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

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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

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

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

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

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