Euler characteristic of the configuration space of a complex

A closed form formula (generating function) for the Euler characteristic of the configuration space of $\scriptstyle n$ particles in a simplicial complex is given.Comment: 6 pages, no figure

Asymptotic dimension and uniform embeddings

We show that the type function of a space with finite asymptotic dimension estimates its Hilbert (or any $l^p$) compression. The method allows to obtain the lower bound of the compression of the lamplighter group $Z\wr Z$, which has infinite asymptotic dimension.Comment: 17 pages, no figure

Photometric validation of a model independent procedure to extract galaxy clusters

By means of CCD photometry in three bands (Gunn g, r, i) we investigate the existence of 12 candidate clusters extracted via a model independent peak finding algorithm (\cite{memsait}) from DPOSS data. The derived color-magnitude diagrams allow us to confirm the physical nature of 9 of the cluster candidates, and to estimate their photometric redshifts. Of the other candidates, one is a fortuitous detection of a true cluster at z~0.4, one is a false detection and the last is undecidable on the basis of the available data. The accuracy of the photometric redshifts is tested on an additional sample of 8 clusters with known spectroscopic redshifts. Photometric redshifts turn out to be accurate within z~0.01 (interquartile range).Comment: A&A in pres

The Universal Aspect Ratio of Vortices in Rotating Stratified Flows: Theory and Simulation

We derive a relationship for the vortex aspect ratio $\alpha$ (vertical half-thickness over horizontal length scale) for steady and slowly evolving vortices in rotating stratified fluids, as a function of the Brunt-Vaisala frequencies within the vortex $N_c$ and in the background fluid outside the vortex $\bar{N}$, the Coriolis parameter $f$, and the Rossby number $Ro$ of the vortex: $\alpha^2 = Ro(1+Ro) f^2/(N_c^2-\bar{N}^2)$. This relation is valid for cyclones and anticyclones in either the cyclostrophic or geostrophic regimes; it works with vortices in Boussinesq fluids or ideal gases, and the background density gradient need not be uniform. Our relation for $\alpha$ has many consequences for equilibrium vortices in rotating stratified flows. For example, cyclones must have $N_c^2 > \bar{N}^2$; weak anticyclones (with $|Ro| \bar{N}^2$. We verify our relation for $\alpha$ with numerical simulations of the three-dimensional Boussinesq equations for a wide variety of vortices, including: vortices that are initially in (dissipationless) equilibrium and then evolve due to an imposed weak viscous dissipation or density radiation; anticyclones created by the geostrophic adjustment of a patch of locally mixed density; cyclones created by fluid suction from a small localised region; vortices created from the remnants of the violent breakups of columnar vortices; and weakly non-axisymmetric vortices. The values of the aspect ratios of our numerically-computed vortices validate our relationship for $\alpha$, and generally they differ significantly from the values obtained from the much-cited conjecture that $\alpha = f/\bar{N}$ in quasi-geostrophic vortices.Comment: Submitted to the Journal of Fluid Mechanics. Also see the companion paper by Aubert et al. "The Universal Aspect Ratio of Vortices in Rotating Stratified Flows: Experiments and Observations" 201

WISeREP - An Interactive Supernova Data Repository

We have entered an era of massive data sets in astronomy. In particular, the number of supernova (SN) discoveries and classifications has substantially increased over the years from few tens to thousands per year. It is no longer the case that observations of a few prototypical events encapsulate most spectroscopic information about SNe, motivating the development of modern tools to collect, archive, organize and distribute spectra in general, and SN spectra in particular. For this reason we have developed the Weizmann Interactive Supernova data REPository - WISeREP - an SQL-based database (DB) with an interactive web-based graphical interface. The system serves as an archive of high quality SN spectra, including both historical (legacy) data as well as data that is accumulated by ongoing modern programs. The archive provides information about objects, their spectra, and related meta-data. Utilizing interactive plots, we provide a graphical interface to visualize data, perform line identification of the major relevant species, determine object redshifts, classify SNe and measure expansion velocities. Guest users may view and download spectra or other data that have been placed in the public domain. Registered users may also view and download data that are proprietary to specific programs with which they are associated. The DB currently holds >8000 spectra, of which >5000 are public; the latter include published spectra from the Palomar Transient Factory, all of the SUSPECT archive, the Caltech-Core-Collapse Program, the CfA SN spectra archive and published spectra from the UC Berkeley SNDB repository. It offers an efficient and convenient way to archive data and share it with colleagues, and we expect that data stored in this way will be easy to access, increasing its visibility, usefulness and scientific impact.Comment: To be published in PASP. WISeREP: http://www.weizmann.ac.il/astrophysics/wiserep