Quantum Doubles from a Class of Noncocommutative Weak Hopf Algebras

The concept of biperfect (noncocommutative) weak Hopf algebras is introduced and their properties are discussed. A new type of quasi-bicrossed products are constructed by means of weak Hopf skew-pairs of the weak Hopf algebras which are generalizations of the Hopf pairs introduced by Takeuchi. As a special case, the quantum double of a finite dimensional biperfect (noncocommutative) weak Hopf algebra is built. Examples of quantum doubles from a Clifford monoid as well as a noncommutative and noncocommutative weak Hopf algebra are given, generalizing quantum doubles from a group and a noncommutative and noncocommutative Hopf algebra, respectively. Moreover, some characterisations of quantum doubles of finite dimensional biperfect weak Hopf algebras are obtained.Comment: LaTex 18 pages, to appear in J. Math. Phys. (To compile, need pb-diagram.sty, pb-lams.sty, pb-xy.sty and lamsarrow.sty

Team to Market (T2M): Creating High Performance Teams in the Digital Age

1. Teams are the essential means of product or service delivery and the fundamental building blocks of modern organisations. An effective team can produce results far outperforming a collection of even the most talented individuals when team members coalesce and jell into a single, well-functioning, fully-aligned organism. This report advances the notion of “Team to Market” (T2M) to help business leaders and knowledge workers understand, create and lead high performance teams in the digital age

The digital transformation of business models in the creative industries: A holistic framework and emerging trends

This paper examines how digital technologies facilitate business model innovations in the creative industries. Through a systematic literature review, a holistic business model framework is developed, which is then used to analyse the empirical evidence from the creative industries. The research found that digital technologies have facilitated pervasive changes in business models, and some significant trends have emerged. However, the reconfigured business models are often not ‘new’ in the unprecedented sense. Business model innovations are primarily reflected in using digital technologies to enable the deployment of a wider range of business models than previously available to a firm. A significant emerging trend is the increasing adoption of multiple business models as a portfolio within one firm. This is happening in firms of all sizes, when one firm uses multiple business models to servedifferent markets segments, sell different products, or engage with multi-sided markets, or to use different business models over time. The holistic business model framework is refined and extended through a recursive learning process, which can serve both as a cognitive instrument for understanding business models and a planning tool for business model innovations. The paper contributes to our understanding of the theory of business models and how digital technologies facilitate business model innovations in the creative industries. Three new themes for future research are highlighted

Empirical risk minimization as parameter choice rule for general linear regularization methods.

We consider the statistical inverse problem to recover f from noisy measurements Y = Tf + sigma xi where xi is Gaussian white noise and T a compact operator between Hilbert spaces. Considering general reconstruction methods of the form (f) over cap (alpha) = q(alpha) (T*T)T*Y with an ordered filter q(alpha), we investigate the choice of the regularization parameter alpha by minimizing an unbiased estiate of the predictive risk E[parallel to T f - T (f) over cap (alpha)parallel to(2)]. The corresponding parameter alpha(pred) and its usage are well-known in the literature, but oracle inequalities and optimality results in this general setting are unknown. We prove a (generalized) oracle inequality, which relates the direct risk E[parallel to f - (f) over cap (alpha pred)parallel to(2)] with the oracle prediction risk inf(alpha>0) E[parallel to T f - T (f) over cap (alpha)parallel to(2)]. From this oracle inequality we are then able to conclude that the investigated parameter choice rule is of optimal order in the minimax sense. Finally we also present numerical simulations, which support the order optimality of the method and the quality of the parameter choice in finite sample situations

Sequential Refinement Solver using Space-Time Domain Decomposition for Non-linear Multiphase Flow Problems

Convergence failure and slow convergence rate are among the biggest challenges with solving the system of non-linear equations numerically. While using strictly small time steps sizes and unconditionally stable fully implicit scheme mitigate the problem, the computational load becomes enormous. We introduce a sequential local refinement scheme in space-time domain that improves convergence rate and prevents convergence failure while not restricting to small time step, thus boosting computational efficiency. We rely on the non-linear two-phase flow model. The algorithm starts by solving the coarsest mesh. Then regions with certain features such as saturation front is refined to the finest resolution sequentially. Such process prevents convergence failure. After each refinement, the solution from the previous mesh is used to estimate initial guess of the current mesh for faster convergence. Numerical results are presented to confirm accuracy of our algorithm as compared to the traditional fine time step approach. We also observe 5 times speedup in the runtime by using our algorithm

Matter Effects in Active-Sterile Solar Neutrino Oscillations

The matter effects for solar neutrino oscillations are studied in a general scheme with an arbitrary number of sterile neutrinos, without any constraint on the mixing, assuming only a realistic hierarchy of neutrino squared-mass differences in which the smallest squared-mass difference is effective in solar neutrino oscillations. The validity of the analytic results are illustrated with a numerical solution of the evolution equation in three examples of the possible mixing matrix in the simplest case of four-neutrino mixing.Comment: 26 pages. Final version published in Phys. Rev. D80 (2009) 11300