Integer symmetric matrices having all their eigenvalues in the interval [-2,2]

We completely describe all integer symmetric matrices that have all their eigenvalues in the interval [-2,2]. Along the way we classify all signed graphs, and then all charged signed graphs, having all their eigenvalues in this same interval. We then classify subsets of the above for which the integer symmetric matrices, signed graphs and charged signed graphs have all their eigenvalues in the open interval (-2,2).Comment: 33 pages, 18 figure

OB associations and giant molecular clouds in the galaxy

Giant molecular clouds (GMC's) are the sites of all OB star formation in the Galaxy. These OB stars typically form in large associations and photoionize the surrounding gas, eventually destroying the clouds from which they were born. CO surveys have revealed the distribution of GMC's in the Galaxy, and radio observations provide data on the distribution of associations. These results are extrapolated to determine Galactic mean distribution functions of each and then combined to determine how GMC's and OB associations are correlated. The resulting probability distribution of luminosity given cloud mass implies that although most of the molecular mass of the Galaxy is in massive star forming complexes, a large number of clouds above which massive star formation is extremely likely and abundant and below which it is almost certainly absent

Star Cluster Formation in Turbulent, Magnetized Dense Clumps with Radiative and Outflow Feedback

We present three Orion simulations of star cluster formation in a 1000 Msun, turbulent molecular cloud clump, including the effects of radiative transfer, protostellar outflows, and magnetic fields. Our simulations all use self-consistent turbulent initial conditions and vary the mean mass-to-flux ratio relative to the critical value over 2, 10, and infinity to gauge the influence of magnetic fields on star cluster formation. We find, in good agreement with previous studies, that magnetic fields of typically observed strengths lower the star formation rate by a factor of 2.4 and reduce the amount of fragmentation by a factor of 2 relative to the zero-field case. We also find that the field increases the characteristic sink particle mass, again by a factor of 2.4. The magnetic field also increases the degree of clustering in our simulations, such that the maximum stellar densities in the strong field case are higher than the others by again a factor of 2. This clustering tends to encourage the formation of multiple systems, which are more common in the rad-MHD runs than the rad-hydro run. The companion frequency in our simulations is consistent with observations of multiplicity in Class I sources, particularly for the strong field case. Finally, we find evidence of primordial mass segregation in our simulations reminiscent of that observed in star clusters like the Orion Nebula Cluster.Comment: 21 pages, 17 figures, accepted by MNRA

Symmetrizable integer matrices having all their eigenvalues in the interval [-2,2]

The adjacency matrices of graphs form a special subset of the set of all integer symmetric matrices. The description of which graphs have all their eigenvalues in the interval [-2,2] (i.e., those having spectral radius at most 2) has been known for several decades. In 2007 we extended this classification to arbitrary integer symmetric matrices. In this paper we turn our attention to symmetrizable matrices. We classify the connected nonsymmetric but symmetrizable matrices which have entries in $\Z$ that are maximal with respect to having all their eigenvalues in [-2,2]. This includes a spectral characterisation of the affine and finite Dynkin diagrams that are not simply laced (much as the graph result gives a spectral characterisation of the simply laced ones).Comment: 20 pages, 11 figure

Diabetes as a tracer condition in international benchmarking of health systems.

OBJECTIVE: To assess the performance of health systems using diabetes as a tracer condition. RESEARCH DESIGN AND METHODS: We generated a measure of "case-fatality" among young people with diabetes using the mortality-to-incidence ratio (M/I ratio) for 29 industrialized countries using published data on diabetes incidence and mortality. Standardized incidence rates for ages 0-14 years were extracted from the World Health Organization DiaMond study for the period 1990-1994; data on death from diabetes for ages 0-39 years were obtained from the World Health Organization mortality database and converted into age-standardized death rates for the period 1994-1998, using the European standard population. RESULTS: The M/I ratio varied >10-fold. These relative differences appear similar to those observed in cohort studies of mortality among young people with type 1 diabetes in five countries. A sensitivity analysis showed that using plausible assumptions about potential overestimation of diabetes as a cause of death and underestimation of incidence rates in the U.S. yields an M/I ratio that would still be twice as high as in the U.K. or Canada. CONCLUSIONS: The M/I ratio for diabetes provides a means of differentiating countries on quality of care for people with diabetes. It is solely an indicator of potential problems, a basis for stimulating more detailed assessments of whether such problems exist, and what can be done to address them