Feedback design for regularizing descriptor systems

This paper surveys numerical techniques for the regularization of descriptor (generalized state-space) systems by proportional and derivative feedback. We review generalizations of controllability and observability to descriptor systems along with definitions of regularity and index in terms of the Weierstraß canonical form. Three condensed forms display the controllability and observability properties of a descriptor system. The condensed forms are obtained through orthogonal equivalence transformations and rank decisions, so they may be computed by numerically stable algorithms. In addition, the condensed forms display whether a descriptor system is regularizable, i.e., when the system pencil can be made to be regular by derivative and/or proportional output feedback, and, if so, what index can be achieved. Also included is a a new characterization of descriptor systems that can be made to be regular with index 1 by proportional and derivative output feedback.

Eigenstructure assignment in descriptor systems

Coordinate free conditions are given for pole assignment by feedback in linear descriptor (singular) systems which guarantee closed-loop regularity. These conditions are shown to be both necessary and sufficient for assignment of the maximum possible number of finite poles. Transformation to special coordinates are not used and the results provide a robust algorithm for the computation of the required feedback.

Algorithms for Robust Pole Assignment in Singular Systems

The solution of the pole assignment problem by feedback in singular systems is parameterized and conditions are given which guarantee the regularity and maximal degree of the closed loop pencil. A robustness measure is defined, and numerical procedures are described for selecting the free parameters in the feedback to give optimal robustness.

Trefftz discontinuous Galerkin methods for acoustic scattering on locally refined meshes

We extend the a priori error analysis of Trefftz-discontinuous Galerkin methods for time-harmonic wave propagation problems developed in previous papers to acoustic scattering problems and locally refined meshes. To this aim, we prove refined regularity and stability results with explicit dependence of the stability constant on the wave number for non convex domains with non connected boundaries. Moreover, we devise a new choice of numerical flux parameters for which we can prove L2-error estimates in the case of locally refined meshes near the scatterer. This is the setting needed to develop a complete hp-convergence analysis.

A spatio-temporal structure-based approach to drought characterisation

Drought characterisation is an intrinsically spatio-temporal problem. A limitation of previous approaches to characterisation is that they discard much of the spatio-temporal information by reducing events to a lower-order subspace. To address this, an explicit 3-dimensional (longitude, latitude, time) structure-based method is described in which drought events are defined by a spatially and temporarily coherent set of points displaying standardised precipitation below a given threshold. Geometric methods can then be used to measure similarity between individual drought structures. Groupings of these similarities provide an alternative to traditional methods for extracting recurrent space-time signals from geophysical data. The explicit consideration of structure encourages the construction of summary statistics which relate to the event geometry. Example measures considered are the event volume, centroid, and aspect ratio. The utility of a 3-dimensional approach is demonstrated by application to the analysis of European droughts (15 °W to 35°E, and 35 °N to 70°N) for the period 1901–2006. Large-scale structure is found to be abundant with 75 events identified lasting for more than 3 months and spanning at least 0.5 × 106 km2. Near-complete dissimilarity is seen between the individual drought structures, and little or no regularity is found in the time evolution of even the most spatially similar drought events. The spatial distribution of the event centroids and the time evolution of the geographic cross-sectional areas strongly suggest that large area, sustained droughts result from the combination of multiple small area (∼106 km2) short duration (∼3 months) events. The small events are not found to occur independently in space. This leads to the hypothesis that local water feedbacks play an important role in the aggregation process.

Endogenous cholinergic tone modulates spontaneous network level neuronal activity in primary cortical cultures grown on multi-electrode arrays

Background Cortical cultures grown long-term on multi-electrode arrays (MEAs) are frequently and extensively used as models of cortical networks in studies of neuronal firing activity, neuropharmacology, toxicology and mechanisms underlying synaptic plasticity. However, in contrast to the predominantly asynchronous neuronal firing activity exhibited by intact cortex, electrophysiological activity of mature cortical cultures is dominated by spontaneous epileptiform-like global burst events which hinders their effective use in network-level studies, particularly for neurally-controlled animat (‘artificial animal’) applications. Thus, the identification of culture features that can be exploited to produce neuronal activity more representative of that seen in vivo could increase the utility and relevance of studies that employ these preparations. Acetylcholine has a recognised neuromodulatory role affecting excitability, rhythmicity, plasticity and information flow in vivo although its endogenous production by cortical cultures and subsequent functional influence upon neuronal excitability remains unknown. Results Consequently, using MEA electrophysiological recording supported by immunohistochemical and RT-qPCR methods, we demonstrate for the first time, the presence of intrinsic cholinergic neurons and significant, endogenous cholinergic tone in cortical cultures with a characterisation of the muscarinic and nicotinic components that underlie modulation of spontaneous neuronal activity. We found that tonic muscarinic ACh receptor (mAChR) activation affects global excitability and burst event regularity in a culture age-dependent manner whilst, in contrast, tonic nicotinic ACh receptor (nAChR) activation can modulate burst duration and the proportion of spikes occurring within bursts in a spatio-temporal fashion. Conclusions We suggest that the presence of significant endogenous cholinergic tone in cortical cultures and the comparability of its modulatory effects to those seen in intact brain tissues support emerging, exploitable commonalities between in vivo and in vitro preparations. We conclude that experimental manipulation of endogenous cholinergic tone could offer a novel opportunity to improve the use of cortical cultures for studies of network-level mechanisms in a manner that remains largely consistent with its functional role.

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.

Explaining sleep duration in adolescents: The impact of socio-demographic and lifestyle factors and working status

Previous studies found students who both work and attend school undergo a partial sleep deprivation that accumulates across the week. The aim of the present study was to obtain information using a questionnaire on a number of variables (e.g., socio-demographics, lifestyle, work timing, and sleep-wake habits) considered to impact on sleep duration of working (n = 51) and non-working (n = 41) high-school students aged 14-21 yrs old attending evening classes (19:00-22:30h) at a public school in the city of Sao Paulo, Brazil. Data were collected for working days and days off. Multiple linear regression analyses were performed to assess the factors associated with sleep duration on weekdays and weekends. Work, sex, age, smoking, consumption of alcohol and caffeine, and physical activity were considered control variables. Significant predictors of sleep duration were: work (p < 0.01), daily work duration (8-10h/day; p < 0.01), sex (p = 0.04), age 18-21 yrs (0.01), smoking (p = 0.02) and drinking habits (p = 0.03), irregular physical exercise (p < 0.01), ease of falling asleep (p = 0.04), and the sleep-wake cycle variables of napping (p < 0.01), nocturnal awakenings (p < 0.01), and mid-sleep regularity (p < 0.01). The results confirm the hypotheses that young students who work and attend school showed a reduction in night-time sleep duration. Sleep deprivation across the week, particularly in students working 8-10h/day, is manifested through a sleep rebound (i.e., extended sleep duration) on Saturdays. However, the different roles played by socio-demographic and lifestyle variables have proven to be factors that intervene with nocturnal sleep duration. The variables related to the sleep-wake cyclenaps and night awakeningsproved to be associated with a slight reduction in night-time sleep, while regularity in sleep and wake-up schedules was shown to be associated with more extended sleep duration, with a distinct expression along the week and the weekend. Having to attend school and work, coupled with other socio-demographic and lifestyle factors, creates an unfavorable scenario for satisfactory sleep duration.