Leptonic μ \mu - and τ \tau -decays: mass effects, polarization effects and O(α) O(\alpha) radiative corrections

We calculate the radiative corrections to the unpolarized and the four polarized spectrum and rate functions in the leptonic decay of a polarized $\mu$ into a polarized electron. The new feature of our calculation is that we keep the mass of the final state electron finite which is mandatory if one wants to investigate the threshold region of the decay. Analytical results are given for the energy spectrum and the polar angle distribution of the final state electron whose longitudinal and transverse polarization is calculated. We also provide analytical results on the integrated spectrum functions. We analyze the $m_e \to 0$ limit of our general results and investigate the quality of the $m_e \to 0$ approximation. In the $m_e \to 0$ case we discuss in some detail the role of the $O(\alpha)$ anomalous helicity flip contribution of the final electron which survives the $m_e \to 0$ limit. The results presented in this 0203048 also apply to the leptonic decays of polarized $\tau$-leptons for which we provide numerical results.Comment: 39 pages, 11 postscript figures added. Updated version. Four references added. A few text improvements. Final version to appear in Phys.Rev.

A research and development (R&D) roadmap for broadly protective coronavirus vaccines: A pandemic preparedness strategy

Broadly protective coronavirus vaccines are an important tool for protecting against future SARS-CoV-2 variants and could play a critical role in mitigating the impact of future outbreaks or pandemics caused by novel coronaviruses. The Coronavirus Vaccines Research and Development (R&D) Roadmap (CVR) is aimed at promoting the development of such vaccines. The CVR, funded by the Bill & Melinda Gates Foundation and The Rockefeller Foundation, was generated through a collaborative and iterative process, which was led by the Center for Infectious Disease Research and Policy (CIDRAP) at the University of Minnesota and involved 50 international subject matter experts and recognized leaders in the field. This report summarizes the major issues and areas of research outlined in the CVR and identifies high-priority milestones. The CVR covers a 6-year timeframe and is organized into five topic areas: virology, immunology, vaccinology, animal and human infection models, and policy and finance. Included in each topic area are key barriers, gaps, strategic goals, milestones, and additional R&D priorities. The roadmap includes 20 goals and 86 R&D milestones, 26 of which are ranked as high priority. By identifying key issues, and milestones for addressing them, the CVR provides a framework to guide funding and research campaigns that promote the development of broadly protective coronavirus vaccines

Faster algorithms for computing plurality points

Let V be a set of n points in R^d, which we call voters, where d is a fixed constant. A point p in R^d is preferred over another point p' in R^d by a voter v in V if dist(v,p) &lt; dist(v,p'). A point p is called a plurality point if it is preferred by at least as many voters as any other point p'. We present an algorithm that decides in O(n log n) time whether V admits a plurality point in the L_2 norm and, if so, finds the (unique) plurality point. We also give efficient algorithms to compute the smallest subset W of V such that V - W admits a plurality point, and to compute a so-called minimum-radius plurality ball. Finally, we consider the problem in the personalized L_1 norm, where each point v in V has a preference vector &lt;w_1(v), ...,w_d(v)&gt; and the distance from v to any point p in R^d is given by sum_{i=1}^d w_i(v) cdot |x_i(v)-x_i(p)|. For this case we can compute in O(n^(d-1)) time the set of all plurality points of V. When all preference vectors are equal, the running time improves to O(n). </p

Finding plurality points in R^d

Let V be a set of n points in R^d, which we call voters, where d is a fixed constant. A point p in R^d is preferred over another point p' in R^d by a voter v in V if dist(v,p) < dist(v,p'). A point p is called a plurality point if it is preferred by at least as many voters as any other point p'. We present an algorithm that decides in O(n log n) time whether V admits a plurality point in the L_2 norm and, if so, finds the (unique) plurality point

Range-clustering queries

In a geometric k-clustering problem the goal is to partition a set of points in R^d into k subsets such that a certain cost function of the clustering is minimized. We present data structures for orthogonal range-clustering queries on a point set S: given a query box Q and an integer k > 2, compute an optimal k-clustering for the subset of S inside Q. We obtain the following results. * We present a general method to compute a (1+epsilon)-approximation to a range-clustering query, where epsilon>0 is a parameter that can be specified as part of the query. Our method applies to a large class of clustering problems, including k-center clustering in any Lp-metric and a variant of k-center clustering where the goal is to minimize the sum (instead of maximum) of the cluster sizes. * We extend our method to deal with capacitated k-clustering problems, where each of the clusters should not contain more than a given number of points. * For the special cases of rectilinear k-center clustering in R^1, and in R^2 for k = 2 or 3, we present data structures that answer range-clustering queries exactly

Minimum perimeter-sum partitions in the plane

Let P be a set of n points in the plane. We consider the problem of partitioning P into two subsets P 1 and P 2 such that the sum of the perimeters of CH(P 1) and CH(P 2) is minimized, where CH(P i) denotes the convex hull of P i. The problem was first studied by Mitchell and Wynters in 1991 who gave an O(n 2) time algorithm. Despite considerable progress on related problems, no subquadratic time algorithm for this problem was found so far. We present an exact algorithm solving the problem in O(n log 4 n) time and a (1 + ϵ)-approximation algorithm running in O(n + 1/ϵ 2 · log 4 (1/ϵ)) time

POLLUTION LIABILITY INSURANCE AND THE INTERNALIZATION OF ENVIRONMENTAL RISKS

This paper summarizes conceptual and empirical research on the effects of using private insurance as an instrument for regulating the risks of the chemical cycle. The paper reviews the following issues: (1) the institutional choices in regulation activities that may cause latent damage; (2) the insurability of pollution liabilities; and (3) the actual problems with using the pollution liability insurance market as a regulatory tool. Copyright 1986 by The Policy Studies Organization.