line with Sorace's (2000, 2003, 2005) notion of interface vulnerability, we maintain that the latter case is more difficult for L2 learners, which is borne out in the data we present. However, the data also show that the indicative/subjunctive distinction with negated epistemics can be acquired by advanced stages of acquisition, questioning the notion of obligatory residual optionality for all properties which require the integration of syntactic and discourse information.

First order k-th moment finite element analysis of nonlinear operator equations with stochastic data

We develop and analyze a class of efficient Galerkin approximation methods for uncertainty quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin discretizations of tensorized linearizations at nominal parameters. Specifically, we consider abstract, nonlinear, parametric operator equations J(\alpha ,u)=0 for random input \alpha (\omega ) with almost sure realizations in a neighborhood of a nominal input parameter \alpha _0. Under some structural assumptions on the parameter dependence, we prove existence and uniqueness of a random solution, u(\omega ) = S(\alpha (\omega )). We derive a multilinear, tensorized operator equation for the deterministic computation of k-th order statistical moments of the random solution's fluctuations u(\omega ) - S(\alpha _0). We introduce and analyse sparse tensor Galerkin discretization schemes for the efficient, deterministic computation of the k-th statistical moment equation. We prove a shift theorem for the k-point correlation equation in anisotropic smoothness scales and deduce that sparse tensor Galerkin discretizations of this equation converge in accuracy vs. complexity which equals, up to logarithmic terms, that of the Galerkin discretization of a single instance of the mean field problem. We illustrate the abstract theory for nonstationary diffusion problems in random domains.

A high frequency $hp$ boundary element method for scattering by convex polygons

In this paper we propose and analyze a hybrid $hp$ boundary element method for the solution of problems of high frequency acoustic scattering by sound-soft convex polygons, in which the approximation space is enriched with oscillatory basis functions which efficiently capture the high frequency asymptotics of the solution. We demonstrate, both theoretically and via numerical examples, exponential convergence with respect to the order of the polynomials, moreover providing rigorous error estimates for our approximations to the solution and to the far field pattern, in which the dependence on the frequency of all constants is explicit. Importantly, these estimates prove that, to achieve any desired accuracy in the computation of these quantities, it is sufficient to increase the number of degrees of freedom in proportion to the logarithm of the frequency as the frequency increases, in contrast to the at least linear growth required by conventional methods.

Gradient recovery in adaptive finite-element methods for parabolic problems

We derive energy-norm a posteriori error bounds, using gradient recovery (ZZ) estimators to control the spatial error, for fully discrete schemes for the linear heat equation. This appears to be the �rst completely rigorous derivation of ZZ estimators for fully discrete schemes for evolution problems, without any restrictive assumption on the timestep size. An essential tool for the analysis is the elliptic reconstruction technique.Our theoretical results are backed with extensive numerical experimentation aimed at (a) testing the practical sharpness and asymptotic behaviour of the error estimator against the error, and (b) deriving an adaptive method based on our estimators. An extra novelty provided is an implementation of a coarsening error "preindicator", with a complete implementation guide in ALBERTA in the appendix.

A finite element method for nonlinear elliptic problems

We present a Galerkin method with piecewise polynomial continuous elements for fully nonlinear elliptic equations. A key tool is the discretization proposed in Lakkis and Pryer, 2011, allowing us to work directly on the strong form of a linear PDE. An added benefit to making use of this discretization method is that a recovered (finite element) Hessian is a byproduct of the solution process. We build on the linear method and ultimately construct two different methodologies for the solution of second order fully nonlinear PDEs. Benchmark numerical results illustrate the convergence properties of the scheme for some test problems as well as the Monge–Amp`ere equation and the Pucci equation.

A finite element method for second order nonvariational elliptic problems

We propose a numerical method to approximate the solution of second order elliptic problems in nonvariational form. The method is of Galerkin type using conforming finite elements and applied directly to the nonvariational (nondivergence) form of a second order linear elliptic problem. The key tools are an appropriate concept of “finite element Hessian” and a Schur complement approach to solving the resulting linear algebra problem. The method is illustrated with computational experiments on three linear and one quasi-linear PDE, all in nonvariational form.

A finite element-spherical harmonics model for radiative transfer in inhomogeneous clouds. Part II. some applications

EVENT has been used to examine the effects of 3D cloud structure, distribution, and inhomogeneity on the scattering of visible solar radiation and the resulting 3D radiation field. Large eddy simulation and aircraft measurements are used to create realistic cloud fields which are continuous or broken with smooth or uneven tops. The values, patterns and variance in the resulting downwelling and upwelling radiation from incident visible solar radiation at different angles are then examined and compared to measurements. The results from EVENT confirm that 3D cloud structure is important in determining the visible radiation field, and that these results are strongly influenced by the solar zenith angle. The results match those from other models using visible solar radiation, and are supported by aircraft measurements of visible radiation, providing confidence in the new model.

Repressor element 1 silencing transcription factor couples loss of pluripotency with neural induction and neural differentiation

Neural differentiation of embryonic stem cells (ESCs) requires coordinated repression of the pluripotency regulatory program and reciprocal activation of the neurogenic regulatory program. Upon neural induction, ESCs rapidly repress expression of pluripotency genes followed by staged activation of neural progenitor and differentiated neuronal and glial genes. The transcriptional factors that underlie maintenance of pluripotency are partially characterized whereas those underlying neural induction are much less explored, and the factors that coordinate these two developmental programs are completely unknown. One transcription factor, REST (repressor element 1 silencing transcription factor), has been linked with terminal differentiation of neural progenitors and more recently, and controversially, with control of pluripotency. Here, we show that in the absence of REST, coordination of pluripotency and neural induction is lost and there is a resultant delay in repression of pluripotency genes and a precocious activation of both neural progenitor and differentiated neuronal and glial genes. Furthermore, we show that REST is not required for production of radial glia-like progenitors but is required for their subsequent maintenance and differentiation into neurons, oligodendrocytes, and astrocytes. We propose that REST acts as a regulatory hub that coordinates timely repression of pluripotency with neural induction and neural differentiation.

A mathematical model of the sterol regulatory element binding protein 2 cholesterol biosynthesis pathway

Cholesterol is one of the key constituents for maintaining the cellular membrane and thus the integrity of the cell itself. In contrast high levels of cholesterol in the blood are known to be a major risk factor in the development of cardiovascular disease. We formulate a deterministic nonlinear ordinary differential equation model of the sterol regulatory element binding protein 2 (SREBP-2) cholesterol genetic regulatory pathway in an hepatocyte. The mathematical model includes a description of genetic transcription by SREBP-2 which is subsequently translated to mRNA leading to the formation of 3-hydroxy-3-methylglutaryl coenzyme A reductase (HMGCR), a main precursor of cholesterol synthesis. Cholesterol synthesis subsequently leads to the regulation of SREBP-2 via a negative feedback formulation. Parameterised with data from the literature, the model is used to understand how SREBP-2 transcription and regulation affects cellular cholesterol concentration. Model stability analysis shows that the only positive steady-state of the system exhibits purely oscillatory, damped oscillatory or monotic behaviour under certain parameter conditions. In light of our findings we postulate how cholesterol homestasis is maintained within the cell and the advantages of our model formulation are discussed with respect to other models of genetic regulation within the literature.

Human monstrosity: rape, ambiguity and performance in Rosemary’s Baby (Roman Polanski, 1968)

The narrative of Rosemary’s Baby hinges on a central hesitation between pregnancy induced madness and the existence of Satanism. Accordingly, the monstrous element is embodied in both the real and the supernatural: Rosemary’s husband Guy (John Cassavetes) is responsible for her victimisation through rape in either explanation. However, I will argue that the inherent ambiguity of the plot makes it difficult to place him as such a figure typical to the archetypal horror binaries of normality/monster, human/inhuman. By displacing generic convention the film complicates the issue of monstrosity, whilst simultaneously offering the possibility for the depiction of female experience of marriage to be at the centre of the narrative, for the real to be possibly of more significance than the supernatural. Previous writing has tended to concentrate on Rosemary and her pregnancy, so through detailed consideration of Cassavetes’ performance and its placement in the mise-en-scène this focus on Guy aims to demonstrate that he changes almost as much as Rosemary does. The chapter will focus on the film’s depiction of rape, during Rosemary’s nightmare and after it, in order to demonstrate how the notion of performance reveals Guy’s monstrousness and the difficulties this represents in our engagement with him.