The Invariant Measures of some Infinite Interval Exchange Maps

We classify the locally finite ergodic invariant measures of certain infinite interval exchange transformations (IETs). These transformations naturally arise from return maps of the straight-line flow on certain translation surfaces, and the study of the invariant measures for these IETs is equivalent to the study of invariant measures for the straight-line flow in some direction on these translation surfaces. For the surfaces and directions for which our methods apply, we can characterize the locally finite ergodic invariant measures of the straight-line flow in a set of directions of Hausdorff dimension larger than 1/2. We promote this characterization to a classification in some cases. For instance, when the surfaces admit a cocompact action by a nilpotent group, we prove each ergodic invariant measure for the straight-line flow is a Maharam measure, and we describe precisely which Maharam measures arise. When the surfaces under consideration are finite area, the straight-line flows in the directions we understand are uniquely ergodic. Our methods apply to translation surfaces admitting multi-twists in a pair of cylinder decompositions in non-parallel directions.Comment: 107 pages, 11 figures. Minor improvement

Restrictions of generalized Verma modules to symmetric pairs

We initiate a new line of investigation on branching problems for generalized Verma modules with respect to complex reductive symmetric pairs (g,k). Here we note that Verma modules of g may not contain any simple module when restricted to a reductive subalgebra k in general. In this article, using the geometry of K_C orbits on the generalized flag variety G_C/P_C, we give a necessary and sufficient condition on the triple (g,k, p) such that the restriction X|_k always contains simple k-modules for any g-module $X$ lying in the parabolic BGG category O^p attached to a parabolic subalgebra p of g. Formulas are derived for the Gelfand-Kirillov dimension of any simple k-module occurring in a simple generalized Verma module of g. We then prove that the restriction X|_k is multiplicity-free for any generic g-module X \in O if and only if (g,k) is isomorphic to a direct sum of (A_n,A_{n-1}), (B_n,D_n), or (D_{n+1},B_n). We also see that the restriction X|_k is multiplicity-free for any symmetric pair (g, k) and any parabolic subalgebra p with abelian nilradical and for any generic g-module X \in O^p. Explicit branching laws are also presented.Comment: 31 pages, To appear in Transformation Group

Non-stationary compositions of Anosov diffeomorphisms

Motivated by non-equilibrium phenomena in nature, we study dynamical systems whose time-evolution is determined by non-stationary compositions of chaotic maps. The constituent maps are topologically transitive Anosov diffeomorphisms on a 2-dimensional compact Riemannian manifold, which are allowed to change with time - slowly, but in a rather arbitrary fashion. In particular, such systems admit no invariant measure. By constructing a coupling, we prove that any two sufficiently regular distributions of the initial state converge exponentially with time. Thus, a system of the kind loses memory of its statistical history rapidly

Ergodic infinite group extensions of geodesic flows on translation surfaces

We show that generic infinite group extensions of geodesic flows on square tiled translation surfaces are ergodic in almost every direction, subject to certain natural constraints. Recently K. Fr\c{a}czek and C. Ulcigrai have shown that certain concrete staircases, covers of square-tiled surfaces, are not ergodic in almost every direction. In contrast we show the almost sure ergodicity of other concrete staircases. An appendix provides a combinatorial approach for the study of square-tiled surfaces

A central limit theorem for time-dependent dynamical systems

The work [8] established memory loss in the time-dependent (non-random) case of uniformly expanding maps of the interval. Here we find conditions under which we have convergence to the normal distribution of the appropriately scaled Birkhoff-like partial sums of appropriate test functions. A substantial part of the problem is to ensure that the variances of the partial sums tend to infinity (cf. the zero-cohomology condition in the autonomous case). In fact, the present paper is the first one where non-random, i. e. specific examples are also found, which are not small perturbations of a given map. Our approach uses martingale approximation technique in the form of [9]

Polyubiquitin binding to ABIN1 is required to prevent autoimmunity

The protein ABIN1 possesses a polyubiquitin-binding domain homologous to that present in nuclear factor kappa B (NF-kappa B) essential modulator (NEMO), a component of the inhibitor of NF-kappa B (I kappa B) kinase (IKK) complex. To address the physiological significance of polyubiquitin binding, we generated knockin mice expressing the ABIN1[D485N] mutant instead of the wild-type (WT) protein. These mice developed all the hallmarks of autoimmunity, including spontaneous formation of germinal centers, isotype switching, and production of autoreactive antibodies. Autoimmunity was suppressed by crossing to MyD88(-/-) mice, demonstrating that toll-like receptor (TLR)-MyD88 signaling pathways are needed for the phenotype to develop. The B cells and myeloid cells of the ABIN1[D485N] mice showed enhanced activation of the protein kinases TAK, IKK-alpha/beta, c-Jun N-terminal kinases, and p38 alpha mitogen-activated protein kinase and produced more IL-6 and IL-12 than WT. The mutant B cells also proliferated more rapidly in response to TLR ligands. Our results indicate that the interaction of ABIN1 with polyubiquitin is required to limit the activation of TLR-MyD88 pathways and prevent autoimmunity

Modular Lie algebras and the Gelfand-Kirillov conjecture

Let g be a finite dimensional simple Lie algebra over an algebraically closed field of characteristic zero. We show that if the Gelfand-Kirillov conjecture holds for g, then g has type A_n, C_n or G_2.Comment: 20 page

Low recurrence rate of a two-layered closure repair for primary and recurrent midline incisional hernia without mesh

Background: Incisional hernia is a serious complication after abdominal surgery and occurs in 11-23% of laparotomies. Repair can be done, for instance, with a direct suture technique, but recurrence rates are high. Recent literature advises the use of mesh repair. In contrast to this development, we studied the use of a direct suture repair in a separate layer technique. The objective of this retrospective observational study is to assess the outcomes (recurrences and complications) of a two-layered open closure repair for primary and recurrent midline incisional hernia without the use of mesh. Methods: In an observational retrospective cohort study, we analysed the hospital and outpatient records of 77 consecutive patients who underwent surgery for a primary or recurrent incisional hernia between 1st May 2002 and 8th November 2006. The repair consisted of separate continuous suturing of the anterior and posterior fascia, including the rectus muscle, after extensive intra-abdominal adhesiolysis. Results: Forty-one men (53.2%) and 36 women (46.8%) underwent surgery. Sixty-three operations (81.8%) were primary repairs and 14 (18.2%) were repairs for a recurrent incisional hernia. Of the 66 patients, on physical examination, three had a recurrence (4.5%) after an average follow-up of 2.6 years. The 30-day postoperative mortality was 1.1%. Wound infection was seen in five patients (6.5%). Conclusions: A two-layered suture repair for primary and recurrent incisional hernia repair without mesh with extensive adhesiolysis was associated with a recurrence rate comparable to mesh repair and had an acceptable complication rate

Effects of mesenchymal stromal cells versus serum on tendon healing in a controlled experimental trial in an equine model

Abstract Background Mesenchymal stromal cells (MSC) have shown promising results in the treatment of tendinopathy in equine medicine, making this therapeutic approach seem favorable for translation to human medicine. Having demonstrated that MSC engraft within the tendon lesions after local injection in an equine model, we hypothesized that they would improve tendon healing superior to serum injection alone. Methods Quadrilateral tendon lesions were induced in six horses by mechanical tissue disruption combined with collagenase application 3 weeks before treatment. Adipose-derived MSC suspended in serum or serum alone were then injected intralesionally. Clinical examinations, ultrasound and magnetic resonance imaging were performed over 24 weeks. Tendon biopsies for histological assessment were taken from the hindlimbs 3 weeks after treatment. Horses were sacrificed after 24 weeks and forelimb tendons were subjected to macroscopic and histological examination as well as analysis of musculoskeletal marker expression. Results Tendons injected with MSC showed a transient increase in inflammation and lesion size, as indicated by clinical and imaging parameters between week 3 and 6 (p < 0.05). Thereafter, symptoms decreased in both groups and, except that in MSC-treated tendons, mean lesion signal intensity as seen in T2w magnetic resonance imaging and cellularity as seen in the histology (p < 0.05) were lower, no major differences could be found at week 24. Conclusions These data suggest that MSC have influenced the inflammatory reaction in a way not described in tendinopathy studies before. However, at the endpoint of the current study, 24 weeks after treatment, no distinct improvement was observed in MSC-treated tendons compared to the serum-injected controls. Future studies are necessary to elucidate whether and under which conditions MSC are beneficial for tendon healing before translation into human medicine