Higher rank numerical ranges of normal matrices

The higher rank numerical range is closely connected to the construction of quantum error correction code for a noisy quantum channel. It is known that if a normal matrix $A \in M_n$ has eigenvalues $a_1, \..., a_n$, then its higher rank numerical range $\Lambda_k(A)$ is the intersection of convex polygons with vertices $a_{j_1}, \..., a_{j_{n-k+1}}$, where $1 \le j_1 < \... < j_{n-k+1} \le n$. In this paper, it is shown that the higher rank numerical range of a normal matrix with $m$ distinct eigenvalues can be written as the intersection of no more than $\max\{m,4\}$ closed half planes. In addition, given a convex polygon ${\mathcal P}$ a construction is given for a normal matrix $A \in M_n$ with minimum $n$ such that $\Lambda_k(A) = {\mathcal P}$. In particular, if ${\mathcal P}$ has $p$ vertices, with $p \ge 3$, there is a normal matrix $A \in M_n$ with $n \le \max\left\{p+k-1, 2k+2 \right\}$ such that $\Lambda_k(A) = {\mathcal P}$.Comment: 12 pages, 9 figures, to appear in SIAM Journal on Matrix Analysis and Application

Feeding Patterns of Barren-ground Grizzly Bears in the Central Canadian Arctic

We collected 169 grizzly bear scats between 1994 and 1997 to determine the dietary habits of barren-ground grizzly bears (Ursus arctos) inhabiting Canada's central Arctic. From personal observations and fecal analysis, we concluded that barren-ground grizzly bears lead a predominantly carnivorous lifestyle and are effective predators of caribou (Rangifer tarandus). Caribou was a predominant diet item during spring, mid-summer, and fall. During early summer, grizzly bears foraged primarily on green vegetation. Berries increased in dietary importance in late summer. Declines in the caribou population of our study area or long-term absences of caribou may threaten the local grizzly bear population.On a prélevé 169 excréments de grizzli entre 1994 et 1997 afin de déterminer les habitudes alimentaires du grizzli de Richardson (Ursus arctos) qui vit dans le centre de l'Arctique canadien. En s'appuyant sur des observations personnelles et un examen coproscopique, on conclut que le grizzli de Richardson est un animal largement carnassier et qu'il est un prédateur efficace du caribou (Rangifer tarandus). Ce dernier constituait un aliment prédominant au printemps, au milieu de l'été et en automne. Au début de l'été, le grizzli se nourrissait surtout de végétation verte. À la fin de l'été, les baies prenaient plus d'importance dans son alimentation. Le déclin de la population du caribou dans la zone d'étude ou son absence prolongée peut constituer une menace pour la population locale de grizzlis

Geometric motivic Poincar\'e series of quasi-ordinary singularities

The geometric motivic Poincar\'e series of a germ $(S,0)$ of complex algebraic variety takes into account the classes in the Grothendieck ring of the jets of arcs through $(S,0)$. Denef and Loeser proved that this series has a rational form. We give an explicit description of this invariant when $(S,0)$ is an irreducible germ of quasi-ordinary hypersurface singularity in terms of the Newton polyhedra of the logarithmic jacobian ideals. These ideals are determined by the characteristic monomials of a quasi-ordinary branch parametrizing $(S,0)$

Predictive Modeling in Post-reform Marketplace

Healthcare reform changes everything. Annual and lifetime dollar limits, underwriting, and preexisting condition exclusion will all be eliminated by 2014. Insurers must offer coverage to any individual regardless of their health status. An overwhelming majority of those who will be mandated to purchase individual insurance is currently uninsured or under-insured. Insurers have insufficient internal data to estimate costs for this new population. A study on how to apply predictive modeling to deal with risks and uncertainties facing healthcare industry in the post-reform marketplace is presented in this article

Movements of Subadult Male Grizzly Bears, Ursus arctos, in the Central Canadian Arctic

Between May 1995 and June 1999, we equipped eight subadult male (3-5 yrs old) Grizzly Bears (Ursus arctos) with satellite radio-collars within a study area of 235,000 km2, centred 400 km northeast of Yellowknife, Northwest Territories, Canada. Subadult male annual home ranges were extraordinarily large (average = 11,407 km2, SE = 3849) due, in part, to their movement's occasional linear directionality. We believe their long-range linear movements may reflect some individuals tracking the migration of Caribou (Rangifer tarandus). Seasonal daily movement patterns were similar to adult males that were previously reported. The areas used by these bears are the largest ranges reported for any Grizzly Bears and the scale of their movements may put individual bears in contact with humans even when developments are hundreds of kilometres from the central home range of an animal

Limits on the Dipole Moments of the τ\tau-Lepton via the Process $e^{+}e^{-}\to \tau^+ \tau^- \gamma in a Left-Right Symmetric Model

Limits on the anomalous magnetic moment and the electric dipole moment of the $\tau$ lepton are calculated through the reaction $e^{+}e^{-}\to \tau^+ \tau^- \gamma$ at the $Z_1$-pole and in the framework of a left-right symmetric model. The results are based on the recent data reported by the L3 Collaboration at CERN LEP. Due to the stringent limit of the model mixing angle $\phi$, the effect of this angle on the dipole moments is quite small.Comment: 15 pages, 3 figure

Population Viability of Barren-ground Grizzly Bears in Nunavut and the Northwest Territories

We modelled probabilities of population decline as a function of annual kill for a population of barren-ground grizzly bears (Ursus arctos) inhabiting Nunavut and the Northwest Territories, Canada. Our results suggest that the population is at risk of decline, especially if annual removal rates increase from the 42-year mean of 13.4 bears per year. Adding six bears to the mean annual kill results in a greater than 40% chance of a decrease by one-quarter in population size over the next 50 years, compared to a 10% chance with the current level of human-caused mortality. Additional mortalities may result from increased problem behaviour by bears at mine sites or hunt and exploration camps, given recent increases in human activity in the region, and may already be present as unreported mortality. We believe any increase in current harvest quotas would considerably lessen conservation prospects for the population.On a simulé les probabilités de baisse de la population en fonction du prélèvement annuel dans le cadre de la chasse pour une population de grizzlis de la toundra (Ursus arctos) habitant le Nunavut et les Territoires du Nord-Ouest, au Canada. Nos résultats suggèrent que la population risque de décliner, surtout si les taux de prélèvement augmentent par rapport à la moyenne établie sur 42 ans qui est de 13,4 ours par an. Le fait d'ajouter 6 ours au prélèvement de chasse annuel augmente à plus de 40 % le risque que la population décline d'un quart au cours des prochains 50 ans, par rapport à 10 % dans le cas du niveau actuel de mortalité provoquée par les humains. Vu l'augmentation récente de l'activité anthropique dans la région, d'autres individus pourraient être abattus à cause du nombre croissant de comportements problématiques des ours résidant à des sites miniers et à des campements d'exploration, et il est possible que ce phénomène existe déjà mais que les morts ne soient pas rapportées. Notre opinion est que toute augmentation des quotas actuels de prélèvement réduirait considérablement les perspectives de conservation pour la population

The Significance of the CC-Numerical Range and the Local CC-Numerical Range in Quantum Control and Quantum Information

This paper shows how C-numerical-range related new strucures may arise from practical problems in quantum control--and vice versa, how an understanding of these structures helps to tackle hot topics in quantum information. We start out with an overview on the role of C-numerical ranges in current research problems in quantum theory: the quantum mechanical task of maximising the projection of a point on the unitary orbit of an initial state onto a target state C relates to the C-numerical radius of A via maximising the trace function |\tr \{C^\dagger UAU^\dagger\}|. In quantum control of n qubits one may be interested (i) in having U\in SU(2^n) for the entire dynamics, or (ii) in restricting the dynamics to {\em local} operations on each qubit, i.e. to the n-fold tensor product SU(2)\otimes SU(2)\otimes >...\otimes SU(2). Interestingly, the latter then leads to a novel entity, the {\em local} C-numerical range W_{\rm loc}(C,A), whose intricate geometry is neither star-shaped nor simply connected in contrast to the conventional C-numerical range. This is shown in the accompanying paper (math-ph/0702005). We present novel applications of the C-numerical range in quantum control assisted by gradient flows on the local unitary group: (1) they serve as powerful tools for deciding whether a quantum interaction can be inverted in time (in a sense generalising Hahn's famous spin echo); (2) they allow for optimising witnesses of quantum entanglement. We conclude by relating the relative C-numerical range to problems of constrained quantum optimisation, for which we also give Lagrange-type gradient flow algorithms.Comment: update relating to math-ph/070200

Templeting of Thin Films Induced by Dewetting on Patterned Surfaces

The instability, dynamics and morphological transitions of patterns in thin liquid films on periodic striped surfaces (consisting of alternating less and more wettable stripes) are investigated based on 3-D nonlinear simulations that account for the inter-site hydrodynamic and surface-energetic interactions. The film breakup is suppressed on some potentially destabilizing nonwettable sites when their spacing is below a characteristic lengthscale of the instability, the upper bound for which is close to the spinodal lengthscale. The thin film pattern replicates the substrate surface energy pattern closely only when, (a) the periodicity of substrate pattern matches closely with the characteristic lengthscale, and (b) the stripe-width is within a range bounded by a lower critical length, below which no heterogeneous rupture occurs, and an upper transition length above which complex morphological features bearing little resemblance to the substrate pattern are formed.Comment: 5 pages TeX (REVTeX 4), other comments: submitted to Phys. Rev.Let