Periaxonal K+ regulation in the small squid Alloteuthis. Studies on isolated and in situ axons

A novel giant axon preparation from the squid Alloteuthis is described. Properties of in situ and isolated axons are similar. Periaxonal K+ accumulation is a function of the physiological state of the animal and of the axon and its sheathing layers. Carefully dissected isolated axons, and axons in situ in a healthy mantle, show much less K+ accumulation than previously reported in squid. It is suggested that the Schwann cells are involved in the observed K+ regulation

Oseledets' Splitting of Standard-like Maps

For the class of differentiable maps of the plane and, in particular, for standard-like maps (McMillan form), a simple relation is shown between the directions of the local invariant manifolds of a generic point and its contribution to the finite-time Lyapunov exponents (FTLE) of the associated orbit. By computing also the point-wise curvature of the manifolds, we produce a comparative study between local Lyapunov exponent, manifold's curvature and splitting angle between stable/unstable manifolds. Interestingly, the analysis of the Chirikov-Taylor standard map suggests that the positive contributions to the FTLE average mostly come from points of the orbit where the structure of the manifolds is locally hyperbolic: where the manifolds are flat and transversal, the one-step exponent is predominantly positive and large; this behaviour is intended in a purely statistical sense, since it exhibits large deviations. Such phenomenon can be understood by analytic arguments which, as a by-product, also suggest an explicit way to point-wise approximate the splitting.Comment: 17 pages, 11 figure

Nonmalignant Features Associated with Inherited Colorectal Cancer Syndromes-Clues for Diagnosis

Simple Summary: Familiarity with nonmalignant features and comorbidities of cancer predisposition syndromes may raise awareness and assist clinicians in the diagnosis and interpretation of molecular test results. Genetic predisposition to colorectal cancer (CRC) should be suspected mainly in young patients, in patients with significant family histories, multiple polyps, mismatch repair-deficient tumors, and in association with malignant or nonmalignant comorbidities. The aim of this review is to describe the main nonmalignant comorbidities associated with selected CRC predisposition syndromes that may serve as valuable diagnostic clues for clinicians and genetic professionals.& nbsp;Genetic diagnosis of affected individuals and predictive testing of their at-risk relatives, combined with intensive cancer surveillance, has an enormous cancer-preventive potential in these families. A lack of awareness may be part of the reason why the underlying germline cause remains unexplained in a large proportion of patients with CRC. Various extracolonic features, mainly dermatologic, ophthalmic, dental, endocrine, vascular, and reproductive manifestations occur in many of the cancer predisposition syndromes associated with CRC and polyposis. Some are mediated via the WNT, TGF-beta, or mTOR pathways. However the pathogenesis of most features is still obscure. Here we review the extracolonic features of the main syndromes, the existing information regarding their prevalence, and the pathways involved in their pathogenesis. This knowledge could be useful for care managers from different professional disciplines, and used to raise awareness, enable diagnosis, and assist in the process of genetic testing and interpretation

A theorem of Tits type for compact Kahler manifolds

We prove a theorem of Tits type about automorphism groups for compact Kahler manifolds, which has been conjectured in the paper [KOZ].Comment: Inventiones Mathematicae (to appear), 11 page

Instability of ion kinetic waves in a weakly ionized plasma

The fundamental higher-order Landau plasma modes are known to be generally heavily damped. We show that these modes for the ion component in a weakly ionized plasma can be substantially modified by ion-neutral collisions and a dc electric field driving ion flow so that some of them can become unstable. This instability is expected to naturally occur in presheaths of gas discharges at sufficiently small pressures and thus affect sheaths and discharge structures.Comment: Published in Phys. Rev. E, see http://link.aps.org/doi/10.1103/PhysRevE.85.02641

Selfsimilar solutions in a sector for a quasilinear parabolic equation

We study a two-point free boundary problem in a sector for a quasilinear parabolic equation. The boundary conditions are assumed to be spatially and temporally "self-similar" in a special way. We prove the existence, uniqueness and asymptotic stability of an expanding solution which is self-similar at discrete times. We also study the existence and uniqueness of a shrinking solution which is self-similar at discrete times.Comment: 23 page