On an upper bound for the arithmetic self-intersection number of the dualizing sheaf on arithmetic surfaces

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The mean dehn functions of Abelian groups

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Higher arithmetic Chow groups

We give a new construction of higher arithmetic Chow groups for quasi-projective arithmetic varieties over a field. Our definition agrees with the higher arithmetic Chow groups defined by Goncharov for projective arithmetic varieties over a field. These groups are the analogue, in the Arakelov context, of the higher algebraic Chow groups defined by Bloch. The degree zero group agrees with the arithmetic Chow groups of Burgos. Our new construction is shown to be a contravariant functor and is endowed with a product structure, which is commutative and associative.

Singular Bott-Chern classes and the arithmetic Grothendieck-Riemann-Roch theorem for closed immersions

We study the singular Bott-Chern classes introduced by Bismut, Gillet and Soulé. Singular Bott-Chern classes are the main ingredient to define direct images for closed immersions in arithmetic K-theory. In this paper we give an axiomatic definition of a theory of singular Bott-Chern classes, study their properties, and classify all possible theories of this kind. We identify the theory defined by Bismut, Gillet and Soulé as the only one that satisfies the additional condition of being homogeneous. We include a proof of the arithmetic Grothendieck-Riemann-Roch theorem for closed immersions that generalizes a result of Bismut, Gillet and Soulé and was already proved by Zha. This result can be combined with the arithmetic Grothendieck-Riemann-Roch theorem for submersions to extend this theorem to arbitrary projective morphisms. As a byproduct of this study we obtain two results of independent interest. First, we prove a Poincaré lemma for the complex of currents with fixed wave front set, and second we prove that certain direct images of Bott-Chern classes are closed.

An irreducibility criterion for group representations, with arithmetic applications

We prove a criterion for the irreducibility of an integral group representation p over the fraction field of a noetherian domain R in terms of suitably defined reductions of p at prime ideals of R. As applications, we give irreducibility results for universal deformations of residual representations, with a special attention to universal deformations of residual Galois representations associated with modular forms of weight at least 2.

Mean-payoff games and propositional proofs

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A survey on recent p-adic integration theories and arithmetic applications

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Changes in wage structure in Mexico going beyond the mean: An analysis of differences in distribution, 1987-2008

This paper conducts an empirical analysis of the relationship between wage inequality, employment structure, and returns to education in urban areas of Mexico during the past two decades (1987-2008). Applying Melly’s (2005) quantile regression based decomposition, we find that changes in wage inequality have been driven mainly by variations in educational wage premia. Additionally, we find that changes in employment structure, including occupation and firm size, have played a vital role. This evidence seems to suggest that the changes in wage inequality in urban Mexico cannot be interpreted in terms of a skill-biased change, but rather they are the result of an increasing demand for skills during that period.

Kriging coordinates: what does that mean?

Kriging is an interpolation technique whose optimality criteria are based on normality assumptions either for observed or for transformed data. This is the case of normal, lognormal and multigaussian kriging.When kriging is applied to transformed scores, optimality of obtained estimators becomes a cumbersome concept: back-transformed optimal interpolations in transformed scores are not optimal in the original sample space, and vice-versa. This lack of compatible criteria of optimality induces a variety of problems in both point and block estimates. For instance, lognormal kriging, widely used to interpolate positivevariables, has no straightforward way to build consistent and optimal confidence intervals for estimates.These problems are ultimately linked to the assumed space structure of the data support: for instance, positive values, when modelled with lognormal distributions, are assumed to be embedded in the whole real space, with the usual real space structure and Lebesgue measure

When zero doesn't mean it and other geomathematical mischief

There is almost not a case in exploration geology, where the studied data doesn’tincludes below detection limits and/or zero values, and since most of the geological dataresponds to lognormal distributions, these “zero data” represent a mathematicalchallenge for the interpretation.We need to start by recognizing that there are zero values in geology. For example theamount of quartz in a foyaite (nepheline syenite) is zero, since quartz cannot co-existswith nepheline. Another common essential zero is a North azimuth, however we canalways change that zero for the value of 360°. These are known as “Essential zeros”, butwhat can we do with “Rounded zeros” that are the result of below the detection limit ofthe equipment?Amalgamation, e.g. adding Na2O and K2O, as total alkalis is a solution, but sometimeswe need to differentiate between a sodic and a potassic alteration. Pre-classification intogroups requires a good knowledge of the distribution of the data and the geochemicalcharacteristics of the groups which is not always available. Considering the zero valuesequal to the limit of detection of the used equipment will generate spuriousdistributions, especially in ternary diagrams. Same situation will occur if we replace thezero values by a small amount using non-parametric or parametric techniques(imputation).The method that we are proposing takes into consideration the well known relationshipsbetween some elements. For example, in copper porphyry deposits, there is always agood direct correlation between the copper values and the molybdenum ones, but whilecopper will always be above the limit of detection, many of the molybdenum values willbe “rounded zeros”. So, we will take the lower quartile of the real molybdenum valuesand establish a regression equation with copper, and then we will estimate the“rounded” zero values of molybdenum by their corresponding copper values.The method could be applied to any type of data, provided we establish first theircorrelation dependency.One of the main advantages of this method is that we do not obtain a fixed value for the“rounded zeros”, but one that depends on the value of the other variable.Key words: compositional data analysis, treatment of zeros, essential zeros, roundedzeros, correlation dependency

Mean intrinsic tensile properties of stone groundwood fibers from softwood

Stone groundwood (SGW) is a fibrous matter commonly prepared in a high yield process, and mainly used for papermaking applications. In this work, the use of SGW fibers is explored as reinforcing element of polypropylene (PP) composites. Due to its chemical and superficial features, the use of coupling agents is needed for a good adhesion and stress transfer across the fiber-matrix interface. The intrinsic strength of the reinforcement is a key parameter to predict the mechanical properties of the composite and to perform an interface analysis. The main objective of the present work was the determination of the intrinsic tensile strength of stone groundwood fibers. Coupled and non-coupled PP composites from stone groundwood fibers were prepared. The influence of the surface morphology and the quality at interface on the final properties of the composite was analyzed and compared to that of fiberglass PP composites. The intrinsic tensile properties of stone groundwood fibers, as well as the fiber orientation factor and the interfacial shear strength of the current composites were determined

Subsampling the mean of heavy-tailed dependent observations

We establish the validity of subsampling confidence intervals for themean of a dependent series with heavy-tailed marginal distributions.Using point process theory, we study both linear and nonlinear GARCH-liketime series models. We propose a data-dependent method for the optimalblock size selection and investigate its performance by means of asimulation study.

Asymptotic robust inferences in the analysis of mean and covariance structures

Structural equation models are widely used in economic, socialand behavioral studies to analyze linear interrelationships amongvariables, some of which may be unobservable or subject to measurementerror. Alternative estimation methods that exploit different distributionalassumptions are now available. The present paper deals with issues ofasymptotic statistical inferences, such as the evaluation of standarderrors of estimates and chi--square goodness--of--fit statistics,in the general context of mean and covariance structures. The emphasisis on drawing correct statistical inferences regardless of thedistribution of the data and the method of estimation employed. A(distribution--free) consistent estimate of $\Gamma$, the matrix ofasymptotic variances of the vector of sample second--order moments,will be used to compute robust standard errors and a robust chi--squaregoodness--of--fit squares. Simple modifications of the usual estimateof $\Gamma$ will also permit correct inferences in the case of multi--stage complex samples. We will also discuss the conditions under which,regardless of the distribution of the data, one can rely on the usual(non--robust) inferential statistics. Finally, a multivariate regressionmodel with errors--in--variables will be used to illustrate, by meansof simulated data, various theoretical aspects of the paper.

Spanning tests in return and stochastic discount factor mean-variance frontiers: A unifying approach

We propose new spanning tests that assess if the initial and additional assets share theeconomically meaningful cost and mean representing portfolios. We prove their asymptoticequivalence to existing tests under local alternatives. We also show that unlike two-step oriterated procedures, single-step methods such as continuously updated GMM yield numericallyidentical overidentifyng restrictions tests, so there is arguably a single spanning test.To prove these results, we extend optimal GMM inference to deal with singularities in thelong run second moment matrix of the influence functions. Finally, we test for spanningusing size and book-to-market sorted US stock portfolios.