Scattering for radial, semi-linear, super-critical wave equations with bounded critical norm

In this paper we study the focusing cubic wave equation in 1+5 dimensions with radial initial data as well as the one-equivariant wave maps equation in 1+3 dimensions with the model target manifolds $\mathbb{S}^3$ and $\mathbb{H}^3$. In both cases the scaling for the equation leaves the $\dot{H}^{\frac{3}{2}} \times \dot{H}^{\frac{1}{2}}$-norm of the solution invariant, which means that the equation is super-critical with respect to the conserved energy. Here we prove a conditional scattering result: If the critical norm of the solution stays bounded on its maximal time of existence, then the solution is global in time and scatters to free waves both forwards and backwards in infinite time. The methods in this paper also apply to all supercritical power-type nonlinearities for both the focusing and defocusing radial semi-linear equation in 1+5 dimensions, yielding analogous results.Comment: 59 pages, minor typos have been correcte

Model-Independent Extraction of ∣Vcb∣|V_{cb}| from Bˉ→D∗ℓν‾\bar{B}\rightarrow D^* \ell \overline{\nu}

We fit the unfolded data of $\bar{B}^0\rightarrow D^{*+} \ell \overline{\nu}$ from the Belle experiment, where $\ell \equiv e, \mu$, using a method independent of heavy quark symmetry to extrapolate to zero-recoil and extract the value of $|V_{cb}|$. This results in $|V_{cb}| = (41.9^{~+2.0}_{~-1.9})\times 10^{-3}$, which is robust to changes in the theoretical inputs and very consistent with the value extracted from inclusive semileptonic $B$ decays.Comment: 8 pages, 3 figures; corrected minor typographical error

Competitiveness partnerships : building and maintaining public-private dialogue to improve the investment climate - a resource drawn from the review of 40 countries'experiences

The authors examine competitiveness partnerships, which consist of structured dialogue between the public and private sector to improve the investment climate. The paper is designed to be used as a resource by donors, governments, or businesspeople who are interested in establishing, maintaining, or improving a competitiveness partnership in their country or region. The political and economic context of a country determines the kind of partnership that is feasible and likely to succeed, and there is no one-size-fits-all approach. But it is possible to distill some ideas and techniques from best practice as many public-private dialogue mechanisms face similar challenges. Drawing on the experiences of 40 countries, the authors make a positive case for building and maintaining competitiveness partnerships, and offer a selection of valuable insights into how practitioners can design them so as to avoid common pitfalls. They demonstrate that reforms that are designed through public-private dialogue are better conceived and more effectively implemented because they arise from increased mutual understanding between government and the businesscommunity. The paper has three parts. Part One outlines what competitiveness partnerships can achieve. Part Two describes how competitiveness partnerships function, presenting issues to consider when designing such partnerships and a range of ways in which they may be approached. Part Three identifies challenges that competitiveness partnerships have frequently faced and strategies that have been used to overcome them.Health Monitoring&Evaluation,National Governance,Health Economics&Finance,ICT Policy and Strategies,Economic Theory&Research

Compositional Vector Space Models for Knowledge Base Completion

Knowledge base (KB) completion adds new facts to a KB by making inferences from existing facts, for example by inferring with high likelihood nationality(X,Y) from bornIn(X,Y). Most previous methods infer simple one-hop relational synonyms like this, or use as evidence a multi-hop relational path treated as an atomic feature, like bornIn(X,Z) -> containedIn(Z,Y). This paper presents an approach that reasons about conjunctions of multi-hop relations non-atomically, composing the implications of a path using a recursive neural network (RNN) that takes as inputs vector embeddings of the binary relation in the path. Not only does this allow us to generalize to paths unseen at training time, but also, with a single high-capacity RNN, to predict new relation types not seen when the compositional model was trained (zero-shot learning). We assemble a new dataset of over 52M relational triples, and show that our method improves over a traditional classifier by 11%, and a method leveraging pre-trained embeddings by 7%.Comment: The 53rd Annual Meeting of the Association for Computational Linguistics and The 7th International Joint Conference of the Asian Federation of Natural Language Processing, 201

Automating the Construction of Jet Observables with Machine Learning

Machine-learning assisted jet substructure tagging techniques have the potential to significantly improve searches for new particles and Standard Model measurements in hadronic final states. Techniques with simple analytic forms are particularly useful for establishing robustness and gaining physical insight. We introduce a procedure to automate the construction of a large class of observables that are chosen to completely specify $M$-body phase space. The procedure is validated on the task of distinguishing $H\rightarrow b\bar{b}$ from $g\rightarrow b\bar{b}$, where $M=3$ and previous brute-force approaches to construct an optimal product observable for the $M$-body phase space have established the baseline performance. We then use the new method to design tailored observables for the boosted $Z'$ search, where $M=4$ and brute-force methods are intractable. The new classifiers outperform standard $2$-prong tagging observables, illustrating the power of the new optimization method for improving searches and measurement at the LHC and beyond.Comment: 15 pages, 8 tables, 12 figure