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

Fractional Superspace Formulation of Generalized Super-Virasoro Algebras

We present a fractional superspace formulation of the centerless parasuper-Viraso-ro and fractional super-Virasoro algebras. These are two different generalizations of the ordinary super-Virasoro algebra generated by the infinitesimal diffeomorphisms of the superline. We work on the fractional superline parametrized by $t$ and $\theta$, with $t$ a real coordinate and $\theta$ a paragrassmann variable of order $M$ and canonical dimension $1/F$. We further describe a more general structure labelled by $M$ and $F$ with $M\geq F$. The case $F=2$ corresponds to the parasuper-Virasoro algebra of order $M$, while the case $F=M$ leads to the fractional super-Virasoro algebra of order $F$. The ordinary super-Virasoro algebra is recovered at $F=M=2$. The connection with $q$-oscillator algebras is discussed.Comment: 9 pages, McGill/92-30 (small corrections and elimination of the parameter "alpha"

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