Monads in double categories

We extend the basic concepts of Street's formal theory of monads from the setting of 2-categories to that of double categories. In particular, we introduce the double category Mnd(C) of monads in a double category C and dene what it means for a double category to admit the construction of free monads. Our main theorem shows that, under some mild conditions, a double category that is a framed bicategory admits the construction of free monads if its horizontal 2-category does. We apply this result to obtain double adjunctions which extend the adjunction between graphs and categories and the adjunction between polynomial endofunctors and polynomial monads.

Estudi de la reformació amb vapor de biocombustibles per a l'obtenció d'hidrogen utilitzant suports estructurats ceràmics funcionalitzats

Donada una aplicació racional en una varietat complexa, Bellon i Viallet van definit l’entropia algebraica d’aquesta aplicació i van provar que aquest valor és un invariant biracional. Un invariant biracional equivalent és el grau asimptòtic, grau dinàmic o complexitat, definit per Boukraa i Maillard. Aquesta noció és propera a la complexitat definida per Arnold. Conjecturalment, el grau asimptòtic satisfà una recurrència lineal amb coeficients enters. Aquesta conjectura ha estat provada en el cas polinòmic en el pla afí complex per Favre i Jonsson i resta oberta en per al cas projectiu global i per al cas local. L’estudi de l’arbre valoratiu de Favre i Jonsson ha resultat clau per resoldre la conjectura en el cas polinòmic en el pla afí complex. El beneficiari ha estudiat l’arbre valoratiu global de Favre i Jonsson i ha reinterpretat algunes nocions i resultats des d’un punt de vista més geomètric. Així mateix, ha estudiat la demostració de la conjectura de Bellon – Viallet en el cas polinòmic en el pla afí complex com a primer pas per trobar una demostració en el cas local i projectiu global en estudis futurs. El projecte inclou un estudi detallat de l'arbre valoratiu global des d'un punt de vista geomètric i els primers passos de la demostració de la conjectura de Bellon - Viallet en el cas polinòmic en el pla afí complex que van efectuar Favre i Jonsson.

Aspectes geomètrics i dinàmics de transformacions racionals planes

Donada una aplicació racional en una varietat complexa, Bellon i Viallet van definit l’entropia algebraica d’aquesta aplicació i van provar que aquest valor és un invariant biracional. Un invariant biracional equivalent és el grau asimptòtic, grau dinàmic o complexitat, definit per Boukraa i Maillard. Aquesta noció és propera a la complexitat definida per Arnold. Conjecturalment, el grau asimptòtic satisfà una recurrència lineal amb coeficients enters. Aquesta conjectura ha estat provada en el cas polinòmic en el pla afí complex per Favre i Jonsson i resta oberta en per al cas projectiu global i per al cas local. L’estudi de l’arbre valoratiu de Favre i Jonsson ha resultat clau per resoldre la conjectura en el cas polinòmic en el pla afí complex. El beneficiari ha estudiat l’arbre valoratiu global de Favre i Jonsson i ha reinterpretat algunes nocions i resultats des d’un punt de vista més geomètric. Així mateix, ha estudiat la demostració de la conjectura de Bellon – Viallet en el cas polinòmic en el pla afí complex com a primer pas per trobar una demostració en el cas local i projectiu global en estudis futurs. El projecte inclou un estudi detallat de l'arbre valoratiu global des d'un punt de vista geomètric i els primers passos de la demostració de la conjectura de Bellon - Viallet en el cas polinòmic en el pla afí complex que van efectuar Favre i Jonsson.

Improving the accuracy of heat balance integral methods applied to thermal problems with time dependent boundary conditions

In this paper the two main drawbacks of the heat balance integral methods are examined. Firstly we investigate the choice of approximating function. For a standard polynomial form it is shown that combining the Heat Balance and Refined Integral methods to determine the power of the highest order term will either lead to the same, or more often, greatly improved accuracy on standard methods. Secondly we examine thermal problems with a time-dependent boundary condition. In doing so we develop a logarithmic approximating function. This new function allows us to model moving peaks in the temperature profile, a feature that previous heat balance methods cannot capture. If the boundary temperature varies so that at some time t & 0 it equals the far-field temperature, then standard methods predict that the temperature is everywhere at this constant value. The new method predicts the correct behaviour. It is also shown that this function provides even more accurate results, when coupled with the new CIM, than the polynomial profile. Analysis primarily focuses on a specified constant boundary temperature and is then extended to constant flux, Newton cooling and time dependent boundary conditions.

Strong isomorphism reductions in complexity theory

We give the first systematic study of strong isomorphism reductions, a notion of reduction more appropriate than polynomial time reduction when, for example, comparing the computational complexity of the isomorphim problem for different classes of structures. We show that the partial ordering of its degrees is quite rich. We analyze its relationship to a further type of reduction between classes of structures based on purely comparing for every n the number of nonisomorphic structures of cardinality at most n in both classes. Furthermore, in a more general setting we address the question of the existence of a maximal element in the partial ordering of the degrees.

Consistency and optimality

Assume that the problem Qo is not solvable in polynomial time. For theories T containing a sufficiently rich part of true arithmetic we characterize T U {ConT} as the minimal extension of T proving for some algorithm that it decides Qo as fast as any algorithm B with the property that T proves that B decides Qo. Here, ConT claims the consistency of T. Moreover, we characterize problems with an optimal algorithm in terms of arithmetical theories.

Computing hypergraph width measures exactly

Hypergraph width measures are a class of hypergraph invariants important in studying the complexity of constraint satisfaction problems (CSPs). We present a general exact exponential algorithm for a large variety of these measures. A connection between these and tree decompositions is established. This enables us to almost seamlessly adapt the combinatorial and algorithmic results known for tree decompositions of graphs to the case of hypergraphs and obtain fast exact algorithms. As a consequence, we provide algorithms which, given a hypergraph H on n vertices and m hyperedges, compute the generalized hypertree-width of H in time O*(2n) and compute the fractional hypertree-width of H in time O(1.734601n.m).1

Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs

In a seminal paper [10], Weitz gave a deterministic fully polynomial approximation scheme for counting exponentially weighted independent sets (which is the same as approximating the partition function of the hard-core model from statistical physics) in graphs of degree at most d, up to the critical activity for the uniqueness of the Gibbs measure on the innite d-regular tree. ore recently Sly [8] (see also [1]) showed that this is optimal in the sense that if here is an FPRAS for the hard-core partition function on graphs of maximum egree d for activities larger than the critical activity on the innite d-regular ree then NP = RP. In this paper we extend Weitz's approach to derive a deterministic fully polynomial approximation scheme for the partition function of general two-state anti-ferromagnetic spin systems on graphs of maximum degree d, up to the corresponding critical point on the d-regular tree. The main ingredient of our result is a proof that for two-state anti-ferromagnetic spin systems on the d-regular tree, weak spatial mixing implies strong spatial mixing. his in turn uses a message-decay argument which extends a similar approach proposed recently for the hard-core model by Restrepo et al [7] to the case of general two-state anti-ferromagnetic spin systems.

Control de márgenes quirúrgicos del carcinoma basocelular según la especialidad del cirujano

Introducción: el principal tratamiento del carcinoma basocelular (CBC) es la extirpación quirúrgica. Objetivo: determinar la prevalencia de márgenes afectados por el tumor, globalmente y en función del especialista que lo interviene. Métodos: se realizó un estudio retrospectivo de de los informes histológicos de CBC (enero de 2009 - marzo de 2010), un análisis estadístico (Chi-cuadrado de Pearson, U de Mann-Whitney, test de Kruskal-Wallis) y multivariable mediante regresión

Estudio de marcadores moleculares en neoplasias mieloproliferativas

Las neoplasias mieloproliferativas (NM) son un grupo de enfermedades clonales de la célula hematopoyética madre. Entre las NM clásicas se encuentran la policitemia vera (PV), la trombocitemia esencial (TE) y la mielofibrosis primaria (MFP). Durante muchos años el diagnóstico de estas patologías se hacía por exclusión utilizando biomarcadores de clonalidad poco específicos. En el año 2005, la descripción de la mutación JAK2V617F supuso un avance importante en el diagnóstico de estas patologías. Posteriormente, se han descrito mutaciones en otros genes como mutaciones en MPL, TET2, ASXL1, IDH1, IDH2, c-CBL, EZH2, IKZF1 y LNK, en distintas neoplasias mieloides y en porcentaje variable. Aun así, ninguno de estos genes son marcadores específicos de ninguna NM y todavía existe un porcentaje elevado de pacientes con TE y MFP sin un marcador de clonalidad conocido. Además, todos estos genes se han descrito como eventos genéticos implicados en la transformación de una NM a leucemia mieloide aguda. El objetivo de este proyecto fue estudiar varios marcadores moleculares en neoplasias mieloproliferativas Philadelphia negativas. En primer lugar, se estudió la modulación de la carga alélica JAK2V617F en pacientes con PV o TE que recibieron tratamiento citoreductor y a su vez se analizó la dinámica natural de la carga alélica en pacientes que no recibieron tratamiento. Posteriormente, se analizaron la presencia de alteraciones en los genes previamente mencionados, en distintos grupos de pacientes. En primer lugar, se analizó la presencia de mutaciones en TET2, ASXL1, IDH1, IDH2 y CBL en un grupo de pacientes JAK2 y MPL negativos, para determinar la frecuencia de alteraciones de estos genes en este grupo de pacientes y determinar su valor en el diagnóstico de estas patologías. En segundo lugar, se estudió la presencia de mutaciones en estos genes incluyendo EZH2, IKZF1 y LNK para estudiar la incidencia y el valor pronóstico de estas alteraciones en las NM que progresan a mielofibrosis.

Analysis of Pleistocene paleodrainage evolution in the Po Basin (Italy) by multivariate statistical techniques

In order to obtain a high-resolution Pleistocene stratigraphy, eleven continuouslycored boreholes, 100 to 220m deep were drilled in the northern part of the PoPlain by Regione Lombardia in the last five years. Quantitative provenanceanalysis (QPA, Weltje and von Eynatten, 2004) of Pleistocene sands was carriedout by using multivariate statistical analysis (principal component analysis, PCA,and similarity analysis) on an integrated data set, including high-resolution bulkpetrography and heavy-mineral analyses on Pleistocene sands and of 250 majorand minor modern rivers draining the southern flank of the Alps from West toEast (Garzanti et al, 2004; 2006). Prior to the onset of major Alpine glaciations,metamorphic and quartzofeldspathic detritus from the Western and Central Alpswas carried from the axial belt to the Po basin longitudinally parallel to theSouthAlpine belt by a trunk river (Vezzoli and Garzanti, 2008). This scenariorapidly changed during the marine isotope stage 22 (0.87 Ma), with the onset ofthe first major Pleistocene glaciation in the Alps (Muttoni et al, 2003). PCA andsimilarity analysis from core samples show that the longitudinal trunk river at thistime was shifted southward by the rapid southward and westward progradation oftransverse alluvial river systems fed from the Central and Southern Alps.Sediments were transported southward by braided river systems as well as glacialsediments transported by Alpine valley glaciers invaded the alluvial plain.Kew words: Detrital modes; Modern sands; Provenance; Principal ComponentsAnalysis; Similarity, Canberra Distance; palaeodrainage

Using self organizing maps on compositional data

Self-organizing maps (Kohonen 1997) is a type of artificial neural network developedto explore patterns in high-dimensional multivariate data. The conventional versionof the algorithm involves the use of Euclidean metric in the process of adaptation ofthe model vectors, thus rendering in theory a whole methodology incompatible withnon-Euclidean geometries.In this contribution we explore the two main aspects of the problem:1. Whether the conventional approach using Euclidean metric can shed valid resultswith compositional data.2. If a modification of the conventional approach replacing vectorial sum and scalarmultiplication by the canonical operators in the simplex (i.e. perturbation andpowering) can converge to an adequate solution.Preliminary tests showed that both methodologies can be used on compositional data.However, the modified version of the algorithm performs poorer than the conventionalversion, in particular, when the data is pathological. Moreover, the conventional ap-proach converges faster to a solution, when data is \well-behaved".Key words: Self Organizing Map; Artificial Neural networks; Compositional data

Compositional data analysis: where we are and where should we be heading?

We take stock of the present position of compositional data analysis, of what has beenachieved in the last 20 years, and then make suggestions as to what may be sensibleavenues of future research. We take an uncompromisingly applied mathematical view,that the challenge of solving practical problems should motivate our theoreticalresearch; and that any new theory should be thoroughly investigated to see if it mayprovide answers to previously abandoned practical considerations. Indeed a main themeof this lecture will be to demonstrate this applied mathematical approach by a number ofchallenging examples

When a data set can be considered compositional?

Traditionally, compositional data has been identified with closed data, and the simplex has been considered as the natural sample space of this kind of data. In our opinion, the emphasis on the constrained nature ofcompositional data has contributed to mask its real nature. More crucial than the constraining property of compositional data is the scale-invariant property of this kind of data. Indeed, when we are considering only few parts of a full composition we are not working with constrained data but our data are still compositional. We believe that it is necessary to give a more precisedefinition of composition. This is the aim of this oral contribution

Comparing correspondence analysis and the log-ratio alternative for representing categorical data

We compare correspondance análisis to the logratio approach based on compositional data. We also compare correspondance análisis and an alternative approach using Hellinger distance, for representing categorical data in a contingency table. We propose a coefficient which globally measures the similarity between these approaches. This coefficient can be decomposed into several components, one component for each principal dimension, indicating the contribution of the dimensions to the difference between the two representations. These three methods of representation can produce quite similar results. One illustrative example is given