Natural boundary for the susceptibility function of generic piecewise expanding unimodal maps

We consider the susceptibility function Psi(z) of a piecewise expanding unimodal interval map f with unique acim mu, a perturbation X, and an observable phi. Combining previous results (deduced from spectral properties of Ruelle transfer operators) with recent work of Breuer-Simon (based on techniques from the spectral theory of Jacobi matrices and a classical paper of Agmon), we show that density of the postcritical orbit (a generic condition) implies that Psi(z) has a strong natural boundary on the unit circle. The Breuer-Simon method provides uncountably many candidates for the outer functions of Psi(z), associated to precritical orbits. If the perturbation X is horizontal, a generic condition (Birkhoff typicality of the postcritical orbit) implies that the nontangential limit of the Psi(z) as z tends to 1 exists and coincides with the derivative of the acim with respect to the map (linear response formula). Applying the Wiener-Wintner theorem, we study the singularity type of nontangential limits as z tends to e^{i\omega}. An additional LIL typicality assumption on the postcritical orbit gives stronger results.Comment: LaTex, 23 pages, to appear ETD

Porcine Epidemic Diarrhea Virus (PEDV) Co-Infection Induced Chlamydial Persistence/Stress Does Not Require Viral Replication

Chlamydiae may exist at the site of infection in an alternative replicative form, called the aberrant body (AB). ABs are produced during a viable but non-infectious developmental state termed persistence or chlamydial stress. As persistent/stressed chlamydiae: (i) may contribute to chronic inflammation observed in diseases like trachoma; and (ii) are more resistant to current anti-chlamydial drugs of choice, it is critical to better understand this developmental stage. We previously demonstrated that porcine epidemic diarrhea virus (PEDV) co-infection induced Chlamydia pecorum persistence/stress in culture. One critical characteristic of persistence/stress is that the chlamydiae remain viable and can reenter the normal developmental cycle when the stressor is removed. Thus, we hypothesized that PEDV-induced persistence would be reversible if viral replication was inhibited. Therefore, we performed time course experiments in which Vero cells were C. pecorum/PEDV infected in the presence of cycloheximide (CHX), which inhibits viral but not chlamydial protein synthesis. CHX-exposure inhibited PEDV replication, but did not inhibit induction of C. pecorum persistence at 24 h post-PEDV infection, as indicated by AB formation and reduced production of infectious EBs. Interestingly, production of infectious EBs resumed when CHX-exposed, co-infected cells were incubated 48-72 h post-PEDV co-infection. These data demonstrate that PEDV co-infection-induced chlamydial persistence/stress is reversible and suggest that this induction (i) does not require viral replication in host cells; and (ii) does not require de novo host or viral protein synthesis. These data also suggest that viral binding and/or entry may be required for this effect. Because the PEDV host cell receptor (CD13 or aminopeptidase N) stimulates cellular signaling pathways in the absence of PEDV infection, we suspect that PEDV co-infection might alter CD13 function and induce the chlamydiae to enter the persistent state

Addendum to `Fake Projective Planes'

The addendum updates the results presented in the paper `Fake Projective Plane, Invent Math 168, 321-370 (2007)' and makes some additions and corrections. The fake projective planes are classified into twenty six classes. Together with a recent work of Donald Cartwright and Tim Steger, there is now a complete list of fake projective planes. There are precisely one hundred fake projective planes as complex surfaces classified up to biholomorphism.Comment: A more refined classification is given in the new versio

The congruence kernel of an arithmetic lattice in a rank one algebraic group over a local field

Let k be a global field and let k_v be the completion of k with respect to v, a non-archimedean place of k. Let \mathbf{G} be a connected, simply-connected algebraic group over k, which is absolutely almost simple of k_v-rank 1. Let G=\mathbf{G}(k_v). Let \Gamma be an arithmetic lattice in G and let C=C(\Gamma) be its congruence kernel. Lubotzky has shown that C is infinite, confirming an earlier conjecture of Serre. Here we provide complete solution of the congruence subgroup problem for \Gamm$ by determining the structure of C. It is shown that C is a free profinite product, one of whose factors is \hat{F}_{\omega}, the free profinite group on countably many generators. The most surprising conclusion from our results is that the structure of C depends only on the characteristic of k. The structure of C is already known for a number of special cases. Perhaps the most important of these is the (non-uniform) example \Gamma=SL_2(\mathcal{O}(S)), where \mathcal{O}(S) is the ring of S-integers in k, with S=\{v\}, which plays a central role in the theory of Drinfeld modules. The proof makes use of a decomposition theorem of Lubotzky, arising from the action of \Gamma on the Bruhat-Tits tree associated with G.Comment: 27 pages, 5 figures, to appear in J. Reine Angew. Mat

Damage/Danger Associated Molecular Patterns (Damps) Modulate Chlamydia Pecorum and C. Trachomatis Serovar E Inclusion Development in Vitro

Persistence, more recently termed the chlamydial stress response, is a viable but non-infectious state constituting a divergence from the characteristic chlamydial biphasic developmental cycle. Damage/danger associated molecular patterns (DAMPs) are normal intracellular components or metabolites that, when released from cells, signal cellular damage/ lysis. Purine metabolite DAMPs, including extracellular ATP and adenosine, inhibit chlamydial development in a species-specific manner. Viral co-infection has been shown to reversibly abrogate Chlamydia inclusion development, suggesting persistence/chlamydial stress. Because viral infection can cause host cell DAMP release, we hypothesized DAMPs may influence chlamydial development. Therefore, we examined the effect of extracellular ATP, adenosine, and cyclic AMP exposure, at 0 and 14 hours post infection, on C. pecorum and C. trachomatis serovar E development. In the absence of de novo host protein synthesis, exposure to DAMPs immediately post or at 14 hours post infection reduced inclusion size; however, the effect was less robust upon 14 hours post infection exposure. Additionally, upon exposure to DAMPs immediately post infection, bacteria per inclusion and subsequent infectivity were reduced in both Chlamydia species. These effects were reversible, and C. pecorum exhibited more pronounced recovery from DAMP exposure. Aberrant bodies, typical in virus-induced chlamydial persistence, were absent upon DAMP exposure. In the presence of de novo host protein synthesis, exposure to DAMPs immediately post infection reduced inclusion size, but only variably modulated chlamydial infectivity. Because chlamydial infection and other infections may increase local DAMP concentrations, DAMPs may influence Chlamydia infection in vivo, particularly in the context of poly-microbial infections. This is an open access article, free of all copyright, and may be freely reproduced, distributed, transmitted, modified, built upon, or otherwise used by anyone for any lawful purpose. The work is made available under the Creative Commons CC0 public domain dedication

A Note on the Equality of Algebraic and Geometric D-Brane Charges in WZW Models

The algebraic definition of charges for symmetry-preserving D-branes in Wess-Zumino-Witten models is shown to coincide with the geometric definition, for all simple Lie groups. The charge group for such branes is computed from the ambiguities inherent in the geometric definition.Comment: 12 pages, fixed typos, added references and a couple of remark

Conjugacy theorems for loop reductive group schemes and Lie algebras

The conjugacy of split Cartan subalgebras in the finite dimensional simple case (Chevalley) and in the symmetrizable Kac-Moody case (Peterson-Kac) are fundamental results of the theory of Lie algebras. Among the Kac-Moody Lie algebras the affine algebras stand out. This paper deals with the problem of conjugacy for a class of algebras --extended affine Lie algebras-- that are in a precise sense higher nullity analogues of the affine algebras. Unlike the methods used by Peterson-Kac, our approach is entirely cohomological and geometric. It is deeply rooted on the theory of reductive group schemes developed by Demazure and Grothendieck, and on the work of J. Tits on buildingsComment: Publi\'e dans Bulletin of Mathematical Sciences 4 (2014), 281-32

Equivariant pretheories and invariants of torsors

In the present paper we introduce and study the notion of an equivariant pretheory: basic examples include equivariant Chow groups, equivariant K-theory and equivariant algebraic cobordism. To extend this set of examples we define an equivariant (co)homology theory with coefficients in a Rost cycle module and provide a version of Merkurjev's (equivariant K-theory) spectral sequence for such a theory. As an application we generalize the theorem of Karpenko-Merkurjev on G-torsors and rational cycles; to every G-torsor E and a G-equivariant pretheory we associate a graded ring which serves as an invariant of E. In the case of Chow groups this ring encodes the information concerning the motivic J-invariant of E and in the case of Grothendieck's K_0 -- indexes of the respective Tits algebras.Comment: 23 pages; this is an essentially extended version of the previous preprint: the construction of an equivariant cycle (co)homology and the spectral sequence (generalizing the long exact localization sequence) are adde

Neisseria gonorrhoeae Limits Chlamydia trachomatis Inclusion Development and Infectivity in a Novel In Vitro Co-Infection Model

Chlamydia trachomatis (Ct) and Neisseria gonorrhoeae (Ng) are the most common bacterial sexually transmitted infections (STIs) worldwide. The primary site of infection for both bacteria is the epithelium of the endocervix in women and the urethra in men; both can also infect the rectum, pharynx and conjunctiva. Ct/Ng co-infections are more common than expected by chance, suggesting Ct/Ng interactions increase susceptibility and/or transmissibility. To date, studies have largely focused on each pathogen individually and models exploring co-infection are limited. We aimed to determine if Ng co-infection influences chlamydial infection and development and we hypothesized that Ng-infected cells are more susceptible to chlamydial infection than uninfected cells. To address this hypothesis, we established an in vitro model of Ct/Ng co-infection in cultured human cervical epithelial cells. Our data show that Ng co-infection elicits an anti-chlamydial effect by reducing chlamydial infection, inclusion size, and subsequent infectivity. Notably, the anti-chlamydial effect is dependent on Ng viability but not extracellular nutrient depletion or pH modulation. Though this finding is not consistent with our hypothesis, it provides evidence that interaction of these bacteria in vitro influences chlamydial infection and development. This Ct/Ng co-infection model, established in an epithelial cell line, will facilitate further exploration into the pathogenic interplay between Ct and Ng

Arbitrarily large families of spaces of the same volume

In any connected non-compact semi-simple Lie group without factors locally isomorphic to SL_2(R), there can be only finitely many lattices (up to isomorphism) of a given covolume. We show that there exist arbitrarily large families of pairwise non-isomorphic arithmetic lattices of the same covolume. We construct these lattices with the help of Bruhat-Tits theory, using Prasad's volume formula to control their covolumes.Comment: 9 pages. Syntax corrected; one reference adde