Inflationary spacetimes are not past-complete

Many inflating spacetimes are likely to violate the weak energy condition, a key assumption of singularity theorems. Here we offer a simple kinematical argument, requiring no energy condition, that a cosmological model which is inflating -- or just expanding sufficiently fast -- must be incomplete in null and timelike past directions. Specifically, we obtain a bound on the integral of the Hubble parameter over a past-directed timelike or null geodesic. Thus inflationary models require physics other than inflation to describe the past boundary of the inflating region of spacetime.Comment: We improve the basic argument to apply to a wider class of spacetimes, use a better title and add a discussion of cyclic models. 4 pages, 1 figure, RevTe

Implications of a Quantum Mechanical Treatment of the Universe

We attempt to treat the very early Universe according to quantum mechanics. Identifying the scale factor of the Universe with the width of the wave packet associated with it, we show that there cannot be an initial singularity and that the Universe expands. Invoking the correspondence principle, we obtain the scale factor of the Universe and demonstrate that the causality problem of the standard model is solved.Comment: LaTex, 5 pages, 1 figure, to be published in Mod. Phys. Lett.

Anatomical variation of the extracranial course of the optic nerve in the floor of the sphenoid sinus: first reported case

Abstract Objective: We report a unique case of anatomical variation of the extracranial course of the optic nerve running in the floor of the sphenoid sinus. Method: Clinical and radiological findings are presented. Results: A 39-year-old woman with Turner syndrome presented with severe headache associated with visual disturbances. Magnetic resonance imaging revealed a mass presumed to be a sella meningioma. Computed tomography of the paranasal sinuses was undertaken to help plan surgical removal via an endoscopic trans-sphenoidal approach; this scan revealed an atypical extracranial course of the optic nerve, running in the floor of the sphenoid sinu

Business cycles, bank credit and crises

This paper investigates how business cycle volatility affects internal and external funding sources of banks. It argues that excessive credit growth, credit cycles, and bank failures are phenomena related to distinct patterns of banks’ financing options over the cycle

Kinefold web server for RNA/DNA folding path and structure prediction including pseudoknots and knots

The Kinefold web server provides a web interface for stochastic folding simulations of nucleic acids on second to minute molecular time scales. Renaturation or co-transcriptional folding paths are simulated at the level of helix formation and dissociation in agreement with the seminal experimental results. Pseudoknots and topologically ‘entangled’ helices (i.e. knots) are efficiently predicted taking into account simple geometrical and topological constraints. To encourage interactivity, simulations launched as immediate jobs are automatically stopped after a few seconds and return adapted recommendations. Users can then choose to continue incomplete simulations using the batch queuing system or go back and modify suggested options in their initial query. Detailed output provide (i) a series of low free energy structures, (ii) an online animated folding path and (iii) a programmable trajectory plot focusing on a few helices of interest to each user. The service can be accessed at