Using zero-norm constraint for sparse probability density function estimation

A new sparse kernel probability density function (pdf) estimator based on zero-norm constraint is constructed using the classical Parzen window (PW) estimate as the target function. The so-called zero-norm of the parameters is used in order to achieve enhanced model sparsity, and it is suggested to minimize an approximate function of the zero-norm. It is shown that under certain condition, the kernel weights of the proposed pdf estimator based on the zero-norm approximation can be updated using the multiplicative nonnegative quadratic programming algorithm. Numerical examples are employed to demonstrate the efficacy of the proposed approach.

L1 transfer in the acquisition of manner and path in Spanish by native speakers of English

In this article the authors argue that L1 transfer from English is not only important in the early stages of L2 acquisition of Spanish, but remains influential in later stages if there is not enough positive evidence for the learners to progress in their development (Lefebvre, White, & Jourdan, 2006). The findings are based on analyses of path and manner of movement in stories told by British students of Spanish (N = 68) of three different proficiency levels. Verbs that conflate motion and path, on the one hand, are mastered early, possibly because the existence of Latinate path verbs, such as enter and ascend in English, facilitate their early acquisition by British learners of Spanish. Contrary to the findings of Cadierno (2004) and Cadierno and Ruiz (2006), the encoding of manner, in particular in boundary crossing contexts, seems to pose enormous difficulties, even among students who had been abroad on a placement in a Spanish-speaking country prior to the data collection. An analysis of the frequency of manner verbs in Spanish corpora shows that one of the key reasons why students struggle with manner is that manner verbs are so infrequent in Spanish. The authors claim that scarce positive evidence in the language exposed to and little or no negative evidence are responsible for the long-lasting effect of transfer on the expression of manner.

Minimum norm regularization of descriptor systems by mixed output feedback

We study the regularization problem for linear, constant coefficient descriptor systems Ex' = Ax+Bu, y1 = Cx, y2 = Γx' by proportional and derivative mixed output feedback. Necessary and sufficient conditions are given, which guarantee that there exist output feedbacks such that the closed-loop system is regular, has index at most one and E+BGΓ has a desired rank, i.e., there is a desired number of differential and algebraic equations. To resolve the freedom in the choice of the feedback matrices we then discuss how to obtain the desired regularizing feedback of minimum norm and show that this approach leads to useful results in the sense of robustness only if the rank of E is decreased. Numerical procedures are derived to construct the desired feedback gains. These numerical procedures are based on orthogonal matrix transformations which can be implemented in a numerically stable way.

Properties of singular vectors using convective available potential energy as final time norm

We study the feasibility of using the singular vector technique to create initial condition perturbations for short-range ensemble prediction systems (SREPS) focussing on predictability of severe local storms and in particular deep convection. For this a new final time semi-norm based on the convective available potential energy (CAPE) is introduced. We compare singular vectors using the CAPE-norm with SVs using the more common total energy (TE) norm for a 2-week summer period in 2007, which includes a case of mesoscale extreme rainfall in the south west of Finland. The CAPE singular vectors perturb the CAPE field by increasing the specific humidity and temperature of the parcel and increase the lapse rate above the parcel in the lower troposphere consistent with physical considerations. The CAPE-SVs are situated in the lower troposphere. This in contrast to TE-SVs with short optimization times which predominantly remain in the high troposphere. By examining the time evolution of the CAPE singular values we observe that the convective event in the south west of Finland is clearly associated with high CAPE singular values.

'Quasi'-norm of an arithmetical convolution operator and the order of the Riemann zeta function

In this paper we study Dirichlet convolution with a given arithmetical function f as a linear mapping 'f that sends a sequence (an) to (bn) where bn = Pdjn f(d)an=d. We investigate when this is a bounded operator on l2 and ¯nd the operator norm. Of particular interest is the case f(n) = n¡® for its connection to the Riemann zeta function on the line 1, 'f is bounded with k'f k = ³(®). For the unbounded case, we show that 'f : M2 ! M2 where M2 is the subset of l2 of multiplicative sequences, for many f 2 M2. Consequently, we study the `quasi'-norm sup kak = T a 2M2 k'fak kak for large T, which measures the `size' of 'f on M2. For the f(n) = n¡® case, we show this quasi-norm has a striking resemblance to the conjectured maximal order of j³(® + iT )j for ® > 12 .

A generalized collectively compact operator theory with an application to integral equations on unbounded domains

In this paper a generalization of collectively compact operator theory in Banach spaces is developed. A feature of the new theory is that the operators involved are no longer required to be compact in the norm topology. Instead it is required that the image of a bounded set under the operator family is sequentially compact in a weaker topology. As an application, the theory developed is used to establish solvability results for a class of systems of second kind integral equations on unbounded domains, this class including in particular systems of Wiener-Hopf integral equations with L1 convolutions kernels

L1 acquisition across Portuguese dialects: modular and interdisciplinary interfaces as sources of explanation

This study investigates the child (L1) acquisition of properties at the interfaces of morpho-syntax, syntax-semantics and syntax-pragmatics, by focusing on inflected infinitives in European Portuguese (EP). Three child groups were tested, 6–7-year-olds, 9–10-year-olds and 11–12-year-olds, as well as an adult control group. The data demonstrate that children as young as 6 have knowledge of the morpho-syntactic properties of inflected infinitives, although they seem at first glance to show partially insufficient knowledge of their syntax–semantic interface properties (i.e. non-obligatory control properties), differently from children aged 9 and older, who show clearer evidence of knowledge of both types of properties. However, in general, both morpho-syntactic and syntax–semantics interface properties are also accessible to 6–7-year-old children, although these children give preference to a range of interpretations partially different from the adults; in certain cases, they may not appeal to certain pragmatic inferences that permit additional interpretations to adults and older children. Crucially, our data demonstrate that EP children master the two types of properties of inflected infinitives years before Brazilian Portuguese children do (Pires and Rothman, 2009a and Pires and Rothman, 2009b), reasons for and implications of which we discuss in detail.

Individual differences and the role of the L1 in L2 processing: an ERP investigation

This study used ERP (event-related potentials) to examine both the role of the L1 and the role of individual differences in the processing of agreement violations. Theories of L2 acquisition differ with regard to whether or not native-like acquisition of L2 features is possible (Schwartz and Sprouse, 1994, 1996; Tsimpli and Mastropavlou, 2007), and the results of previous ERP studies are inconsistent when it comes to whether or not native-like processing is observed in response to L2 agreement violations (e.g., Sabourin, 2003; Tokowicz and MacWhinney, 2005). Furthermore, studies of learners in early stages of L2 acquisition have found variability in the emergence of native-like responses (e.g., McLaughlin et al., 2010; Tanner et al., 2009), but sources of variability have not been investigated. The current study examines responses to gender and number agreement violations in English-speaking learners of Spanish (n=24). Stimuli targeted agreement in three conditions: subject-verb agreement (el barco flota/*flotan), which is similar in Spanish and English; number agreement on adjectival predicates (la isla rocosa/*rocosas), a context in which agreement is not instantiated in English; and gender agreement on adjectival predicates (la isla rocosa/*rocoso), which is unique to Spanish. Grammaticality judgments and ERP responses were also tested for correlations with aptitude scores on the Modern Languages Aptitude Test (MLAT; Carroll and Sapon, 1959) and the Raven Advanced Progressive Matrices (Raven, 1965). Results are in line with theories that claim native-like processing is acquirable, since learners demonstrated similar ERP responses to a control group of native Spanish-speakers (n=8) with regard to all three agreement types. Additionally, the MLAT (but not the Raven) was significantly correlated with sensitivity to number violations, both in terms of grammaticality judgments and ERP amplitudes, indicating a role for verbal but not nonverbal aptitude in L2 processing.

Morphosyntactic processing in advanced second language (L2) learners: An event-related potential investigation of the effects of L1-L2 similarity and structural distance

Different theoretical accounts of second language (L2) acquisition differ with respect to whether or not advanced learners are predicted to show native like processing for features not instantiated in the native language (L1). We examined how native speakers of English, a language with number but not gender agreement, process number and gender agreement in Spanish. We compare agreement within a determiner phrase (órgano muy complejo “[DP organ-MASC-SG very complex-MASC-SG]”) and across a verb phrase (cuadro es auténtico “painting-MASC-SG [VP is authentic-MASC-SG]”) in order to investigate whether native like processing is limited to local domains (e.g. within the phrase), in line with Clahsen and Felser (2006). We also examine whether morphological differences in how the L1 and L2 realize a shared feature impact processing by comparing number agreement between nouns and adjectives, where only Spanish instantiates agreement, and between demonstratives and nouns, where English also instantiates agreement. Similar to Spanish natives, advanced learners showed a P600 for both number and gender violations overall, in line with the Full Transfer/Full Access Hypothesis (Schwartz and Sprouse, 1996), which predicts that learners can show native-like processing for novel features. Results also show that learners can establish syntactic dependencies outside of local domains, as suggested by the presence of a P600 for both within and across phrase violations. Moreover, similar to native speakers, learners were impacted by the structural distance (number of intervening phrases) between the agreeing elements, as suggested by the more positive waveforms for within than across-phrase agreement overall. These results are consistent with the proposal that learners are sensitive to hierarchical structure.