Journal Articles

Permanent URI for this collection

https://unbscholar.lib.unb.ca/handle/1882/12771

Articles. Typically the realization of research papers reporting original research findings published in a journal issue. (URI: http://purl.org/coar/resource_type/c_6501) Item types include:

  • editorial
  • journal article
    • corrigendum
    • data paper
    • research article
    • review article
    • software paper
  • letter to the editor

Browse

Browsing Journal Articles by Subject "Mathematics and Statistics"

Now showing 1 - 4 of 4
  • Thumbnail Image
    Item
    A folded model for compositional data analysis
    (Wiley, 2020) Tsagris, Michail; Stewart, Connie
    A folded type model is developed for analysing compositional data. The proposed model involves an extension of the α-transformation for compositional data and provides a new and flexible class of distributions for modelling data defined on the simplex sample space. Despite its rather seemingly complex structure, employment of the EM algorithm guarantees efficient parameter estimation. The model is validated through simulation studies and examples which illustrate that the proposed model performs better in terms of capturing the data structure, when compared to the popular logistic normal distribution, and can be advantageous over a similar model without folding.
  • Thumbnail Image
    Item
    An approach to measure distance between compositional diet estimates containing essential zeros
    (Taylor & Francis, 2016) Stewart, Connie
    For many applications involving compositional data, it is necessary to establish a valid measure of distance, yet when essential zeros are present traditional distance measures are problematic. In quantitative fatty acid signature analysis (QFASA), compositional diet estimates are produced that often contain many zeros. In order to test for a difference in diet between two populations of predators using the QFASA diet estimates, a legitimate measure of distance for use in the test statistic is necessary. Since ecologists using QFASA must first select the potential species of prey in the predator's diet, the chosen measure of distance should be such that the distance between samples does not decrease as the number of species considered increases, a property known in general as subcompositional coherence. In this paper we compare three measures of distance for compositional data capable of handling zeros, but not satisfying some of the well-accepted principles of compositional data analysis. For compositional diet estimates, the most relevant of these is the property of subcompositionally coherence and we show that this property may be approximately satisfied. Based on the results of a simulation study and an application to real-life QFASA diet estimates of grey seals, we recommend the chi-square measure of distance.
  • Thumbnail Image
    Item
    Gauge theory on noncommutative Riemannian principal bundles
    (Springer, 2021-10-11) Ćaćić, Branimir; Mesland, Bram
    We present a new, general approach to gauge theory on principal G-spectral triples, where G is a compact connected Lie group. We introduce a notion of vertical Riemannian geometry for G-C∗-algebras and prove that the resulting noncommutative orbitwise family of Kostant’s cubic Dirac operators defines a natural unbounded K K G-cycle in the case of a principal G-action. Then, we introduce a notion of principal G-spectral triple and prove, in particular, that any such spectral triple admits a canonical factorisation in unbounded K K G-theory with respect to such a cycle: up to a remainder, the total geometry is the twisting of the basic geometry by a noncommutative superconnection encoding the vertical geometry and underlying principal connection. Using these notions, we formulate an approach to gauge theory that explicitly generalises the classical case up to a groupoid cocycle and is compatible in general with this factorisation; in the unital case, it correctly yields a real affine space of noncommutative principal connections with affine gauge action. Our definitions cover all locally compact classical principal G-bundles and are compatible with θ-deformation; in particular, they cover the θ-deformed quaternionic Hopf fibration C∞(S7 θ ) ← C∞(S4 θ ) as a noncommutative principal SU(2)-bundle.
  • Thumbnail Image
    Item
    Geometric foundations for classical U(1)-gauge theory on noncommutative manifolds
    (Springer, 2024-08-22) Ćaćić, Branimir
    We systematically extend the elementary differential and Riemannian geometry of classical U(1)-gauge theory to the noncommutative setting by combining recent advances in noncommutative Riemannian geometry with the theory of coherent 2-groups. We show that Hermitian line bimodules with Hermitian bimodule connection over a unital pre-C∗-algebra with ∗-exterior algebra form a coherent 2-group, and we prove that weak monoidal functors between coherent 2-groups canonically define bar or involutive monoidal functors in the sense of Beggs–Majid and Egger, respectively. Using this, we prove that a suitable Hermitian line bimodule with Hermitian bimodule connection yields an essentially unique differentiable quantum principal U(1)-bundle with principal connection and vice versa; here, U(1) is q-deformed for q a numerical invariant of the bimodule connection. Finally, we formulate and solve the interrelated lifting problems for noncommutative Riemannian structure in terms of abstract Hodge star operators and formal spectral triples, respectively; all the while, we account precisely for emergent modular phenomena. Thus, the spin Dirac spectral triple on quantum CP1 does not lift to a non-pathological twisted spectral triple on 3-dimensional quantum SU(2), but its formal lift nonetheless induces Kaad–Kyed’s compact quantum metric space on quantum SU(2) for a canonical choice of parameters