Amplitude ambiguities in pseudoscalar meson photoproduction

We consider the problem of determining amplitudes from observables for the case of pseudoscalar meson photoproduction. We find a number of surprisingly simple constraints which give necessary conditions for a complete set of measurements. These results contradict one of the selection rules derived previously.Comment: 7 page

Ambiguities in the partial-wave analysis of pseudoscalar-meson photoproduction

Ambiguities in pseudoscalar-meson photoproduction, arising from incomplete experimental data, have analogs in pion-nucleon scattering. Amplitude ambiguities have important implications for the problems of amplitude extraction and resonance identification in partial-wave analysis. The effect of these ambiguities on observables is described. We compare our results with those found in earlier studies.Comment: 12 pages of text. No figure

Multi-Level Weighted Additive Spanners

Given a graph G = (V, E), a subgraph H is an additive +β spanner if distH(u, v) ≤ distG(u, v) + β for all u, v ∈ V. A pairwise spanner is a spanner for which the above inequality is only required to hold for specific pairs P ⊆ V × V given on input; when the pairs have the structure P = S × S for some S ⊆ V, it is called a subsetwise spanner. Additive spanners in unweighted graphs have been studied extensively in the literature, but have only recently been generalized to weighted graphs. In this paper, we consider a multi-level version of the subsetwise additive spanner in weighted graphs motivated by multi-level network design and visualization, where the vertices in S possess varying level, priority, or quality of service (QoS) requirements. The goal is to compute a nested sequence of spanners with the minimum total number of edges. We first generalize the +2 subsetwise spanner of [Pettie 2008, Cygan et al., 2013] to the weighted setting. We experimentally measure the performance of this and several existing algorithms by [Ahmed et al., 2020] for weighted additive spanners, both in terms of runtime and sparsity of the output spanner, when applied as a subroutine to multi-level problem. We provide an experimental evaluation on graphs using several different random graph generators and show that these spanner algorithms typically achieve much better guarantees in terms of sparsity and additive error compared with the theoretical maximum. By analyzing our experimental results, we additionally developed a new technique of changing a certain initialization parameter which provides better spanners in practice at the expense of a small increase in running time. © Reyan Ahmed, Greg Bodwin, Faryad Darabi Sahneh, Keaton Hamm, Stephen Kobourov, and Richard Spence; licensed under Creative Commons License CC-BY 4.0 19th International Symposium on Experimental Algorithms (SEA 2021).Open access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

On Additive Spanners in Weighted Graphs with Local Error

An additive + β spanner of a graph G is a subgraph which preserves distances up to an additive + β error. Additive spanners are well-studied in unweighted graphs but have only recently received attention in weighted graphs [Elkin et al. 2019 and 2020, Ahmed et al. 2020]. This paper makes two new contributions to the theory of weighted additive spanners. For weighted graphs, [Ahmed et al. 2020] provided constructions of sparse spanners with global error β= cW, where W is the maximum edge weight in G and c is constant. We improve these to local error by giving spanners with additive error + cW(s, t) for each vertex pair (s, t), where W(s, t) is the maximum edge weight along the shortest s–t path in G. These include pairwise + (2 + ε) W(·, · ) and + (6 + ε) W(·, · ) spanners over vertex pairs P⊆ V× V on Oε(n| P|1 / 3) and Oε(n| P|1 / 4) edges for all ε> 0, which extend previously known unweighted results up to ε dependence, as well as an all-pairs + 4 W(·, · ) spanner on O~ (n7 / 5) edges. Besides sparsity, another natural way to measure the quality of a spanner in weighted graphs is by its lightness, defined as the total edge weight of the spanner divided by the weight of an MST of G. We provide a + εW(·, · ) spanner with Oε(n) lightness, and a + (4 + ε) W(·, · ) spanner with Oε(n2 / 3) lightness. These are the first known additive spanners with nontrivial lightness guarantees. All of the above spanners can be constructed in polynomial time.12 month embargo; first online: 20 September 2021This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

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