On Exceptional Times for generalized Fleming-Viot Processes with Mutations

If $\mathbf Y$ is a standard Fleming-Viot process with constant mutation rate (in the infinitely many sites model) then it is well known that for each $t>0$ the measure $\mathbf Y_t$ is purely atomic with infinitely many atoms. However, Schmuland proved that there is a critical value for the mutation rate under which almost surely there are exceptional times at which $\mathbf Y$ is a finite sum of weighted Dirac masses. In the present work we discuss the existence of such exceptional times for the generalized Fleming-Viot processes. In the case of Beta-Fleming-Viot processes with index $\alpha\in\,]1,2[$ we show that - irrespectively of the mutation rate and $\alpha$ - the number of atoms is almost surely always infinite. The proof combines a Pitman-Yor type representation with a disintegration formula, Lamperti's transformation for self-similar processes and covering results for Poisson point processes

Exceptional Sequences of Line Bundles and Spherical Twists - a Toric Example

Exceptional sequences of line bundles on a smooth projective toric surface are automatically full when they can be constructed via augmentation. By using spherical twists, we give examples that there are also exceptional sequences which can not be constructed this way but are nevertheless full.Comment: 12 pages, 3 figure

Quenched large deviation principle for words in a letter sequence

When we cut an i.i.d. sequence of letters into words according to an independent renewal process, we obtain an i.i.d. sequence of words. In the \emph{annealed} large deviation principle (LDP) for the empirical process of words, the rate function is the specific relative entropy of the observed law of words w.r.t. the reference law of words. In the present paper we consider the \emph{quenched} LDP, i.e., we condition on a typical letter sequence. We focus on the case where the renewal process has an \emph{algebraic} tail. The rate function turns out to be a sum of two terms, one being the annealed rate function, the other being proportional to the specific relative entropy of the observed law of letters w.r.t. the reference law of letters, with the former being obtained by concatenating the words and randomising the location of the origin. The proportionality constant equals the tail exponent of the renewal process. Earlier work by Birkner considered the case where the renewal process has an exponential tail, in which case the rate function turns out to be the first term on the set where the second term vanishes and to be infinite elsewhere. In a companion paper the annealed and the quenched LDP are applied to the collision local time of transient random walks, and the existence of an intermediate phase for a class of interacting stochastic systems is established.Comment: 41 pages, 2 figures. Acronym LDP spelled out in title, main result strengthened to cover more general "letter" spaces, application to collision local times removed (this part will become a separate manuscript

Hydrophobic gating of mechanosensitive channel of large conductance evidenced by single-subunit resolution

Mechanosensitive (MS) ion channels are membrane proteins that detect and respond to membrane tension in all branches of life. In bacteria, MS channels prevent cells from lysing upon sudden hypoosmotic shock by opening and releasing solutes and water. Despite the importance of MS channels and ongoing efforts to explain their functioning, the molecular mechanism of MS channel gating remains elusive and controversial. Here we report a method that allows single-subunit resolution for manipulating and monitoring “mechanosensitive channel of large conductance” from Escherichia coli. We gradually changed the hydrophobicity of the pore constriction in this homopentameric protein by modifying a critical pore residue one subunit at a time. Our experimental results suggest that both channel opening and closing are initiated by the transmembrane 1 helix of a single subunit and that the participation of each of the five identical subunits in the structural transitions between the closed and open states is asymmetrical. Such a minimal change in the pore environment seems ideal for a fast and energy-efficient response to changes in the membrane tension.

The 1+1-dimensional Kardar-Parisi-Zhang equation and its universality class

We explain the exact solution of the 1+1 dimensional Kardar-Parisi-Zhang equation with sharp wedge initial conditions. Thereby it is confirmed that the continuum model belongs to the KPZ universality class, not only as regards to scaling exponents but also as regards to the full probability distribution of the height in the long time limit.Comment: Proceedings StatPhys 2

Terahertz radiation driven chiral edge currents in graphene

We observe photocurrents induced in single layer graphene samples by illumination of the graphene edges with circularly polarized terahertz radiation at normal incidence. The photocurrent flows along the sample edges and forms a vortex. Its winding direction reverses by switching the light helicity from left- to right-handed. We demonstrate that the photocurrent stems from the sample edges, which reduce the spatial symmetry and result in an asymmetric scattering of carriers driven by the radiation electric field. The developed theory is in a good agreement with the experiment. We show that the edge photocurrents can be applied for determination of the conductivity type and the momentum scattering time of the charge carriers in the graphene edge vicinity.Comment: 4 pages, 4 figure, additional Supplemental Material (3 pages, 1 figure

Vibrational Spectra of a Mechanosensitive Channel

We report the simulated vibrational spectra of a mechanosensitive membrane channel in different gating states. Our results show that while linear absorption is insensitive to structural differences, linear dichroism and sum-frequency generation spectroscopies are sensitive to the orientation of the transmembrane helices, which is changing during the opening process. Linear dichroism cannot distinguish an intermediate structure from the closed structure, but sum-frequency generation can. In addition, we find that two-dimensional infrared spectroscopy can be used to distinguish all three investigated gating states of the mechanosensitive membrane channel.

Ketamine Dysregulates the Amplitude and Connectivity of High-Frequency Oscillations in Cortical-Subcortical Networks in Humans: Evidence From Resting-State Magnetoencephalography-Recordings

Hypofunctioning of the N-methyl-D-aspartate (NMDA)-receptor (NMDA-R) has been prominently implicated in the pathophysiology of schizophrenia (ScZ). The current study tested the effects of ketamine, a dissociative anesthetic and NMDA-R antagonist, on resting-state activity recorded with magnetoencephalography (MEG) in healthy volunteers. In a single-blind cross-over design, each participant (n = 12) received, on two different sessions, a subanesthetic dose of S-ketamine (0.006 mg/Kg) and saline injection. MEG-data were analyzed at sensorand source- level in the beta (13-30 Hz) and gamma (30-90 Hz) frequency ranges. In addition, connectivity analysis at source-level was performed using transfer entropy (TE). Ketamine increased gamma-power while beta-band activity was decreased. Specifically, elevated 30-90 Hz activity was pronounced in subcortical (thalamus and hippocampus) and cortical (frontal and temporal cortex) regions, whilst reductions in beta-band power were localized to the precuneus, cerebellum, anterior cingulate, temporal and visual cortex. TE analysis demonstrated increased information transfer in a thalamo-cortical network after ketamine administration. The findings are consistent with the pronounced dysregulation of highfrequency oscillations following the inhibition of NMDA-R in animal models of ScZ as well as with evidence from EEG-data in ScZ-patients and increased functional connectivity during early illness stages. Moreover, our data highlight the potential contribution of thalamo-cortical connectivity patterns towards ketamine-induced neuronal dysregulation, which may be relevant for the understanding of schizophrenia as a disorder of disinhibition of neural circuits