Error bounds for initial value problems by optimization

The computation of the error bounds for approximate solutions of initial value problems for ordinary differential equations has a long and successful history. This paper presents a new scheme to compute such bounds with uncertain initial conditions using preconditioned defect estimates and optimization techniques. These bounds are based on the newly developed concept of conditional differential inequalities. The scheme is implemented in MATLAB and AMPL. The resulting enclosures are compared with the packages VALENCIA-IVP, VNODE-LP and VSPODE for bounding solutions of ODEs. The current prototype uses heuristics to solve the global optimization subproblems. Hence the bounds obtained in the numerical experiments are not fully rigorous. The latter can be achieved by using rigorous global optimization and rounding error control, but the effect on the bounds is likely to be marginal only.     

PET regularization by envelope guided conjugate gradients

The authors propose a new way to iteratively solve large scale ill-posed problems and in particular the image reconstruction problem in positron emission tomography by exploiting the relation between Tikhonov regularization and multiobjective optimization to obtain iteratively approximations to the Tikhonov L-curve and its corner. Monitoring the change of the approximate L-curves allows the authors to adjust the regularization parameter adaptively during a preconditioned conjugate gradient iteration, so that the desired solution can be reconstructed with a small number of iterations.     

Hamstrings and psoas lengths during normal and crouch gait: implications for muscle-tendon surgery

OBJECTIVE: To study the relative contribution of the lung and the chest wall on the total respiratory system mechanics, gas exchange, and work of breathing in sedated-paralyzed normal subjects and morbidly obese patients, in the postoperative period. SETTING: Policlinico Hospital, University of Milan, Italy. METHODS: In ten normal subjects (normal) and ten morbidly obese patients (obese), we partitioned the total respiratory mechanics (rs) into its lung (L) and chest wall (w) components using the esophageal balloon technique together with airway occlusion technique, during constant flow inflation. We measured, after abdominal surgery, static respiratory system compliance (Cst,rs), lung compliance (Cst,L), chest wall compliance (Cst,w), total lung (Rmax,L) and chest wall (Rmax,w) resistance. Rmax,L includes airway (Rmin,L) and "additional" lung resistance (DR,L). DR,L represents the component due to viscoelastic phenomena of the lung tissue and time constant inequalities (pendelluft). Functional residual capacity (FRC) was measured by helium dilution technique. RESULTS: We found that morbidly obese patients compared with normal subjects are characterized by the following: (1) reduced Cst,rs (p < 0.01), due to lower Cst,L (55.3 +/- 15.3 mL x cm H2O-1 vs 106.6 +/- 31.7 mL x cm H2O-1; p < 0.01) and Cst,w (112.4 +/- 47.4 mL x cm H2O-1 vs 190.7 +/- 45.1 mL x cm H2O-1; p < 0.01); (2) increased Rmin,L (4.7 +/- 3.1 mL x cm H2O x L-1 x s; vs 1.0 +/- 0.8 mL x cm H2O x L-1 x s; p < 0.01) and DR,L (4.9 +/- 2.6 mL x cm H2O x L-1 x s; vs 1.5 +/- 0.8 mL x cm H2O x L-1 x s; p < 0.01); (3) reduced FRC (0.665 +/- 0.191 L vs 1.691 +/- 0.325 L; p < 0.01); (4) increased work performed to inflate both the lung (0.91 +/- 0.25 J/L vs 0.34 +/- 0.08 J/L; p < 0.01) and the chest wall (0.39 +/- 0.13 J/L vs 0.18 +/- 0.04 J/L; p < 0.01); and (5) a reduced pulmonary oxygenation index (PaO2/PAO2 ratio). CONCLUSION: Sedated-paralyzed morbidly obese patients, compared with normal subjects, are characterized by marked derangements in lung and chest wall mechanics and reduced lung volume after abdominal surgery. These alterations may account for impaired arterial oxygenation in the postoperative period.     

Prediction of the Poisson's ratio of porous materials

An equation is presented for the prediction of the Poisson's ratio of porous materials. The equation is strictly derived for spherical porosity and isotropic materials and it is valid for the whole porosity range. For low porosity, the equation coincides with a published equation, which has been verified in the past by comparison with extensive experimental data. For the high-porosity range, the theoretical variation of the Poisson's ratio exhibits a trend converging to a value _P =0.5, when the porosity increases to P=1, A similar converging trend has been found in other theoretical studies, but a rigorous experimental verification of such variations has still to be carried out.     

Smooth velocity approximation for constrained systems in real-time simulation

The rapidly increasing complexity of multi-body system models in applications like vehicle dynamics, robotics and bio-mechanics requires qualitative new solution methods to slash computing times for the dynamical simulation.     

Corrected upper bounds for free-cut elimination

Free-cut elimination allows cut elimination to be carried out in the presence of non-logical axioms. Formulas in a proof are anchored provided they originate in a non-logical axiom or non-logical inference. This paper corrects and strengthens earlier upper bounds on the size of free-cut elimination. The correction requires that the notion of a free cut be modified so that a cut formula is anchored provided that all of its introductions are anchored, instead of only requiring that one of its introductions is anchored. With the correction, the originally proved size upper bounds remain unchanged. These results also apply to partial cut elimination. We also apply these bounds to elimination of cuts in propositional logic.If the non-logical inferences are closed under cut and infer only atomic formulas, then all cuts can be eliminated. This extends earlier results of Takeuti and of Negri and von Plato.     

Evolution strategies with cumulative step length adaptation on the noisy parabolic ridge

This paper presents an analysis of the performance of the (μ/μ,λ)-ES with isotropically distributed mutations and cumulative step length adaptation on the noisy parabolic ridge. Several forms of dependency of the noise strength on the distance from the ridge axis are considered. Closed form expressions are derived that describe the mutation strength and the progress rate of the strategy in high-dimensional search spaces. It is seen that as for the sphere model, larger levels of noise present lead to cumulative step length adaptation generating increasingly inadequate mutation strengths, and that the problem can be ameliorated to some degree by working with larger populations.     

Exploring the Interaction between Java's Implicitly Thrown Exceptions and Instruction Scheduling

The frequent occurrence of implicitly thrown exceptions poses one of the challenges present in a Java compiler. Not only do these implicitly thrown exceptions directly affect the performance by requiring explicit checks, they also indirectly impact the performance by restricting code movement in order to satisfy the precise exception model in Java. In particular, instruction scheduling is one transformation that is restricted by implicitly thrown exceptions due to the heavy reliance on reordering instructions to exploit maximum hardware performance. The goal of this study is two-fold: first, investigate the degree to which implicitly thrown exceptions in Java hinder instruction scheduling, and second, find new techniques for allowing more efficient execution of Java programs containing implicitly thrown exceptions. Experimental results show that with aggressive scheduling techniques, such as superblock scheduling, the negative performance impact can be greatly reduced.