Stable variable step stiff methods for ordinary differential equations

The (alpha)-type variable step variable formula method was first shown to be stable by Zlatev in 1978 and more generally in 1981. These methods are studied for their use in the numerical solution of stiff ordinary differential equations with initial conditions;Two parameter families of these (alpha)-type formulas for orders 2-5 are analyzed. Theorems characterizing A(,0)-stability and A-stability are proved. It is shown that no order 5 A(,0)-stable member exists. A((theta))-stability is also discussed;A generalization of the above types of stability is defined for the variable coefficient methods with a variable grid spacing. Theorems for orders 2-3 are proved which provide bounds on the parameters and allowable step size changing sequences in order to increase generalized A((theta))-stability is discussed. A numerical solution for the order 4 case is given. Selection of these formulas is done and comparisons with the variable coefficient backward differentiation formulas are made;A general purpose computer code which uses the (alpha)-type variable step variable formula method is given. Numerical testing on a set of test problems is performed and comparisons are made to three different computer codes

Bayesian hierarchical EMAX model for doseâ response in early phase efficacy clinical trials

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/149669/1/sim8167_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/149669/2/sim8167.pd

Subacute normobaric oxygen and hyperbaric oxygen therapy in drowning, reversal of brain volume loss: a case report

A 2-year-old girl experienced cardiac arrest after cold water drowning. Magnetic resonance imaging (MRI) showed deep gray matter injury on day 4 and cerebral atrophy with gray and white matter loss on day 32. Patient had no speech, gait, or responsiveness to commands on day 48 at hospital discharge. She received normobaric 100% oxygen treatment (2 L/minute for 45 minutes by nasal cannula, twice/day) since day 56 and then hyperbaric oxygen treatment (HBOT) at 1.3 atmosphere absolute (131.7 kPa) air/45 minutes, 5 days/week for 40 sessions since day 79; visually apparent and/or physical examination-documented neurological improvement occurred upon initiating each therapy. After HBOT, the patient had normal speech and cognition, assisted gait, residual fine motor and temperament deficits. MRI at 5 months after injury and 27 days after HBOT showed near-normalization of ventricles and reversal of atrophy. Subacute normobaric oxygen and HBOT were able to restore drowning-induced cortical gray matter and white matter loss, as documented by sequential MRI, and simultaneous neurological function, as documented by video and physical examinations

Symptomatic intracranial abscess after treating lower cervical spine fracture with halo vest: a case report and review of literature

We present the case of a nineteen year old male, who sustained a fracture of anterior-superior surface of C7, combined with anterior subluxation at the level of C6–C7 vertebrae. After x-ray and CT examination, he was treated conservatively by a Halo-vest. After mobilization, the patient was discharged from the hospital with instructions to visit the outpatient's clinic at regular bases

Hyperbaric treatment for children with autism: a multicenter, randomized, double-blind, controlled trial

<p>Abstract</p> <p>Background</p> <p>Several uncontrolled studies of hyperbaric treatment in children with autism have reported clinical improvements; however, this treatment has not been evaluated to date with a controlled study. We performed a multicenter, randomized, double-blind, controlled trial to assess the efficacy of hyperbaric treatment in children with autism.</p> <p>Methods</p> <p>62 children with autism recruited from 6 centers, ages 2–7 years (mean 4.92 ± 1.21), were randomly assigned to 40 hourly treatments of either hyperbaric treatment at 1.3 atmosphere (atm) and 24% oxygen ("treatment group", n = 33) or slightly pressurized room air at 1.03 atm and 21% oxygen ("control group", n = 29). Outcome measures included Clinical Global Impression (CGI) scale, Aberrant Behavior Checklist (ABC), and Autism Treatment Evaluation Checklist (ATEC).</p> <p>Results</p> <p>After 40 sessions, mean physician CGI scores significantly improved in the treatment group compared to controls in overall functioning (p = 0.0008), receptive language (p < 0.0001), social interaction (p = 0.0473), and eye contact (p = 0.0102); 9/30 children (30%) in the treatment group were rated as "very much improved" or "much improved" compared to 2/26 (8%) of controls (p = 0.0471); 24/30 (80%) in the treatment group improved compared to 10/26 (38%) of controls (p = 0.0024). Mean parental CGI scores significantly improved in the treatment group compared to controls in overall functioning (p = 0.0336), receptive language (p = 0.0168), and eye contact (p = 0.0322). On the ABC, significant improvements were observed in the treatment group in total score, irritability, stereotypy, hyperactivity, and speech (p < 0.03 for each), but not in the control group. In the treatment group compared to the control group, mean changes on the ABC total score and subscales were similar except a greater number of children improved in irritability (p = 0.0311). On the ATEC, sensory/cognitive awareness significantly improved (p = 0.0367) in the treatment group compared to the control group. Post-hoc analysis indicated that children over age 5 and children with lower initial autism severity had the most robust improvements. Hyperbaric treatment was safe and well-tolerated.</p> <p>Conclusion</p> <p>Children with autism who received hyperbaric treatment at 1.3 atm and 24% oxygen for 40 hourly sessions had significant improvements in overall functioning, receptive language, social interaction, eye contact, and sensory/cognitive awareness compared to children who received slightly pressurized room air.</p> <p>Trial Registration</p> <p>clinicaltrials.gov NCT00335790</p

College Algebra with Modeling and Visualization

https://cornerstone.lib.mnsu.edu/university-archives-msu-authors/1298/thumbnail.jp

College Algebra with Modeling and Visualization

https://cornerstone.lib.mnsu.edu/university-archives-msu-authors/1299/thumbnail.jp