The topological dimension of type I C*-algebras

While there is only one natural dimension concept for separable, metric spaces, the theory of dimension in noncommutative topology ramifies into different important concepts. To accommodate this, we introduce the abstract notion of a noncommutative dimension theory by proposing a natural set of axioms. These axioms are inspired by properties of commutative dimension theory, and they are for instance satisfied by the real and stable rank, the decomposition rank and the nuclear dimension. We add another theory to this list by showing that the topological dimension, as introduced by Brown and Pedersen, is a noncommutative dimension theory of type I C*-algebras. We also give estimates of the real and stable rank of a type I C*-algebra in terms of its topological dimension.Comment: 20 pages; minor correction

Dimerization of inositol monophosphatase Mycobacterium tuberculosis SuhB is not constitutive, but induced by binding of the activator Mg2+

Background The cell wall of Mycobacterium tuberculosis contains a wide range of phosphatidyl inositol-based glycolipids that play critical structural roles and, in part, govern pathogen-host interactions. Synthesis of phosphatidyl inositol is dependent on free myo-inositol, generated through dephosphorylation of myo-inositol-1-phosphate by inositol monophosphatase (IMPase). Human IMPase, the putative target of lithium therapy, has been studied extensively, but the function of four IMPase-like genes in M. tuberculosis is unclear. Results We determined the crystal structure, to 2.6 Å resolution, of the IMPase M. tuberculosis SuhB in the apo form, and analysed self-assembly by analytical ultracentrifugation. Contrary to the paradigm of constitutive dimerization of IMPases, SuhB is predominantly monomeric in the absence of the physiological activator Mg2+, in spite of a conserved fold and apparent dimerization in the crystal. However, Mg2+ concentrations that result in enzymatic activation of SuhB decisively promote dimerization, with the inhibitor Li+ amplifying the effect of Mg2+, but failing to induce dimerization on its own. Conclusion The correlation of Mg2+-driven enzymatic activity with dimerization suggests that catalytic activity is linked to the dimer form. Current models of lithium inhibition of IMPases posit that Li+ competes for one of three catalytic Mg2+ sites in the active site, stabilized by a mobile loop at the dimer interface. Our data suggest that Mg2+/Li+-induced ordering of this loop may promote dimerization by expanding the dimer interface of SuhB. The dynamic nature of the monomer-dimer equilibrium may also explain the extended concentration range over which Mg2+ maintains SuhB activity

Fredholm Modules on P.C.F. Self-Similar Fractals and their Conformal Geometry

The aim of the present work is to show how, using the differential calculus associated to Dirichlet forms, it is possible to construct Fredholm modules on post critically finite fractals by regular harmonic structures. The modules are d-summable, the summability exponent d coinciding with the spectral dimension of the generalized laplacian operator associated with the regular harmonic structures. The characteristic tools of the noncommutative infinitesimal calculus allow to define a d-energy functional which is shown to be a self-similar conformal invariant.Comment: 16 page

The application of big data and AI in the upstream supply chain

The use of Big Data has grown in popularity in organisations to exploit the purpose of their primary data to enhance their competitiveness. In conjunction with the increased use of Big Data, there has also been a growth in the use of Artificial Intelligence (AI) to analyse the vast amounts of data generated and provide a mechanism for locating and constructing useable patterns that organisations can incorporate in their supply chain strategy programme. As these organisations embrace the use of technology and embed this in their supply chain strategy, there are questions as to how this may affect their upstream supply chains especially with regards to how SME’s may be able to cope with the potential changes. There exists the opportunity to conduct further research into this area, mainly focusing on three key industry sectors of aerospace, rail and automotive supply chains.N/

Temperature dependence of the Casimir effect between metallic mirrors

We calculate the Casimir force and free energy for plane metallic mirrors at non-zero temperature. Numerical evaluations are given with temperature and conductivity effects treated simultaneously. The results are compared with the approximation where both effects are treated independently and the corrections simply multiplied. The deviation between the exact and approximated results takes the form of a temperature dependent function for which an analytical expression is given. The knowledge of this function allows simple and accurate estimations at the % level.Comment: 8 pages, 4 figures, uses RevTe

Nonstable K-Theory for graph algebras

We compute the monoid V (LK(E)) of isomorphism classes of finitely generated projective modules over certain graph algebras LK(E), and we show that this monoid satisfies the refinement property and separative cancellation. We also show that there is a natural isomorphism between the lattice of graded ideals of LK(E) and the lattice of order-ideals of V (LK(E)). When K is the field C of complex numbers, the algebra LC(E) is a dense subalgebra of the graph C -algebra C (E), and we show that the inclusion map induces an isomorphism between the corresponding monoids. As a consequence, the graph C*-algebra of any row-finite graph turns out to satisfy the stable weak cancellation propert

Classification of graph C*-algebras with no more than four primitive ideals

We describe the status quo of the classification problem of graph C*-algebras with four primitive ideals or less

Loop effects and non-decoupling property of SUSY QCD in gb→tH−g b\to tH^{-}

One-loop SUSY QCD radiative correction to $gb \to tH^{-}$ cross section is calculated in the Minimal Supersymmetric Standard Model. We found that SUSY QCD is non-decoupling if the gluino mass and the parameter $\mu$, $A_t$ or $A_b$ are at the same order and get large. The non-decoupling contribution can be enhanced by large $\tan\beta$ and therefore large corrections to the hadronic production rates at the Tevatron and LHC are expected in the large $\tan\beta$ limit. The fundamental reason for such non-decoupling behavior is found to be some couplings in the loops being proportional to SUSY mass parameters.Comment: 15 pages, 5 PS figures. A proof of non-decouplings of SUSY-QCD, Comments on corresponding QCD correction and references adde

Symmetries and the identity of physical states

The paper proposes a combined account of identity for physical states and direct empirical significance for symmetries according to which symmetry-related state variables designate distinct physical states if and only if the symmetry that relates them has direct empirical significance. Strengthening an earlier result, I show that, given this combined account, the local gauge symmetries in our leading contemporary theories of particle physics do not have any direct empirical significance