A Causal Order for Spacetimes with C0C^0 Lorentzian Metrics: Proof of Compactness of the Space of Causal Curves

We recast the tools of ``global causal analysis'' in accord with an approach to the subject animated by two distinctive features: a thoroughgoing reliance on order-theoretic concepts, and a utilization of the Vietoris topology for the space of closed subsets of a compact set. We are led to work with a new causal relation which we call $K^+$, and in terms of it we formulate extended definitions of concepts like causal curve and global hyperbolicity. In particular we prove that, in a spacetime \M which is free of causal cycles, one may define a causal curve simply as a compact connected subset of \M which is linearly ordered by $K^+$. Our definitions all make sense for arbitrary $C^0$ metrics (and even for certain metrics which fail to be invertible in places). Using this feature, we prove for a general $C^0$ metric, the familiar theorem that the space of causal curves between any two compact subsets of a globally hyperbolic spacetime is compact. We feel that our approach, in addition to yielding a more general theorem, simplifies and clarifies the reasoning involved. Our results have application in a recent positive energy theorem, and may also prove useful in the study of topology change. We have tried to make our treatment self-contained by including proofs of all the facts we use which are not widely available in reference works on topology and differential geometry.Comment: Two small revisions to accomodate errors brought to our attention by R.S. Garcia. No change to chief results. 33 page

The Role of a Hot Gas Environment on the Evolution of Galaxies

Most spiral galaxies are found in galaxy groups with low velocity dispersions; most E/S0 galaxies are found in galaxy groups with relatively high velocity dispersions. The mass of the hot gas we can observe in the E/S0 groups via their thermal X-ray emission is, on average, as much as the baryonic mass of the galaxies in these groups. By comparison, galaxy clusters have as much or more hot gas than stellar mass. Hot gas in S-rich groups, however, is of low enough temperature for its X-ray emission to suffer heavy absorption due to Galactic HI and related observational effects, and hence is hard to detect. We postulate that such lower temperature hot gas does exist in low velocity dispersion, S-rich groups, and explore the consequences of this assumption. For a wide range of metallicity and density, hot gas in S-rich groups can cool in far less than a Hubble time. If such gas exists and can cool, especially when interacting with HI in existing galaxies, then it can help link together a number of disparate observations, both Galactic and extragalactic, that are otherwise difficult to understand.Comment: 16 pages with one figure. ApJ Letters, in pres

Forman's Ricci curvature - From networks to hypernetworks

Networks and their higher order generalizations, such as hypernetworks or multiplex networks are ever more popular models in the applied sciences. However, methods developed for the study of their structural properties go little beyond the common name and the heavy reliance of combinatorial tools. We show that, in fact, a geometric unifying approach is possible, by viewing them as polyhedral complexes endowed with a simple, yet, the powerful notion of curvature - the Forman Ricci curvature. We systematically explore some aspects related to the modeling of weighted and directed hypernetworks and present expressive and natural choices involved in their definitions. A benefit of this approach is a simple method of structure-preserving embedding of hypernetworks in Euclidean N-space. Furthermore, we introduce a simple and efficient manner of computing the well established Ollivier-Ricci curvature of a hypernetwork.Comment: to appear: Complex Networks '18 (oral presentation

Inverse Compton Scattering as the Source of Diffuse EUV Emission in the Coma Cluster of Galaxies

We have examined the hypothesis that the majority of the diffuse EUV flux in the Coma cluster is due to inverse Compton scattering of low energy cosmic ray electrons (0.16 < epsilon < 0.31 GeV) against the 3K black-body background. We present data on the two-dimensional spatial distribution of the EUV flux and show that these data provide strong support for a non-thermal origin for the EUV flux. However, we show that this emission cannot be produced by an extrapolation to lower energies of the observed synchrotron radio emitting electrons and an additional component of low energy cosmic ray electrons is required.Comment: 11 pages, 5 figure

Toward a conceptual framework of emotional relationship marketing: an examination of two UK political parties

The purpose of this paper is to review the notion of branding and evaluate its applicability to political parties. As ideological politics is in decline, branding may provide a consistent narrative where voters feel a sense of warmth and belonging. The paper aims to build an understanding of the complexity of building a political brand where a combination of image, logo, leadership, and values can all contribute to a compelling brand narrative. It investigates how competing positive and negative messages attempt to build and distort the brand identity. A critical review of bran ding, relationship marketing, and political science literature articulates the conceptual development of branding and its applicability to political parties. The success or failure of negative campaigning is due to the authenticity of a political party’s brand values — creating a coherent brand story — if there is no distance between the brand values articulated by the political party and the values their community perceives then this creates an "authentic" brand. However, if there is a gap this paper illustrates how negative campaigning can be used to build a "doppelganger brand," which undermines the credibility of the authentic political brand. The paper argues that political parties need to understand how brand stories are developed but also how they can be used to protect against negative advertising. This has implications for political marketing strategists and political parties. This paper draws together branding theory and relationship marketing and incorporates them into a framework that makes a contribution to the political marketing literature

Spectroscopy of 194^{194}Po

Prompt, in-beam $\gamma$ rays following the reaction $^{170}$Yb + 142 MeV $^{28}$Si were measured at the ATLAS facility using 10 Compton-suppressed Ge detectors and the Fragment Mass Analyzer. Transitions in $^{194}$Po were identified and placed using $\gamma$-ray singles and coincidence data gated on the mass of the evaporation residues. A level spectrum up to J$\approx$10$\hbar$ was established. The structure of $^{194}$Po is more collective than that observed in the heavier polonium isotopes and indicates that the structure has started to evolve towards the more collective nature expected for deformed nuclei.Comment: 8 pages, revtex 3.0, 4 figs. available upon reques

Algebras generated by two bounded holomorphic functions

We study the closure in the Hardy space or the disk algebra of algebras generated by two bounded functions, of which one is a finite Blaschke product. We give necessary and sufficient conditions for density or finite codimension of such algebras. The conditions are expressed in terms of the inner part of a function which is explicitly derived from each pair of generators. Our results are based on identifying z-invariant subspaces included in the closure of the algebra. Versions of these results for the case of the disk algebra are given.Comment: 22 pages ; a number of minor mistakes have been corrected, and some points clarified. Conditionally accepted by Journal d'Analyse Mathematiqu

Patenting and licensing of university research: promoting innovation or undermining academic values?

Since the 1980s in the US and the 1990s in Europe, patenting and licensing activities by universities have massively increased. This is strongly encouraged by governments throughout the Western world. Many regard academic patenting as essential to achieve 'knowledge transfer' from academia to industry. This trend has far-reaching consequences for access to the fruits of academic research and so the question arises whether the current policies are indeed promoting innovation or whether they are instead a symptom of a pro-intellectual property (IP) culture which is blind to adverse effects. Addressing this question requires both empirical analysis (how real is the link between academic patenting and licensing and 'development' of academic research by industry?) and normative assessment (which justifications are given for the current policies and to what extent do they threaten important academic values?). After illustrating the major rise of academic patenting and licensing in the US and Europe and commenting on the increasing trend of 'upstream' patenting and the focus on exclusive as opposed to non-exclusive licences, this paper will discuss five negative effects of these trends. Subsequently, the question as to why policymakers seem to ignore these adverse effects will be addressed. Finally, a number of proposals for improving university policies will be made