A pure jump Markov process with a random singularity spectrum

We construct a non-decreasing pure jump Markov process, whose jump measure heavily depends on the values taken by the process. We determine the singularity spectrum of this process, which turns out to be random and to depend locally on the values taken by the process. The result relies on fine properties of the distribution of Poisson point processes and on ubiquity theorems.Comment: 20 pages, 4 figure

Electroweak and Heavy Flavor Physics at SLD

We review recent electroweak and B physics results obtained in polarized e+e- interactions at the SLC by the SLD experiment. Unique and precise measurements of the electroweak parameters Ae, Ab, Ac, Rb and Rc provide powerful constraints on the Standard Model. The excellent 3-D vertexing capabilities of SLD are further exploited to extract precise B+ and B0 lifetimes, as well as measurements of the time evolution of B0-B0-bar mixing.Comment: 11 pages, 5 figures. Presented at the Workshop on Physics at the First Muon Collider and at the Front End of a Muon Collider, 6-9 November 1997, Fermilab, Batavia, I

Can Rats Reason?

Since at least the mid-1980s claims have been made for rationality in rats. For example, that rats are capable of inferential reasoning (Blaisdell, Sawa, Leising, & Waldmann, 2006; Bunsey & Eichenbaum, 1996), or that they can make adaptive decisions about future behavior (Foote & Crystal, 2007), or that they are capable of knowledge in propositional-like form (Dickinson, 1985). The stakes are rather high, because these capacities imply concept possession and on some views (e.g., Rödl, 2007; Savanah, 2012) rationality indicates self-consciousness. I evaluate the case for rat rationality by analyzing 5 key research paradigms: spatial navigation, metacognition, transitive inference, causal reasoning, and goal orientation. I conclude that the observed behaviors need not imply rationality by the subjects. Rather, the behavior can be accounted for by noncognitive processes such as hard-wired species typical predispositions or associative learning or (nonconceptual) affordance detection. These mechanisms do not necessarily require or implicate the capacity for rationality. As such there is as yet insufficient evidence that rats can reason. I end by proposing the ‘Staircase Test,’ an experiment designed to provide convincing evidence of rationality in rats

Local extremality of the Calabi-Croke sphere for the length of the shortest closed geodesic

Recently, F. Balacheff proved that the Calabi-Croke sphere made of two flat 1-unit-side equilateral triangles glued along their boundaries is a local extremum for the length of the shortest closed geodesic among the Riemannian spheres with conical singularities of fixed area. We give an alternative proof of this theorem, which does not make use of the uniformization theorem, and extend the result to Finsler metrics

Marked length spectrum of magnetized surfaces

The main result presented here is that the flow associated with a riemannian metric and a non zero magnetic field on a compact oriented surface without boundary, under assumptions of hyperbolic type, cannot have the same length spectrum of topologically corresponding periodic orbits as the geodesic flow associated with another riemannian metric having a negative curvature and the same total volume. The main tool is a regularization inspired by U. Hamenst\"adt's methods

A reciprocal Wald theorem for varying gravitational function

We study when a cosmological constant is a natural issue if it is mimicked by the potential of a massive Hyperextended Scalar Tensor theory with a perfect fluid for Bianchi type I and V models. We then deduce a reciprocal Wald theorem giving the conditions such that the potential tends to a non vanishing constant when the gravitational function varies. We also get the conditions allowing the potentiel to vanish or diverge.Comment: 13 page

Vlasov-Poisson in 1D for initially cold systems: post-collapse Lagrangian perturbation theory

We study analytically the collapse of an initially smooth, cold, self-gravitating collisionless system in one dimension. The system is described as a central "S" shape in phase-space surrounded by a nearly stationary halo acting locally like a harmonic background on the S. To resolve the dynamics of the S under its self-gravity and under the influence of the halo, we introduce a novel approach using post-collapse Lagrangian perturbation theory. This approach allows us to follow the evolution of the system between successive crossing times and to describe in an iterative way the interplay between the central S and the halo. Our theoretical predictions are checked against measurements in entropy conserving numerical simulations based on the waterbag method. While our post-collapse Lagrangian approach does not allow us to compute rigorously the long term behavior of the system, i.e. after many crossing times, it explains the close to power-law behavior of the projected density observed in numerical simulations. Pushing the model at late time suggests that the system could build at some point a very small flat core, but this is very speculative. This analysis shows that understanding the dynamics of initially cold systems requires a fine grained approach for a correct description of their very central part. The analyses performed here can certainly be extended to spherical symmetry.Comment: 20 pages, 9 figures, accepted for publication in MNRA