Pseudometrics, The Complex of Ultrametrics, and Iterated Cycle Structures

Every set X, finite of cardinality n say, carries a set M(X) of all possible pseudometrics. It is well known that M(X) forms a convex polyhedral cone whose faces correspond to triangle inequalities. Every point in a convex cone can be expressed as a conical sum of its extreme rays, hence the interest around discovering and classifying such rays. We shall give examples of extreme rays for M(X) exhibiting all integral edge lengths up to half the cardinality of X. By intersecting the cone with the unit cube we obtain the convex polytope of bounded-by-one pseudometrics BM(X). Analogous to extreme rays, every point in a convex polytope arises as a convex combination of extreme points. Extreme rays of BM(X) give rise to very special extreme points of ̄BM(X) as we may normalize a nonzero pseudometric to make its largest distance 1. We shall give a simple and complete characterization of extremeness for metrics with only edge lengths equal to 1/2 and 1. Then we shall use this characterization to give a decomposition result for the upper half of BM(X). BM(X) contains the set of bounded-by-1 pseudoultrametrics, U(X). Ultrametrics satisfy a stronger version of the triangle inequality, and have an interesting structure expressed in terms of partition chains. We will describe the topology of U(X) and its subset of scaled ultrametrics, SU(X), up to homotopy equivalence. Every permutation on a set X can be written as a product of disjoint cycles that cover X. In this way, a permutation generalizes a partition. An iterated cycle structure (ICS) will then be the associated generalization of a partition chain. Analogously, we will compute the “Euler-characteristic” of the set of iterated cycle structures

Dysregulation of ACE-1 in Normal Aging and the Early Stages of Alzheimer's Disease

An imbalance in the renin–angiotensin system (RAS) is associated with cognitive decline and disease pathology in Alzheimer’s disease (AD). In this study, we have investigated changes in the brain angiotensin-converting enzyme-1 (ACE-1) and angiotensin-II (Ang-II), and the counter-regulatory angiotensin-converting enzyme-2 (ACE-2), in the frontal and temporal cortex during normal aging and in the early stages of AD. We studied a cohort of normal aging (n = 121; 19–95 years age-at-death) from the Sudden Death Brain Bank, University of Edinburgh, United Kingdom, and AD and age-matched controls (n = 60) from the South West Dementia Brain Bank, University of Bristol, United Kingdom, stratified according to Braak tangle stage (BS): 0–II, III–IV (intermediate disease), and V–VI (end-stage disease). ACE-1 and ACE-2 enzyme activity were measured using fluorogenic peptide activity assays. ACE-1, ACE-2, and Ang-II protein level were measured by enzyme-linked immunosorbent assay (ELISA). In both regions, ACE-1 protein and Ang-II levels correlated positively with age whereas ACE-1 enzyme activity was inversely related to age. ACE-1 protein correlated positively with Ang-II, whilst ACE-1 activity correlated inversely with Ang-II in normal aging. ACE-1 enzyme activity was elevated at an early/intermediate stage, BS III–IV compared to BS 0–II in the temporal cortex in AD. ACE-2 protein and enzyme activity were unchanged with aging and in AD. In conclusion, ACE-1 activity is induced in the early stages of AD independently from normal physiological age-related changes in ACE-1 protein

An Untriggered Search for Optical Bursts

We present an untriggered search for optical bursts with the ROTSE-I telephoto array. Observations were taken which monitor an effective 256 square degree field continuously over 125 hours to m_{ROTSE}=15.7. The uniquely large field, moderate limiting magnitude and fast cadence of $\sim$10 minutes permits transient searches in a new region of sensitivity. Our search reveals no candidate events. To quantify this result, we simulate potential optical bursts with peak magnitude, m_{p}, at t=10 s, which fade as f=(\frac{t}{t_{0}}) ^{\alpha_{t}}, where \alpha_t < 0. Simple estimates based on observational evidence indicate that a search of this sensitivity begins to probe the possible region occupied by GRB orphan afterglows. Our observing protocol and image sensitivity result in a broad region of high detection efficiency for light curves to the bright and slowly varying side of a boundary running from [\alpha_{t},m_{p}]=[-2.0,6.0] to [-0.3,13.2]. Within this region, the integrated rate of brief optical bursts is less than 1.1\times 10^{-8} {\rm s}^{-1} {\rm deg}^{-2}. At $\sim$22 times the observed GRB rate from BATSE, this suggests a limit on \frac{\theta_{opt}}{\theta_{\gamma}}\lesssim 5 where \theta_{opt} and \theta_{\gamma} are the optical and gamma-ray collimation angles, respectively. Several effects might explain the absence of optical bursts, and a search of the kind described here but more sensitive by about 4 magnitudes should offer a more definitive probe.Comment: 8 pages, 6 figures, 1 tabl

"Sorry to hear you're going through a difficult time": Investigating online discussions of consumer debt

As recent years have witnessed increasing pressure on personal finances, compounded by the current cost of living crisis, online forums have become an important resource for people dealing with financial precarity. In this article, we offer a corpus linguistic analysis of data from MoneySavingExpert.com, the UK's largest online money management advice forum, studying 207 threads and 41.4 million words of text posted from 2005 to 2021. Through measures of word frequency and word association, we uncover similarities and differences in language use on the debt-free wannabe (DFW) and mortgage-free wannabe (MFW) forums. Our findings show that the DFW forum focuses on interactive exchanges involving requests for help and offers of advice, while the MFW forum is characterised by goal setting and community building. We thus contribute new insights into the discursive construction of debt in digital media and provide further understanding of the role online forums play in supporting vulnerable people

A Search for Early Optical Emission from Short and Long Duration Gamma-ray Bursts

Gamma-ray bursts of short duration may harbor vital clues to the range of phenomena producing bursts. However, recent progress from the observation of optical counterparts has not benefitted the study of short bursts. We have searched for early optical emission from six gamma-ray bursts using the ROTSE-I telephoto array. Three of these events were of short duration, including GRB 980527 which is among the brightest short bursts yet observed. The data consist of unfiltered CCD optical images taken in response to BATSE triggers delivered via the GCN. For the first time, we have analyzed the entire 16 degree by 16 degree field covered for five of these bursts. In addition, we discuss a search for the optical counterpart to GRB 000201, a well-localized long burst. Single image sensitivities range from 13th to 14th magnitude around 10 s after the initial burst detection, and 14 - 15.8 one hour later. No new optical counterparts were discovered in this analysis suggesting short burst optical and gamma-ray fluxes are uncorrelated.Comment: 8 pages, 2 figures, subm. to ApJ Let

The effect of endothelial cell overexpression of plasminogen activator inhibitor-1 on smooth muscle cell migration

AbstractIntroduction: Plasminogen activator inhibitor-1 (PAI-1), a known inhibitor of plasminogen activators, may regulate smooth muscle cell migration (SMC) through alteration in matrix metalloproteinase (MMP) activity. Methods: To study the effect of endothelial cell (EC) PAI-1 overexpression on SMC migration, RT-PCR was used to clone the full length PAI-1 gene, which was ligated into the pCMV/myc/ER expression vector. With electroporation, bovine aortic ECs were transfected with either the PAI-1 construct or the empty vector as control. EC PAI-1 overexpression was shown with a specific PAI-1 activity assay and enzyme-linked immunosorbent assay. The effect of EC PAI-1 overexpression on SMC migration was measured with a modified Boyden-chamber assay. SMC MMP expression was measured with zymography. Results: Selected clones (EC9, EC21) had a three-fold to five-fold increase in PAI-1 activity compared with untransfected EC and empty vector EC (ECC). Similarly, enzyme-linked immunosorbent assay results showed a 3.5-fold to 5.5-fold increase in PAI-1 levels in EC9 and EC21 versus ECC. Untransfected EC and ECC had similar effects on SMC migratory patterns. Migration of SMC exposed to PAI-1 overexpressing EC was inhibited by 35% to 57% compared with ECC. This inhibitory effect was reversed with addition of exogenous urokinase-type plasminogen activator (uPA). Zymography showed downregulation of MMP-2 and MMP-9 in SMCs exposed to PAI-1 overexpressing EC. Conclusion: PAI-1 overexpression with transfected EC inhibits SMC migration. This effect may be mediated through decreased SMC MMP activity. (J Vasc Surg 2002;36:164-71.

Prompt Optical Observations of Gamma-ray Bursts

The Robotic Optical Transient Search Experiment (ROTSE) seeks to measure simultaneous and early afterglow optical emission from gamma-ray bursts (GRBs). A search for optical counterparts to six GRBs with localization errors of 1 square degree or better produced no detections. The earliest limiting sensitivity is m(ROTSE) > 13.1 at 10.85 seconds (5 second exposure) after the gamma-ray rise, and the best limit is m(ROTSE) > 16.0 at 62 minutes (897 second exposure). These are the most stringent limits obtained for GRB optical counterpart brightness in the first hour after the burst. Consideration of the gamma-ray fluence and peak flux for these bursts and for GRB990123 indicates that there is not a strong positive correlation between optical flux and gamma-ray emission.Comment: 4 pages, 3 figures, submitted to ApJ Letter