Robustness: a New Form of Heredity Motivated by Dynamic Networks

We investigate a special case of hereditary property in graphs, referred to as {\em robustness}. A property (or structure) is called robust in a graph $G$ if it is inherited by all the connected spanning subgraphs of $G$. We motivate this definition using two different settings of dynamic networks. The first corresponds to networks of low dynamicity, where some links may be permanently removed so long as the network remains connected. The second corresponds to highly-dynamic networks, where communication links appear and disappear arbitrarily often, subject only to the requirement that the entities are temporally connected in a recurrent fashion ({\it i.e.} they can always reach each other through temporal paths). Each context induces a different interpretation of the notion of robustness. We start by motivating the definition and discussing the two interpretations, after what we consider the notion independently from its interpretation, taking as our focus the robustness of {\em maximal independent sets} (MIS). A graph may or may not admit a robust MIS. We characterize the set of graphs \forallMIS in which {\em all} MISs are robust. Then, we turn our attention to the graphs that {\em admit} a robust MIS (\existsMIS). This class has a more complex structure; we give a partial characterization in terms of elementary graph properties, then a complete characterization by means of a (polynomial time) decision algorithm that accepts if and only if a robust MIS exists. This algorithm can be adapted to construct such a solution if one exists

An investigation into the relationship between preceding break crops and weed populations in barley crops in organic ley/arable rotations

This report was presented at the UK Organic Research 2002 Conference. The relationship between weed populations and cereal crops following nine organic break crops was investigated in field trials in Warwickshire, Aberdeenshire and Ceredigion in 2001. Weed biodiversity was high on all sites and varied between sites in terms of species present. Severity of weed infestation differed significantly between sites and between cereals following different break crops. The impact of break crop species on the incidence and severity of the weed burden in the following cereal is discussed in relation to the field trials at the three sites

Incoherent single pion electroproduction on the deuteron with polarization effects

Incoherent pion electroproduction on the deuteron is studied from threshold up to the second resonance region with special emphasis on the influence of final state interaction, in particular on polarization observables. The elementary $\gamma N\to\pi N$ amplitude is taken from the MAID-2003 model. Final state interaction is included by considering complete rescattering in the final $NN$ and $\pi N$ subsystems. Their influence on the structure functions governing the semi-exclusive differential cross section, where besides the scattered electron only the produced pion is detected, is investigated in detail. For charged pion-production the effect of $NN$-rescattering is moderate whereas $\pi N$-rescattering is almost negligible, except very close to threshold. $NN$-rescattering appears much stronger in neutral pion production for which the primary mechanism is the elimination of a significant spurious coherent contribution in the impulse approximation. Sizeable effects are also found in some of the polarization structure functions for beam and/or target polarizations.Comment: 20 pages including 14 figure

UK policy options and the South Atlantic

This is the final version of the article. Available from Universidade Federal do Rio Grande do Sul via the DOI in this record.This article assesses the utility of International Relations 'role theory' for understanding the United Kingdom's policy options in the South Atlantic, with specific reference to UK-Argentine relations. The article does not ignore the geo-strategic realities of Anglo-Argentine relations, but posits that recent interactions in the economic sphere can be seen as the beginning of a normalisation process. The cause of this economic rapprochement, it is argued, is less to do with UK policy and instead is due to changes in domestic Argentine politics which have offered a window of opportunity for the UK

Remarks on separating words

The separating words problem asks for the size of the smallest DFA needed to distinguish between two words of length <= n (by accepting one and rejecting the other). In this paper we survey what is known and unknown about the problem, consider some variations, and prove several new results

Incoherent pion photoproduction on the deuteron with polarization observables I: Formal expressions

Formal expressions are developed for the general five-fold differential cross section of incoherent $\pi$-photoproduction on the deuteron including beam and target polarization. The polarization observables of the cross section are described by various beam, target and beam-target asymmetries for polarized photons and/or polarized deuterons. They are given as bilinear hermitean forms in the reaction matrix elements divided by the unpolarized cross section. In addition, the corresponding observables for the semi-exclusive reaction $\vec d(\vec \gamma,\pi)NN$ are also given.Comment: 11 pages, 1 figur

Multi-waveband observations of colliding galaxies

Colliding galaxies represent a major challenge to both theorists and observers because of the large variety of phenomena which are expected to come into play during the interaction. Strong gravitational fluctuations may drive non-linear waves and instabilities throughout the stars and gas leading to enhanced star formation, nuclear activity and ultimately a mixing of the morphological components of the original galaxies. One relatively uncomplicated class of colliding galaxy where stellar waves play an important role in star formation are ring galaxies. Ring galaxies are probably formed when a companion galaxy passes through the center of a disk system driving circular waves through the disk (Lynds and Toomre 1976, Toomre 1978, Struck-Marcell 1990). Off-center collisions can generate non-circular waves and can be loosely described as banana-shaped although they may exhibit more complex forms as the waves expand into the disk. The propagation of such stellar and gaseous waves through the disk leads to enhanced star formation (e.g., Appleton and Struck-Marcell 1987a; Jeske 1986) and provides a unique probe of the response of the interstellar medium (ISM) to a propagating wave (see Appleton and Struck-Marcell 1987b). Here, the authors report results for 3 systems; the irregular ring Arp 143 (=VV 117); Wakamatsu's Seyfert ring (A0959-755; see Wakamatsu and Nishida 1987) and the brighter member of the pair of ring galaxies comprising of AM 1358-221. The most complete multi-wavelength data is for Arp 143. Optical charge coupled device (CCD) observations made with the 60 inch Palomar telescope at BV and r band, near-IR images at J (1.25 microns), H (1.65 microns) and k (2.2 microns) bands from the infrared camera (IRCAM) InSb array camera on the 3.8m United Kingdon Infrared Telescope (UKIRT) telescope and very large array (VLA) observations at 20cm in both the neutral hydrogen line and radio continuum are described. The observations of Wakamatsu's ring and AM 1358 were made only in the near-IR, and a comparison is made with available optical plate material