Polynominals related to powers of the Dedekind eta function

The vanishing properties of Fourier coefficients of integral powers of the Dedekind eta function correspond to the existence of integral roots of integer-valued polynomials Pn(x) introduced by M. Newman. In this paper we study the derivatives of these polynomials. We obtain non-vanishing results at integral points. As an application we prove that integral roots are simple if the index n of the polynomial is equal to a prime power pm or to pm + 1. We obtain a formula for the derivative of Pn(x) involving the polynomials of lower degree

Hudson's Theorem for finite-dimensional quantum systems

We show that, on a Hilbert space of odd dimension, the only pure states to possess a non-negative Wigner function are stabilizer states. The Clifford group is identified as the set of unitary operations which preserve positivity. The result can be seen as a discrete version of Hudson's Theorem. Hudson established that for continuous variable systems, the Wigner function of a pure state has no negative values if and only if the state is Gaussian. Turning to mixed states, it might be surmised that only convex combinations of stabilizer states give rise to non-negative Wigner distributions. We refute this conjecture by means of a counter-example. Further, we give an axiomatic characterization which completely fixes the definition of the Wigner function and compare two approaches to stabilizer states for Hilbert spaces of prime-power dimensions. In the course of the discussion, we derive explicit formulas for the number of stabilizer codes defined on such systems.Comment: 17 pages, 3 figures; References updated. Title changed to match published version. See also quant-ph/070200

Raman cooling and heating of two trapped Ba+ ions

We study cooling of the collective vibrational motion of two 138Ba+ ions confined in an electrodynamic trap and irradiated with laser light close to the resonances S_1/2-P_1/2 (493 nm) and P_1/2-D_3/2 (650 nm). The motional state of the ions is monitored by a spatially resolving photo multiplier. Depending on detuning and intensity of the cooling lasers, macroscopically different motional states corresponding to different ion temperatures are observed. We also derive the ions' temperature from detailed analytical calculations of laser cooling taking into account the Zeeman structure of the energy levels involved. The observed motional states perfectly match the calculated temperatures. Significant heating is observed in the vicinity of the dark resonances of the Zeeman-split S_1/2-D_3/2 Raman transitions. Here two-photon processes dominate the interaction between lasers and ions. Parameter regimes of laser light are identified that imply most efficient laser cooling.Comment: 8 pages, 5 figure

Activity at the Deuterium-Burning Mass Limit in Orion

We report very intense and variable Halpha emission (pseudo-equivalent widths of ~180, 410 A) of S Ori 55, a probable free-floating, M9-type substellar member of the young sigma Orionis open star cluster. After comparison with state-of-the-art evolutionary models, we infer that S Ori 55 is near or below the cluster deuterium-burning mass borderline, which separates brown dwarfs and planetary-mass objects. We find its mass to be 0.008-0.015 Msun for ages between 1 Myr and 8 Myr, with ~0.012 Msun the most likely value at the cluster age of 3 Myr. The largest Halpha intensity reached the saturation level of log L(Halpha)/L(bol) = -3. We discuss several possible scenarios for such a strong emission. We also show that sigma Orionis M and L dwarfs have in general more Halpha emission than their older field spectral counterparts. This could be due to a decline in the strength of the magnetic field with age in brown dwarfs and isolated planetary-mass objects, or to a likely mass accretion from disks in the very young sigma Orionis substellar members.Comment: Accepted for publication in ApJ Letters. Nine pages (figures included

Cancer Biology Data Curation at the Mouse Tumor Biology Database (MTB)

Many advances in the field of cancer biology have been made using mouse models of human cancer. The Mouse Tumor Biology (MTB, "http://tumor.informatics.jax.org":http://tumor.informatics.jax.org) database provides web-based access to data on spontaneous and induced tumors from genetically defined mice (inbred, hybrid, mutant, and genetically engineered strains of mice). These data include standardized tumor names and classifications, pathology reports and images, mouse genetics, genomic and cytogenetic changes occurring in the tumor, strain names, tumor frequency and latency, and literature citations.

Although primary source for the data represented in MTB is peer-reviewed scientific literature an increasing amount of data is derived from disparate sources. MTB includes annotated histopathology images and cytogenetic assay images for mouse tumors where these data are available from The Jackson Laboratory’s mouse colonies and from outside contributors. MTB encourages direct submission of mouse tumor data and images from the cancer research community and provides investigators with a web-accessible tool for image submission and annotation. 

Integrated searches of the data in MTB are facilitated by the use of several controlled vocabularies and by adherence to standard nomenclature. MTB also provides links to other related online resources such as the Mouse Genome Database, Mouse Phenome Database, the Biology of the Mammary Gland Web Site, Festing's Listing of Inbred Strains of Mice, the JAX® Mice Web Site, and the Mouse Models of Human Cancers Consortium's Mouse Repository. 

MTB provides access to data on mouse models of cancer via the internet and has been designed to facilitate the selection of experimental models for cancer research, the evaluation of mouse genetic models of human cancer, the review of patterns of mutations in specific cancers, and the identification of genes that are commonly mutated across a spectrum of cancers.

MTB is supported by NCI grant CA089713

Symmetries of the finite Heisenberg group for composite systems

Symmetries of the finite Heisenberg group represent an important tool for the study of deeper structure of finite-dimensional quantum mechanics. As is well known, these symmetries are properly expressed in terms of certain normalizer. This paper extends previous investigations to composite quantum systems consisting of two subsystems - qudits - with arbitrary dimensions n and m. In this paper we present detailed descriptions - in the group of inner automorphisms of GL(nm,C) - of the normalizer of the Abelian subgroup generated by tensor products of generalized Pauli matrices of orders n and m. The symmetry group is then given by the quotient group of the normalizer.Comment: Submitted to J. Phys. A: Math. Theo