Optimal maintenance policies under different operational schedules

In the reliability literature, maintenance time is usually ignored during the optimization of maintenance policies. In some scenarios, costs due to system failures may vary with time, and the ignorance of maintenance time will lead to unrealistic results. This paper develops maintenance policies for such situations where the system under study operates iteratively at two successive states: up or down. The costs due to system failure at the up state consist of both business losses & maintenance costs, whereas those at the down state only include maintenance costs. We consider three models: Model A, B, and C: Model A makes only corrective maintenance (CM). Model B performs imperfect preventive maintenance (PM) sequentially, and CM. Model C executes PM periodically, and CM; this PM can restore the system as good as the state just after the latest CM. The CM in this paper is imperfect repair. Finally, the impact of these maintenance policies is illustrated through numerical examples.

Role of oxygen radicals in DNA damage and cancer incidence

The development of cancer in humans and animals is a multistep process. The complex series of cellular and molecular changes participating in cancer development are mediated by a diversity of endogenous and exogenous stimuli. One type of endogenous damage is that arising from intermediates of oxygen (dioxygen) reduction - oxygen-free radicals (OFR), which attacks not only the bases but also the deoxyribosyl backbone of DNA. Thanks to improvements in analytical techniques, a major achievement in the understanding of carcinogenesis in the past two decades has been the identification and quantification of various adducts of OFR with DNA. OFR are also known to attack other cellular components such as lipids, leaving behind reactive species that in turn can couple to DNA bases. Endogenous DNA lesions are genotoxic and induce mutations. The most extensively studied lesion is the formation of 8-OH-dG. This lesion is important because it is relatively easily formed and is mutagenic and therefore is a potential biomarker of carcinogenesis. Mutations that may arise from formation of 8-OH-dG involve GC. TA transversions. In view of these findings, OFR are considered as an important class of carcinogens. The effect of OFR is balanced by the antioxidant action of non-enzymatic antioxidants as well as antioxidant enzymes. Non-enzymatic antioxidants involve vitamin C, vitamin E, carotenoids (CAR), selenium and others. However, under certain conditions, some antioxidants can also exhibit a pro-oxidant mechanism of action. For example, beta-carotene at high concentration and with increased partial pressure of dioxygen is known to behave as a pro-oxidant. Some concerns have also been raised over the potentially deleterious transition metal ion-mediated (iron, copper) pro-oxidant effect of vitamin C. Clinical studies mapping the effect of preventive antioxidants have shown surprisingly little or no effect on cancer incidence. The epidemiological trials together with in vitro experiments suggest that the optimal approach is to reduce endogenous and exogenous sources of oxidative stress, rather than increase intake of anti-oxidants. In this review, we highlight some major achievements in the study of DNA damage caused by OFR and the role in carcinogenesis played by oxidatively damaged DNA. The protective effect of antioxidants against free radicals is also discussed.

Influence of apolipoprotein E genotype and dietary alpha-tocopherol on redox status and C-reactive protein levels in apolipoprotein E3 and E4 targeted replacement mice

The molecular basis of the positive association between apoE4 genotype and CVD remains unclear. There is direct in vitro evidence indicating that apoE4 is a poorer antioxidant relative to the apoE3 isoform, with some indirect in vivo evidence also available. Therefore it was hypothesised that apoE4 carriers may benefit from alpha-tocopherol (alpha-Toc) supplementation. Targeted replacement mice expressing the human apoE3 and apoE4 were fed with a diet poor (0 mg/kg diet) or rich (200 mg/kg diet) in alpha-Toc for 12 weeks. Neither apoE genotype nor dietary alpha-Toc exerted any effects on the antioxidant defence system, including glutathione, catalase, superoxide dismutase, glutathione peroxidase and glutathione reductase activities. In addition, no differences were observed in mitogen-induced lymphocyte proliferation. alpha-Toc concentrations were modestly higher in plasma and lower in tissues of apoE4 compared with apoE3 mice, with the greatest differences evident in the lung, suggesting that an apoE4 genotype may reduce alpha-Toc delivery to tissues. A tendency towards increased plasma F-2-isoprostanes in apoE4 mice was observed, while liver thiobarbituric acid-reactive substances did not differ between apoE3 and apoE4 mice. In addition, C-reactive protein (CRP) concentrations were reduced in apoE4 mice indicating that this positive effect on CRP may in part negate the increased CVD risk associated with an apoE4 genotype.

Targeting C-reactive protein for the treatment of cardiovascular disease

Complement-mediated inflammation exacerbates the tissue injury of ischaemic necrosis in heart attacks and strokes, the most common causes of death in developed countries. Large infarct size increases immediate morbidity and mortality and, in survivors of the acute event, larger non-functional scars adversely affect long-term prognosis. There is thus an important unmet medical need for new cardioprotective and neuroprotective treatments. We have previously shown that human C-reactive protein (CRP), the classical acute-phase protein that binds to ligands exposed in damaged tissue and then activates complement(1), increases myocardial and cerebral infarct size in rats subjected to coronary or cerebral artery ligation, respectively(2,3). Rat CRP does not activate rat complement, whereas human CRP activates both rat and human complement(4). Administration of human CRP to rats is thus an excellent model for the actions of endogenous human CRP2,3. Here we report the design, synthesis and efficacy of 1,6-bis(phosphocholine)-hexane as a specific small-molecule inhibitor of CRP. Five molecules of this palindromic compound are bound by two pentameric CRP molecules, crosslinking and occluding the ligand-binding B-face of CRP and blocking its functions. Administration of 1,6-bis(phosphocholine)-hexane to rats undergoing acute myocardial infarction abrogated the increase in infarct size and cardiac dysfunction produced by injection of human CRP. Therapeutic inhibition of CRP is thus a promising new approach to cardioprotection in acute myocardial infarction, and may also provide neuroprotection in stroke. Potential wider applications include other inflammatory, infective and tissue-damaging conditions characterized by increased CRP production, in which binding of CRP to exposed ligands in damaged cells may lead to complement-mediated exacerbation of tissue injury.

The geometry of optimal control solutions on some six dimensional lie groups

This paper examines optimal solutions of control systems with drift defined on the orthonormal frame bundle of particular Riemannian manifolds of constant curvature. The manifolds considered here are the space forms Euclidean space E-3, the spheres S-3 and the hyperboloids H-3 with the corresponding frame bundles equal to the Euclidean group of motions SE(3), the rotation group SO(4) and the Lorentz group SO(1,3). The optimal controls of these systems are solved explicitly in terms of elliptic functions. In this paper, a geometric interpretation of the extremal solutions is given with particular emphasis to a singularity in the explicit solutions. Using a reduced form of the Casimir functions the geometry of these solutions are illustrated.

Optimal 3D surface reconstruction from multiview photographic images

This paper describes a new method for reconstructing 3D surface using a small number, e.g. 10, of 2D photographic images. The images are taken at different viewing directions by a perspective camera with full prior knowledge of the camera configurations. The reconstructed object's surface is represented a set of triangular facets. We empirically demonstrate that if the viewing directions are uniformly distributed around the object's viewing sphere, then the reconstructed 3D points optimally cluster closely on a highly curved part of the surface and are widely, spread on smooth or fat parts. The advantage of this property is that the reconstructed points along a surface or a contour generator are not undersampled or underrepresented because surfaces or contours should be sampled or represented with more densely points where their curvatures are high. The more complex the contour's shape, the greater is the number of points required, but the greater the number of points is automatically generated by the proposed method Given that the viewing directions are uniformly distributed, the number and distribution of the reconstructed points depend on the shape or the curvature of the surface regardless of the size of the surface or the size of the object.

Exact error estimates and optimal randomized algorithms for integration

Exact error estimates for evaluating multi-dimensional integrals are considered. An estimate is called exact if the rates of convergence for the low- and upper-bound estimate coincide. The algorithm with such an exact rate is called optimal. Such an algorithm has an unimprovable rate of convergence. The problem of existing exact estimates and optimal algorithms is discussed for some functional spaces that define the regularity of the integrand. Important for practical computations data classes are considered: classes of functions with bounded derivatives and Holder type conditions. The aim of the paper is to analyze the performance of two optimal classes of algorithms: deterministic and randomized for computing multidimensional integrals. It is also shown how the smoothness of the integrand can be exploited to construct better randomized algorithms.

Solving optimal control problems with state constraints using nonlinear programming and simulation tools

This paper illustrates how nonlinear programming and simulation tools, which are available in packages such as MATLAB and SIMULINK, can easily be used to solve optimal control problems with state- and/or input-dependent inequality constraints. The method presented is illustrated with a model of a single-link manipulator. The method is suitable to be taught to advanced undergraduate and Master's level students in control engineering.

Optimal kinematic control of an autonomous underwater vehicle

This note investigates the motion control of an autonomous underwater vehicle (AUV). The AUV is modeled as a nonholonomic system as any lateral motion of a conventional, slender AUV is quickly damped out. The problem is formulated as an optimal kinematic control problem on the Euclidean Group of Motions SE(3), where the cost function to be minimized is equal to the integral of a quadratic function of the velocity components. An application of the Maximum Principle to this optimal control problem yields the appropriate Hamiltonian and the corresponding vector fields give the necessary conditions for optimality. For a special case of the cost function, the necessary conditions for optimality can be characterized more easily and we proceed to investigate its solutions. Finally, it is shown that a particular set of optimal motions trace helical paths. Throughout this note we highlight a particular case where the quadratic cost function is weighted in such a way that it equates to the Lagrangian (kinetic energy) of the AUV. For this case, the regular extremal curves are constrained to equate to the AUV's components of momentum and the resulting vector fields are the d'Alembert-Lagrange equations in Hamiltonian form.

Singularities of optimal control problems on some 6-D lie groups

This paper considers the motion planning problem for oriented vehicles travelling at unit speed in a 3-D space. A Lie group formulation arises naturally and the vehicles are modeled as kinematic control systems with drift defined on the orthonormal frame bundles of particular Riemannian manifolds, specifically, the 3-D space forms Euclidean space E-3, the sphere S-3, and the hyperboloid H'. The corresponding frame bundles are equal to the Euclidean group of motions SE(3), the rotation group SO(4), and the Lorentz group SO (1, 3). The maximum principle of optimal control shifts the emphasis for these systems to the associated Hamiltonian formalism. For an integrable case, the extremal curves are explicitly expressed in terms of elliptic functions. In this paper, a study at the singularities of the extremal curves are given, which correspond to critical points of these elliptic functions. The extremal curves are characterized as the intersections of invariant surfaces and are illustrated graphically at the singular points. It. is then shown that the projections, of the extremals onto the base space, called elastica, at these singular points, are curves of constant curvature and torsion, which in turn implies that the oriented vehicles trace helices.