An efficient numerical scheme for solving multi-dimensional fractional optimal control problems with a quadratic performance index

The shifted Legendre orthogonal polynomials are used for the numerical solution of a new formulation for the multi-dimensional fractional optimal control problem (M-DFOCP) with a quadratic performance index. The fractional derivatives are described in the Caputo sense. The Lagrange multiplier method for the constrained extremum and the operational matrix of fractional integrals are used together with the help of the properties of the shifted Legendre orthonormal polynomials. The method reduces the M-DFOCP to a simpler problem that consists of solving a system of algebraic equations. For confirming the efficiency and accuracy of the proposed scheme, some test problems are implemented with their approximate solutions.

Optimal choice between even- and uneven-aged forestry: the case of non-industrial private forest owners

An infinite-horizon discrete time model with multiple size-class structures using a transition matrix is built to assess optimal harvesting schedules in the context of Non-Industrial Private Forest (NIPF) owners. Three model specifications accounting for forest income, financial return on an asset and amenity valuations are considered. Numerical simulations suggest uneven-aged forest management where a rational forest owner adapts her or his forest policy by influencing the regeneration of trees or adjusting consumption dynamics depending on subjective time preference and market return rate dynamics on the financial asset. Moreover she or he does not value significantly non-market benefits captured by amenity valuations relatively to forest income.

Harvest control rule vs optimal harvesting of an age-structured population: The case of the Ibero-Atlantic Sardine Fishery

Research Masters

Resting metabolic rate and protein turnover in apparently healthy elderly Gambian men.

Body composition, resting energy expenditure (REE), and whole body protein metabolism were studied in 26 young and 28 elderly Gambian men matched for body mass index during the dry season in a rural village in The Gambia. REE was measured by indirect calorimetry (hood system) in the fasting state and after five successive meals. Rates of whole body nitrogen flux, protein synthesis, and protein breakdown were determined in the fed state from the level of isotopic enrichment of urinary ammonia over a period of 12 h after a single oral dose of [15N]glycine. Expressed in absolute value, REE was significantly lower in the elderly compared with the young group (3.21 +/- 0.07 vs. 4.04 +/- 0.07 kJ/min, P < 0.001) and when adjusted to body weight (3.29 +/- 0.05 vs. 3.96 +/- 0.05 kJ/min, P < 0.0001) and fat-free mass (FFM; 3.38 +/- 0.01 vs. 3.87 +/- 0.01 kJ/min, P < 0.0001). The rate of protein synthesis averaged 207 +/- 13 g protein/day in the elderly and 230 +/- 13 g protein/day in the young group, whereas protein breakdown averaged 184 +/- 13 g protein/day in the elderly and 203 +/- 13 g protein/day in the young group (nonsignificant). When values were adjusted for body weight or FFM, they did not reveal any difference between the two groups. It is concluded that the reduced REE adjusted for body composition observed in elderly Gambian men is not explained by a decrease in protein turnover.

In vivo enzymatic activity of acetylCoA synthetase in skeletal muscle revealed by 13C turnover from hyperpolarized [1-13C]acetate to [1-13C]acetylcarnitine

BACKGROUND: Acetate metabolism in skeletal muscle is regulated by acetylCoA synthetase (ACS). The main function of ACS is to provide cells with acetylCoA, a key molecule for numerous metabolic pathways including fatty acid and cholesterol synthesis and the Krebs cycle. METHODS: Hyperpolarized [1-(13)C]acetate prepared via dissolution dynamic nuclear polarization was injected intravenously at different concentrations into rats. The (13)C magnetic resonance signals of [1-(13)C]acetate and [1-(13)C]acetylcarnitine were recorded in vivo for 1min. The kinetic rate constants related to the transformation of acetate into acetylcarnitine were deduced from the 3s time resolution measurements using two approaches, either mathematical modeling or relative metabolite ratios. RESULTS: Although separated by two biochemical transformations, a kinetic analysis of the (13)C label flow from [1-(13)C]acetate to [1-(13)C]acetylcarnitine led to a unique determination of the activity of ACS. The in vivo Michaelis constants for ACS were KM=0.35±0.13mM and Vmax=0.199±0.031μmol/g/min. CONCLUSIONS: The conversion rates from hyperpolarized acetate into acetylcarnitine were quantified in vivo and, although separated by two enzymatic reactions, these rates uniquely defined the activity of ACS. The conversion rates associated with ACS were obtained using two analytical approaches, both methods yielding similar results. GENERAL SIGNIFICANCE: This study demonstrates the feasibility of directly measuring ACS activity in vivo and, since the activity of ACS can be affected by various pathological states such as cancer or diabetes, the proposed method could be used to non-invasively probe metabolic signatures of ACS in diseased tissue.

The optimal dividend barrier in the Gamma-Omega model

In the traditional actuarial risk model, if the surplus is negative, the company is ruined and has to go out of business. In this paper we distinguish between ruin (negative surplus) and bankruptcy (going out of business), where the probability of bankruptcy is a function of the level of negative surplus. The idea for this notion of bankruptcy comes from the observation that in some industries, companies can continue doing business even though they are technically ruined. Assuming that dividends can only be paid with a certain probability at each point of time, we derive closed-form formulas for the expected discounted dividends until bankruptcy under a barrier strategy. Subsequently, the optimal barrier is determined, and several explicit identities for the optimal value are found. The surplus process of the company is modeled by a Wiener process (Brownian motion).

Blood pressure and LDL-cholesterol targets for prevention of recurrent strokes and cognitive decline in the hypertensive patient: design of the European Society of Hypertension-Chinese Hypertension League Stroke in Hypertension Optimal Treatment randomized trial.

BACKGROUND AND OBJECTIVES: The SBP values to be achieved by antihypertensive therapy in order to maximize reduction of cardiovascular outcomes are unknown; neither is it clear whether in patients with a previous cardiovascular event, the optimal values are lower than in the low-to-moderate risk hypertensive patients, or a more cautious blood pressure (BP) reduction should be obtained. Because of the uncertainty whether 'the lower the better' or the 'J-curve' hypothesis is correct, the European Society of Hypertension and the Chinese Hypertension League have promoted a randomized trial comparing antihypertensive treatment strategies aiming at three different SBP targets in hypertensive patients with a recent stroke or transient ischaemic attack. As the optimal level of low-density lipoprotein cholesterol (LDL-C) level is also unknown in these patients, LDL-C-lowering has been included in the design. PROTOCOL DESIGN: The European Society of Hypertension-Chinese Hypertension League Stroke in Hypertension Optimal Treatment trial is a prospective multinational, randomized trial with a 3 × 2 factorial design comparing: three different SBP targets (1, <145-135; 2, <135-125; 3, <125 mmHg); two different LDL-C targets (target A, 2.8-1.8; target B, <1.8 mmol/l). The trial is to be conducted on 7500 patients aged at least 65 years (2500 in Europe, 5000 in China) with hypertension and a stroke or transient ischaemic attack 1-6 months before randomization. Antihypertensive and statin treatments will be initiated or modified using suitable registered agents chosen by the investigators, in order to maintain patients within the randomized SBP and LDL-C windows. All patients will be followed up every 3 months for BP and every 6 months for LDL-C. Ambulatory BP will be measured yearly. OUTCOMES: Primary outcome is time to stroke (fatal and non-fatal). Important secondary outcomes are: time to first major cardiovascular event; cognitive decline (Montreal Cognitive Assessment) and dementia. All major outcomes will be adjudicated by committees blind to randomized allocation. A Data and Safety Monitoring Board has open access to data and can recommend trial interruption for safety. SAMPLE SIZE CALCULATION: It has been calculated that 925 patients would reach the primary outcome after a mean 4-year follow-up, and this should provide at least 80% power to detect a 25% stroke difference between SBP targets and a 20% difference between LDL-C targets.

Optimal dividend strategies for a compound Poisson risk process under transaction costs and power utility

We characterize the value function of maximizing the total discounted utility of dividend payments for a compound Poisson insurance risk model when strictly positive transaction costs are included, leading to an impulse control problem. We illustrate that well known simple strategies can be optimal in the case of exponential claim amounts. Finally we develop a numerical procedure to deal with general claim amount distributions.

Calpain 3, the "gatekeeper" of proper sarcomere assembly, turnover and maintenance.

Calpain 3 is a member of the calpain family of calcium-dependent intracellular proteases. Thirteen years ago it was discovered that mutations in calpain 3 (CAPN3) result in an autosomal recessive and progressive form of limb girdle muscular dystrophy called limb girdle muscular dystrophy type 2A. While calpain 3 mRNA is expressed at high levels in muscle and appears to have some role in developmental processes, muscles of patients and mice lacking calpain 3 still form apparently normal muscle during prenatal development; thus, a functional calpain 3 protease is not mandatory for muscle to form in vivo but it is a pre-requisite for muscle to remain healthy. Despite intensive research in this field, the physiological substrates of the calpain 3 protein (hereafter referred to as CAPN3) and its alternatively spliced isoforms remain elusive. The existence of these multiple isoforms complicates the search for the physiological functions of CAPN3 and its pathophysiological role. In this review, we summarize the genetic and biochemical evidence that point to loss of function of the full-length isoform of CAPN3, also known as p94, as the pathogenic isoform. We also argue that its natural substrates must reside in its proximity within the sarcomere where it is stored in an inactive state anchored to titin. We further propose that CAPN3 has many attributes that make it ideally suited as a sensor of sarcomeric integrity and function, involved in its repair and maintenance. Loss of these CAPN3-mediated activities can explain the "progressive" development of muscular dystrophy.

Optimal slopes and speeds in uphill ski mountaineering: a laboratory study.

The purpose of this study was to estimate the energy cost of linear (EC) and vertical displacement (ECvert), mechanical efficiency and main stride parameters during simulated ski mountaineering at different speeds and gradients, to identify an optimal speed and gradient that maximizes performance. 12 subjects roller skied on a treadmill at three different inclines (10, 17 and 24 %) at three different speeds (approximately 70, 80 and 85 % of estimated peak heart rate). Energy expenditure was calculated by indirect calorimetry, while biomechanical parameters were measured with an inertial sensor-based system. At 10 % there was no significant change with speed in EC, ECvert and mechanical efficiency. At 17 and 24 % the fastest speed was significantly more economical. There was a significant effect of gradient on EC, ECvert and mechanical efficiency. The most economical gradient was the steepest one. There was a significant increase of stride frequency with speed. At steep gradients only, relative thrust phase duration decreased significantly, while stride length increased significantly with speed. There was a significant effect of gradient on stride length (decrease with steepness) and relative thrust phase duration (increase with steepness). A combination of a decreased relative thrust phase duration with increased stride length and frequency decreases ECvert. To minimize the energy expenditure to reach the top of a mountain and to optimize performance, ski-mountaineers should choose a steep gradient (~24 %) and, provided they possess sufficient metabolic scope, combine it with a fast speed (~6 km h(-1)).

Implementing the OPTIMAL model : the impact on students' motivation in an elementary school games environment

Optimal challenge occurs when an individual perceives the challenge of the task to be equaled or matched by his or her own skill level (Csikszentmihalyi, 1990). The purpose of this study was to test the impact of the OPTIMAL model on physical education students' motivation and perceptions of optimal challenge across four games categories (i. e. target, batting/fielding, net/wall, invasion). Enjoyment, competence, student goal orientation and activity level were examined in relation to the OPTIMAL model. A total of 22 (17 M; 5 F) students and their parents provided informed consent to take part in the study and were taught four OPTIMAL lessons and four non-OPTIMAL lessons ranging across the four different games categories by their own teacher. All students completed the Task and Ego in Sport Questionnaire (TEOSQ; Duda & Whitehead, 1998), the Intrinsic Motivation Inventory (IMI; McAuley, Duncan, & Tanmien, 1987) and the Children's Perception of Optimal Challenge Instrument (CPOCI; Mandigo, 2001). Sixteen students (two each lesson) were observed by using the System for Observing Fitness Instruction Time tool (SOFTT; McKenzie, 2002). As well, they participated in a structured interview which took place after each lesson was completed. Quantitative results concluded that no overall significant difference was found in motivational outcomes when comparing OPTIMAL and non-OPTIMAL lessons. However, when the lessons were broken down into games categories, significant differences emerged. Levels of perceived competence were found to be higher in non-OPTIMAL batting/fielding lessons compared to OPTIMAL lessons, whereas levels of enjoyment and perceived competence were found to be higher in OPTIMAL invasion lessons in comparison to non-OPTIMAL invasion lessons. Qualitative results revealed significance in feehngs of skill/challenge balance, enjoyment and competence in the OPTIMAL lessons. Moreover, a significance of practically twice the active movement time percentage was found in OPTIMAL lessons in comparison to non-OPTIMAL lessons.

Effects of dietary restraint and oral contraceptives on bone strength and bone turnover in young women

ABSTRACT Introduction The purpose of this study was to assess specific osteoporosis-related health behaviours and physiological outcomes including daily calcium intake, physical activity levels, bone strength, as assessed by quantitative ultrasound, and bone turnover among women between the ages of 18 and 25. Respective differences on relevant study variables, based on dietary restraint and oral contraceptive use were also examined. Methods One hundred women (20.6 ± 0.2 years of age) volunteered to participate in the study. Informed written consent was obtained by all subjects prior to participation. The study and all related procedures were approved by the Brock University Research Ethics Board. Body mass, height, relative body fat, as well as chest, waist and hip circumferences were measured using standard procedures. The 10-item restrained eating subscale of the Dutch Eating Behaviour Questionnaire (DEBQ) was used to assess dietary restraint (van Strien et al., 1986). Daily calcium intake was assessed by the Rapid Assessment Method (RAM) (Hertzler & Frary 1994). Weekly physical activity was documented by the 4-item Godin Leisure-Time Exercise Questionnaire (Godin & Shephard 1985). Bone strength was determined from the speed of sound (SOS) as measured by QUS (Sunlight 7000S). SOS measurements (m/s) were taken of the dominant and non-dominant sides of the distal one third of the radius and the mid-shaft of the tibia. Resting blood samples were collected from all subjects between 9am and 12pm, in order to evaluate the impact of lifestyle factors on biochemical markers of bone turnover. Blood was collected during the early follicular phase of the menstrual cycle (approximately days 1-5) for all subjects. Samples were centrifliged and the serum or plasma was aliquoted into separate tubes and stored at -80°C until analysis. The bone formation markers measured were Osteocalcin (OC), bone specific alkaline phosphatase (BAP) and 25-OH vitamin D. The bone resorption markers measured were the carboxy (CTx) and amino (NTx) terminal telopeptides of type-I collagen crosslinks. All markers were assessed by ELISA. Subjects were divided into high (HDR) and low dietary restrainers (LDR) based on the median DEBQ score, and also into users (BC) and non-users (nBC) of oral contraceptives. A series of multiple one way ANOVA's were then conducted to identify differences between each set of groups for all relevant variables. A two-way ANOVA analysis was used to explore significant interactions between dietary restraint and use of oral contraceptives while a univariate follow-up analysis was also performed when appropriate. Pearson Product Moment Correlations were used to determine relationships among study variables. Results HDR had significantly higher BMI, %BF and circumference measures but lower daily calcium intake than LDR. There were no significant differences in physical activity levels between HDR and LDR. No significant differences were found between BC and nBC in body composition, calcium intake and physical activity. HDR had significantly lower tibial SOS scores than LDR in both the dominant and non-dominant sites. The post-hoc analysis showed that within the non-birth control group, the HDR had significantly lower tibial SOS scores of bone strength when compared to the LDR but Aere were no significant differences found between the two dietary restraint groups for those currently on birth control. HDR had significantly lower levels of OC than LDR and the BC group had lower levels of BAP than the nBC group. Consistently, the follow-up analysis revealed that within those not on birth control, subjects who were classified as HDR had significantly (f*<0.05) lower levels of OC when compared with LDR but no significant differences were observed in bone turnover between the two dietary restraint groups for those currently on birth control. Physical activity was not correlated with SOS scores and bone turnover markers possibly due to the low physical activity variability in this group of women. Conclusion This is the first study to examine the effects of dietary restraint on bone strength and turnover among this population of women. The most important finding of this study was that bone strength and turnover are negatively influenced by dietary restraint independent of relative body fat. In general, the results of the present thesis suggest that dietary restraint, oral contraceptive use, as well as low daily calcium intake and low physical activity levels were widespread behaviours among this population of college-aged women. The young women who were using dietary restraint as a strategy to lose weight, and thus were in the HDR group, despite their higher relative body fat and weight, had lower scores of bone strength and lower levels of markers of bone turnover compared to the low dietary restrainers. Additionally, bone turnover seemed to be negatively affected by oral contraceptives, while bone strength, as assessed by QUS, seemed unaffected by their use in this population of young women. Physical activity (weekly energy expenditure), on the other hand, was not associated with either bone strength or bone tiimover possibly due to the low variability of this variable in this population of young Canadian women.

Bone speed of sound, biochemical markers of bone turnover and IGF-1 in competetive synchronized swimmers

The purpose of this study was to compare bone speed of sound (SOS) measured by quantitative ultrasound, circulating levels of IGF- 1 and biochemical markers of bone turnover in pre- (Pr) and post-menarcheal (Po) synchronized swimmers (SS) and controls (NS). Seventy participants were recruited: 8 PrSS, 22 PoSS, 20 PrNS, and 20 PoNS. Anthropometric measures of height, weight, skeletal maturity and percent body fat were taken, and dietary intake evaluated using 24-hour recall. Bone SOS was measured at the distal radius and mid-tibia and blood samples analyzed for IGF-1, osteocalcin, NTx, and 25-OH vitamin D. Results demonstrated maturational effects on bone SOS, IGF-1 and bone turnover (p<0.05), with no differences observed between SS and NS. Main effects were observed for a reduced caloric intake in SS compared to NS (p<0.05). Therefore, SS does not offer additive affects on bone strength but imparts no adverse affects to skeletal health in these athletes.

Protein Turnover in Rat Skeletal Muscle During In Vitro Hypo-Osmotic Stress

Hypo-osmolality influences tissue metabolism, but research on protein turnover in skeletal muscle is limited. The purpose of this investigation was to examine the effects of hypo-osmotic stress on protein turnover in rat skeletal muscle. We hypothesized increased protein synthesis and reduced degradation following hypo-osmotic exposure. EDL muscles (n=8/group) were incubated in iso-osmotic (290 Osm/kg) or hypo-osmotic (190 Osm/kg) modified medium 199 (95% O2, 5% CO2, pH 7.4, 30±2 °C) for 60 min, followed by 75 min incubations with L-U[14C]phenylalanine or cycloheximide to determine protein synthesis and degradation. Immunoblotting was performed to assess signalling pathways involved. Phenylalanine uptake and incorporation were increased by 199% and 169% respectively in HYPO from ISO (p < 0.05). This was supported by elevated phosphorylation of mTOR Ser2448 (+12.5%) and increased Thr389 phosphorylation on p70s6 kinase (+23.6%) (p < 0.05). Hypo-osmotic stress increased protein synthesis and potentially amino acid uptake. Future studies should examine the upstream mechanisms involved.