Continuous Nowhere Differentiable Functions

In this presentation we study functions that are continuous everywhere on their domain but differentiable nowhere.  One such function is the function whose graph is called the Kiesswetter curve.  First we construct the curve and the piece-wise function that represents that curve.  We prove several key properties of the function that gives us insight to why this function is continuous on the unit interval.  We then prove the continuity and nondifferentiability of the function

Scintillator-based ion beam profiler for diagnosing laser-accelerated ion beams

Next generation intense, short-pulse laser facilities require new high repetition rate diagnostics for the detection of ionizing radiation. We have designed a new scintillator-based ion beam profiler capable of measuring the ion beam transverse profile for a number of discrete energy ranges. The optical response and emission characteristics of four common plastic scintillators has been investigated for a range of proton energies and fluxes. The scintillator light output (for 1 MeV > Ep < 28 MeV) was found to have a non-linear scaling with proton energy but a linear response to incident flux. Initial measurements with a prototype diagnostic have been successful, although further calibration work is required to characterize the total system response and limitations under the high flux, short pulse duration conditions of a typical high intensity laser-plasma interaction

Dysfunctional Voiding: Does a validated urine color scale correlate with dysfunctional voiding severity score?

Introduction Dysfunctional voiding (DV), defined as abnormal coordination between the urinary sphincter and the detrusor muscle in a neurologically intact individual, affects approximately 40% of patients that populate pediatric urology clinics. Improper hydration affects the specific gravity and concentration of urinary irritants, resulting in symptoms similar to those seen in DV patients. Methods Herein, we administered a validated DV survey (the Dysfunctional Voiding Symptom Score [DVSS]) and a validated dehydration severity chart (the Urine Color Chart [UCC]) to toilet trained pediatric patients and compared DV patients to patients presenting with non-urologic concerns. Data was analyzed on an item-for-item basis and by the total DVSS and UCC between the two groups. A total of 29 DV pediatric patients and 21 non-urologic pediatric patients were recruited from 2016 to 2018. Results Both patient groups were equivalent with regards to age, sex, height, weight, and BMI. The DV population had significantly higher scores in 7 out of 10 individual items within the DVSS when compared to those presenting for non-urologic complaints (p \u3c 0.05). In addition, DV patients had significantly higher total scores on the DVSS than non-urologic patients (p = 0.0004). No significant difference was noted in UCC scores between patient groups (p = 0.753). Regression analysis showed that within the dysfunctional voiding group, there was a linear relationship between DVSS and UCC scores. Conclusion The present study suggests the DVSS results yield significantly different results for DV patients when compared to age, sex, and BMI matched children with no urologic complaints. The UCC does not reliably vary between DV and non-urologic patients; however, there appears to be a linear relationship between DVSS and UCC scores within the DV cohort. Further studies may elucidate a validated metric by which DV and non-urologic pediatric patients may be differentiated

Pediatric testicular torsion: does patient transfer affect time to intervention or surgical outcomes at a rural tertiary care center?

Background: Testicular torsion (TT) is a urologic emergency that requires prompt surgical intervention. In rural Appalachia, patients are often transferred from surrounding communities due to lack of urologic care. We hypothesized that those transferred would have delayed intervention and higher rates of orchiectomy when compared to those who presented directly to our hospital. Methods: We performed a retrospective review of patient charts with an ICD-9 diagnosis of TT from 2008 to 2016. Patients met inclusion criteria if diagnosis was confirmed by operative exploration. We compared rate of testicular loss and time until surgical intervention between groups. Results: Twenty-three patients met inclusion criteria (12 transferred, 11 direct). Patient demographics did not significantly differ between groups. Transferred patients had a higher orchiectomy rate (33% v 22%,p = 0.41) although this was not statistically significant. Time to surgery from symptom onset was significantly longer in those transferred (12.9 h) compared to those not transferred (6.9 h, p = 0.02). Distance of transfer was not correlated with time of delay (r2 = 0.063). Conclusions: Transferred patients with TT have numerically higher rates of orchiectomy which may reach significance in an appropriately powered study, and relative delays in surgical intervention. This study highlights the need for improved access to urologic care in rural areas