On the integral Hodge conjecture for real varieties, I

We formulate the "real integral Hodge conjecture", a version of the integral Hodge conjecture for real varieties, and raise the question of its validity for cycles of dimension 1 on uniruled and Calabi-Yau threefolds and on rationally connected varieties. We relate it to the problem of determining the image of the Borel-Haefliger cycle class map for 1-cycles, with the problem of deciding whether a real variety with no real point contains a curve of even geometric genus and with the problem of computing the torsion of the Chow group of 1-cycles of real threefolds. New results about these problems are obtained along the way.Comment: 67 pages; v2: minor modifications; v3: Section 1.1.3 slightly expanded, final versio

The role of African Union law in integrating Africa

This article traces how the development of regional law is linked to the state of regional integration in Africa. Given the prominent role European Union law plays in the functioning of the European Union, the question is posed whether there is similar scope for the development of ‘African Union law’, a term not established hitherto. Initially devoid from the necessary supranational elements required to adopt law that would automatically bind member states, the African Union is leaning towards a functionalist approach paving the way for transfer of sovereign powers to African Union institutions. It is argued that law-making capacity, be it through the activities of the Pan-African Parliament, the Peace and Security Council or the African court system are necessary requirements to accelerate the process of regional integration. African Union law will hold member states accountable to comply with international and continentally agreed standards on inter alia democracy, good governance and human rights

Polishness of some topologies related to word or tree automata

We prove that the B\"uchi topology and the automatic topology are Polish. We also show that this cannot be fully extended to the case of a space of infinite labelled binary trees; in particular the B\"uchi and the Muller topologies are not Polish in this case.Comment: This paper is an extended version of a paper which appeared in the proceedings of the 26th EACSL Annual Conference on Computer Science and Logic, CSL 2017. The main addition with regard to the conference paper consists in the study of the B\"uchi topology and of the Muller topology in the case of a space of trees, which now forms Section

Semiparametric inference for the recurrent event process by means of a single-index model

In this paper, we introduce new parametric and semiparametric regression techniques for a recurrent event process subject to random right censoring. We develop models for the cumula- tive mean function and provide asymptotically normal estimators. Our semiparametric model which relies on a single-index assumption can be seen as a dimension reduction technique that, contrary to a fully nonparametric approach, is not stroke by the curse of dimensional- ity when the number of covariates is high. We discuss data-driven techniques to choose the parameters involved in the estimation procedures and provide a simulation study to support our theoretical results

Connecting dispersion models and wall temperature prediction for laminar and turbulent flows in channels

In a former paper, Drouin et al. (2010) proposed a model for dispersion phenomena in heated channels that works for both laminar and turbulent regimes. This model, derived according to the double averaging procedure, leads to satisfactory predictions of mean temperature. In order to derive dispersion coefficients, the so called ‘‘closure problem’’ was solved, which gave us access to the temperature deviation at sub filter scale. We now propose to capitalize on this useful information in order to connect dispersion modeling to wall temperature prediction. As a first step, we use the temperature deviation modeling in order to connect wall to mean temperatures within the asymptotic limit of well established pipe flows. Since temperature in wall vicinity is mostly controlled by boundary conditions, it might evolve according to different time and length scales than averaged temperature. Hence, this asymptotic limit provides poor prediction of wall temperature when flow conditions encounter fast transients and stiff heat flux gradients. To overcome this limitation we derive a transport equation for temperature deviation. The resulting two-temperature model is then compared with fine scale simulations used as reference results. Wall temperature predictions are found to be in good agreement for various Prandtl and Reynolds numbers, from laminar to fully turbulent regimes and improvement with respect to classical models is noticeable

Spatio-Temporal Patterns for a Generalized Innovation Diffusion Model

We construct a model of innovation diffusion that incorporates a spatial component into a classical imitation-innovation dynamics first introduced by F. Bass. Relevant for situations where the imitation process explicitly depends on the spatial proximity between agents, the resulting nonlinear field dynamics is exactly solvable. As expected for nonlinear collective dynamics, the imitation mechanism generates spatio-temporal patterns, possessing here the remarkable feature that they can be explicitly and analytically discussed. The simplicity of the model, its intimate connection with the original Bass' modeling framework and the exact transient solutions offer a rather unique theoretical stylized framework to describe how innovation jointly develops in space and time.Comment: 20 pages, 4 figure

Counting coloured planar maps: differential equations

We address the enumeration of q-coloured planar maps counted bythe number of edges and the number of monochromatic edges. We prove that the associated generating function is differentially algebraic,that is, satisfies a non-trivial polynomial differential equation withrespect to the edge variable. We give explicitly a differential systemthat characterizes this series. We then prove a similar result for planar triangulations, thus generalizing a result of Tutte dealing with their proper q-colourings. Instatistical physics terms, we solvethe q-state Potts model on random planar lattices. This work follows a first paper by the same authors, where the generating functionwas proved to be algebraic for certain values of q,including q=1, 2 and 3. It isknown to be transcendental in general. In contrast, our differential system holds for an indeterminate q.For certain special cases of combinatorial interest (four colours; properq-colourings; maps equipped with a spanning forest), we derive from this system, in the case of triangulations, an explicit differential equation of order 2 defining the generating function. For general planar maps, we also obtain a differential equation of order 3 for the four-colour case and for the self-dual Potts model.Comment: 43 p

A Theory of Child Targeting

There is a large empirical literature on policy measures targeted at children but surprisingly very little theoretical foundation to ground the debate on the optimality of the different instruments. In the present paper, we examine the merit of targeting children through two general policies, namely selective commodity taxation and cash transfer to family with children. We consider a household that comprises an adult and a child. The household behavior is described by the maximization of the adult’s utility function, which depends on the child’s welfare, subject to a budget constraint. The relative effects of a price subsidy and of a cash benefit on child welfare are then derived. In particular, it is shown that ‘favorable’ distortions from the price subsidies may allow to redistribute toward the child. The framework is extended to account for possible paternalistic preferences of the State. Finally, it is shown that, in contrast to the traditional view, well-chosen subsidies can be more cost effective than cash transfers in alleviating child poverty.commodity taxation, child benefit, targeting, intrahousehold distribution, social welfare, paternalism, labeling

On the Way to Recovery: A Nonparametric Bias Free Estimation of Recovery Rate Densities

In this paper we analyse recovery rates on defaulted bonds using the Standard and Poor’s/PMD database for the years 1981-1999. Due to the specific nature of the data (observations lie within 0 and 1), we must rely on nonstandard econometric techniques. The recovery rate density is estimated nonparametrically using a beta kernel method. This method is free of boundary bias, and Monte Carlo comparison with competing nonparametric estimators show that the beta kernel density estimator is particularly well suited for density estimation on the unit interval. We challenge the usual market practice to model parametrically recovery rates using a beta distribution calibrated on the empirical mean and variance. This assumption is unable to replicate multimodal distributions or concentration of data at total recovery and total loss. We evaluate the impact of choosing the beta distribution on the estimation of credit Value-at-Risk.default, recovery, kernel estimation, credit risk