Twisted limit formula for torsion and cyclic base change

Let $G$ be the group of complex points of a real semi-simple Lie group whose fundamental rank is equal to 1, e.g. G= \SL_2 (\C) \times \SL_2 (\C) or \SL_3 (\C). Then the fundamental rank of $G$ is $2,$ and according to the conjecture made in \cite{BV}, lattices in $G$ should have 'little' --- in the very weak sense of 'subexponential in the co-volume' --- torsion homology. Using base change, we exhibit sequences of lattices where the torsion homology grows exponentially with the \emph{square root} of the volume. This is deduced from a general theorem that compares twisted and untwisted $L^2$-torsions in the general base-change situation. This also makes uses of a precise equivariant 'Cheeger-M\"uller Theorem' proved by the second author \cite{Lip1}.Comment: 23 page

Sums of two s{s}-units via frey-hellegouarch curves

In this paper, we develop a new method for finding all perfect powers which can be expressed as the sum of two rational S-units, where S is a finite set of primes. Our approach is based upon the modularity of Galois representations and, for the most part, does not require lower bounds for linear forms in logarithms. Its main virtue is that it enables to carry out such a program explicitly, at least for certain small sets of primes S; we do so for S = {2, 3} and S = {3, 5, 7}.Comment: Missing solution in Prop. 5.4 added. To appear in Mathematics of Computatio

The impact of the global financial turmoil and recession on Mediterranean countries’ economies

This paper reviews the impact of the global financial turmoil and the subsequent recession on the economies of southern and eastern Mediterranean countries. The major effects on the economies of this region have come through transmission channels associated with the real economy, i.e. the global recession. These are, in particular, declines in exports, oil revenues, tourism receipts, remittances and foreign direct investment (FDI) inflows, with the drop in exports so far appearing to have had the strongest impact. As a result, real GDP growth has weakened in the wake of the global crisis. However, the weakening of economic activity in the Mediterranean region has been less pronounced than in advanced economies and most other emerging market regions. The main reason for this is that the direct impact of the global financial turmoil on banking sectors and financial markets in Mediterranean countries has been relatively limited. This is mainly due to (i) their lack of exposure to US mortgage-related assets that turned “toxic”, a feature the region shares with other emerging markets, and (ii) the limited financial development of many countries in the region and their limited integration into global financial markets, a feature that distinguishes the region from other emerging markets and, in particular, from the euro area’s neighbours to the east. Notwithstanding the relative resilience of southern and eastern Mediterranean countries in the wake of the global crisis, the region faces significant challenges. In particular, many countries need significantly higher growth rates to address the employment challenge posed as a consequence of demographic developments. JEL Classification: C43, C51, D91financial sector, Global economic crisis, International spillovers, Mediterranean countries

Corporate Lobbying and Commitment Failure in Capital Taxation

This paper investigates the effects of lobbying by corporations when investments are irreversible and government cannot commit to tax policies. We show that industries which rely more heavily on sunk capital lobby more vigorously and are generally more successful in obtaining tax breaks. Thus lobbying can mitigate the capital levy problem. Nevertheless, these industries invest less in long-run equilibrium than more flexible ones. We then consider the effects of relaxing legal restrictions on corporate lobbying. When the deadweight costs of lobbying fall, taxes on sunk capital tend to fall, but political contributions may rise, as lobbyists compete more intensively for political favors. On balance, a ban of lobbying may therefore cause investment to rise or fall.

Business Tax Lobbying

This paper investigates the effects of business tax lobbying in the presence of investments that are sunk or costly to adjust in the short run. We show that industries which rely more heavily on sunk capital are generally more successful in obtaining tax breaks through lobbying; this reverses the usual logic of the capital levy problem. Nevertheless, these industries invest less in long-run equilibrium than more flexible ones. We then consider the effects of relaxing legal restrictions on corporate lobbying. When politicians give more weight to lobbyists' preferences, taxes fall on average and investment rises. But investment is misallocated among industries, so that welfare may fall. Thus restrictions on business lobbyists may be desirable. Dans ce texte, nous étudions le lobbying des sociétés visant à réduire leurs impôts lorsque le capital qu'elles utilisent est irrécupérable ou coûteux à ajuster à court terme. Il est démontré que grâce au lobbying, les industries utilisant un capital relativement coûteux à ajuster obtiennent les baisses d'impôt les plus substantielles. Néanmoins, ces industries investissent moins à long terme que celles utilisant un capital plus flexible. Nous étudions également l'effet d'une libéralisation des règles encadrant le lobbying des sociétés. Lorsque les politiciens attachent plus d'importance aux préférences des lobbies, le niveau moyen de taxation diminue et l'investissement augmente. Le bien-être peut cependant diminuer à cause de la mauvaise répartition de l'investissement entre les industries. Un certain encadrement du lobbying des sociétés peut donc être désirable.Lobbying, Business taxation, Investment

Maxmin convolutional neural networks for image classification

Convolutional neural networks (CNN) are widely used in computer vision, especially in image classification. However, the way in which information and invariance properties are encoded through in deep CNN architectures is still an open question. In this paper, we propose to modify the standard convo- lutional block of CNN in order to transfer more information layer after layer while keeping some invariance within the net- work. Our main idea is to exploit both positive and negative high scores obtained in the convolution maps. This behav- ior is obtained by modifying the traditional activation func- tion step before pooling. We are doubling the maps with spe- cific activations functions, called MaxMin strategy, in order to achieve our pipeline. Extensive experiments on two classical datasets, MNIST and CIFAR-10, show that our deep MaxMin convolutional net outperforms standard CNN