Randomized Rounding for the Largest Simplex Problem

The maximum volume $j$-simplex problem asks to compute the $j$-dimensional simplex of maximum volume inside the convex hull of a given set of $n$ points in $\mathbb{Q}^d$. We give a deterministic approximation algorithm for this problem which achieves an approximation ratio of $e^{j/2 + o(j)}$. The problem is known to be $\mathrm{NP}$-hard to approximate within a factor of $c^{j}$ for some constant $c > 1$. Our algorithm also gives a factor $e^{j + o(j)}$ approximation for the problem of finding the principal $j\times j$ submatrix of a rank $d$ positive semidefinite matrix with the largest determinant. We achieve our approximation by rounding solutions to a generalization of the $D$-optimal design problem, or, equivalently, the dual of an appropriate smallest enclosing ellipsoid problem. Our arguments give a short and simple proof of a restricted invertibility principle for determinants

Hidden and Generalized Conformal Symmetry of Kerr-Sen Spacetimes

It is recently conjectured that generic non-extremal Kerr black hole could be holographically dual to a hidden conformal field theory in two dimensions. Moreover, it is known that there are two CFT duals (pictures) to describe the charged rotating black holes which correspond to angular momentum $J$ and electric charge $Q$ of the black hole. Furthermore these two pictures can be incorporated by the CFT duals (general picture) that are generated by $SL(2,\mathbb{Z})$ modular group. The general conformal structure can be revealed by looking at charged scalar wave equation in some appropriate values of frequency and charge. In this regard, we consider the wave equation of a charged massless scalar field in background of Kerr-Sen black hole and show in the "near region", the wave equation can be reproduced by the Casimir operator of a local $SL(2,\mathbb{R})_L \times SL(2,\mathbb{R})_R$ hidden conformal symmetry. We can find the exact agreement between macroscopic and microscopic physical quantities like entropy and absorption cross section of scalars for Kerr-Sen black hole. We then find an extension of vector fields that in turn yields an extended local family of $SL(2,\mathbb{R})_L \times SL(2,\mathbb{R})_R$ hidden conformal symmetries, parameterized by one parameter. For some special values of the parameter, we find a copy of $SL(2,\mathbb{R})$ hidden conformal algebra for the charged Gibbons-Maeda-Garfinkle-Horowitz-Strominger black hole in the strong deflection limit.Comment: 16 pages, new material and results added, extensive improvements in interpretation of results, references adde

Separability of Black Holes in String Theory

We analyze the origin of separability for rotating black holes in string theory, considering both massless and massive geodesic equations as well as the corresponding wave equations. We construct a conformal Killing-Stackel tensor for a general class of black holes with four independent charges, then identify two-charge configurations where enhancement to an exact Killing-Stackel tensor is possible. We show that further enhancement to a conserved Killing-Yano tensor is possible only for the special case of Kerr-Newman black holes. We construct natural null congruences for all these black holes and use the results to show that only the Kerr-Newman black holes are algebraically special in the sense of Petrov. Modifying the asymptotic behavior by the subtraction procedure that induces an exact SL(2)^2 also preserves only the conformal Killing-Stackel tensor. Similarly, we find that a rotating Kaluza-Klein black hole possesses a conformal Killing-Stackel tensor but has no further enhancements.Comment: 27 page

Investigating the biological properties of carbohydrate derived fulvic acid (CHD-FA) as a potential novel therapy for the management of oral biofilm infections.

Background: A number of oral diseases, including periodontitis, derive from microbial biofilms and are associated with increased antimicrobial resistance. Despite the widespread use of mouthwashes being used as adjunctive measures to control these biofilms, their prolonged use is not recommended due to various side effects. Therefore, alternative broad-spectrum antimicrobials that minimise these effects are highly sought after. Carbohydrate derived fulvic acid (CHD-FA) is an organic acid which has previously demonstrated to be microbiocidal against Candida albicans biofilms, therefore, the aims of this study were to evaluate the antibacterial activity of CHD-FA against orally derived biofilms and to investigate adjunctive biological effects.<p></p> Methods: Minimum inhibitory concentrations were evaluated for CHD-FA and chlorhexidine (CHX) against a range of oral bacteria using standardised microdilution testing for planktonic and sessile. Scanning electron microscopy was also employed to visualise changes in oral biofilms after antimicrobial treatment. Cytotoxicity of these compounds was assessed against oral epithelial cells, and the effect of CHD-FA on host inflammatory markers was assessed by measuring mRNA and protein expression.<p></p> Results: CHD-FA was highly active against all of the oral bacteria tested, including Porphyromonas gingivalis, with a sessile minimum inhibitory concentration of 0.5%. This concentration was shown to kill multi-species biofilms by approximately 90%, levels comparable to that of chlorhexidine (CHX). In a mammalian cell culture model, pretreatment of epithelial cells with buffered CHD-FA was shown to significantly down-regulate key inflammatory mediators, including interleukin-8 (IL-8), after stimulation with a multi-species biofilm.<p></p> Conclusions: Overall, CHD-FA was shown to possess broad-spectrum antibacterial activity, with a supplementary function of being able to down-regulate inflammation. These properties offer an attractive spectrum of function from a naturally derived compound, which could be used as an alternative topical treatment strategy for oral biofilm diseases. Further studies in vitro and in vivo are required to determine the precise mechanism by which CHD-FA modulates the host immune response.<p></p&gt

Classification of the Weyl Tensor in Higher Dimensions and Applications

We review the theory of alignment in Lorentzian geometry and apply it to the algebraic classification of the Weyl tensor in higher dimensions. This classification reduces to the the well-known Petrov classification of the Weyl tensor in four dimensions. We discuss the algebraic classification of a number of known higher dimensional spacetimes. There are many applications of the Weyl classification scheme, especially in conjunction with the higher dimensional frame formalism that has been developed in order to generalize the four dimensional Newman--Penrose formalism. For example, we discuss higher dimensional generalizations of the Goldberg-Sachs theorem and the Peeling theorem. We also discuss the higher dimensional Lorentzian spacetimes with vanishing scalar curvature invariants and constant scalar curvature invariants, which are of interest since they are solutions of supergravity theory.Comment: Topical Review for Classical and Quantum Gravity. Final published versio

Massless geodesics in AdS5×Y(p,q)AdS_5\times Y(p,q) as a superintegrable system

A Carter like constant for the geodesic motion in the $Y(p,q)$ Einstein-Sasaki geometries is presented. This constant is functionally independent with respect to the five known constants for the geometry. Since the geometry is five dimensional and the number of independent constants of motion is at least six, the geodesic equations are superintegrable. We point out that this result applies to the configuration of massless geodesic in $AdS_5\times Y(p,q)$ studied by Benvenuti and Kruczenski, which are matched to long BPS operators in the dual N=1 supersymmetric gauge theory.Comment: 20 pages, no figures. Small misprint is corrected in the Killing-Yano tensor. No change in any result or conclusion

Adherence to treatment in allergic rhinitis using mobile technology. The MASK Study

Background: Mobile technology may help to better understand the adherence to treatment. MASK-rhinitis (Mobile Airways Sentinel NetworK for allergic rhinitis) is a patient-centred ICT system. A mobile phone app (the Allergy Diary) central to MASK is available in 22 countries. Objectives: To assess the adherence to treatment in allergic rhinitis patients using the Allergy Diary App. Methods: An observational cross-sectional study was carried out on all users who filled in the Allergy Diary from 1 January 2016 to 1 August 2017. Secondary adherence was assessed by using the modified Medication Possession Ratio (MPR) and the Proportion of days covered (PDC) approach. Results: A total of 12143 users were registered. A total of 6949 users reported at least one VAS data recording. Among them, 1887 users reported >= 7 VAS data. About 1195 subjects were included in the analysis of adherence. One hundred and thirty-six (11.28%) users were adherent (MPR >= 70% and PDC = 70% and PDC = 1.50) and 176 (14.60%) were switchers. On the other hand, 832 (69.05%) users were non-adherent to medications (MPR Conclusion and clinical relevance: Adherence to treatment is low. The relative efficacy of continuous vs on-demand treatment for allergic rhinitis symptoms is still a matter of debate. This study shows an approach for measuring retrospective adherence based on a mobile app. This also represents a novel approach for analysing medication-taking behaviour in a real-world setting.Peer reviewe