Recognising a partitionable simplicial complex is in NP

We show that the problem of recognising a partitionable simplicial complex is a member of the complexity class NP, thus answering a question raised in [1

Finding next-to-shortest paths in a graph

We study the problem of finding the next-to-shortest paths in a graph. A next-to-shortest $(u,v)$-path is a shortest $(u,v)$-path amongst $(u,v)$-paths with length strictly greater than the length of the shortest $(u,v)$-path. In constrast to the situation in directed graphs, where the problem has been shown to be NP-hard, providing edges of length zero are allowed, we prove the somewhat surprising result that there is a polynomial time algorithm for the undirected version of the problem

Domination Analysis of Greedy Heuristics For The Frequency Assignment Problem

We introduce the greedy expectation algorithm for the fixed spectrum version of the frequency assignment problem. This algorithm was previously studied for the travelling salesman problem. We show that the domination number of this algorithm is at least $\sigma^{n-\lceil\log_2 n\rceil-1}$ where $\sigma$ is the available span and $n$ the number of vertices in the constraint graph. In contrast to this we show that the standard greedy algorithm has domination number strictly less than $\sigma^{n}e^{-\frac{5(n-1)}{144}}$ for large n and fixed $\sigma$

The calibration of the Sudbury Neutrino Observatory using uniformly distributed radioactive sources

The production and analysis of distributed sources of 24Na and 222Rn in the Sudbury Neutrino Observatory (SNO) are described. These unique sources provided accurate calibrations of the response to neutrons, produced through photodisintegration of the deuterons in the heavy water target, and to low energy betas and gammas. The application of these sources in determining the neutron detection efficiency and response of the 3He proportional counter array, and the characteristics of background Cherenkov light from trace amounts of natural radioactivity is described.Comment: 24 pages, 13 figure

Fast Evaluation of Interlace Polynomials on Graphs of Bounded Treewidth

We consider the multivariate interlace polynomial introduced by Courcelle (2008), which generalizes several interlace polynomials defined by Arratia, Bollobas, and Sorkin (2004) and by Aigner and van der Holst (2004). We present an algorithm to evaluate the multivariate interlace polynomial of a graph with n vertices given a tree decomposition of the graph of width k. The best previously known result (Courcelle 2008) employs a general logical framework and leads to an algorithm with running time f(k)*n, where f(k) is doubly exponential in k. Analyzing the GF(2)-rank of adjacency matrices in the context of tree decompositions, we give a faster and more direct algorithm. Our algorithm uses 2^{3k^2+O(k)}*n arithmetic operations and can be efficiently implemented in parallel.Comment: v4: Minor error in Lemma 5.5 fixed, Section 6.6 added, minor improvements. 44 pages, 14 figure

On the Potts model partition function in an external field

We study the partition function of Potts model in an external (magnetic) field, and its connections with the zero-field Potts model partition function. Using a deletion-contraction formulation for the partition function Z for this model, we show that it can be expanded in terms of the zero-field partition function. We also show that Z can be written as a sum over the spanning trees, and the spanning forests, of a graph G. Our results extend to Z the well-known spanning tree expansion for the zero-field partition function that arises though its connections with the Tutte polynomial

Grain Surface Models and Data for Astrochemistry

AbstractThe cross-disciplinary field of astrochemistry exists to understand the formation, destruction, and survival of molecules in astrophysical environments. Molecules in space are synthesized via a large variety of gas-phase reactions, and reactions on dust-grain surfaces, where the surface acts as a catalyst. A broad consensus has been reached in the astrochemistry community on how to suitably treat gas-phase processes in models, and also on how to present the necessary reaction data in databases; however, no such consensus has yet been reached for grain-surface processes. A team of ∼25 experts covering observational, laboratory and theoretical (astro)chemistry met in summer of 2014 at the Lorentz Center in Leiden with the aim to provide solutions for this problem and to review the current state-of-the-art of grain surface models, both in terms of technical implementation into models as well as the most up-to-date information available from experiments and chemical computations. This review builds on the results of this workshop and gives an outlook for future directions

The WEBT BL Lacertae Campaign 2001 and its extension : Optical light curves and colour analysis 1994–2002

BL Lacertae has been the target of four observing campaigns by the Whole Earth Blazar Telescope (WEBT) collaboration. In this paper we present UBVRI light curves obtained by theWEBT from 1994 to 2002, including the last, extended BL Lac 2001 campaign. A total of about 7500 optical observations performed by 31 telescopes from Japan to Mexico have been collected, to be added to the ∼15 600 observations of the BL Lac Campaign 2000. All these data allow one to follow the source optical emission behaviour with unprecedented detail. The analysis of the colour indices reveals that the flux variability can be interpreted in terms of two components: longer-term variations occurring on a fewday time scale appear as mildly-chromatic events, while a strong bluer-when-brighter chromatism characterizes very fast (intraday) flares. By decoupling the two components, we quantify the degree of chromatism inferring that longer-term flux changes imply moving along a ∼0.1 bluerwhen- brighter slope in the B − R versus R plane; a steeper slope of ∼0.4 would distinguish the shorter-term variations. This means that, when considering the long-term trend, the B-band flux level is related to the R-band one according to a power law of index ∼1.1. Doppler factor variations on a “convex” spectrum could be the mechanism accounting for both the long-term variations and their slight chromatism.Reig Torres, Pablo, [email protected]