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Recently we were presented with an interesting twist to the sliding ladder problem viewed in the related rates section of most calculus textbooks. Our problem concerning a sliding ladder that eventually hits the ground. At first, those attempting this problem fell into the calculus trap using only related rates. Previous work for this problem included higher order systems of differential equations in the solution. This paper discusses a new direction with modeling issues, several modeling based solutions, and numerical methods to solve these models using a spreadsheet. (Contains 2 figures and 3 tables.)

Focal Electrically-Administered Seizure Therapy (FEAST) is a form of electroconvulsive therapy (ECT) that spatially focuses the electrical stimulus to initiate seizure activity in right prefrontal cortex. Two open-label non-comparative studies suggested that FEAST has reduced cognitive side effects when compared to historical data from other forms of ECT. In two different ECT clinics, we compared the efficacy and cognitive side effects of FEAST and Right Unilateral Ultrabrief Pulse (RUL-UBP) ECT. Using a non-randomized, open-label design, 39 depressed adults were recruited after referral for ECT. Twenty patients received FEAST (14 women; age 45.2 ± 12.7), and 19 received RUL-UBP ECT (16 women; age 43.2 ± 16.4). Key cognitive outcome measures were the postictal time to reorientation and the Columbia University Autobiographical Memory Interview: Short-Form (CUAMI-SF). Antidepressant effects were assessed using the Hamilton Rating Scale for Depression (HRSD 24). In the Intent-to-treat sample, a repeated measures mixed model suggested no between group difference in HRSD 24 score over time (F 1,35 = 0.82, p = 0.37), while the response rate favored FEAST (FEAST: 65%; RUL-UBP ECT: 57.9%), and the remission rate favored RUL-UBP ECT (FEAST: 35%; RUL-UBP ECT: 47.4%). The FEAST group had numeric superiority in average time to reorientation (FEAST: 6.6 ± 5.0 min; RUL-UBP ECT: 8.8 ± 5.8 min; Cohens d = 0.41), and CUAMI-SF consistency score (FEAST: 69.2 ± 14.2%; RUL-UBP ECT: 63.9 ± 9.9%; Cohens d = 0.43); findings that failed to meet statistical significance. FEAST exerts similar efficacy relative to an optimal form of conventional ECT and may have milder cognitive side effects. A blinded, randomized, non-inferiority trial is needed. • This trial compared FEAST and RUL-UBP ECT to determine preliminary differences. • Using an open-label, non-randomized design, we assessed efficacy and amnestic effects. • There were no significant differences between the two groups in any primary outcome. • Our preliminary findings, however, suggest a larger comparative study is indicated. [ABSTRACT FROM AUTHOR]

Recently we were presented with an interesting twist to the sliding ladder problem viewed in the related rates section of most calculus textbooks. Our problem concerning a sliding ladder that eventually hits the ground. At first, those attempting this problem fell into the calculus trap using only related rates. Previous work for this problem included higher order systems of differential equations in the solution. This paper discusses a new direction with modeling issues, several modeling based solutions, and numerical methods to solve these models using a spreadsheet. [ABSTRACT FROM AUTHOR]