Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

Lesions impairing regular versus irregular past tense production

We investigated selective impairments in the production of regular and irregular past tense by examining language performance and lesion sites in a sample of twelve stroke patients. A disadvantage in regular past tense production was observed in six patients when phonological complexity was greater for regular than irregular verbs, and in three patients when phonological complexity was closely matched across regularity. These deficits were not consistently related to grammatical difficulties or phonological errors but were consistently related to lesion site. All six patients with a regular past tense disadvantage had damage to the left ventral pars opercularis (in the inferior frontal cortex), an area associated with articulatory sequencing in prior functional imaging studies. In addition, those that maintained a disadvantage for regular verbs when phonological complexity was controlled had damage to the left ventral supramarginal gyrus (in the inferior parietal lobe), an area associated with phonological short-term memory. When these frontal and parietal regions were spared in patients who had damage to subcortical (n = 2) or posterior temporo-parietal regions (n = 3), past tense production was relatively unimpaired for both regular and irregular forms. The remaining (12th) patient was impaired in producing regular past tense but was significantly less accurate when producing irregular past tense. This patient had frontal, parietal, subcortical and posterior temporo-parietal damage, but was distinguished from the other patients by damage to the left anterior temporal cortex, an area associated with semantic processing. We consider how our lesion site and behavioral observations have implications for theoretical accounts of past tense production.

Morphological decomposition in Broca's aphasia

Background: Few studies have investigated how individuals diagnosed with post-stroke Broca’s aphasia decompose words into their constituent morphemes in real-time processing. Previous research has focused on morphologically complex words in non-time-constrained settings or in syntactic frames, but not in the lexicon. Aims: We examined real-time processing of morphologically complex words in a group of five Greek-speaking individuals with Broca’s aphasia to determine: (1) whether their morphological decomposition mechanisms are sensitive to lexical (orthography and frequency) vs. morphological (stem-suffix combinatory features) factors during visual word recognition, (2) whether these mechanisms are different in inflected vs. derived forms during lexical access, and (3) whether there is a preferred unit of lexical access (syllables vs. morphemes) for inflected vs. derived forms. Methods & Procedures: The study included two real-time experiments. The first was a semantic judgment task necessitating participants’ categorical judgments for high- and low-frequency inflected real words and pseudohomophones of the real words created by either an orthographic error at the stem or a homophonous (but incorrect) inflectional suffix. The second experiment was a letter-priming task at the syllabic or morphemic boundary of morphologically transparent inflected and derived words whose stems and suffixes were matched for length, lemma and surface frequency. Outcomes & Results: The majority of the individuals with Broca’s aphasia were sensitive to lexical frequency and stem orthography, while ignoring the morphological combinatory information encoded in the inflectional suffix that control participants were sensitive to. The letter-priming task, on the other hand, showed that individuals with aphasia—in contrast to controls—showed preferences with regard to the unit of lexical access, i.e., they were overall faster on syllabically than morphemically parsed words and their morphological decomposition mechanisms for inflected and derived forms were modulated by the unit of lexical access. Conclusions: Our results show that in morphological processing, Greek-speaking persons with aphasia rely mainly on stem access and thus are only sensitive to orthographic violations of the stem morphemes, but not to illegal morphological combinations of stems and suffixes. This possibly indicates an intact orthographic lexicon but deficient morphological decomposition mechanisms, possibly stemming from an underspecification of inflectional suffixes in the participants’ grammar. Syllabic information, however, appears to facilitate lexical access and elicits repair mechanisms that compensate for deviant morphological parsing procedures.

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.

Contrasting effects of changing rhythm and content on auditory distraction in immediate memory

Across five experiments, the temporal regularity and content of an irrelevant speech stream were varied and their effects on a serial recall task examined. Variations of the content, but not the rhythm, of the irrelevant speech stimuli reliably disrupted serial recall performance in all experiments. Bayesian analyses supported the null hypothesis over the hypothesis that irregular rhythms would disrupt memory to a greater extent than regular rhythms. Pooling the data in a combined analysis revealed that regular presentation of the irrelevant speech was significantly more disruptive to serial recall than irregular presentation. These results are consistent with the idea that auditory distraction is sensitive to both intra-item and inter-item relations and challenge an orienting-based account of auditory distraction.

Emotional responses to Hindustani raga music: the role of musical structure

In Indian classical music, ragas constitute specific combinations of tonic intervals potentially capable of evoking distinct emotions. A raga composition is typically presented in two modes, namely, alaap and gat. Alaap is the note by note delineation of a raga bound by a slow tempo, but not bound by a rhythmic cycle. Gat on the other hand is rendered at a faster tempo and follows a rhythmic cycle. Our primary objective was to (1) discriminate the emotions experienced across alaap and gat of ragas, (2) investigate the association of tonic intervals, tempo and rhythmic regularity with emotional response. 122 participants rated their experienced emotion across alaap and gat of 12 ragas. Analysis of the emotional responses revealed that (1) ragas elicit distinct emotions across the two presentation modes, and (2) specific tonic intervals are robust predictors of emotional response. Specifically, our results showed that the ‘minor second’ is a direct predictor of negative valence. (3) Tonality determines the emotion experienced for a raga where as rhythmic regularity and tempo modulate levels of arousal. Our findings provide new insights into the emotional response to Indian ragas and the impact of tempo, rhythmic regularity and tonality on it.

Serial clustering of extratropical cyclones in a multi-model ensemble of historical and future simulations

This study has investigated serial (temporal) clustering of extra-tropical cyclones simulated by 17 climate models that participated in CMIP5. Clustering was estimated by calculating the dispersion (ratio of variance to mean) of 30 December-February counts of Atlantic storm tracks passing nearby each grid point. Results from single historical simulations of 1975-2005 were compared to those from historical ERA40 reanalyses from 1958-2001 ERA40 and single future model projections of 2069-2099 under the RCP4.5 climate change scenario. Models were generally able to capture the broad features in reanalyses reported previously: underdispersion/regularity (i.e. variance less than mean) in the western core of the Atlantic storm track surrounded by overdispersion/clustering (i.e. variance greater than mean) to the north and south and over western Europe. Regression of counts onto North Atlantic Oscillation (NAO) indices revealed that much of the overdispersion in the historical reanalyses and model simulations can be accounted for by NAO variability. Future changes in dispersion were generally found to be small and not consistent across models. The overdispersion statistic, for any 30 year sample, is prone to large amounts of sampling uncertainty that obscures the climate change signal. For example, the projected increase in dispersion for storm counts near London in the CNRMCM5 model is 0.1 compared to a standard deviation of 0.25. Projected changes in the mean and variance of NAO are insufficient to create changes in overdispersion that are discernible above natural sampling variations.

The signature of a rough path: uniqueness

In the context of controlled differential equations, the signature is the exponential function on paths. B. Hambly and T. Lyons proved that the signature of a bounded variation path is trivial if and only if the path is tree-like. We extend Hambly–Lyons' result and their notion of tree-like paths to the setting of weakly geometric rough paths in a Banach space. At the heart of our approach is a new definition for reduced path and a lemma identifying the reduced path group with the space of signatures.