Reachability in Higher-Order-Counters

Higher-order counter automata (\HOCS) can be either seen as a restriction of higher-order pushdown automata (\HOPS) to a unary stack alphabet, or as an extension of counter automata to higher levels. We distinguish two principal kinds of \HOCS: those that can test whether the topmost counter value is zero and those which cannot. We show that control-state reachability for level $k$ \HOCS with $0$-test is complete for \mbox{$(k-2)$}-fold exponential space; leaving out the $0$-test leads to completeness for \mbox{$(k-2)$}-fold exponential time. Restricting \HOCS (without $0$-test) to level $2$, we prove that global (forward or backward) reachability analysis is \PTIME-complete. This enhances the known result for pushdown systems which are subsumed by level $2$ \HOCS without $0$-test. We transfer our results to the formal language setting. Assuming that \PTIME \subsetneq \PSPACE \subsetneq \mathbf{EXPTIME}, we apply proof ideas of Engelfriet and conclude that the hierarchies of languages of \HOPS and of \HOCS form strictly interleaving hierarchies. Interestingly, Engelfriet's constructions also allow to conclude immediately that the hierarchy of collapsible pushdown languages is strict level-by-level due to the existing complexity results for reachability on collapsible pushdown graphs. This answers an open question independently asked by Parys and by Kobayashi.Comment: Version with Full Proofs of a paper that appears at MFCS 201

Completed cohomology of Shimura curves and a p-adic Jacquet-Langlands correspondence

We study indefinite quaternion algebras over totally real fields F, and give an example of a cohomological construction of p-adic Jacquet-Langlands functoriality using completed cohomology. We also study the (tame) levels of p-adic automorphic forms on these quaternion algebras and give an analogue of Mazur's `level lowering' principle.Comment: Updated version. Contains some minor corrections compared to the published versio

Genetic Susceptibility Determines β-Cell Function and Fasting Glycemia Trajectories Throughout Childhood: A 12-Year Cohort Study (EarlyBird 76)

No embargo require

On elliptic factors in real endoscopic transfer I

This paper is concerned with the structure of packets of representations and some refinements that are helpful in endoscopic transfer for real groups. It includes results on the structure and transfer of packets of limits of discrete series representations. It also reinterprets the Adams-Johnson transfer of certain nontempered representations via spectral analogues of the Langlands-Shelstad factors, thereby providing structure and transfer compatible with the associated transfer of orbital integrals. The results come from two simple tools introduced here. The first concerns a family of splittings of the algebraic group G under consideration; such a splitting is based on a fundamental maximal torus of G rather than a maximally split maximal torus. The second concerns a family of Levi groups attached to the dual data of a Langlands or an Arthur parameter for the group G. The introduced splittings provide explicit realizations of these Levi groups. The tools also apply to maps on stable conjugacy classes associated with the transfer of orbital integrals. In particular, they allow for a simpler version of the definitions of Kottwitz-Shelstad for twisted endoscopic transfer in certain critical cases. The paper prepares for spectral factors in twisted endoscopic transfer that are compatible in a certain sense with the standard factors discussed here. This compatibility is needed for Arthur's global theory. The twisted factors themselves will be defined in a separate paper.Comment: 48 pages, to appear in Progress in Mathematics, Volume 312, Birkha\"user. Also renumbering to match that of submitted versio

Elliptic Curves over Real Quadratic Fields are Modular

We prove that all elliptic curves defined over real quadratic fields are modular.Comment: 38 pages. Magma scripts available as ancillary files with this arXiv versio

The supercuspidal representations of p-adic classical groups

Let G be a unitary, symplectic or special orthogonal group over a locally compact non-archimedean local field of odd residual characteristic. We construct many new supercuspidal representations of G, and Bushnell-Kutzko types for these representations. Moreover, we prove that every irreducible supercuspidal representation of G arises from our constructions.Comment: 55 pages -- minor changes from 1st version (mostly in sections 2.2, 4.2 and 6.2). To appear in Inventiones mathematicae, 2008 (DOI is not yet active as at 12 Nov 2007

On a Conjecture of Rapoport and Zink

In their book Rapoport and Zink constructed rigid analytic period spaces $F^{wa}$ for Fontaine's filtered isocrystals, and period morphisms from PEL moduli spaces of $p$-divisible groups to some of these period spaces. They conjectured the existence of an \'etale bijective morphism $F^a \to F^{wa}$ of rigid analytic spaces and of a universal local system of $Q_p$-vector spaces on $F^a$. For Hodge-Tate weights $n-1$ and $n$ we construct in this article an intrinsic Berkovich open subspace $F^0$ of $F^{wa}$ and the universal local system on $F^0$. We conjecture that the rigid-analytic space associated with $F^0$ is the maximal possible $F^a$, and that $F^0$ is connected. We give evidence for these conjectures and we show that for those period spaces possessing PEL period morphisms, $F^0$ equals the image of the period morphism. Then our local system is the rational Tate module of the universal $p$-divisible group and enjoys additional functoriality properties. We show that only in exceptional cases $F^0$ equals all of $F^{wa}$ and when the Shimura group is $GL_n$ we determine all these cases.Comment: v2: 48 pages; many new results added, v3: final version that will appear in Inventiones Mathematica

Genomic history of the Italian population recapitulates key evolutionary dynamics of both Continental and Southern Europeans

Background: The cline of human genetic diversity observable across Europe is recapitulated at a micro-geographic scale by variation within the Italian population. Besides resulting from extensive gene flow, this might be ascribable also to local adaptations to diverse ecological contexts evolved by people who anciently spread along the Italian Peninsula. Dissecting the evolutionary history of the ancestors of present-day Italians may thus improve the understanding of demographic and biological processes that contributed to shape the gene pool of European populations. However, previous SNP array-based studies failed to investigate the full spectrum of Italian variation, generally neglecting low-frequency genetic variants and examining a limited set of small effect size alleles, which may represent important determinants of population structure and complex adaptive traits. To overcome these issues, we analyzed 38 high-coverage whole-genome sequences representative of population clusters at the opposite ends of the cline of Italian variation, along with a large panel of modern and ancient Euro-Mediterranean genomes. Results: We provided evidence for the early divergence of Italian groups dating back to the Late Glacial and for Neolithic and distinct Bronze Age migrations having further differentiated their gene pools. We inferred adaptive evolution at insulin-related loci in people from Italian regions with a temperate climate, while possible adaptations to pathogens and ultraviolet radiation were observed in Mediterranean Italians. Some of these adaptive events may also have secondarily modulated population disease or longevity predisposition. Conclusions: We disentangled the contribution of multiple migratory and adaptive events in shaping the heterogeneous Italian genomic background, which exemplify population dynamics and gene-environment interactions that played significant roles also in the formation of the Continental and Southern European genomic landscapes

Academic patenting: the importance of industry support

This paper provides evidence that university-industry collaboration is important for turning commercial opportunities into patents. The results suggest that researchers who receive a large share of research grants from industry have a higher propensity to file a patent. Small dissemination grants generally exert a positive effect, whether they come from industry or not. It also finds that these interactions do not increase the number of industry owned patents alone but benefit universities’ commercialisation efforts in general

The dynamics of university units as a multi-level process. Credibility cycles and resource dependencies

This paper presents an analysis of resource acquisition and profile development of institutional units within universities. We conceptualize resource acquisition as a two level nested process, where units compete for external resources based on their credibility, but at the same time are granted faculty positions from the larger units (department) to which they belong. Our model implies that the growth of university units is constrained by the decisions of their parent department on the allocation of professorial positions, which represent the critical resource for most units’ activities. In our field of study this allocation is largely based on educational activities, and therefore, units with high scientific credibility are not necessarily able to grow, despite an increasing reliance on external funds. Our paper therefore sheds light on the implications that the dual funding system of European universities has for the development of units, while taking into account the interaction between institutional funding and third-party funding