Heights of pre-special points of Shimura varieties

Let s be a special point on a Shimura variety, and x a pre-image of s in a fixed fundamental set of the associated Hermitian symmetric domain. We prove that the height of x is polynomially bounded with respect to the discriminant of the centre of the endomorphism ring of the corresponding ZZ -Hodge structure. Our bound is the final step needed to complete a proof of the André–Oort conjecture under the conjectural lower bounds for the sizes of Galois orbits of special points, using a strategy of Pila and Zannier

Bridge over Olduvai Gorge: Capacity building and conservation of lithics and fossils

This paper explores decision-making processes involved in the conservation of lithics and fossils excavated at Olduvai Gorge, Tanzania. The site is renowned for discoveries of early humans from the Palaeolithic period, lithics and fossils that document the evolutionary history of humans, vertebrate fauna and their environment over the last two million years. Excavated specimens are treated in situ, at the field laboratory and at the UCL Institute of Archaeology in London. Factors such as accessibility, ease of transportation and preparation, disposal, Tg and toxicity of resins, and ease of re-treatability are considered to decide what can be used in treatments and how. Frequently used materials include Paraloid B-44 and cyclododecane for temporary consolidation and Paraloid B-44 for adhesion and gap-filling. We have found that, in such complex contexts, the more one engages with colleagues across the disciplines and local community groups, the smoother, stronger and more sustainable one’s efforts become

A generalization of the Bombieri-Pila determinant method

The so-called determinant method was developed by Bombieri and Pila in 1989 for counting integral points of bounded height on affine plane curves. In this paper we give a generalization of that method to varieties of higher dimension, yielding a proof of Heath-Brown's 'Theorem 14' by real-analytic considerations alone.Comment: 13 page

Remoción de plaguicidas MCPA e Imazapic de solución acuosa con materiales carbonosos

El objetivo general de este trabajo se orienta a la búsqueda de alternativas simples y accesibles para la remediación de aguas contaminadas, teniendo en cuenta que la presencia de contaminantes emergentes en nuestros recursos hídricos, tales como fármacos y pesticidas, es motivo de preocupación para la salud y seguridad ambiental. Se realizaron estudios de adsorción de dos pesticidas: MCPA (ácido 4-cloro-2-metil fenoxiacético) e Imazapic (ácido 2-[4,5-dihidro-4-metil-4-(1-metiletil)-5-oxo-1H-imidazol-2-il]-5-metil-3-piridin carboxílico), en dos diferentes tipos de material carbonoso. Fueron utilizados dos tipos de carbón activado, cada uno con diferentes características físicas y químicas, CAT-Ox 4 sulfuro de hidrógeno, adquirido en pellets de 4mm y CARBOPAL MB 4S (Donau). Se realizaron diferentes experimentos en batch de los herbicidas MCPA e Imazapic sobre dos tipos de carbón activado, CAT y CARBOPAL, bajo diferentes condiciones. Ambos materiales parecen ser muy efectivos removiendo estos contaminantes, pero CAT parece tener una mayor capacidad. Ambos pesticidas siguen cinéticas de adsorción de pseudo segundo orden en ambos materiales, lo que indicaría una mayor contribución de quimisorción con formación de monocapa. La capacidad de adsorción (qe) de herbicidas es significativamente influenciada por el valor de pH. En el presente estudio, ambos pesticidas tienen una disminución en la capacidad de adsorción cuando se utilizan condiciones básicas debido a que la superficie de los carbones están cargadas negativamente y en estas condiciones los herbicidas se encuentran en forma aniónica. Además, diferentes modelos fueron analizados para predecir propiedades de cada proceso de adsorción. MCPA se adapta al modelo teórico de Langmuir en ambos materiales. Debido a esto, se predice un proceso de quimisorción con la formación de una monocapa. Por otro lado, Imazapic se adapta al modelo GAB sobre CAT y CARBOPAL, con la formación de multicapas. La capacidad de adsorción es muy alta, por lo que ambos materiales pueden ser usados como método efectivo y de bajo costo para remover MCPA e Imazapic de recursos acuosos.Trabajo presentado por el Centro de Estudio de Compuestos Orgánicos (CEDECOR

Section Extension from Hyperbolic Geometry of Punctured Disk and Holomorphic Family of Flat Bundles

The construction of sections of bundles with prescribed jet values plays a fundamental role in problems of algebraic and complex geometry. When the jet values are prescribed on a positive dimensional subvariety, it is handled by theorems of Ohsawa-Takegoshi type which give extension of line bundle valued square-integrable top-degree holomorphic forms from the fiber at the origin of a family of complex manifolds over the open unit 1-disk when the curvature of the metric of line bundle is semipositive. We prove here an extension result when the curvature of the line bundle is only semipositive on each fiber with negativity on the total space assumed bounded from below and the connection of the metric locally bounded, if a square-integrable extension is known to be possible over a double point at the origin. It is a Hensel-lemma-type result analogous to Artin's application of the generalized implicit function theorem to the theory of obstruction in deformation theory. The motivation is the need in the abundance conjecture to construct pluricanonical sections from flatly twisted pluricanonical sections. We also give here a new approach to the original theorem of Ohsawa-Takegoshi by using the hyperbolic geometry of the punctured open unit 1-disk to reduce the original theorem of Ohsawa-Takegoshi to a simple application of the standard method of constructing holomorphic functions by solving the d-bar equation with cut-off functions and additional blowup weight functions

Counting points on hyperelliptic curves over finite fields

International audienceWe describe some algorithms for computing the cardinality of hyperelliptic curves and their Jacobians over finite fields. They include several methods for obtaining the result modulo small primes and prime powers, in particular an algorithm à la Schoof for genus 2 using Cantor's division polynomials. These are combined with a birthday paradox algorithm to calculate the cardinality. Our methods are practical and we give actual results computed using our current implementation. The Jacobian groups we handle are larger than those previously reported in the literature

A quantitative risk assessment of waterborne infectious disease in the inundation area of a tropical monsoon region

Flooding and inundation are annual events that occur during the rainy season in Cambodia, and inundation has a strong relationship with human health. This study simulated the coliform bacteria distribution using a hydraulic model and estimated the impact of inundation on public health using a dose–response model. The model parameters were calibrated using field survey data from Cambodia and obtained good agreement with the coliform group count distribution. The results suggest that the impact of inundation on human health is most noticeable in residential areas. The annual average risk of infection during medium-sized flood events is 0.21. The risk due to groundwater use ranges from 0.12 to 0.17 in inundation areas and reaches as high as 0.23 outside the inundation areas. The risk attributed to groundwater use is therefore higher than that for surface water use (0.02–0.06), except in densely populated areas at the city center. There is a high risk for infection with waterborne disease in residential areas, and the annual average risk during small flood events is 0.94. An assessment of possible countermeasures to reduce the risk shows that the control of inundation may bring more risk to public health in Cambodia. Shallower inundation water (<0.3 m) leads to a higher risk of infection, but if the depth is greater than 2 m, the risk is low in residential areas.The simulated results explain the spatial distributions of infection risk, which are vitally important for determining the highest priority places with relatively high risk and will be helpful for decision makers when considering the implementation of countermeasures

Quantum numbers of the X(3872)X(3872) state and orbital angular momentum in its ρ0Jψ\rho^0 J\psi decay

Angular correlations in $B^+\to X(3872) K^+$ decays, with $X(3872)\to \rho^0 J/\psi$, $\rho^0\to\pi^+\pi^-$ and $J/\psi \to\mu^+\mu^-$, are used to measure orbital angular momentum contributions and to determine the $J^{PC}$ value of the $X(3872)$ meson. The data correspond to an integrated luminosity of 3.0 fb$^{-1}$ of proton-proton collisions collected with the LHCb detector. This determination, for the first time performed without assuming a value for the orbital angular momentum, confirms the quantum numbers to be $J^{PC}=1^{++}$. The $X(3872)$ is found to decay predominantly through S wave and an upper limit of $4\%$ at $95\%$ C.L. is set on the fraction of D wave.Comment: 16 pages, 4 figure

Riding on the Coat-Tails of Traditional Cultural Expressions

Matters related to the protection of traditional cultural expressions (‘TCEs’) or expressions of folklore (‘EoFs’) are sensitive and intricate as a blend of legal, economic, philosophical and anthropological considerations jostle to capture their core features. This results in disparate views surrounding what should qualify as TCEs or EoFs, who should be considered their ‘owner’ (assuming that ownership per se is conceptually compatible with these items), which is the most appropriate legal protection regime and how broad their scope of protection should be. Drawing from these various accounts on TCEs, this article focuses on the interaction between TCEs and EoFs originating on the European continent and the European Union (‘EU’) trade mark legislation. Specifically, this article examines whether the limitations of the effects of trade mark rights and of the absolute grounds of refusal, as developed by the case law of the Court of Justice of the European Union, are effective in preserving the cohesion of TCEs. This article advances the thesis that registration of TCEs and EoFs as trade marks generates an imbalance between the rights of the trade mark owner and the defences available to others under the EU trade mark law framework. Furthermore, such an imbalance is likely to hinder the unfettered circulation of TCEs and undermine their original meaning. Lastly, in some cases, trade mark registration of TCEs contributes to their appropriation and misappropriation. The article concludes that, de lege ferenda, the direct exclusion of TCEs as eligible subject matter for trade mark registration is preferable to seeking a post factum remedy