Computing a Minimum-Dilation Spanning Tree is NP-hard

In a geometric network G = (S, E), the graph distance between two vertices u, v in S is the length of the shortest path in G connecting u to v. The dilation of G is the maximum factor by which the graph distance of a pair of vertices differs from their Euclidean distance. We show that given a set S of n points with integer coordinates in the plane and a rational dilation delta > 1, it is NP-hard to determine whether a spanning tree of S with dilation at most delta exists

Two new sum rules for octet-baryon magnetic moments (\mu) and constraints on QCD sum rules from new experimental determination of \mu-s for the decuplet

Recently the \mu_{\Delta ^{++}} was found from a fit to (\pi^+)p scattering. This enable us to pinpoint condensate parameters more precisely in the context of QCD sum rules (QCDSR). In the octet sector, the Coleman-Glashow sum rule (CGSR) is violated by the experimental \mu-s. QCDSR allows us to write down two sum rules similar to the CGSR, which are obeyed by the experimental magnetic moments, whereas they rule out a specific model using the Wilson loop approach and a particular chiral quark model. It is amusing to note that the QCDSR allows us to write down the quark and gluon condensates in terms of measurables like the \mu-s of the nucleons and the \Sigma^{+/-}

The Future of Flexible Work and Hybrid Work Culture Beyond Covid-19: Challenges, Opportunities and Lessons Learned at UVA Library

The COVID-19 pandemic led to some significant changes in how many of us work and live. It also exposed deep infrastructure problems and systemic equity issues around income, race, and employment and redefined the meaning of front-line essential worker. The pandemic’s acceleration of the move to remote and hybrid work in many areas, coupled with the redefining of essential work, will result in many libraries having to adapt operations and culture around a hybrid work environment. While libraries prior to the pandemic did allow for some flexible work arrangements, telework was not an expected benefit nor was it universal enough to be a pervasive part of library culture. During the pandemic many libraries provided staff with more opportunities to work from home but are now wrestling with how the situation will evolve post pandemic. This paper will describe the University of Virginia Library’s journey from the shift to an all-remote workforce in the early days of the pandemic to its current and projected future hybrid work environment and provide a framework for other libraries to consider. Throughout the paper, challenges, opportunities, and lessons learned will be highlighted and issues around equity, recruitment and retention, culture and teambuilding, and management will be explored

Magnetic Moment of the Ω−\Omega^- in QCD sumrule (QCDSR)

The $\Omega ^-$ magnetic moment was measured very accurately and experimentalists remarked that it differs from the theoretical estimates, thus posing a challenge to the latter. One such estimation uses QCDSR. We revisit this sumrule method, using condensate parameters which were obtained from fitting the differences ($\mu_p - \mu_n$), ($\mu_{\Sigma^+}- \mu_{\Sigma^-}$) and ($\mu_{\Xi^0} - \mu_{\Xi^-}$) and confirm the experimental number. The $\mu_{\Delta^{++}}$ is also found to agree with the experimental estimate.Comment: 5 pages latex paper, no figur

Farthest-Polygon Voronoi Diagrams

Given a family of k disjoint connected polygonal sites in general position and of total complexity n, we consider the farthest-site Voronoi diagram of these sites, where the distance to a site is the distance to a closest point on it. We show that the complexity of this diagram is O(n), and give an O(n log^3 n) time algorithm to compute it. We also prove a number of structural properties of this diagram. In particular, a Voronoi region may consist of k-1 connected components, but if one component is bounded, then it is equal to the entire region

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