Biplots of compositional data

The singular value decomposition and its interpretation as alinear biplot has proved to be a powerful tool for analysing many formsof multivariate data. Here we adapt biplot methodology to the specifficcase of compositional data consisting of positive vectors each of whichis constrained to have unit sum. These relative variation biplots haveproperties relating to special features of compositional data: the studyof ratios, subcompositions and models of compositional relationships. Themethodology is demonstrated on a data set consisting of six-part colourcompositions in 22 abstract paintings, showing how the singular valuedecomposition can achieve an accurate biplot of the colour ratios and howpossible models interrelating the colours can be diagnosed.

Tying up the loose ends in simple correspondence analysis

Although correspondence analysis is now widely available in statistical software packages and applied in a variety of contexts, notably the social and environmental sciences, there are still some misconceptions about this method as well as unresolved issues which remain controversial to this day. In this paper we hope to settle these matters, namely (i) the way CA measures variance in a two-way table and how to compare variances between tables of different sizes, (ii) the influence, or rather lack of influence, of outliers in the usual CA maps, (iii) the scaling issue and the biplot interpretation of maps,(iv) whether or not to rotate a solution, and (v) statistical significance of results.

Weighted Euclidean biplots

We construct a weighted Euclidean distance that approximates any distance or dissimilarity measure between individuals that is based on a rectangular cases-by-variables data matrix. In contrast to regular multidimensional scaling methods for dissimilarity data, the method leads to biplots of individuals and variables while preserving all the good properties of dimension-reduction methods that are based on the singular-value decomposition. The main benefits are the decomposition of variance into components along principal axes, which provide the numerical diagnostics known as contributions, and the estimation of nonnegative weights for each variable. The idea is inspired by the distance functions used in correspondence analysis and in principal component analysis of standardized data, where the normalizations inherent in the distances can be considered as differential weighting of the variables. In weighted Euclidean biplots we allow these weights to be unknown parameters, which are estimated from the data to maximize the fit to the chosen distances or dissimilarities. These weights are estimated using a majorization algorithm. Once this extra weight-estimation step is accomplished, the procedure follows the classical path in decomposing the matrix and displaying its rows and columns in biplots.

Els Aiguamolls de la Puda de Banyoles: una proposta de gestió

La Puda, no fa pas tants anys, constituïa un espai emblemàtic de Banyoles i, en canvi, avui dia ha esdevingut un àmbit totalment al marge de la dinàmica de la ciutat. La realitat actual mostra que és un espai que no ha desenvolupat les seves potencialitats, fet que l'ha portat a no posseir plenament les característiques d'un parc urbà ni les pròpies d'una àrea natural. L'objectiu principal d'aquest article és proposar un model de gestió per als aiguamolls de la Puda, amb el propòsit de regenerar i protegir ambientalment la zona i recuperar per a la societat banyolina un espai oblidat. Es tracta, dones, de contemplar-ne tant la vessant natural com la social i de fer-ho prenent en consideració diferents escales d’anàlisi. Les raons que condueixen a tal objectiu es fonamenten en la convicció que tot i la precària salut ambiental que pateix la lona, encara està en condicions de desenvolupar plenament el seu alt valor ecològic, i que tot i la marginalitat que presenta respecte a la resta del municipi, manté la possibilitat d'esdevenir un espai singular i atractiu que participi activament de la vida banyolina

Morfogénesis del valle de Sant Miquel de Campmajor

A series of circumstances which converge in a little valley in the province of Girona, result in a peculiar type of morphogenetic evolution and a quite singular mechanical instability of its buttons. Very recent tectonic movements as well as dissolution phenomena of its subsoil due to pressurized underground water have played an important role in the morphogenesis. Such conditions have resulted in a fast morphological evolution which a progressive lowering of the valley floor as well as peculiar morphological features which favour the existence of numerous pits caused by sudden collapses distributed in altitude and time

L’Edició en lletra gòtica de l’Speculum al foder (1917). Història d’un misteriós exemplar d’infern

La filologia, tret de rares excepcions, acostuma a prestar poc interès a la bibliofília. Potser perquè es considera que un text acurat i fiable està renyit amb un llibre imprès en bon paper Japó o de fil, del amb una tipografia impecable, sovint il·lustrat i a un preu que sol ser alt, com correspon a un desplegament artesanal d’aquesta mena. Filologia i bibliofília, en una paraula, tenen vies diferents de difusió. I, amb tot, l’univers de la bibliofília custodia secrets molt ben guardats de la nostra història lingüística i literària, tan singular i plena de sotracs de diversa mena. Secrets que criden poderosament l’atenció del filòleg. El cens i descripció de testimonis del tractadet eròtic medieval conegut com a Speculum al foder, per exemple, amaga un curiós enigma bibliogràfic: un imprès en tipografia gòtica i sense peu editorial, un veritable incunable modern, fruit rar del mateix impuls que cent anys enrere es va ensenyorir de les arts plàstiques i constructives d’aquest país per omplir-lo de magnífiques fantasies medievalitzants. És d’aquest misteriós exemplar d’infern que s’ocupa el treballet que segueix

A Small Baseline DIFSAR Approach for Investigating Deformations on Full Resolution SAR Interferograms

This paper presents a differential synthetic apertureradar (SAR) interferometry (DIFSAR) approach for investigatingdeformation phenomena on full-resolution DIFSAR interferograms.In particular, our algorithm extends the capabilityof the small-baseline subset (SBAS) technique that relies onsmall-baseline DIFSAR interferograms only and is mainly focusedon investigating large-scale deformations with spatial resolutionsof about 100 100 m. The proposed technique is implemented byusing two different sets of data generated at low (multilook data)and full (single-look data) spatial resolution, respectively. Theformer is used to identify and estimate, via the conventional SBAStechnique, large spatial scale deformation patterns, topographicerrors in the available digital elevation model, and possibleatmospheric phase artifacts; the latter allows us to detect, onthe full-resolution residual phase components, structures highlycoherent over time (buildings, rocks, lava, structures, etc.), as wellas their height and displacements. In particular, the estimation ofthe temporal evolution of these local deformations is easily implementedby applying the singular value decomposition technique.The proposed algorithm has been tested with data acquired by theEuropean Remote Sensing satellites relative to the Campania area(Italy) and validated by using geodetic measurements.

Homotopy Batalin-Vilkovisky algebras

This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution we extend the theory of Koszul duality to operads and properads that are defind by quadratic and linear relations. The operad encoding Batalin-Vilkovisky algebras is shown to be Koszul in this sense. This allows us to prove a Poincare-Birkhoff-Witt Theorem for such an operad and to give an explicit small quasi-free resolution for it. This particular resolution enables us to describe the deformation theory and homotopy theory of BV-algebras and of homotopy BV-algebras. We show that any topological conformal field theory carries a homotopy BV-algebra structure which lifts the BV-algebra structure on homology. The same result is proved for the singular chain complex of the double loop space of a topological space endowed with an action of the circle. We also prove the cyclic Deligne conjecture with this cofibrant resolution of the operad BV. We develop the general obstruction theory for algebras over the Koszul resolution of a properad and apply it to extend a conjecture of Lian-Zuckerman, showing that certain vertex algebras have an explicit homotopy BV-algebra structure.

Alteritzar la singularitat: veus per a una pedagogia de l'experiència

Parte de la investigación en torno a la realidad educativa que se ha desarrollado durante los últimos años se caracteriza por intentar encontrar formas de interpretación orientadas a significar los procesos formativos centrados en las vivencias singulares de los agentes que participan de la educación así como en la posibilidad que éstas ofrecen de devenir experiencia, eso es,vivencia concienciada. A raíz de las mismas podemos observar como la biografía apunta a ser una de las más emblemáticas formalizaciones del proceso de narración de vivencias. Pero, aún cuando la misma se perfila como una de las narraciones que más promueven la interpretación e intercambio de vivencias, posibilitando la reflexión e, incluso, formación mediada, la biografía todavía presenta como forma teorética algunos escollos. Los cuales, pueden ser utilizados como preguntas base para formular una voz de las pedagogías de la experiencia. Justamente, interrogarse y repensar su factibilidad es el tema que se ensaya en el presente artículo.

Veus ignorades: representacions socials, subjectivitat i resiliència en persones grans amb pèrdua d’autonomia funcional

Els processos per a l’aprovació i la implementació de la Llei per a l’Autonomia personal i l’Atenció a les Persones en situació de Dependència (LAPAD) han donat lloc a un intens debat polític i social que, coincidint també amb les millores en la provisió de serveis i els avenços mèdics, ha contribuït a un procés de classificació i d’etiquetatge basats en els dèficits de les persones que es troben en aquestes circumstàncies. Aquesta visió anul·la el subjecte i la seva experiència singular i condiciona l’abordatge dels models d’atenció i de cura. L’estudi pretén fer una aproximació a les persones grans amb pèrdua d’autonomia funcional, fent emergir les seves veus, que expressen com perceben, interpreten, afronten i es reajusten a la nova situació. Partint d’un enfocament constructivista, basat en la subjectivitat, es fa un recorregut sobre els models de la discapacitat que han reeixit en l’activitat científica dels darrers anys, els mecanismes de regulació de les pèrdues que defensen les teories del cicle vital i les aportacions que s’han fet sobre el model de la resiliència aplicat a les persones que envelleixen. El resultats de l’estudi mostren com les representacions i els significats que les persones grans atribueixen a la seva experiència s’inscriuen en les seves trajectòries vitals, donant un sentit únic i singular a la forma de viure i de respondre a la pèrdua d’autonomia funcional i les seves conseqüències. Aquelles que expressen una vivència d’integritat respecte de la vida viscuda, amb predomini d’afectes positius envers un mateix i els altres, que conserven l’esperança i el desig de continuar vivint, s’ajusten a les pèrdues de manera més satisfactòria que aquelles que expressen desconfiança i una certa amargor respecte de la pròpia vida. D’això se’n deriva que els espais d’escolta i d’acompanyament poden ser un recurs vàlid i necessari en el qual, a través de la paraula i el testimoni narrat, el subjecte pugui repensar i resignificar les seves experiències.

Bounds on multisecant lines

The purpose of this paper is two fold. First, we give an upper bound on the orderof a multisecant line to an integral arithmetically Cohen-Macaulay subscheme in Pn of codimension two in terms of the Hilbert function. Secondly, we givean explicit description of the singular locus of the blow up of an arbitrary local ring at a complete intersection ideal. This description is used to refine standardlinking theorem. These results are tied together by the construction of sharp examples for the bound, which uses the linking theorems.

Stability of a nonequilibrium steady-state interface

We study the interfacial modes of a driven diffusive model under suitable nonequilibrium conditions leading to possible instability. The external field parallel to the interface, which sets up a steady-state parallel flux, enhances the growth or decay rates of the interfacial modes. More dramatically, asymmetry in the model can introduce an oscillatory component into the interfacial dispersion relation. In certain circumstances, the applied field behaves as a singular perturbation.

Transient and preparation colored-noise effects: The nonlinear relaxation-time approach

We develop a singular perturbation approach to the problem of the calculation of a characteristic time (the nonlinear relaxation time) for non-Markovian processes driven by Gaussian colored noise with small correlation time. Transient and initial preparation effects are discussed and explicit results for prototype situations are obtained. New effects on the relaxation of unstable states are predicted. The approach is compared with previous techniques.

Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study

We study the singular effects of vanishingly small surface tension on the dynamics of finger competition in the Saffman-Taylor problem, using the asymptotic techniques described by Tanveer [Philos. Trans. R. Soc. London, Ser. A 343, 155 (1993)] and Siegel and Tanveer [Phys. Rev. Lett. 76, 419 (1996)], as well as direct numerical computation, following the numerical scheme of Hou, Lowengrub, and Shelley [J. Comput. Phys. 114, 312 (1994)]. We demonstrate the dramatic effects of small surface tension on the late time evolution of two-finger configurations with respect to exact (nonsingular) zero-surface-tension solutions. The effect is present even when the relevant zero-surface-tension solution has asymptotic behavior consistent with selection theory. Such singular effects, therefore, cannot be traced back to steady state selection theory, and imply a drastic global change in the structure of phase-space flow. They can be interpreted in the framework of a recently introduced dynamical solvability scenario according to which surface tension unfolds the structurally unstable flow, restoring the hyperbolicity of multifinger fixed points.

Kinematic reduction of reaction-diffusion fronts with multiplicative noise. Derivation of stochastic sharp-interface equations

We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the kinematic (eikonal) description in terms of a stochastic moving-boundary or sharp-interface approximation. We find that the effective noise is additive and we relate its strength to the noise parameters in the original field equations, to first order in noise strength, but including a partial resummation to all orders which captures the singular dependence on the microscopic cutoff associated with the spatial correlation of the noise. This dependence is essential for a quantitative and qualitative understanding of fluctuating fronts, affecting both scaling properties and nonuniversal quantities. Our results predict phenomena such as the shift of the transition point between the pushed and pulled regimes of front propagation, in terms of the noise parameters, and the corresponding transition to a non-Kardar-Parisi-Zhang universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations and kinetic roughening. We also predict and observe a noise-induced pushed-pulled transition. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reaction-diffusion field equations with multiplicative noise.