On the solvability of a class of second kind integral equations on unbounded domains

We consider integral equations of the form ψ(x) = φ(x) + ∫Ωk(x, y)z(y)ψ(y) dy(in operator form ψ = φ + Kzψ), where Ω is some subset ofRn(n ≥ 1). The functionsk,z, and φ are assumed known, withz ∈ L∞(Ω) and φ ∈ Y, the space of bounded continuous functions on Ω. The function ψ ∈ Yis to be determined. The class of domains Ω and kernelskconsidered includes the case Ω = Rnandk(x, y) = κ(x − y) with κ ∈ L1(Rn), in which case, ifzis the characteristic function of some setG, the integral equation is one of Wiener–Hopf type. The main theorems, proved using arguments derived from collectively compact operator theory, are conditions on a setW ⊂ L∞(Ω) which ensure that ifI − Kzis injective for allz ∈ WthenI − Kzis also surjective and, moreover, the inverse operators (I − Kz)−1onYare bounded uniformly inz. These general theorems are used to recover classical results on Wiener–Hopf integral operators of21and19, and generalisations of these results, and are applied to analyse the Lippmann–Schwinger integral equation.

Subject-to-subject raising and the syntax of tense in L2 Spanish: a full access approach

This paper investigates the acquisition of syntax in L2 grammars. We tested adult L2 speakers of Spanish (English L1) on the feature specification of T(ense), which is different in English and Spanish in so-called subject-to-subject raising structures. We present experimental results with the verb parecer “to seem/to appear” in different tenses, with and without experiencers, and with Tense Phrase (TP), verb phrase (vP) and Adjectival Phrase (AP) complements. The results show that advanced L2 learners can perform just like native Spanish speakers regarding grammatical knowledge in this domain, although the subtle differences between both languages are not explicitly taught. We argue that these results support Full Access approaches to Universal Grammar (UG) in L2 acquisition, by providing evidence that uninterpretable syntactic features can be learned in adult L2, even when such features are not directly instantiated in the same grammatical domain in the L1 grammar.

L3 syntactic transfer selectivity and typological determinacy: the typological primacy model

The present article addresses the following question: what variables condition syntactic transfer? Evidence is provided in support of the position that third language (L3) transfer is selective, whereby, at least under certain conditions, it is driven by the typological proximity of the target L3 measured against the other previously acquired linguistic systems (cf. Rothman and Cabrelli Amaro, 2007, 2010; Rothman, 2010; Montrul et al., 2011). To show this, we compare data in the domain of adjectival interpretation between successful first language (L1) Italian learners of English as a second language (L2) at the low to intermediate proficiency level of L3 Spanish, and successful L1 English learners of L2 Spanish at the same levels for L3 Brazilian Portuguese. The data show that, irrespective of the L1 or the L2, these L3 learners demonstrate target knowledge of subtle adjectival semantic nuances obtained via noun-raising, which English lacks and the other languages share. We maintain that such knowledge is transferred to the L3 from Italian (L1) and Spanish (L2) respectively in light of important differences between the L3 learners herein compared to what is known of the L2 Spanish performance of L1 English speakers at the same level of proficiency (see, for example, Judy et al., 2008; Rothman et al., 2010). While the present data are consistent with Flynn et al.’s (2004) Cumulative Enhancement Model, we discuss why a coupling of these data with evidence from other recent L3 studies suggests necessary modifications to this model, offering in its stead the Typological Primacy Model (TPM) for multilingual transfer.

Linguistic interfaces and language acquisition in childhood: introduction to the special issue

Much contemporary L1 acquisition theory and empirical research are guided by the hypothesis that acquisition delays in children are often related to the integration of information across grammatical and other cognitive modules, such as syntax and discourse-pragmatics (see e.g., Grinstead, 2010). This special issue brings together cutting edge research from all relevant paradigms addressing interface issues in child language acquisition and provides a platform for the study of the interaction between different levels of linguistic knowledge. In this introduction, we present the reader with the tools needed to best understand the contributions of the individual studies and what they bring to bear on larger theoretical questions as a collective.

The syntax-semantics of bare and definite plural subjects in the L2 Spanish of English natives

This study investigates the extent to which advanced native-English L2 learners of Spanish come to acquire restrictions on bare plural preverbal subjects in L2 Spanish (e.g. gatos “cats” vs. definite plurals such as los gatos “the cats”). It tests L2 knowledge of available semantic readings of bare plurals and definite plurals in Spanish, where [+specific] and [+generic] interpretations are syntactically represented differently from English. Assuming L1 transfer, and in view of a potential subset/superset relationship of the two grammars, the learning task in this domain is not a straightforward one. Target acquisition requires both grammatical expansion and retraction; Spanish definite plural subjects require the addition of an L1-unavailable [+generic] reading, while a loss of an L1-available [+generic] reading for preverbal subject bare plurals is required. The results and analysis show that advanced L2 learners of Spanish (English L1) can circumvent a superficial subset/superset learnability problem by means of feature resetting in line with the Nominal Mapping Parameter.

On the typological economy of syntactic transfer: word order and relative clause high/low attachment preference in L3 Brazilian Portuguese

One central question in the formal linguistic study of adult multilingual morphosyntax (i.e., L3/Ln acquisition) involves determining the role(s) the L1 and/or the L2 play(s) at the L3 initial state (e.g., Bardel & Falk, Second Language Research 23: 459–484, 2007; Falk & Bardel, Second Language Research: forthcoming; Flynn et al., The International Journal of Multilingualism 8: 3–16, 2004; Rothman, Second Language Research: forthcoming; Rothman & Cabrelli, On the initial state of L3 (Ln) acquisition: Selective or absolute transfer?: 2007; Rothman & Cabrelli Amaro, Second Language Research 26: 219–289, 2010). The present article adds to this general program, testing Rothman's (Second Language Research: forthcoming) model for L3 initial state transfer, which when relevant in light of specific language pairings, maintains that typological proximity between the languages is the most deterministic variable determining the selection of syntactic transfer. Herein, I present empirical evidence from the later part of the beginning stages of L3 Brazilian Portuguese (BP) by native speakers of English and Spanish, who have attained an advanced level of proficiency in either English or Spanish as an L2. Examining the related domains of syntactic word order and relative clause attachment preference in L3 BP, the data clearly indicate that Spanish is transferred for both experimental groups irrespective of whether it was the L1 or L2. These results are expected by Rothman's (Second Language Research: forthcoming) model, but not necessarily predicted by other current hypotheses of multilingual syntactic transfer; the implications of this are discussed.

What variables condition syntactic transfer? A look at the L3 initial state

This study investigates transfer at the third-language (L3) initial state, testing between the following possibilities: (1) the first language (L1) transfer hypothesis (an L1 effect for all adult acquisition), (2) the second language (L2) transfer hypothesis, where the L2 blocks L1 transfer (often referred to in the recent literature as the ‘L2 status factor’; Williams and Hammarberg, 1998), and (3) the Cumulative Enhancement Model (Flynn et al., 2004), which proposes selective transfer from all previous linguistic knowledge. We provide data from successful English-speaking learners of L2 Spanish at the initial state of acquiring L3 French and L3 Italian relating to properties of the Null-Subject Parameter (e.g. Chomsky, 1981; Rizzi, 1982). We compare these groups to each other, as well as to groups of English learners of L2 French and L2 Italian at the initial state, and conclude that the data are consistent with the predictions of the ‘L2 status factor’. However, we discuss an alternative possible interpretation based on (psycho)typologically-motivated transfer (borrowing from Kellerman, 1983), providing a methodology for future research in this domain to meaningfully tease apart the ‘L2 status factor’ from this alternative account.

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).

Knowledge of A/A'-dependencies on subject extraction with two types of infinitives in non-native Portuguese adult bilingualism

Within generative L2 acquisition research there is a longstanding debate as to what underlies observable differences in L1/L2 knowledge/ performance. On the one hand, Full Accessibility approaches maintain that target L2 syntactic representations (new functional categories and features) are acquirable (e.g., Schwartz & Sprouse, 1996). Conversely, Partial Accessibility approaches claim that L2 variability and/or optionality, even at advanced levels, obtains as a result of inevitable deficits in L2 narrow syntax and is conditioned upon a maturational failure in adulthood to acquire (some) new functional features (e.g., Beck, 1998; Hawkins & Chan, 1997; Hawkins & Hattori, 2006; Tsimpli & Dimitrakopoulou, 2007). The present study tests the predictions of these two sets of approaches with advanced English learners of L2 Brazilian Portuguese (n = 21) in the domain of inflected infinitives. These advanced L2 learners reliably differentiate syntactically between finite verbs, uninflected and inflected infinitives, which, as argued, only supports Full Accessibility approaches. Moreover, we will discuss how testing the domain of inflected infinitives is especially interesting in light of recent proposals that Brazilian Portuguese colloquial dialects no longer actively instantiate them (Lightfoot, 1991; Pires, 2002, 2006; Pires & Rothman, 2009; Rothman, 2007).

Polynomial-based noise variance estimation for MIMO-SCBT systems

In this paper, we present a polynomial-based noise variance estimator for multiple-input multiple-output single-carrier block transmission (MIMO-SCBT) systems. It is shown that the optimal pilots for noise variance estimation satisfy the same condition as that for channel estimation. Theoretical analysis indicates that the proposed estimator is statistically more efficient than the conventional sum of squared residuals (SSR) based estimator. Furthermore, we obtain an efficient implementation of the estimator by exploiting its special structure. Numerical results confirm our theoretical analysis.

Model estimation of cerebral hemodynamics between blood flow and volume changes: A data-based modeling approach

It is well known that there is a dynamic relationship between cerebral blood flow (CBF) and cerebral blood volume (CBV). With increasing applications of functional MRI, where the blood oxygen-level-dependent signals are recorded, the understanding and accurate modeling of the hemodynamic relationship between CBF and CBV becomes increasingly important. This study presents an empirical and data-based modeling framework for model identification from CBF and CBV experimental data. It is shown that the relationship between the changes in CBF and CBV can be described using a parsimonious autoregressive with exogenous input model structure. It is observed that neither the ordinary least-squares (LS) method nor the classical total least-squares (TLS) method can produce accurate estimates from the original noisy CBF and CBV data. A regularized total least-squares (RTLS) method is thus introduced and extended to solve such an error-in-the-variables problem. Quantitative results show that the RTLS method works very well on the noisy CBF and CBV data. Finally, a combination of RTLS with a filtering method can lead to a parsimonious but very effective model that can characterize the relationship between the changes in CBF and CBV.

An investigation of working memory effects on oral grammatical accuracy and fluency in producing questions in English

This article addresses the question of how far working memory may affect second language (L2) learners' improvement in spoken language during a period of immersion. Research is presented testing the hypothesis that individual differences in working memory (WM) capacity are associated with individual variation in improvements in oral production of questions in English. Thirty-two Chinese adult speakers of English were tested, before and after a year's postgraduate study in the United Kingdom, to measure grammatical accuracy and fluency using a question elicitation task, and to measure WM using a battery of first language (L1) and L2 WM tests. Story recall in L1 (Mandarin) was significantly associated with individuals' improvement in oral grammatical measures (p < .05). However, there was no significant mean improvement across the cohort in grammatical accuracy, although there was for fluency. The findings suggest that WM may aid certain aspects of individuals' L2 oral proficiency during academic immersion through postgraduate study. They also indicate that academic immersion in itself can lead to improvements in oral proficiency, independent of WM capacity, but there is no general guarantee of significant grammatical change. Further research to clarify the opportunities for input and interaction available in academic immersion settings is called for.

Sparse model construction using coordinate descent optimization

We propose a new sparse model construction method aimed at maximizing a model’s generalisation capability for a large class of linear-in-the-parameters models. The coordinate descent optimization algorithm is employed with a modified l1- penalized least squares cost function in order to estimate a single parameter and its regularization parameter simultaneously based on the leave one out mean square error (LOOMSE). Our original contribution is to derive a closed form of optimal LOOMSE regularization parameter for a single term model, for which we show that the LOOMSE can be analytically computed without actually splitting the data set leading to a very simple parameter estimation method. We then integrate the new results within the coordinate descent optimization algorithm to update model parameters one at the time for linear-in-the-parameters models. Consequently a fully automated procedure is achieved without resort to any other validation data set for iterative model evaluation. Illustrative examples are included to demonstrate the effectiveness of the new approaches.

Tracking the momentum flux of a CME and quantifying its influence on geomagnetically induced currents at Earth

We investigate a coronal mass ejection (CME) propagating toward Earth on 29 March 2011. This event is specifically chosen for its predominately northward directed magnetic field, so that the influence from the momentum flux onto Earth can be isolated. We focus our study on understanding how a small Earth-directed segment propagates. Mass images are created from the white-light cameras onboard STEREO which are also converted into mass height-time maps (mass J-maps). The mass tracks on these J-maps correspond to the sheath region between the CME and its associated shock front as detected by in situ measurements at L1. A time series of mass measurements from the STEREO COR-2A instrument is made along the Earth propagation direction. Qualitatively, this mass time series shows a remarkable resemblance to the L1 in situ density series. The in situ measurements are used as inputs into a three-dimensional (3-D) magnetospheric space weather simulation from the Community Coordinated Modeling Center. These simulations display a sudden compression of the magnetosphere from the large momentum flux at the leading edge of the CME, and predictions are made for the time derivative of the magnetic field (dB/dt) on the ground. The predicted dB/dt values were then compared with the observations from specific equatorially located ground stations and showed notable similarity. This study of the momentum of a CME from the Sun down to its influence on magnetic ground stations on Earth is presented as a preliminary proof of concept, such that future attempts may try to use remote sensing to create density and velocity time series as inputs to magnetospheric simulations.

The time-course of morphological processing in a second language

We report findings from psycholinguistic experiments investigating the detailed timing of processing morphologically complex words by proficient adult second (L2) language learners of English in comparison to adult native (L1) speakers of English. The first study employed the masked priming technique to investigate -ed forms with a group of advanced Arabic-speaking learners of English. The results replicate previously found L1/L2 differences in morphological priming, even though in the present experiment an extra temporal delay was offered after the presentation of the prime words. The second study examined the timing of constraints against inflected forms inside derived words in English using the eye-movement monitoring technique and an additional acceptability judgment task with highly advanced Dutch L2 learners of English in comparison to adult L1 English controls. Whilst offline the L2 learners performed native-like, the eye-movement data showed that their online processing was not affected by the morphological constraint against regular plurals inside derived words in the same way as in native speakers. Taken together, these findings indicate that L2 learners are not just slower than native speakers in processing morphologically complex words, but that the L2 comprehension system employs real-time grammatical analysis (in this case, morphological information) less than the L1 system.