Recognizing Planar Laman Graphs

Laman graphs are the minimally rigid graphs in the plane. We present two algorithms for recognizing planar Laman graphs. A simple algorithm with running time O(n^(3/2)) and a more complicated algorithm with running time O(n log^3 n) based on involved planar network flow algorithms. Both improve upon the previously fastest algorithm for general graphs by Gabow and Westermann [Algorithmica, 7(5-6):465 - 497, 1992] with running time O(n sqrt{n log n}). To solve this problem we introduce two algorithms (with the running times stated above) that check whether for a directed planar graph G, disjoint sets S, T subseteq V(G), and a fixed k the following connectivity condition holds: for each vertex s in S there are k directed paths from s to T pairwise having only vertex s in common. This variant of connectivity seems interesting on its own

Optimization Algorithm for the Generation of ONCV Pseudopotentials

We present an optimization algorithm to construct pseudopotentials and use it to generate a set of Optimized Norm-Conserving Vanderbilt (ONCV) pseudopotentials for elements up to Z=83 (Bi) (excluding Lanthanides). We introduce a quality function that assesses the agreement of a pseudopotential calculation with all-electron FLAPW results, and the necessary plane-wave energy cutoff. This quality function allows us to use a Nelder-Mead optimization algorithm on a training set of materials to optimize the input parameters of the pseudopotential construction for most of the periodic table. We control the accuracy of the resulting pseudopotentials on a test set of materials independent of the training set. We find that the automatically constructed pseudopotentials provide a good agreement with the all-electron results obtained using the FLEUR code with a plane-wave energy cutoff of approximately 60 Ry.Comment: 11 pages, 6 figure

Edge-Orders

Canonical orderings and their relatives such as st-numberings have been used as a key tool in algorithmic graph theory for the last decades. Recently, a unifying concept behind all these orders has been shown: they can be described by a graph decomposition into parts that have a prescribed vertex-connectivity. Despite extensive interest in canonical orderings, no analogue of this unifying concept is known for edge-connectivity. In this paper, we establish such a concept named edge-orders and show how to compute (1,1)-edge-orders of 2-edge-connected graphs as well as (2,1)-edge-orders of 3-edge-connected graphs in linear time, respectively. While the former can be seen as the edge-variants of st-numberings, the latter are the edge-variants of Mondshein sequences and non-separating ear decompositions. The methods that we use for obtaining such edge-orders differ considerably in almost all details from the ones used for their vertex-counterparts, as different graph-theoretic constructions are used in the inductive proof and standard reductions from edge- to vertex-connectivity are bound to fail. As a first application, we consider the famous Edge-Independent Spanning Tree Conjecture, which asserts that every k-edge-connected graph contains k rooted spanning trees that are pairwise edge-independent. We illustrate the impact of the above edge-orders by deducing algorithms that construct 2- and 3-edge independent spanning trees of 2- and 3-edge-connected graphs, the latter of which improves the best known running time from O(n^2) to linear time

Quasiparticle GWGW band structures and Fermi surfaces of bulk and monolayer NbS2_2

In this work we employ the $GW$ approximation in the framework of the SternheimerGW method to investigate the effects of many-body corrections to the band structures and Fermi surfaces of bulk and monolayer NbS$_2$. For the bulk system, we find that the inclusion of these many-body effects leads to important changes in the band structure, especially in the low-energy regime around the Fermi level, and that our calculations are in good agreement with recent ARPES measurements. In the case of a free-standing monolayer NbS$_2$, we observe a strong increase of the screened Coulomb interaction and the quasiparticle corrections as compared to bulk. In this case we also perform calculations to include the effect of screening by a substrate. We report in detail the results of our convergence tests and computational parameters, to serve as a solid basis for future studies.Comment: 15 pages, 18 figure

Remodeling and expanding Carnegie-era library buildings

One of the most satisfying undertakings in library building design can be the expansion and remodeling of historic public libraries from the early twentieth century. However, although the logic of preservation and conservation leads to strong public interest in the reuse of existing structures, the costs can be extremely high and the results can be functionally disappointing. Among the major problems frequently faced are modern building codes, load-bearing walls, the difficulty of installing modern HVAC systems, flimsy original construction materials, locations that no longer meet community needs, poor electrical wiring, elderly windows, historic brickwork that is difficult to match, inadequate sites, total inaccessibility for users with disabilities, bad modern lighting, and basements with low ceilings. However, many of these problems can be solved—or at least dealt with—with careful programming and planning, and expansion projects can result in handsome libraries that can serve for a second century.published or submitted for publicationOpe