Ergodic properties of countable extensions

First, we study countably piecewise continuous, piecewise monotone interval maps. We establish a necessary and sufficient criterion for the existence of a non-decreasing semiconjugacy to an interval map of constant slope in terms of the existence of an eigenvector of an operator acting on a space of measures. Then we give examples, both Markov and non-Markov, for which the criterion is violated. ^ Next, we establish a criterion for the existence of a constant slope map on the extended real line conjugate to a given countably piecewise monotone interval map. We require the given interval map to be continuous, Markov, and topologically mixing, and show by example that the mixing hypothesis is essential. ^ Next, we study a class of countable state subshifts of finite type which admit finite-state factors. Our systems carry a displacement function, analogous to that used in the rotation theory of circle maps. Among those invariant measures on the factor system for which the average displacement is zero, we identify a unique measure of maximal entropy. As a corollary we obtain an efficient computational tool for the Gurevich entropy of the countable state system. We also prove that the countable state systems in our class do not admit any measure of maximal entropy. ^ Finally, we apply our findings to the study of degree one circle maps with Markov partitions and with transitive liftings to the real line. After compactifying by adjoining fixed points at plus and minus infinity, we show how to compute the topological entropy of the lifting and how to find all conjugate maps of constant slope. We prove that there are conjugate maps of constant slope for every slope greater than or equal to the exponential of the entropy

Morphometric approach to many-body correlations in hard spheres

We model the thermodynamics of local structures within the hard sphere liquid at arbitrary volume fractions through the \textit{morphometric} calculation of $n$-body correlations. We calculate absolute free energies of local geometric motifs in excellent quantitative agreement with molecular dynamics simulations across the liquid and supercooled liquid regimes. We find a bimodality in the density library of states where five-fold symmetric structures appear lower in free energy than four-fold symmetric structures, and from a single reaction path predict a relaxation barrier which scales linearly in the compressibility factor. The method provides a new route to assess changes in the free energy landscape at volume fractions dynamically inaccessible to conventional techniques.Comment: 6+17 pages, 3 figure

Long Term Sequela of Pediatric Bladder Reconstruction

Children with refractory neurogenic bladder (NGB) who have failed maximal medical management are presented with options for bladder reconstruction. It is critical to understand the long-term sequela of bladder augmentation and bladder neck reconstruction to properly counsel families regarding these procedures. Benefits may include preservation of renal function, continence, reduced risk of renal-related mortality, and potential improvements in quality of life (QOL). However, these advantages must be balanced with the risks of bladder calculi, perforation, need for additional surgery, acid/base disturbances, vitamin B12 deficiency, and malignancy. Therefore, careful patient selection and preoperative counseling are paramount for those undergoing bladder reconstruction which includes intestinal bladder augmentation, as these patients require lifelong vigilant follow-up

Morphological thermodynamics for hard bodies from a controlled expansion

The morphometric approach is a powerful ansatz for decomposing the chemical potential for a complex solute into purely geometrical terms. This method has proven accuracy in hard spheres, presenting an alternative to comparatively expensive (classical) density functional theory approaches. Despite this, fundamental questions remain over why it is accurate and how one might include higher-order terms to improve accuracy. We derive the morphometric approach as the exact resummation of terms in the virial series, providing further justification of the approach. The resulting theory is less accurate than previous morphometric theories, but provides fundamental insights into the inclusion of higher-order terms and to extensions to mixtures of convex bodies of arbitrary shape.Comment: 10 pages, 2 figure

Epidural Analgesia Decreases Narcotic Requirements in Low Level Spina Bifida Patients Undergoing Urologic Laparotomy for Neurogenic Bladder and Bowel

Purpose Concern of anatomical anomalies and worsening neurologic symptoms has prevented widespread use of epidural catheters in patients with low level spina bifida (LLSB). We hypothesize that thoracic epidural placement in the T9-T10 interspace is safe and decreases narcotic requirements in LLSB patients following major open lower urinary tract reconstruction (LUTR). Materials and Methods We reviewed consecutive LLSB patients who had LUTR and epidurals for post-operative pain control. Controls were LLSB patients who received single shot transversus abdominis plane (TAP) blocks with similar procedures. Complications from epidural placement, including changes in motor and sensory status were recorded. Opioid consumption was calculated utilizing equivalent IV morphine doses. Mean and maximum pain scores on post-operative day (POD) 0-3 were calculated. Results 10 LLSB patients who had lower urinary tract reconstruction and epidurals were matched to 10 LLSB patients who had lower urinary tract reconstruction and transverse abdominis plane blocks. Groups were demographically similar. All had full abdominal sensation and functional levels at or below L3. No epidural complications or changes in neurological status were noted. The epidural group had decreased opioid consumption on POD 0-3 (0.75 mg/kg vs. 1.29 mg/kg, p=0.04). Pain scores were similar or improved in the epidural group. Conclusions Thoracic epidural analgesia appears to be a safe and effective opioid sparing option to assist with post-operative pain management following lower urinary tract reconstruction in LLSB patients

Many-body correlations from integral geometry

In a recent letter we presented a framework for predicting the concentrations of many-particle local structures inside the bulk liquid as a route to assessing changes in the liquid approaching dynamical arrest. Central to this framework was the morphometric approach, a synthesis of integral geometry and liquid state theory, which has traditionally been derived from fundamental measure theory. We present the morphometric approach in a new context as a generalisation of scaled particle theory, and derive several morphometric theories for hard spheres of fundamental and practical interest. Our central result is a new theory which is particularly suited to the treatment of many-body correlation functions in the hard sphere liquid, which we demonstrate by numerical tests against simulation.Comment: 12 pages, 6 figure

The need for specialized training for adults with congenital urologic conditions: differences in opinion among specialties

Introduction: The aim of this study was to survey pediatric urology fellowship directors (PFD) and adult reconstruction fellowship directors (AFD) to assess who they believe has sufficient training to care for adults with congenital urologic conditions (ACUC). Material and methods: An online survey was created to assess attitudes towards specific training to care for ACUC. The survey was administered to 27 PFD and 26 AFD [16 from genitourinary reconstructive surgery (GURS) and 10 from female pelvic medicine and reconstructive surgery (FPMRS)]. Both groups were asked if specific training is warranted, and if general urologists, pediatric urologists or adult reconstructive urologists were sufficiently trained to care for ACUC. Results: A total of 26 (96%) PFD and 10 (39%) AFD completed the survey. All PFD were fellowship trained in pediatrics. Of the AFD, 5 were GURS trained, 4 were FPMRS trained and 1 was not fellowship trained. The majority (65% PFD, 90% AFD) believed specific training is warranted. Few believed general urologists have sufficient training (8% PFD, 20% AFD). Most PFD believed pediatric urologists have sufficient training (85%), but a minority believed those with adult reconstructive training do (40%). Conversely, a minority of AFD believed that pediatric urologists have sufficient training (40%), while those with adult reconstructive training do (FPMRS: 67%, GURS: 60%). Conclusions: Both pediatric and adult reconstructive urologists believe specific training to care for adults with congenital urologic conditions is warranted. Neither group considers the other to be ideally suited to care for this co