Ursinus College Bulletin Vol. 13, No. 5, February 1897

A digitized copy of the February 1897 Ursinus College Bulletin.https://digitalcommons.ursinus.edu/ucbulletin/1122/thumbnail.jp

Large Deviations Behavior of the Logarithmic Error Probability of Random Codes

This work studies the deviations of the error exponent of the constant composition code ensemble around its expectation, known as the error exponent of the typical random code (TRC). In particular, it is shown that the probability of randomly drawing a codebook whose error exponent is smaller than the TRC exponent is exponentially small; upper and lower bounds for this exponent are given, which coincide in some cases. In addition, the probability of randomly drawing a codebook whose error exponent is larger than the TRC exponent is shown to be double–exponentially small; upper and lower bounds to the double–exponential exponent are given. The results suggest that codebooks whose error exponent is larger than the error exponent of the TRC are extremely rare. The key ingredient in the proofs is a new large deviations result of type class enumerators with dependent variables

Achalasia: unusual cause of chronic cough in children

Achalasia is a rare motility disorder of the esophagus which results from lack of enervation of the lower esophageal sphincter muscles and leads to dilatation of proximal esophagus. Patients with achalasia presents typically with dysphagia, vomiting of undigested food and failure to thrive. Cough can be present in achalasia patients due to aspiration of food or due to airway compression by the dilated esophagus. We report two cases of achalasia presenting primarily with prolonged cough. Diagnosis of achalasia in both cases was delayed due to this atypical presentation. This highlights the importance of recognizing achalasia as a potential cause of chronic cough in order to avoid delayed diagnosis and mismanagement