Exponential tail bounds for loop-erased random walk in two dimensions

Let $M_n$ be the number of steps of the loop-erasure of a simple random walk on $\mathbb{Z}^2$ from the origin to the circle of radius $n$. We relate the moments of $M_n$ to $Es(n)$, the probability that a random walk and an independent loop-erased random walk both started at the origin do not intersect up to leaving the ball of radius $n$. This allows us to show that there exists $C$ such that for all $n$ and all $k=1,2,...,\mathbf{E}[M_n^k]\leq C^kk!\mathbf{E}[M_n]^k$ and hence to establish exponential moment bounds for $M_n$. This implies that there exists $c>0$ such that for all $n$ and all $\lambda\geq0$, $$\mathbf{P}\{M_n>\lambda\mathbf{E}[M_n]\}\leq2e^{-c\lambda}.$$ Using similar techniques, we then establish a second moment result for a specific conditioned random walk which enables us to prove that for any $\alpha0$ such that for all $n$ and $\lambda>0$, $$\mathbf{P}\{M_n<\lambda^{-1}\mathbf{E}[M_n]\}\leq Ce^{-c'\lambda ^{\alpha}}.$$Comment: Published in at http://dx.doi.org/10.1214/10-AOP539 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Oligopolistic Agreement and/or Superiority?: New Findings from New Methodologies and Data

The influential Scherer and Ross text (1990, p. 411) states that the main question in empirical industrial organization in the latter part of the twentieth century is Bains (1951) collusion or agreement hypothesis versus Demsetzs (1973) superior firm hypothesis. Prior to the Federal Trade Commission Line-of-Business (LOB) studies the contending schools were deadlocked, but these studies led to a win being declared for the superiority hypothesis by Scherer writing with seven other LOB researchers (1987). These studies found that the effect of concentration on profits disappeared when controlling for firm shares. As many economists agreed, merger policy shifted away from a focus on agreement to applying a unilateral effects (non-cooperative Nash) approach. We develop a nine year panel LOB data set for Korea. We perform three types of tests, all of which support both hypotheses, but which show that the agreement effect overwhelmingly dominates the superiority effect in pricing. First we examine a secondary implication of the superiority model: profit aggregation should imply that if share is negatively related to firm profits, so should concentration be negatively related to industry profits. Instead, we find that for those industries with a negative share relationship, the concentration profits relationship is positive and virtually identical to the relationship for the full sample in both within and between panel tests. Next we introduce a commonly cited model in the empirical literature. This model is cited to motivate the proposition that both share and concentration should have an effect on firm profits. However, authors who cite this model then typically use an ad hoc specification rather than estimating this as a structural model. We develop our structural model and define latent variables to distinguish between domestic and export price cost margins (PCMs) and to identify firm conjectures as they impact the domestic PCM. Demand elasticities are captured in non-linear industry fixed effects. We show that concentration plays an overwhelming role in determining firm PCMs, with firm share playing a far smaller role. We additionally exploit the structural characteristics of the model to deal with the possibility that deviations between marginal costs and average costs might be driving the results. For supporting evidence we construct a new latent variable identifying the domestic/export price ratio. We find a strong within relationship between concentration and the domestic/export price ratio, again firm shares play a weaker role. Finally, we discuss why our results differ from the FTC-LOB studies and provide evidence that would suggest that the FTC studies conclusions are biased due to the 1973 removal of price controls and energy crisis, the stagflation of the 1970s, and the use of national firm shares along with geographically weighted averages of concentration ratios.Industrial Organization,

Report on the 2022 excavations at Wogan Cavern (Pembroke, Pembrokeshire, UK)

Publisher Copyright: © 2023 British Cave Research Association. All rights reserved.Peer reviewe

Cirene : air-sea iInteractions in the Seychelles-Chagos thermocline ridge region

Author Posting. © American Meteorological Society, 2009. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Bulletin of the American Meteorological Society 90 (2009): 1337-1350, doi:10.1175/2008BAMS2499.1.The Vasco—Cirene program ex-plores how strong air—sea inter-actions promoted by the shallow thermocline and high sea surface temperature in the Seychelles—Chagos thermocline ridge results in marked variability at synoptic, intraseasonal, and interannual time scales. The Cirene oceano-graphic cruise collected oceanic, atmospheric, and air—sea flux observations in this region in Jan-uary—February 2007. The contem-poraneous Vasco field experiment complemented these measure-ments with balloon deployments from the Seychelles. Cirene also contributed to the development of the Indian Ocean observing system via deployment of a moor-ing and 12 Argo profilers. Unusual conditions prevailed in the Indian Ocean during Janu-ary and February 2007, following the Indian Ocean dipole climate anomaly of late 2006. Cirene measurements show that the Seychelles—Chagos thermocline ridge had higher-than-usual heat content with subsurface anomalies up to 7°C. The ocean surface was warmer and fresher than average, and unusual eastward currents prevailed down to 800 m. These anomalous conditions had a major impact on tuna fishing in early 2007. Our dataset also sampled the genesis and maturation of Tropical Cyclone Dora, including high surface temperatures and a strong diurnal cycle before the cyclone, followed by a 1.5°C cool-ing over 10 days. Balloonborne instruments sampled the surface and boundary layer dynamics of Dora. We observed small-scale structures like dry-air layers in the atmosphere and diurnal warm layers in the near-surface ocean. The Cirene data will quantify the impact of these finescale features on the upper-ocean heat budget and atmospheric deep convection.CNES funded the Vasco part of the experiment; INSU funded the Cirene part. R/V Suroît is an Ifremer ship. The contributions from ODU, WHOI, and FOI (Sweden) are supported by the National Science Foundation under Grant Number 0525657. The participation of the University of Miami group was funded though NASA (NNG04HZ33C). PMEL participation was supported through NOAA’s Office of Climate Observation

Identification and Characterization of Antifungal Compounds Using a Saccharomyces cerevisiae Reporter Bioassay

New antifungal drugs are urgently needed due to the currently limited selection, the emergence of drug resistance, and the toxicity of several commonly used drugs. To identify drug leads, we screened small molecules using a Saccharomyces cerevisiae reporter bioassay in which S. cerevisiae heterologously expresses Hik1, a group III hybrid histidine kinase (HHK) from Magnaporthe grisea. Group III HHKs are integral in fungal cell physiology, and highly conserved throughout this kingdom; they are absent in mammals, making them an attractive drug target. Our screen identified compounds 13 and 33, which showed robust activity against numerous fungal genera including Candida spp., Cryptococcus spp. and molds such as Aspergillus fumigatus and Rhizopus oryzae. Drug-resistant Candida albicans from patients were also highly susceptible to compounds 13 and 33. While the compounds do not act directly on HHKs, microarray analysis showed that compound 13 induced transcripts associated with oxidative stress, and compound 33, transcripts linked with heavy metal stress. Both compounds were highly active against C. albicans biofilm, in vitro and in vivo, and exerted synergy with fluconazole, which was inactive alone. Thus, we identified potent, broad-spectrum antifungal drug leads from a small molecule screen using a high-throughput, S. cerevisiae reporter bioassay