Polynomial (chaos) approximation of maximum eigenvalue functions: efficiency and limitations

This paper is concerned with polynomial approximations of the spectral abscissa function (the supremum of the real parts of the eigenvalues) of a parameterized eigenvalue problem, which are closely related to polynomial chaos approximations if the parameters correspond to realizations of random variables. Unlike in existing works, we highlight the major role of the smoothness properties of the spectral abscissa function. Even if the matrices of the eigenvalue problem are analytic functions of the parameters, the spectral abscissa function may not be everywhere differentiable, even not everywhere Lipschitz continuous, which is related to multiple rightmost eigenvalues or rightmost eigenvalues with multiplicity higher than one. The presented analysis demonstrates that the smoothness properties heavily affect the approximation errors of the Galerkin and collocation-based polynomial approximations, and the numerical errors of the evaluation of coefficients with integration methods. A documentation of the experiments, conducted on the benchmark problems through the software Chebfun, is publicly available.Comment: This is a pre-print of an article published in Numerical Algorithms. The final authenticated version is available online at: https://doi.org/10.1007/s11075-018-00648-

Dante ghibellino. Note per una discussione

The essay proposes a chronlogical hypothesis which will clarify the diverse yet related moments of the request for the Black Guelfs' pardon in the canzone Tre donne, and the marked Ghibelline spirit which gives life to the eulogy of Frederick II and Manfredi in De vulgari eloquentia. Dante’s progressive estrangement from the Guelf viewpoint of his mentor Brunetto Latini is also considered as it leads to an openly pro-imperial stance that the Inferno neither denies nor hides, as some have indeed thought

Il canto XXX dell'Inferno

La lettura del XXX dell'Inferno mostra i legami stilistici e tematici tra questo canto e i precedenti VII e VIII (in particolare l'episodio di Filippo Argenti). Mostra l'importanza del contesto «canino» e generalmente bestiale entro il quale va collocato il latrato di Ecuba e l'importanza della sua funzione demitizzante nel momento che immette l'eredità classica nel mondo moderno. Del discorso di maestro Adamo, si rilevano gli echi complessi impliciti nel suo biblico esordio, e se ne analizzano le parole in chiave di «discours de la mauvaise foi» (seguendo una precisa indicazione della studiosa francese Claude Perrus). Dante si serve della zuffa tra i due personaggi per condannare lo sterile e pericoloso esercizio di falsificazione verbale costituito dall a tenzone.The reading of the XXX of Hell shows the stylistic and thematic links between that canto and the previous VII and VIII (particularly the episode of Filippo Argenti). It shows the significance of the «canine» and the generally brutal context in which the howling of Hecuba is placed and the importance of his demystifying function at the moment he releases the classical inheritance into the modern world. From the speech by Maestro Adamo, the complex echoes implicit in his Biblical debut point themselves out, and the words in the key of the «discours de la mauvaise foi» (following a precise indication from the French scholar Claude Perrus) are analysed within it. Dante used the fight between the two characters to condemn that sterile and dangerous exercise of verbal falsification constituted by the fight

«Et havrà Barcellona il suo poeta». Benet Garret, il Cariteo

Il saggio considera lo sfondo storico e politico contro il quale va collocata la vita (1450 circa - 1514 circa) e l'opera del poeta di origine barcellonese Benet Garret, detto Cariteo, il quale fu constantemente fedele ai suoi re. Tutta la sua opera è segnata in profondità da questa esperienza e dà forma al vero e proprio mito della Napoli aragonese. Si esaminano inoltre le testimonianze dell'opera giunte sino a noi, per passare poi a considerare la struttura del canzioniere intitolato Endimione. L'amore per Luna e l'amore per i re aragonesi e quello per gli amici e quello per Napoli non sono, in essenza, cose diverse rispetto a quella che è, appunto, la struttura profonda del canzionere. Essa finisce per comprendere anche l'amore per la patria perduta, che constituisce l'ultimo e forse più struggente mito di Cariteo il quale, alla fine della propria vita, sogna di tornare a Barcellona per affidare alla città nella quale era nato la custodia dell'intero tesoro della sua esperienza poetica e umana.The thesis considers the historical and political background to the work of the Barcelona poet Benet Garret (1450 approx - 1514 approx) alias Cariteo, who was constantly faithful to his king. His work is deeply marked by this experience and relates the truth behind the myth of Aragonese Naples. Testimonies are taken toward an examination of committee work, in order to then consider the structure of the canzoniere or songbook entitled Endimione. Love for Luna, for the Aragonese king, for friends and for Naples is essentially the same thing in relation to the deep structure of the canzoniere. It terminates by also comprehending love for the lost patria that constitutes Cariteo's ultimate and perhaps most compelling myth, and expressing his lifelong dream of returning to Barcelona in order to entrust the treasure of his poetic and human experience to the city in which he was born

Etica, estetica e politica del cibo in Petrarca

Il saggio considera l'insieme degli atteggiamenti di Petrarca nei confronti del cibo, testimoniati da una lunga serie di passi sparsi nella sua opera, e in particolare in alcune importanti lettere «Senili». Da questo esame risultano varie funzioni assegnate al discorso sull'alimentazione: quella oppositiva, che distingue tra gozzoviglia e moderazione, tra cibi artefatti e cibi naturali, tra sporcizia e pulizia, e infine, sul piano sociale e politico, tra lusso e corruzione da una parte, e modestia e virtù dall'altro; quella positiva, che associa la buona e semplice alimentazione naturale alla salute e alla vita tranquilla e solitaria; quella estetica, non meno importante delle altre, che fa del modo di nutrirsi un «test» particolarmente importante sulla civiltà e la buona educazione. Cibarsi, insomma, è per Petrarca un fatto assolutamente culturale, e con ciò egli chiaramente supera i dilemmi della morale cristiana, e pone per primo le basi per una riflessione moderna sull'argomento.The research considers the combined attitudes of Petrarch in comparison with food, attested by a long series of scattered steps in his work and, in particular, in some significant «Senile» letters. There are various functions resulting from this research, aimed at the discussion of nutrition: The opposing, which distinguishes between gluttony and moderate eating, artificial and natural foods, cleanliness and dirtiness -on both a social and political level, between luxury and depravation, on the one hand, and modesty and virtue, on the other. The positive, associates a good, simple natural diet with health and a peaceful, private life. The aesthetic, of no less importance than the others, tests eating habits, proven particularly important with regard to civilisation and good education. In short, for Petrarch, eating was a completely cultural event, with which one clearly overcame Christian moral dilemmas and which firmly stood by its foundations for a modern reflection on the debate

Longitudinal analysis of maize diversity in Yucatan, Mexico: influence of agro-ecological factors on landraces conservation and modern variety introduction

Transformations that farmers bring to their traditional farming systems and their impacts on the conservation and evolution of maize varieties over a 12-year period are investigated using a longitudinal analysis. Despite the increased introduction and supply of improved maize variety seeds in the Yucatan Peninsula, Mexico, over the last 12 years farmers continue to maintain a substantial amount of traditional maize variety diversity. Even with the increased availability of hybrid seeds, farmers in the community of Yaxcaba on average plant more than three quarters of their milpa fields to traditional maize varieties, with the latter one fourth predominately planted to a locally improved variety Nal Xoy, a farm cross of a traditional variety and an improved variety. We observed a significant reduction in yellow – x-Nuuk nal, a long-cycle traditional landrace, paralleled by an increase in short- and intermediate-cycle locally adapted improved maize varieties. We found great differences in the distribution of maize varieties by soil type, with modern varieties being targeted for the rarer, deeper and fine-grained soils, while traditional varieties predominate on the more prevalent stony and thin soils. Our results provide a picture in which most traditional maize varieties in Yaxcaba continue to be maintained by farmers, coexisting with locally adapted improved varieties on the same landscape, and allowing the continued evolution of maize populationsPeer Revie

X-ray and radio observations of the magnetar Swift J1834.9-0846 and its dust-scattering halo

We present a long-term study of the 2011 outburst of the magnetar Swift J1834.9-0846 carried out using new Chandra observations, as well as all the available Swift, RXTE, and XMM-Newton data. The last observation was performed on 2011 November 12, about 100 days after the onset of the bursting activity that had led to the discovery of the source on 2011 August 07. This long time span enabled us to refine the rotational ephemeris and observe a downturn in the decay of the X-ray flux. Assuming a broken power law for the long-term light curve, the break was at ~46 d after the outburst onset, when the decay index changed from alpha ~ 0.4 to ~4.5. The flux decreased by a factor ~2 in the first ~50 d and then by a factor ~40 until November 2011 (overall, by a factor ~70 in ~100 d). At the same time, the spectrum, which was well described by an absorbed blackbody all along the outburst, softened, the temperature dropping from ~1 to ~0.6 keV. Diffuse X-ray emission extending up to 20" from the source was clearly detected in all Chandra observations. Its spatial and spectral properties, as well as its time evolution, are consistent with a dust-scattering halo due to a single cloud located at a distance of $\approx$200 pc from Swift J1834.9-0846, which should be in turn located at a distance of ~5 kpc. Considering the time delay of the scattered photons, the same dust cloud might also be responsible for the more extended emission detected in XMM-Newton data taken in September 2011. We searched for the radio signature of Swift J1834.9-0846 at radio frequencies using the Green Bank Radio Telescope and in archival data collected at Parkes from 1998 to 2003. No evidence for radio emission was found, down to a flux density of 0.05 mJy (at 2 GHz) during the outburst and ~0.2-0.3 mJy (at 1.4 GHz) in the older data.Comment: 11 pages, 9 figures and 4 tables, accepted for publication in MNRA