The dimension of the Brownian frontier is greater than 1

Consider a planar Brownian motion run for finite time. The frontier or ``outer boundary'' of the path is the boundary of the unbounded component of the complement. Burdzy (1989) showed that the frontier has infinite length. We improve this by showing that the Hausdorff dimension of the frontier is strictly greater than 1. (It has been conjectured that the Brownian frontier has dimension $4/3$, but this is still open.) The proof uses Jones's Traveling Salesman Theorem and a self-similar tiling of the plane by fractal tiles known as Gosper Islands

Do Stock Prices Really Reflect Fundamental Values? The Case of REITs

Real estate investment trust (REIT) stock prices deviate substantially from net asset values (NAV). Using REIT data since 1990, we find large positive excess returns to a strategy of buying stocks that trade at a discount to NAV, and shorting stocks trading at a premium to NAV. Estimated alphas from this strategy are between 0.9% and 1.8% per month, with little risk. Trading costs and short-sale constraints are not prohibitive and the results strengthen when we control for differences in liquidity or the extent of institutional ownership. We find that some variation in P/NAV makes sense, as premiums are positively related to recent and future NAV growth. However, there appears to be too much volatility in P/NAV, giving rise to potential profits from short-term mean reversion. The closed-end fund literature has some similar findings on stock price deviations from fundamental value, but compared to closed-end funds REITs are much larger and have much higher insider and institutional ownership. These differences suggest that REIT premiums and discounts reflect more than just small investor sentiment, which is a common explanation of why closed-end fund prices deviate from their fundamental value.

Genetic basis of human circadian rhythm disorders.

Circadian rhythm disorders constitute a group of phenotypes that usually present as altered sleep-wake schedules. Until a human genetics approach was applied to investigate these traits, the genetic components regulating human circadian rhythm and sleep behaviors remained mysterious. Steady advances in the last decade have dramatically improved our understanding of the genes involved in circadian rhythmicity and sleep regulation. Finding these genes presents new opportunities to use a wide range of approaches, including in vitro molecular studies and in vivo animal modeling, to elevate our understanding of how sleep and circadian rhythms are regulated and maintained. Ultimately, this knowledge will reveal how circadian and sleep disruption contribute to various ailments and shed light on how best to maintain and recover good health

Split-plot designs: What, why, and how

The past decade has seen rapid advances in the development of new methods for the design and analysis of split-plot experiments. Unfortunately, the value of these designs for industrial experimentation has not been fully appreciated. In this paper, we review recent developments and provide guidelines for the use of split-plot designs in industrial applications

A role for the extracellular calcium-sensing receptor in cell-cell communication in pancreatic islets of Langerhans

Background: The extracellular calcium-sensing receptor (CaR) is expressed in many tissues that are not associated with Ca2+ homeostasis, including the endocrine cells in pancreatic islets of Langerhans. We have demonstrated previously that pharmacological activation of the CaR stimulates insulin secretion from islet -cells and insulin-secreting MIN6 cells. Methods: In the present study we have investigated the effects of CaR activation on MIN6 cell proliferation and have used shRNA-mediated CaR knockdown to determine whether the CaR is involved in the regulation of insulin secretion via cell-cell communication. Results: CaR activation caused the phosphorylation and activation of the p42/44 MAPK signalling cascade, and this activation was prevented by the shRNA-induced down-regulation of CaR mRNA expression. CaR activation also resulted in increased proliferation of MIN6 cells, consistent with the known role of the p42/44 MAPK system in the regulation of -cell proliferation. Down-regulation of CaR expression had no detectable effects on glucose-induced insulin secretion from MIN6 cells maintained as monolayers, but blocked the increases in insulin secretion that were observed when the cells were configured as three-dimensional islet-like structures (pseudoislets), consistent with a role for the CaR in cell-cell communication in pseudoislets. Conclusion: It is well established that islet function is dependent on communication between islet cells and the results of this study suggest that the CaR is required for -cell to -cell interactions within islet-like structures