SUSY vertex algebras and supercurves

This article is a continuation of math.QA/0603633 Given a strongly conformal SUSY vertex algebra V and a supercurve X we construct a vector bundle V_X on X, the fiber of which, is isomorphic to V. Moreover, the state-field correspondence of V canonically gives rise to (local) sections of these vector bundles. We also define chiral algebras on any supercurve X, and show that the vector bundle V_X, corresponding to a SUSY vertex algebra, carries the structure of a chiral algebra.Comment: 50 page

MDL Convergence Speed for Bernoulli Sequences

The Minimum Description Length principle for online sequence estimation/prediction in a proper learning setup is studied. If the underlying model class is discrete, then the total expected square loss is a particularly interesting performance measure: (a) this quantity is finitely bounded, implying convergence with probability one, and (b) it additionally specifies the convergence speed. For MDL, in general one can only have loss bounds which are finite but exponentially larger than those for Bayes mixtures. We show that this is even the case if the model class contains only Bernoulli distributions. We derive a new upper bound on the prediction error for countable Bernoulli classes. This implies a small bound (comparable to the one for Bayes mixtures) for certain important model classes. We discuss the application to Machine Learning tasks such as classification and hypothesis testing, and generalization to countable classes of i.i.d. models.Comment: 28 page

On Convergence Properties of Shannon Entropy

Convergence properties of Shannon Entropy are studied. In the differential setting, it is shown that weak convergence of probability measures, or convergence in distribution, is not enough for convergence of the associated differential entropies. A general result for the desired differential entropy convergence is provided, taking into account both compactly and uncompactly supported densities. Convergence of differential entropy is also characterized in terms of the Kullback-Liebler discriminant for densities with fairly general supports, and it is shown that convergence in variation of probability measures guarantees such convergence under an appropriate boundedness condition on the densities involved. Results for the discrete setting are also provided, allowing for infinitely supported probability measures, by taking advantage of the equivalence between weak convergence and convergence in variation in this setting.Comment: Submitted to IEEE Transactions on Information Theor

Experimental determination of the degree of quantum polarisation of continuous variable states

We demonstrate excitation-manifold resolved polarisation characterisation of continuous-variable (CV) quantum states. In contrast to traditional characterisation of polarisation that is based on the Stokes parameters, we experimentally determine the Stokes vector of each excitation manifold separately. Only for states with a given photon number does the methods coincide. For states with an indeterminate photon number, for example Gaussian states, the employed method gives a richer and more accurate description. We apply the method both in theory and in experiment to some common states to demonstrate its advantages.Comment: 5 page

Free-of-charge medicine schemes in the NHS: A local and regional drug and therapeutic committee's experience

INTRODUCTION: Free-of-charge (FoC) medicine schemes are increasingly available and allow access to investigational treatments outside clinical trials or in advance of licensing or NHS commissioning. METHODS: We retrospectively reviewed FoC medicine schemes evaluated between 2013 and 2019 by a single NHS trust and a regional drug and therapeutics committee (DTC). The details of each locally reviewed FoC scheme, and any nationally available Medicines and Healthcare products Regulatory Agency Early Access to Medicines Scheme (MHRA EAMS) in the same period, were recorded and categorised. RESULTS: Most FoC schemes (95%) allowed access to medicines intended to address an unmet clinical need. Over 7 years, 90% were company-FoC schemes and 10% were MHRA EAMS that were locally reviewed. Phase 3 clinical trial data were available for 44% of FoC schemes, 37% had phase 2 data and 19% were supported only by phase 1 data, retrospective observational studies or preclinical data. Utilisation of company-FoC schemes increased on average by 50% per year, while MHRA EAMS schemes showed little growth. CONCLUSION: Company-FoC medicine schemes are increasingly common. This may indicate a preference for pharmaceutical companies to independently co-ordinate schemes. Motivations for company-FoC schemes remain unclear and many provide access to treatments that are yet to be evaluated in appropriately conducted clinical trials, and whose efficacy and risk of harm remain uncertain. There is no standardisation of this practice and there is no regulatory oversight. Moreover, no standardised data collection framework is in place that could demonstrate the utility of such programmes in addressing unmet clinical need or to allow generation of further evidence

Approximation and learning by greedy algorithms

We consider the problem of approximating a given element $f$ from a Hilbert space $\mathcal{H}$ by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the existing theory of convergence rates for both the orthogonal greedy algorithm and the relaxed greedy algorithm, as well as for the forward stepwise projection algorithm. For all these algorithms, we prove convergence results for a variety of function classes and not simply those that are related to the convex hull of the dictionary. We then show how these bounds for convergence rates lead to a new theory for the performance of greedy algorithms in learning. In particular, we build upon the results in [IEEE Trans. Inform. Theory 42 (1996) 2118--2132] to construct learning algorithms based on greedy approximations which are universally consistent and provide provable convergence rates for large classes of functions. The use of greedy algorithms in the context of learning is very appealing since it greatly reduces the computational burden when compared with standard model selection using general dictionaries.Comment: Published in at http://dx.doi.org/10.1214/009053607000000631 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Biochar-based wastewater treatment to combat antimicrobial resistance

Antimicrobial resistance (AMR) is driven in part by environmental reservoirs of antimicrobial-resistant organisms and genes, as well as antimicrobials themselves, which drive resistance via selective pressure. According to the UN, 80% of all wastewater flows into the environment untreated. When wastewater is treated, treatment plants can act as hotspots of horizontal gene transfer from resistant to non-resistant organisms. There is therefore an urgent need to filter wastewater from sources rich in resistant bacteria and antimicrobials, like hospitals and pharmaceutical plants, before they reach environmental reservoirs where resistance can spread. Biochars produced from waste lignocellulosic biomass are ideal for this purpose, as they are highly adsorbent, affordable, and sustainable, with morphologies and surface chemistries that are tunable by choice of production conditions. Here, we link peak pyrolysis temperatures and alkaline pretreatment of walnut shell biochars to their filtration performance, showing these materials are suitable for in-line filtration of wastewater to combat AMR

Overview of the CLEF-2019 Checkthat! LAB: Automatic identification and verification of claims. Task 2: Evidence and factuality

We present an overview of Task 2 of the second edition of the CheckThat! Lab at CLEF 2019. Task 2 asked (A) to rank a given set of Web pages with respect to a check-worthy claim based on their usefulness for fact-checking that claim, (B) to classify these same Web pages according to their degree of usefulness for fact-checking the target claim, (C) to identify useful passages from these pages, and (D) to use the useful pages to predict the claim's factuality. Task 2 at CheckThat! provided a full evaluation framework, consisting of data in Arabic (gathered and annotated from scratch) and evaluation based on normalized discounted cumulative gain (nDCG) for ranking, and F1 for classification. Four teams submitted runs. The most successful approach to subtask A used learning-to-rank, while different classifiers were used in the other subtasks. We release to the research community all datasets from the lab as well as the evaluation scripts, which should enable further research in the important task of evidence-based automatic claim verification