The Influence of Quadrature Errors on Isogeometric Mortar Methods

Mortar methods have recently been shown to be well suited for isogeometric analysis. We review the recent mathematical analysis and then investigate the variational crime introduced by quadrature formulas for the coupling integrals. Motivated by finite element observations, we consider a quadrature rule purely based on the slave mesh as well as a method using quadrature rules based on the slave mesh and on the master mesh, resulting in a non-symmetric saddle point problem. While in the first case reduced convergence rates can be observed, in the second case the influence of the variational crime is less significant

Two-Qubit Separability Probabilities and Beta Functions

Due to recent important work of Zyczkowski and Sommers (quant-ph/0302197 and quant-ph/0304041), exact formulas are available (both in terms of the Hilbert-Schmidt and Bures metrics) for the (n^2-1)-dimensional and (n(n-1)/2-1)-dimensional volumes of the complex and real n x n density matrices. However, no comparable formulas are available for the volumes (and, hence, probabilities) of various separable subsets of them. We seek to clarify this situation for the Hilbert-Schmidt metric for the simplest possible case of n=4, that is, the two-qubit systems. Making use of the density matrix (rho) parameterization of Bloore (J. Phys. A 9, 2059 [1976]), we are able to reduce each of the real and complex volume problems to the calculation of a one-dimensional integral, the single relevant variable being a certain ratio of diagonal entries, nu = (rho_{11} rho_{44})/{rho_{22} rho_{33})$. The associated integrand in each case is the product of a known (highly oscillatory near nu=1) jacobian and a certain unknown univariate function, which our extensive numerical (quasi-Monte Carlo) computations indicate is very closely proportional to an (incomplete) beta function B_{nu}(a,b), with a=1/2, b=sqrt{3}in the real case, and a=2 sqrt{6}/5, b =3/sqrt{2} in the complex case. Assuming the full applicability of these specific incomplete beta functions, we undertake separable volume calculations.Comment: 17 pages, 4 figures, paper is substantially rewritten and reorganized, with the quasi-Monte Carlo integration sample size being greatly increase

Evolutionary patterns of morphometrics, allozymes and mitochondrial DNA in thrashers (Genus Toxostoma)

We examined patterns of variation in skeletal morphometrics (29 characters), allozymes (34 loci), mitochondrial DNA (mtDNA) restriction sites (n = 74) and fragments (n = 395), and mtDNA sequences (1,739 bp from cytochrome b, ND2, ND6, and the control region) among all species of Toxostoma. The phenetic pattern of variation in skeletal morphometrics generally matched traditional taxonomic groupings (based on plumage patterns) with the exceptions of T. redivivum, which because of its large size clusters outside of its proper evolutionary group (lecontei), and T. occelatum, which did not cluster with T. curvirostre. Skull characters contributed highly to species discrimination, suggesting that unique feeding adaptations arose in different species groups. Although genetic variation was detected at isozyme loci (average heterozygosity = 3.6%), these data yielded little phylogenetic resolution. Similarly, mtDNA restriction sites were relatively uninformative; hence, phylogenetic conclusions were based on sequence data. Phylogenetic analyses confirmed the monophyly of these traditionally recognized assemblages: rufum group (T. rufum, T. longirostre, and T. guttatum), lecontei group (T. lecontei, T. crissale, and T. redivivum), and cinereum group (T. bendirei and T. cinereum). The cinereum and lecontei groups appear to be sister lineages. Monophyly of the curvirostre group (which also includes T. occelatum) was not confirmed. Sequence data suggest that T. occelatum and T. curvirostre, which differ by 7.7% sequence divergence, are probably most closely related to the rufum group. Toxostoma rufum and T. longirostre have similar external appearances and differ by 5.0%. Toxostoma guttatum is restricted to Cozumel Island and often is considered a subspecies of T. longirostre; it differs by more than 5% from the other two members of the rufum group and is a distinct species constituting the basal member of this group. The phenotypically distinctive T. bendirei and T. cinereum differ in sequence divergence by only 1.6%. Overall, mtDNA distances computed from coding genes (mean 8.5%) exceeded distances computed from the control region (mean 7.6%), contrary to expectation. Because neither allozymes nor mtDNA could unambiguously resolve the placement of T. occelatum and T. curvirostre, a scenario involving contemporaneous speciation is suggested. Application of a molecular clock suggested that most speciation occurred in the late Pliocene or early Pleistocene

Bures volume of the set of mixed quantum states

We compute the volume of the N^2-1 dimensional set M_N of density matrices of size N with respect to the Bures measure and show that it is equal to that of a N^2-1 dimensional hyper-halfsphere of radius 1/2. For N=2 we obtain the volume of the Uhlmann 3-D hemisphere, embedded in R^4. We find also the area of the boundary of the set M_N and obtain analogous results for the smaller set of all real density matrices. An explicit formula for the Bures-Hall normalization constants is derived for an arbitrary N.Comment: 15 revtex pages, 2 figures in .eps; ver. 3, Eq. (4.19) correcte

Minimization of the receiver cost in an all-optical ring with a limited number of wavelengths

A new all-optical node architecture, known as \emph{Packet Optical Add-Drop Multiplexer} (POADM), may lead to a considerable cost reduction for the infrastructure of the all-optical metropolitan rings if associated with proper dimensioning studies. We present a dimensioning problem which consists of minimizing the total number of receivers located in POADMs for a metropolitan all-optical ring with a fixed number of wavelengths and a given traffic matrix. We prove that this problem is NP-complete and provide a heuristic. The heuristic principle is to match and to group transmissions instead of considering them independently. We justify the transmission group matching approach by confronting the results of our algorithm with its simplified version. The results obtained allow us to recommend the heuristic in the planning of POADM configurations in all-optical rings with a limited number of wavelengths

Effective lattice theories for Polyakov loops

We derive effective actions for SU(2) Polyakov loops using inverse Monte Carlo techniques. In a first approach, we determine the effective couplings by requiring that the effective ensemble reproduces the single-site distribution of the Polyakov loops. The latter is flat below the critical temperature implying that the (untraced) Polyakov loop is distributed uniformly over its target space, the SU(2) group manifold. This allows for an analytic determination of the Binder cumulant and the distribution of the mean-field, which turns out to be approximately Gaussian. In a second approach, we employ novel lattice Schwinger-Dyson equations which reflect the SU(2) x SU(2) invariance of the functional Haar measure. Expanding the effective action in terms of SU(2) group characters makes the numerics sufficiently stable so that we are able to extract a total number of 14 couplings. The resulting action is short-ranged and reproduces the Yang-Mills correlators very well.Comment: 27 pages, 8 figures, v2: method refined, chapter and references adde

Sampling locality is more detectable than taxonomy or ecology in the gut microbiota of the brood-parasitic Brown-headed Cowbird (Molothrus ater)

Brown-headed Cowbirds (Molothrus ater) are the most widespread avian brood parasite in North America, laying their eggs in the nests of approximately 250 host species that raise the cowbird nestlings as their own. It is currently unknown how these heterospecific hosts influence the cowbird gut microbiota relative to other factors, such as the local environment and genetics. We test a Nature Hypothesis (positing the importance of cowbird genetics) and a Nurture Hypothesis (where the host parents are most influential to cowbird gut microbiota) using the V6 region of 16S rRNA as a microbial fingerprint of the gut from 32 cowbird samples and 16 potential hosts from nine species. We test additional hypotheses regarding the influence of the local environment and age of the birds.We found no evidence for the Nature Hypothesis and little support for the Nurture Hypothesis. Cowbird gut microbiota did not forma clade, but neither did members of the host species. Rather, the physical location, diet and age of the bird, whether cowbird or host, were the most significant categorical variables. Thus, passerine gut microbiota may be most strongly influenced by environmental factors. To put this variation in a broader context, we compared the bird data to a fecal microbiota dataset of 38 mammal species and 22 insect species. Insects were always the most variable; on some axes, we found more variation within cowbirds than across all mammals. Taken together, passerine gut microbiota may be more variable and environmentally determined than other taxonomic groups examined to date. © 2014 Hird et al

Hall Normalization Constants for the Bures Volumes of the n-State Quantum Systems

We report the results of certain integrations of quantum-theoretic interest, relying, in this regard, upon recently developed parameterizations of Boya et al of the n x n density matrices, in terms of squared components of the unit (n-1)-sphere and the n x n unitary matrices. Firstly, we express the normalized volume elements of the Bures (minimal monotone) metric for n = 2 and 3, obtaining thereby "Bures prior probability distributions" over the two- and three-state systems. Then, as an essential first step in extending these results to n > 3, we determine that the "Hall normalization constant" (C_{n}) for the marginal Bures prior probability distribution over the (n-1)-dimensional simplex of the n eigenvalues of the n x n density matrices is, for n = 4, equal to 71680/pi^2. Since we also find that C_{3} = 35/pi, it follows that C_{4} is simply equal to 2^{11} C_{3}/pi. (C_{2} itself is known to equal 2/pi.) The constant C_{5} is also found. It too is associated with a remarkably simple decompositon, involving the product of the eight consecutive prime numbers from 2 to 23. We also preliminarily investigate several cases, n > 5, with the use of quasi-Monte Carlo integration. We hope that the various analyses reported will prove useful in deriving a general formula (which evidence suggests will involve the Bernoulli numbers) for the Hall normalization constant for arbitrary n. This would have diverse applications, including quantum inference and universal quantum coding.Comment: 14 pages, LaTeX, 6 postscript figures. Revised version to appear in J. Phys. A. We make a few slight changes from the previous version, but also add a subsection (III G) in which several variations of the basic problem are newly studied. Rather strong evidence is adduced that the Hall constants are related to partial sums of denominators of the even-indexed Bernoulli numbers, although a general formula is still lackin

A priori probability that a qubit-qutrit pair is separable

We extend to arbitrarily coupled pairs of qubits (two-state quantum systems) and qutrits (three-state quantum systems) our earlier study (quant-ph/0207181), which was concerned with the simplest instance of entangled quantum systems, pairs of qubits. As in that analysis -- again on the basis of numerical (quasi-Monte Carlo) integration results, but now in a still higher-dimensional space (35-d vs. 15-d) -- we examine a conjecture that the Bures/SD (statistical distinguishability) probability that arbitrarily paired qubits and qutrits are separable (unentangled) has a simple exact value, u/(v Pi^3)= >.00124706, where u = 2^20 3^3 5 7 and v = 19 23 29 31 37 41 43 (the product of consecutive primes). This is considerably less than the conjectured value of the Bures/SD probability, 8/(11 Pi^2) = 0736881, in the qubit-qubit case. Both of these conjectures, in turn, rely upon ones to the effect that the SD volumes of separable states assume certain remarkable forms, involving "primorial" numbers. We also estimate the SD area of the boundary of separable qubit-qutrit states, and provide preliminary calculations of the Bures/SD probability of separability in the general qubit-qubit-qubit and qutrit-qutrit cases.Comment: 9 pages, 3 figures, 2 tables, LaTeX, we utilize recent exact computations of Sommers and Zyczkowski (quant-ph/0304041) of "the Bures volume of mixed quantum states" to refine our conjecture

Probing orbital ordering in LaVO3_{3} epitaxial films by Raman scattering

Single crystals of Mott-Hubbard insulator LaVO3 exhibit spin and orbital ordering along with a structural change below ≈140 K. The occurrence of orbital ordering in epitaxial LaVO3films has, however, been little investigated. By temperature-dependent Raman scatteringspectroscopy, we probed and evidenced the transition to orbital ordering in epitaxial LaVO3film samples fabricated by pulsed-laser deposition. This opens up the possibility to explore the influence of different epitaxial strain (compressive vs. tensile) and of epitaxy-induced distortions of oxygen octahedra on the orbital ordering, in epitaxial perovskite vanadate films