CM cycles on Kuga–Sato varieties over Shimura curves and Selmer groups

Given a modular form f of even weight larger than two and an imaginary quadratic field K satisfying a relaxed Heegner hypothesis, we construct a collection of CM cycles on a Kuga–Sato variety over a suitable Shimura curve which gives rise to a system of Galois cohomology classes attached to f enjoying the compatibility properties of an Euler system. Then we use Kolyvagin’s method [21], as adapted by Nekova´¿r [28] to higher weight modular forms, to bound the size of the relevant Selmer group associated to f and K and prove the finiteness of the (primary part) of the Shafarevich–Tate group, provided that a suitable cohomology class does not vanish.Peer ReviewedPostprint (author's final draft

New bounds for truthful scheduling on two unrelated selfish machines

We consider the minimum makespan problem for $n$ tasks and two unrelated parallel selfish machines. Let $R_n$ be the best approximation ratio of randomized monotone scale-free algorithms. This class contains the most efficient algorithms known for truthful scheduling on two machines. We propose a new $Min-Max$ formulation for $R_n$, as well as upper and lower bounds on $R_n$ based on this formulation. For the lower bound, we exploit pointwise approximations of cumulative distribution functions (CDFs). For the upper bound, we construct randomized algorithms using distributions with piecewise rational CDFs. Our method improves upon the existing bounds on $R_n$ for small $n$. In particular, we obtain almost tight bounds for $n=2$ showing that $|R_2-1.505996|<10^{-6}$.Comment: 28 pages, 3 tables, 1 figure. Theory Comput Syst (2019

Baseline report on the evaluation of Familias en Acción

This report describes the survey that was carried out in 122 communities in rural Colombia by the consortium formed by the Institute for Fiscal Studies, Econometria and SEI as the baseline for the impact evaluation of Familias en Acción, a programme to foster the accumulation of human capital in rural Colombia, run by the Colombian government. In this report, we will not describe in detail the programme or the methodology of the proposed evaluation, as this was done in IFS-Econometria-SEI (2003a). The main aim of the document is to discuss the first, baseline survey that was collected for this evaluation. While the baseline survey cannot, by definition, be used to perform impact evaluation, towards the end of the report we exploit the slightly peculiar way in which the programme was started and have a first very preliminary glance at some of the impacts that the programme might have. The methodological caveats on interpreting these results should be taken very seriously. This report does not contain an extensive ‘fieldwork’ report. This is included in SEI (2003). Analogously, we do not discuss extensively the operation of the programme and the evidence that emerged on related issues and on targeting. These issues are covered in IFS-Econometria- SEI (2003b, 2003c). We will be referring to some of the issues raised in those reports, however. This report is divided into five chapters. In Chapter 1, we briefly summarise the main features of the programme and its proposed evaluation. A more detailed description of both of these aspects is contained in IFS-Econometria-SEI (2003a). Here, however, we give some details on the expansion of the programme and on the features of this expansion that allow a first and preliminary analysis of the impact of the programme. In Chapter 2, we describe the statistical methodology that will be used in the report. This includes the methodology for the data description that constitutes the largest part of the report and for the preliminary impact evaluation. Chapter 3 describes the baseline survey. This chapter is divided into several sections, each referring to a particular module. In each section, we first describe the ‘treatment’ population – that is, the households eligible for the programme that were living in villages targeted by the programme. We then move on to the population living in ‘control’ villages – that is, in villages that were not targeted by the programme and yet are, nonetheless, reasonably similar to the treatment villages. Chapter 4 presents the preliminary impact evaluation

Using the BFKL resummation to fit DIS data: collinear and running coupling effects

The proton structure function F2 is studied in the low x regime using BFKL evolution. The next to leading logarithmic (NLL) analysis requires the inclusion of running coupling effects which lead to off-diagonal terms in the evolution kernel. An all-orders resummation is used to improve the collinear behavior of the NLL BFKL result. We emphasize the theoretical uncertainties that appear throughout the analysis and give a comparison to the combined HERA data.Comment: 4 pages, 5 figures, proceedings of the XX Workshop on Deep-Inelastic Scattering and Related Subjects, 26-30 March, University of Bonn (2012

Interior Structures and Tidal Heating in the TRAPPIST-1 Planets

With seven planets, the TRAPPIST-1 system has the largest number of exoplanets discovered in a single system so far. The system is of astrobiological interest, because three of its planets orbit in the habitable zone of the ultracool M dwarf. Assuming the planets are composed of non-compressible iron, rock, and H$_2$O, we determine possible interior structures for each planet. To determine how much tidal heat may be dissipated within each planet, we construct a tidal heat generation model using a single uniform viscosity and rigidity for each planet based on the planet's composition. With the exception of TRAPPIST-1c, all seven of the planets have densities low enough to indicate the presence of significant H$_2$O in some form. Planets b and c experience enough heating from planetary tides to maintain magma oceans in their rock mantles; planet c may have eruptions of silicate magma on its surface, which may be detectable with next-generation instrumentation. Tidal heat fluxes on planets d, e, and f are lower, but are still twenty times higher than Earth's mean heat flow. Planets d and e are the most likely to be habitable. Planet d avoids the runaway greenhouse state if its albedo is $\gtrsim$ 0.3. Determining the planet's masses within $\sim0.1$ to 0.5 Earth masses would confirm or rule out the presence of H$_2$O and/or iron in each planet, and permit detailed models of heat production and transport in each planet. Understanding the geodynamics of ice-rich planets f, g, and h requires more sophisticated modeling that can self-consistently balance heat production and transport in both rock and ice layers.Comment: 34 pages, 3 tables, 4 figures. Accepted for publication in Astronomy & Astrophysics -- final version including corrections made in proof stag