Birational boundedness for holomorphic symplectic varieties, Zarhin's trick for K3K3 surfaces, and the Tate conjecture

We investigate boundedness results for families of holomorphic symplectic varieties up to birational equivalence. We prove the analogue of Zarhin's trick by for $K3$ surfaces by constructing big line bundles of low degree on certain moduli spaces of stable sheaves, and proving birational versions of Matsusaka's big theorem for holomorphic symplectic varieties. As a consequence of these results, we give a new geometric proof of the Tate conjecture for $K3$ surfaces over finite fields of characteristic at least $5$, and a simple proof of the Tate conjecture for $K3$ surfaces with Picard number at least $2$ over arbitrary finite fields -- including characteristic $2$.Comment: 27 pages. Zarhin's trick for K3 surfaces is now stated for arbitrary fields, and the proof of Theorem 3.3 has been fixed. Minor typos fixe

Raviart-Thomas finite elements of Petrov-Galerkin type

The mixed finite element method for the Poisson problem with the Raviart-Thomas elements of low-level can be interpreted as a finite volume method with a non-local gradient. In this contribution, we propose a variant of Petrov-Galerkin type for this problem to ensure a local computation of the gradient at the interfaces of the elements. The shape functions are the Raviart-Thomas finite elements. Our goal is to define test functions that are in duality with these shape functions: Precisely, the shape and test functions will be asked to satisfy a L2-orthogonality property. The general theory of Babu\v{s}ka brings necessary and sufficient stability conditions for a Petrov-Galerkin mixed problem to be convergent. We propose specific constraints for the dual test functions in order to ensure stability. With this choice, we prove that the mixed Petrov-Galerkin scheme is identical to the four point finite volumes scheme of Herbin, and to the mass lumping approach developed by Baranger, Maitre and Oudin. Finally, we construct a family of dual test functions that satisfy the stability conditions. Convergence is proven with the usual techniques of mixed finite elements

A Study of Deep Learning Robustness Against Computation Failures

For many types of integrated circuits, accepting larger failure rates in computations can be used to improve energy efficiency. We study the performance of faulty implementations of certain deep neural networks based on pessimistic and optimistic models of the effect of hardware faults. After identifying the impact of hyperparameters such as the number of layers on robustness, we study the ability of the network to compensate for computational failures through an increase of the network size. We show that some networks can achieve equivalent performance under faulty implementations, and quantify the required increase in computational complexity

Longitudinal evidence on financial expectations in Albania: Do remittances matter?

This paper focuses on the role of remittances on financial expectations in Albania using longitudinal data covering the period 2002-2004. To study the dynamics of income satisfaction at the household level, we use subjective data on past, current and future financial situations and estimate random and fixed effect ordered Probit models. We find that households are more optimistic about the future when they have experienced an improvement in their financial situation in the past and when they have received private transfers from foreign countries.Albania; Income expectations: Longitudinal data; Remittances

Outsourcing ship management: Implications for the logistics chain

The purpose of this paper is to contribute to a better understanding of the probability that shipping companies outsource the management of vessels to ship management companies, a decision with many implications for the logistics chain. Data on 39,925 vessels are used to investigate to the extent to which 4,049 different ship-owners (each operating a fleet of at least two vessels) outsource to ship-management service providers. We rely on multinomial Logit random and fixed effects regressions to explain how the characteristics of the owners and vessels influence this decision. We find that the size of the firm in terms of the number of vessels and the number of different types of vessels influence the likelihood of outsourcing. Also, ship-owners frequently implement a mixed strategy and outsource only some of their vessels.

Remittances matter: Longitudinal evidence from Albania

Using the LSMS panel data collected by the World Bank in Albania from 2002 to 2004, this paper focuses on the determinants and financial implication of remittances sent by family members and adult children living abroad. Our econometric analysis draws on random and fixed effects discrete choice models. We find that the proportion of households receiving remittances is large. These transfers are negatively correlated with both the donor's and the recipient's level of education. Finally, remittances have a positive impact on economic indicators like satisfaction with current situation, adequateness of food consumption and number of affordable expenditures