Integral Modular Categories of Frobenius-Perron Dimension <Emphasis Type="Italic">pq</Emphasis><Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

Integral modular categories of Frobenius-Perron dimension pq ⁿ , where p and q are primes, are considered. It is already known that such categories are group-theoretical in the cases of 0 ≤ n ≤ 4. In the general case we determine that these categories are either group-theoretical or contain a Tannakian subcategory of dimension q ⁱ for i > 1. We then show that all integral modular categories \(\mathcal {C}\) with \(\text {FPdim}(\mathcal {C})=pq^{5}\) are group-theoretical, and, if in addition p < q, all with \(\text {FPdim}(\mathcal {C})=pq^{6}\) or pq ⁷ are group-theoretical. In the process we generalize an existing criterion for an integral modular category to be group-theoretical.     

A new look at Bergström’s theorem on convergence in distribution for sums of dependent random variables

In his 1972Periodica Mathematica Hungarica paper, H. Bergström stated a theorem on convergence in distribution for triangular arrays of dependent random variables satisfying, a ?-mixing condition. A gap in his proof of this theorem is explained and a more general version is proved under weakened hypotheses. The method used consists of comparisons between the given array and associated arrays which are parameterized by a truncation variable. In addition to the main theorem, this method yields a proof of equality of limiting finite-dimensional distributions for processes generated by the given associated arrays as well as the result that if a limit distribution for the centered row sums does exist, it must be infinitely divisible. Several corollaries to the main theorem specialize this result for convergence to distributions within certain subclasses of the infinitely divisible laws.     

Partition Complete Boolean Algebras and Almost Compact Cardinals

For an infinite cardinal K a stronger version of K-distributivity for Boolean algebras, called k-partition completeness, is defined and investigated (e. g. every K-Suslin algebra is a K-partition complete Boolean algebra). It is shown that every k-partition complete Boolean algebra is K-weakly representable, and for strongly inaccessible K these concepts coincide. For regular K ≥ u, it is proved that an atomless K-partition complete Boolean algebra is an updirected union of basic K-tree algebras. Using K-partition completeness, the concept of γ-almost compactness is introduced for γ ≥ K. For strongly inaccessible K we show that K is K-almost compact iff K is weakly compact, and if K is 2^K-almost compact, then K is measurable. Further K is strongly compact iff it is γ-almost compact for all γ ≥ K.     

Non-parametric efficiency, progress and regress measures for panel data: Methodological aspects

This purely methodological paper deals with the rôle of time in non-parametric efficiency analysis. Using both FDH and DEA technologies, it first shows how each observation in a panel can be characterized in efficiency terms vis-à-vis three different kinds of frontiers: (i) ‘contemporaneous’, (ii) ‘sequential’, and (iii) ‘intertemporal’. These are then compared with window analysis. Next, frontier shifts ‘outward’ and ‘inward’, interpreted as progress or regress are considered for the two kinds of technologies, and computational methods are described in detail for evaluating such shifts in either case. These are also contrasted with what is measured by the ‘Malmquist’ productivity index. Finally, an alternative way of identifying progress and regress, independent of the frontier notion and referring instead to some ‘benchmark’ notion, is extended here to panel data.     

Comments on “quantum theory does not require action at a distance”

Kraus claims that the argument for action at a distance depends upon the classical prejudice that a measurement always measures something that already exists. It is shown that in the example considered by Kraus no assumption about pre-existing results is needed. A criterion proposed by Kraus for a theory to be compatible with locality is shown to be untenable.     

On the Coriolis effect in acoustic waveguides

Rotation of an elastic medium gives rise to a shift of frequency of its acoustic modes, i.e., the time-period vibrations that exist in it. This frequency shift is investigated by applying perturbation theory in the regime of small ratios of the rotation velocity and the frequency of the acoustic mode. In an expansion of the relative frequency shift in powers of this ratio, upper bounds are derived for the first-order and the second-order terms. The derivation of the theoretical upper bounds of the first-order term is presented for linear vibration modes as well as for stable nonlinear vibrations with periodic time dependence that can be represented by a Fourier series.     

Deficiency of optineurin enhances osteoclast differentiation by attenuating the NRF2-mediated antioxidant response

Abnormally increased resorption contributes to bone degenerative diseases such as Paget’s disease of bone (PDB) through unclear mechanisms. Recently, the optineurin (OPTN) gene has been implicated in PDB, and global OPTN knockout mice (Optn^−/−) were shown to exhibit increased formation of osteoclasts (osteoclastogenesis). Growing evidence, including our own, has demonstrated that intracellular reactive oxygen species (ROS) stimulated by receptor activator of nuclear factor kappa-B ligand (RANKL) can act as signaling molecules to promote osteoclastogenesis. Here, we report that OPTN interacts with nuclear factor erythroid-derived factor 2-related factor 2 (NRF2), the master regulator of the antioxidant response, defining a pathway through which RANKL-induced ROS could be regulated for osteoclastogenesis. In this study, monocytes from Optn^−/− and wild-type (Optn^+/+) mice were utilized to differentiate into osteoclasts, and both qRT-PCR and tartrate-resistant acid phosphatase (TRAP) staining showed that the Optn^−/− monocytes exhibited enhanced osteoclastogenesis compared to the Optn^+/+ cells. CellROX^® staining, qRT-PCR, and Western blotting indicated that OPTN deficiency reduced the basal expression of Nrf2, inhibited the expression of NRF2-responsive antioxidants, and increased basal and RANKL-induced intracellular ROS levels, leading to enhanced osteoclastogenesis. Coimmunoprecipitation (co-IP) showed direct interaction, and immunofluorescence staining showed perinuclear colocalization of the OPTN-NRF2 granular structures during differentiation. Finally, curcumin and the other NRF2 activators attenuated the hyperactive osteoclastogenesis induced by OPTN deficiency. Collectively, our findings reveal a novel OPTN-mediated mechanism for regulating the NRF2-mediated antioxidant response in osteoclasts and extend the therapeutic potential of OPTN in the aging process resulting from ROS-triggered oxidative stress, which is associated with PDB and many other degenerative diseases.Subject terms: Mechanisms of disease, Stress signalling     

Coordination and Redox Isomerization in the Reduction of a Uranium(III) Monoarene Complex

Synthetic studies on the redox chemistry of trivalent uranium monoarene complexes were undertaken with a complex derived from the chelating tris(aryloxide)arene ligand (^Ad,MeArO)₃mes^3?. Cyclic voltammetry of [{(^Ad,MeArO)₃mes}U^III] ( 1 ) revealed a nearly reversible and chemically accessible reduction at ?2.495 V vs. Fc/Fc⁺—the first electrochemical evidence for a formally divalent uranium complex. Chemical reduction of 1 indicates that reduction induces coordination and redox isomerization to form a uranium(IV) hydride, and addition of a crown ether results in hydride insertion into the coordinated arene to afford uranium(IV) complexes. This stoichiometric reaction sequence provides structural insight into the mechanism of arene functionalization at diuranium inverted sandwich complexes.     

Application of a rapid screening method to detect irradiated meat in Brazil

Based on the enormous potential for food irradiation in Brazil, and to ensure free consumer choice, there is a need to find a convenient and rapid method for detection of irradiated food. Since treatment with ionising radiation causes DNA fragmentation, the analysis of DNA damage might be promising. In this paper, the DNA Comet Assay was used to identify exotic meat (boar, jacaré and capybara), irradiated with ⁶⁰Co gamma rays. The applied radiation doses were 0, 1.5, 3.0 and 4.5 kGy. Analysis of the DNA migration enabled a rapid identification of the radiation treatment.