376 research outputs found
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 \HOCS with -test is
complete for \mbox{}-fold exponential space; leaving out the -test
leads to completeness for \mbox{}-fold exponential time. Restricting
\HOCS (without -test) to level , 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 \HOCS without
-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
Linearly bounded infinite graphs
Linearly bounded Turing machines have been mainly studied as acceptors for
context-sensitive languages. We define a natural class of infinite automata
representing their observable computational behavior, called linearly bounded
graphs. These automata naturally accept the same languages as the linearly
bounded machines defining them. We present some of their structural properties
as well as alternative characterizations in terms of rewriting systems and
context-sensitive transductions. Finally, we compare these graphs to rational
graphs, which are another class of automata accepting the context-sensitive
languages, and prove that in the bounded-degree case, rational graphs are a
strict sub-class of linearly bounded graphs
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
Genetic Susceptibility Determines β-Cell Function and Fasting Glycemia Trajectories Throughout Childhood: A 12-Year Cohort Study (EarlyBird 76)
No embargo require
Symbolic Backwards-Reachability Analysis for Higher-Order Pushdown Systems
Higher-order pushdown systems (PDSs) generalise pushdown systems through the
use of higher-order stacks, that is, a nested "stack of stacks" structure.
These systems may be used to model higher-order programs and are closely
related to the Caucal hierarchy of infinite graphs and safe higher-order
recursion schemes.
We consider the backwards-reachability problem over higher-order Alternating
PDSs (APDSs), a generalisation of higher-order PDSs. This builds on and extends
previous work on pushdown systems and context-free higher-order processes in a
non-trivial manner. In particular, we show that the set of configurations from
which a regular set of higher-order APDS configurations is reachable is regular
and computable in n-EXPTIME. In fact, the problem is n-EXPTIME-complete.
We show that this work has several applications in the verification of
higher-order PDSs, such as linear-time model-checking, alternation-free
mu-calculus model-checking and the computation of winning regions of
reachability games
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
Metabolic profiles of male meat eaters, fish eaters, vegetarians, and vegans from the EPIC-Oxford cohort
Background: Human metabolism is influenced by dietary factors and lifestyle, environmental, and genetic factors; thus, men who exclude some or all animal products from their diet might have different metabolic profiles than meat eaters. Objective: We aimed to investigate differences in concentrations of 118 circulating metabolites, including acylcarnitines, amino acids, biogenic amines, glycerophospholipids, hexose, and sphingolipids related to lipid, protein, and carbohydrate metabolism between male meat eaters, fish eaters, vegetarians, and vegans from the Oxford arm of the European Prospective Investigation into Cancer and Nutrition. Design: In this cross-sectional study, concentrations of metabolites were measured by mass spectrometry in plasma from 379 men categorized according to their diet group. Differences in mean metabolite concentrations across diet groups were tested by using ANOVA, and a false discovery rate–controlling procedure was used to account for multiple testing. Principal component analysis was used to investigate patterns in metabolic profiles. Results: Concentrations of 79% of metabolites differed significantly by diet group. In the vast majority of these cases, vegans had the lowest concentration, whereas meat eaters most often had the highest concentrations of the acylcarnitines, glycerophospholipids, and sphingolipids, and fish eaters or vegetarians most often had the highest concentrations of the amino acids and a biogenic amine. A clear separation between patterns in the metabolic profiles of the 4 diet groups was seen, with vegans being noticeably different from the other groups because of lower concentrations of some glycerophospholipids and sphingolipids. Conclusions: Metabolic profiles in plasma could effectively differentiate between men from different habitual diet groups, especially vegan men compared with men who consume animal products. The difference in metabolic profiles was mainly explained by the lower concentrations of glycerophospholipids and sphingolipids in vegans
Delay Games with WMSO+U Winning Conditions
Delay games are two-player games of infinite duration in which one player may
delay her moves to obtain a lookahead on her opponent's moves. We consider
delay games with winning conditions expressed in weak monadic second order
logic with the unbounding quantifier, which is able to express (un)boundedness
properties. We show that it is decidable whether the delaying player has a
winning strategy using bounded lookahead and give a doubly-exponential upper
bound on the necessary lookahead. In contrast, we show that bounded lookahead
is not always sufficient to win such a game.Comment: A short version appears in the proceedings of CSR 2015. The
definition of the equivalence relation introduced in Section 3 is updated:
the previous one was inadequate, which invalidates the proof of Lemma 2. The
correction presented here suffices to prove Lemma 2 and does not affect our
main theorem. arXiv admin note: text overlap with arXiv:1412.370
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