Codimension formulae for the intersection of fractal subsets of Cantor spaces

We examine the dimensions of the intersection of a subset $E$ of an $m$-ary Cantor space $\mathcal{C}^m$ with the image of a subset $F$ under a random isometry with respect to a natural metric. We obtain almost sure upper bounds for the Hausdorff and upper box-counting dimensions of the intersection, and a lower bound for the essential supremum of the Hausdorff dimension. The dimensions of the intersections are typically $\max\{\dim E +\dim F -\dim \mathcal{C}^m, 0\}$, akin to other codimension theorems. The upper estimates come from the expected sizes of coverings, whilst the lower estimate is more intricate, using martingales to define a random measure on the intersection to facilitate a potential theoretic argument.Comment: Accepted version, Proc. Amer. Math. So

TOWARD A NEUROPHYSIOLOGY OF PAIN

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75094/1/j.1526-4610.1969.hed0804141.x.pd

Neural Mechanisms of Pain: an Overview

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65716/1/j.1399-6576.1982.tb01838.x.pd

An empirical analysis of the effects of climate variables on national level economic growth

The influence of climate on economic growth is a topic of growing interest. Few studies have investigated the potential role that climate hazards and their cumulative effects have on the growth prospects for a country. Due to the relatively stationary spatial patterns of global climate, some regions and countries are more prone to climate hazards and climate variability than others. This study uses a precipitation index that preserves the spatial and temporal variability of precipitation and differentiates between precipitation maximums (such as floods) and minimums (such as droughts). The authors develop a year and country fixed effects regression model to test the influence of climate variables on measures of economic growth and activity. The results indicate that precipitation extremes (floods and droughts) are the dominant climate influence on economic growth and that the effects are significant and negative. The drought index is associated with a highly significant negative influence on growth of growth domestic product, while the flood index is associated with a negative influence on growth of gross domestic product and lagged effects on growth. Temperature has little significant effect. These results have important implications for economic projections of climate change impacts. In addition, adaptation strategies should give new consideration to the importance of water resources given the identification of precipitation extremes as the key climate influence on historical growth of gross domestic product.Climate Change Mitigation and Green House Gases,Science of Climate Change,Global Environment Facility,Climate Change Economics,Climate Change Impacts

Sweet Georgia Brown

With Ukulele arrangement. Contains advertisements and/or short musical examples of pieces being sold by publisher.https://digitalcommons.library.umaine.edu/mmb-vp/6923/thumbnail.jp

Supraspinal nocifensive responses of cats: Spinal cord pathways, monoamines, and modulation

These experiments were conducted to determine (1) whether dorsal and ventral ascending spinal pathways can each mediate unlearned supraspinal nocifensive responses of cats to noxious thermal stimuli and (2) whether interrupting the spinal projection of supraspinal monoaminergic neurons alters the excitability and natural modulation of these responses. In partially restrained cats, thermal pulses (≥ 47°C) delivered to the hindlimbs of intact cats or rostral to lesions of the thoracic spinal cord elicited abrupt body movements and interruption of eating (or of exploring for) liquified food. These electronically monitored responses automatically terminated the stimulus. Natural modulation of responsiveness was produced by delivering food and thermal stimuli simultaneously; this reduced response probability by an average of 41%. Complete transection of the thoracic spinal cord eliminated both thermally elicited responses, and orienting responses to noxious and tactile mechanical stimulation of the hindlimbs. Ventral bilateral thoracic spinal cord lesions that spared only the dorsal funiculus and portions of the dorsolateral funiculus (three cats) significantly reduced orienting responses to all mechanical hindlimb stimuli and reduced, but did not eliminate, movement and interrupt responses to noxious thermal hindlimb stimuli. Response latency was unaffected. Food-induced response supression persisted although lumbar spinal cord concentrations of serotonin (5HT) and norepinephrine (NE) were markedly reduced. A bilateral lesion of the dorsal funiculi and dorsal portions of the dorsolateral funiculi (one cat) also reduced nocifensive responsiveness, but only the NE concentration in lumbar spinal cord was reduced significantly relative to a matched cervical sample. In contrast, deep bilateral lesions of the dorsolateral funiculi (two cats) produced an increase in the probability of movement and interrupt responses without affecting either response latency or food-induced response supression. Lumbar spinal cord concentrations of NE and, in one cat, 5HT were reduced. We conclude that (1) the dorsal and ventral spinal funiculi are each sufficient to initiate and necessary to maintain normal supraspinally organized nocifensive behavior in the cat; (2) descending monoaminergic pathways are not necessary for the phasic modulation of these responses; and (3) the tonic excitability, but not the phasic modulation, of these responses is determined in part by fibers in the dorsolateral funiculus.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/50039/1/902700412_ftp.pd

A Note On The Determinants Of Equity Payouts

This study develops an equity distribution model to analyze dividend and share repurchase pay- ments to shareholders. Transaction costs increase and agency costs decrease as equity cash dis- tributions increase, suggesting that an optimal equity distribution exists that minimizes the sum of these two costs. A Tobit model relates the equity distribution yield (dividend and share repurchase distributions as a percent of market capitalization) to proxies of perceived undervaluation, finan- cial leverage, asset productivity, investment cash outflows, and agency costs. The results suggest that firms appearing undervalued, using little financial leverage, employing more productive as- sets, having fewer investment opportunities, or having greater dispersion of ownership distribute relatively more cash to shareholders through dividends and/or share repurchases. These findings support the existence of an optimal equity cash distribution policy that is unique to each firm

Estimates of the Costs and Benefits of Expanding the Early Childhood Education Program in Kentucky

Excerpt from the executive summary: Kentucky officials are being encouraged to expand the availability of Kentucky’s state-funded preschool program. The current program restricts eligibility to three- and four-year-old students with disabilities and four-year-old students with family incomes up to 150 percent of the federal poverty level

Sweet Georgia Brown.

Text only; Tan backgroundhttps://scholarsjunction.msstate.edu/cht-sheet-music/10391/thumbnail.jp