Random permutations and unique fully supported ergodicity for the Euler adic transformation

There is only one fully supported ergodic invariant probability measure for the adic transformation on the space of infinite paths in the graph that underlies the Eulerian numbers. This result may partially justify a frequent assumption about the equidistribution of random permutations.Comment: 12 pages, 7 figures, to appear Ann. Inst. H. Poincar\'e Prob. and Sta

Periodic codings of Bratteli-Vershik systems

We develop conditions for the coding of a Bratteli-Vershik system according to initial path segments to be periodic, equivalently for a constructive symbolic recursive scheme corresponding to a cutting and stacking process to produce a periodic sequence. This is a step toward understanding when a Bratteli-Vershik system can be essentially faithfully represented by means of a natural coding as a subshift on a finite alphabet.Comment: Fixed a few typos. Version to appear in Mathematica Scandinavic

Dynamical properties of some adic systems with arbitrary orderings

We consider arbitrary orderings of the edges entering each vertex of the (downward directed) Pascal graph. Each ordering determines an adic (Bratteli–Vershik) system, with a transformation that is defined on most of the space of infinite paths that begin at the root. We prove that for every ordering the coding of orbits according to the partition of the path space determined by the first three edges is essentially faithful, meaning that it is one-to-one on a set of paths that has full measure for every fully supported invariant probability measure. We also show that for every $k$ the subshift that arises from coding orbits according to the first $k$ edges is topologically weakly mixing. We give a necessary and sufficient condition for any adic system to be topologically conjugate to an odometer and use this condition to determine the probability that a random order on a fixed diagram, or a diagram constructed at random in some way, is topologically conjugate to an odometer. We also show that the closure of the union over all orderings of the subshifts arising from codings of the Pascal adic by the first edge has superpolynomial complexity, is not topologically transitive, and has no periodic points besides the two fixed points, while the intersection over all orderings consists of just four orbits

On the effects of turbulence on a screw dynamo

In an experiment in the Institute of Continuous Media Mechanics in Perm (Russia) an non--stationary screw dynamo is intended to be realized with a helical flow of liquid sodium in a torus. The flow is necessarily turbulent, that is, may be considered as a mean flow and a superimposed turbulence. In this paper the induction processes of the turbulence are investigated within the framework of mean--field electrodynamics. They imply of course a part which leads to an enhanced dissipation of the mean magnetic field. As a consequence of the helical mean flow there are also helical structures in the turbulence. They lead to some kind of $\alpha$--effect, which might basically support the screw dynamo. The peculiarity of this $\alpha$--effect explains measurements made at a smaller version of the device envisaged for the dynamo experiment. The helical structures of the turbulence lead also to other effects, which in combination with a rotational shear are potentially capable of dynamo action. A part of them can basically support the screw dynamo. Under the conditions of the experiment all induction effects of the turbulence prove to be rather weak in comparison to that of the main flow. Numerical solutions of the mean--field induction equation show that all the induction effects of the turbulence together let the screw dynamo threshold slightly, at most by one per cent, rise. The numerical results give also some insights into the action of the individual induction effects of the turbulence.Comment: 15 pages, 7 figures, in GAFD prin

Revealing the secrets of neuronal circuits with recombinant rabies virus technology

An understanding of how the brain processes information requires knowledge of the architecture of its underlying neuronal circuits, as well as insights into the relationship between architecture and physiological function. A range of sophisticated tools is needed to acquire this knowledge, and recombinant rabies virus (RABV) is becoming an increasingly important part of this essential toolbox. RABV has been recognized for years for its properties as a synapse-specific trans-neuronal tracer. A novel genetically modified variant now enables the investigation of specific monosynaptic connections. This technology, in combination with other genetic, physiological, optical, and computational tools, has enormous potential for the visualization of neuronal circuits, and for monitoring and manipulating their activity. Here we will summarize the latest developments in this fast moving field and provide a perspective for the use of this technology for the dissection of neuronal circuit structure and function in the normal and diseased brain

Hasard et destin dans le Anton Reiser de Karl Philipp Moritz

International audienceThe distinction between literary chance and chance as experience (E. Köhler) allows the originality of Moritz's autobiographical novel to be disengaged. This study of the motif of chance in book II ofAnton Reiser shows the establishment of a narrative method characterized by repressing the literary treatment of chance and maintaining of chance as a category of lived experience. In this text, the fortunate and unfortunate chances do not found the literary necessity of an exemplary destiny, but are the occasion for throwing light on the double determination, exterior and interior, that affects the character's existence, an existence that is experienced under the sign of a radical contingency. It is in this first obscurity that psychological analysis operates, not to establish the horizon of Providence, but to disengage the general lessons of an existence, and to give to its hero, at this moment, the consistency of a novelistic character.La distinction entre les deux catégories du « hasard vécu » (erlebter Zufall) et du « hasard littéraire » (literarischer Zufall), empruntée à Erich Köhler, permet d'aborder l'étude du roman autobiographique de Karl Philipp Moritz, Anton Reiser, en faisant ressortir l'ambivalence d'un projet "romanesque" en un sens nouveau. On montre ici comment le recul de la figuration du hasard littéraire au profit de la figuration du hasard vécu exprime la remise en cause du roman traditionnel et la recherche de nouvelles formes permettant de saisir et de donner forme à la consistance de la vie intérieure

Fusion pore expansion is a slow, discontinuous, and Ca2+-dependent process regulating secretion from alveolar type II cells

In alveolar type II cells, the release of surfactant is considerably delayed after the formation of exocytotic fusion pores, suggesting that content dispersal may be limited by fusion pore diameter and subject to regulation at a postfusion level. To address this issue, we used confocal FRAP and N-(3-triethylammoniumpropyl)-4-(4-[dibutylamino]styryl) pyridinium dibromide (FM 1-43), a dye yielding intense localized fluorescence of surfactant when entering the vesicle lumen through the fusion pore (Haller, T., J. Ortmayr, F. Friedrich, H. Volkl, and P. Dietl. 1998. Proc. Natl. Acad. Sci. USA. 95:1579–1584). Thus, we have been able to monitor the dynamics of individual fusion pores up to hours in intact cells, and to calculate pore diameters using a diffusion model derived from Fick's law. After formation, fusion pores were arrested in a state impeding the release of vesicle contents, and expanded at irregular times thereafter. The expansion rate of initial pores and the probability of late expansions were increased by elevation of the cytoplasmic Ca2+ concentration. Consistently, content release correlated with the occurrence of Ca2+ oscillations in ATP-treated cells, and expanded fusion pores were detectable by EM. This study supports a new concept in exocytosis, implicating fusion pores in the regulation of content release for extended periods after initial formation

The mean electromotive force due to turbulence of a conducting fluid in the presence of mean flow

The mean electromotive force caused by turbulence of an electrically conducting fluid, which plays a central part in mean--field electrodynamics, is calculated for a rotating fluid. Going beyond most of the investigations on this topic, an additional mean motion in the rotating frame is taken into account. One motivation for our investigation originates from a planned laboratory experiment with a Ponomarenko-like dynamo. In view of this application the second--order correlation approximation is used. The investigation is of high interest in astrophysical context, too. Some contributions to the mean electromotive are revealed which have not been considered so far, in particular contributions to the $\alpha$--effect and related effects due to the gradient of the mean velocity. Their relevance for dynamo processes is discussed. In a forthcoming paper the results reported here will be specified to the situation in the laboratory and partially compared with experimental findings.Comment: 16 pages, 2 figures, in PRE pres