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Determining the optimal mix of exercise activities using mathematical programming.

Several mathematical programming models designed to develop optimal exercise programs are described. The models can be adapted to various individuals so that unique objectives and constraints can be met. The models can be used to design individualized exercise programs for a wide variety of people. Models can meet the needs of those who exercise for recreational purposes, athletic achievements and/or rehabilitative purposes. As the objectives of an exercise program and the constraints on it change over time, individuals must occasionally review the relevancy of the objective function and constraints. The model must then be updated so that the updated optimal exercise program can be designed. An illustrative example that deals with the development of an overall fitness program for individuals exercising for recreational reasons is described.

Exercise↗

A national study of the efficiency of hospitals in urban markets.

Using a sample of 3,000 urban hospitals, this article examines the contributions of selected hospital characteristics to variations in hospital technical efficiencies, while it accounts for multiple products and inputs, and controls for local environmental variations. Four hospital characteristics are examined: hospital size, membership in a multihospital system, ownership, and payer mix (managed care contracts, percent Medicare, and percent Medicaid). Ownership and percent Medicare are consistently found to be related significantly to hospital efficiency. Within the ownership variable, government hospitals tend to be more efficient and for-profit hospitals less efficient than other hospitals. Higher percentages of Medicare payment are negatively related to efficiency. While not consistently significant across all five of the MSA size categories in which the analyses are conducted, possession of managed care contracts, membership in a multihospital system, and size all are consistently related positively to hospital technical efficiency. These variables are also all significant when the hospitals are examined in a combined analysis. Percent Medicaid was not significant in any of the analyses. Implications for policy and the need for methodological work are discussed.

Analysis of Variance↗

Comparison between linear and nonlinear in-season training programs in freshman football players.

The purpose of this study was to compare linear (LT) with nonlinear (NL) in-season training programs in freshman football players during the course of 2 separate seasons. During the first year (n = 14, mean +/- SD = 177.3 +/- 4.8 cm, 88.0 +/- 9.7 kg), the LT program was employed 2 days per week. In the second year (n = 14, 175.0 +/- 7.1 cm, 94.2 +/- 20.5 kg), a 2 days per week LT was used. Subjects were tested for maximal strength in the squat (1 repetition maximum [1RM]) and bench press (1RM) exercises. A significant improvement in 1RM squat was seen in LT, but not in NL. No significant improvement in 1RM bench press was seen in either group. A significant difference between LT and NL was observed in Delta1RM squat (13.8 +/- 7.4 kg compared with 1.6 +/- 2.6 kg, respectively). Results of this study suggest that LT may be more effective in eliciting strength gains than NL in freshman football players during an in-season training program.

Adolescent↗

Electronic spreadsheet program for estimating two-compartment intravenous pharmacokinetic parameters by least squares linear regression analysis.

A microcomputer program using an electronic spreadsheet program was developed to calculate pharmacokinetic values of thiacetarsamide sodium, a drug used to kill the adult heartworm (Dirofilaria immitis) parasite of the dog. A least squares, semilogarithmic regression analysis was done on data using a two compartment intravenous model. The data entered includes the time after injection and the drug concentration at that time. A graph of the points can be viewed or plotted, with the time on the x-axis, and the natural log of the drug concentration on the y-axis. The program was developed on a Televideo (512 kbytes) microcomputer. The spreadsheet used was Lotus 123 with the pharmacokinetics program occupying 16 kbytes of memory (720 cells) out of the 400 kbytes available with Lotus.

Animals↗

A longitudinal study of changes in evoked otoacoustic emissions and pure-tone thresholds as measured in a hearing conservation program.

Non-linear transient-evoked otoacoustic emissions (TEOAEs) at 74dB pSPL, distortion-product otoacoustic emissions (DPOAEs) at 65/45dB SPL and pure-tone audiometry were used to detect noise-induced, inner car changes in a longitudinal study. Repeated-measures ANOVAs were made on the Noise (n=69) and Quiet (n=42) groups. The Noise group's hearing thresholds increased by 1.2 dB and DPOAE amplitude decreased by -0.9 dB. For both groups, TEOAE amplitude decreased by approximately -0.6 dB. Eight of 12 ears with permanent threshold shift (PTS) and 10 of 13 ears with temporary threshold shift (TTS) showed TEOAE decrements or low baseline TEOAE amplitudes. Fewer TTS and PTS ears also showed DPOAE decrements, and there was never a DPOAE decrement without a corresponding TEOAE decrement or low TEOAE baseline. Some TTS ears showed permanent emission decrements. Although otoacoustic emissions show promise in detecting noise-induced inner ear changes, it is premature to use them in hearing conservation programs.

Adolescent↗

A simplified method to determine binding parameters in a two-site case using linear regression.

A program using a simplified method to compute estimates of binding parameters in a system with two independent classes of binding sites is presented. An iterative method is used to approximate step-by-step the two lines describing the binding activities separately, starting from a curvilinear Scatchard or Hofstee plot. This method is designed for use on microcomputers with graphic facilities and on programmable hand-held calculators.

Binding Sites↗

Three-dimensional imaging for brachytherapy planning.

A computerized 3-D brachytherapy treatment planning program has been developed which simulates catheter trajectories, radioisotope seed positioning and percentage dosimetry zones about a catheter/seed array in relationship to CT or MRI images. The high activity 125I seed is used in this program. A visual and a non-linear mathematical optimization program will also be described.

Brachytherapy↗

A practical computer-based approach to the analysis of radioligand binding experiments.

EBDA is a computer program designed to process raw data (dpm) obtained from radioligand binding experiments into a form suitable for use by a non-linear curve fitting program. Processing of the data is facilitated by graphical representation in the form of Scatchard and Hill plots for saturation data, and competition curves and Hofstee plots for drug displacement studies. Preliminary estimates of binding constants required by a non-linear curve fitting program can also be obtained.

Computers↗

[Scale-up preparation of hydrophobic interaction chromatographic packing materials based on inorganic matrix].

Based on inorganic matrix controlled pore glass (CPG) and macro-pore silica sphere, by using polyethylene glycol (PEG 1000) as a ligand, a preparation method of hydrophobic interaction chromatographic (HIC) packing material was improved by adding a proper catalyst during the bonding process. The packing material can be synthesized in a scale-up batch, for example 150g for each batch, both for analytical and preparative columns. The retention of proteins, such as cytochrome C (Cyt-C), chymotrypsingen-A (Chy-A), lysozyme (Lys) and ribonuclease(Rnase), is increased with the increasing of (NH4)2SO4 concentration in the eluant 2.5 mol/L of salt concentration for the mobile phase was chosen by considering the separation efficiency and equipment life. After comparing the effect of pH for the retention of proteins it is found that the proteins are well separated at pH 7. The time of linear gradient elution program was optimized in considering the separation efficiency and speed. It is better to take 30 minutes of the gradient program for the separation. Six standard proteins can be well separated with the high-performance HIC column in the linear gradient elution program from 2.5 to 0 mol/L of (NH4)2SO4 in 50 mmol/L of phosphate buffer solution within 30 minutes. Cyt-C, Rnase, Lys and Chy-A can be separated by the HIC column based on CPG matrix. Six proteins, Cyt-C, Rnase, Lys, Chy-A, insulin(Ins) and lipase (Lip) can be well separated on the column based on silica matrix with gradient elution program. The recovery of trypsin detected with BAEE method is over 95% after purification with the HIC column.

Chromatography↗

Software for linear and non-linear optimization in external radiotherapy.

The study presents a set of programs designed to determine optimum dose distribution either by calculation of beam intensities and field width (in linear programming) or, in addition, by calculation of beam geometry (non-linear optimization). Various optimization criteria can be selected: homogeneity, concentration on target, entire dose in a sensitive area. The optimization method used is the gradient projection method, and doses are calculated by Cunningham formulae. The article describes the program operating modes, the main subroutines and their functions and specifications, and outlines an example.

Computers↗

[Linear tomography and the Zonarc TMJ program. Reproducibility of condylar position of TMJ after surgical correction of dysgnathia].

In this clinical study the position of the mandibular condyles of 40 patients treated for malocclusion by surgical splitting of the mandibular ramus alone or combined with Le Fort I osteotomies was studied on lateral linear TMJ tomograms. Linear tomograms of the right and left TMJ with the mandible closed were taken from each patient prior to surgery and 6 months postoperatively. The postoperative changes in condylar position wee assessed in terms of direction and amount. Condylar displacements were found in 89% of the examined joints, most of them were less than 2mm. All types and combinations of displacement occurred, however, general trends in direction depending on the type of treatment could not be established with statistical significance. The type of surgical correction, its direction and amount did not seem to have an effect on the direction and amount of condylar displacement resulting. A comparison of the measured values with data in the literature showed that the amount of condylar displacement was markedly less--this seemed to be attributable to our precise evaluation method and a more sophisticated surgical technique.

Adolescent↗

A memory-efficient dynamic programming algorithm for optimal alignment of a sequence to an RNA secondary structure.

BACKGROUND: Covariance models (CMs) are probabilistic models of RNA secondary structure, analogous to profile hidden Markov models of linear sequence. The dynamic programming algorithm for aligning a CM to an RNA sequence of length N is O(N3) in memory. This is only practical for small RNAs. RESULTS: I describe a divide and conquer variant of the alignment algorithm that is analogous to memory-efficient Myers/Miller dynamic programming algorithms for linear sequence alignment. The new algorithm has an O(N2 log N) memory complexity, at the expense of a small constant factor in time. CONCLUSIONS: Optimal ribosomal RNA structural alignments that previously required up to 150 GB of memory now require less than 270 MB.

Algorithms↗