Cotorsion torsion triples and the representation theory of filtered hierarchical clustering

We give a full classification of representation types of the subcategories of representations of an $m \times n$ rectangular grid with monomorphisms (dually, epimorphisms) in one or both directions, which appear naturally in the context of clustering as two-parameter persistent homology in degree zero. We show that these subcategories are equivalent to the category of all representations of a smaller grid, modulo a finite number of indecomposables. This equivalence is constructed from a certain cotorsion torsion triple, which is obtained from a tilting subcategory generated by said indecomposables.Comment: 39 pages; corrected the lists appearing in Cor. 1.6 and minor changes throughou

Alas, the dark matter structures were not that trivial

The radial density profile of dark matter structures has been observed to have an almost universal behaviour in numerical simulations, however, the physical reason for this behaviour remains unclear. It has previously been shown that if the pseudo phase-space density, rho/sigma_d^epsilon, is a beautifully simple power-law in radius, with the "golden values" epsilon=3 and d=r (i.e., the phase-space density is only dependent on the radial component of the velocity dispersion), then one can analytically derive the radial variation of the mass profile, dispersion profile etc. That would imply, if correct, that we just have to explain why rho/sigma^3_r ~r^{-alpha}, and then we would understand everything about equilibrated DM structures. Here we use a set of simulated galaxies and clusters of galaxies to demonstrate that there are no such golden values, but that each structure instead has its own set of values. Considering the same structure at different redshifts shows no evolution of the phase-space parameters towards fixed points. There is also no clear connection between the halo virialized mass and these parameters. This implies that we still do not understand the origin of the profiles of dark matter structures.Comment: 4 pages, 3 figures, accepted for publication in ApJ

Vulnerability : a view from different disciplines

Practitioners from different disciplines use different meanings and concepts of vulnerability, which, in turn, have led to diverse methods of measuring it. This paper presents a selective review of the literature from several disciplines to examine how they define and measure vulnerability. The disciplines include economics, sociology/anthropology, disaster management, environmental science, and health/nutrition. Differences between the disciplines can be explained by their tendency to focus on different components of risk, household responses to risk and welfare outcomes. In general, they focus either on the risks (at one extreme) or the underlying conditions (or outcomes) at the other. Trade-offs exist between simple measurement schemes and rich conceptual understanding.Environmental Economics&Policies,Health Economics&Finance,Insurance&Risk Mitigation,Economic Theory&Research,Rural Poverty Reduction

Vaginal yeasts in the era of "over the counter" antifungals

OBJECTIVE: To establish whether there has been any rise in the prevalence of non-albicans Candida species isolated from vaginal swabs since the introduction of “over the counter” antifungal treatments. METHOD: A retrospective review looking at all positive vaginal yeast isolates collected from women attending one genitourinary medicine clinic during the 6 year period from 1993 to 1998 inclusive. All positive vaginal yeast isolates were included, regardless of whether or not the patients were symptomatic. Isolates from HIV positive women were excluded from the analysis. RESULT: No increase in non-albicans vaginal yeast isolates was shown during the period studied. The proportion of non-albicans yeasts remained constant at approximately 5% of the total yeasts isolated. The most common non-albicans yeast isolated was C glabrata. CONCLUSION: There is no evidence from this study to suggest that the increasing use of “over the counter” antifungal treatment has selected for atypical, possibly inherently azole resistant, strains of vaginal yeasts in HIV seronegative women