Improving the cost effectiveness equation of cascade testing for Familial Hypercholesterolaemia (FH)

Purpose of Review : Many International recommendations for the management of Familial Hypercholesterolaemia (FH) propose the use of Cascade Testing (CT) using the family mutation to unambiguously identify affected relatives. In the current economic climate DNA information is often regarded as too expensive. Here we review the literature and suggest strategies to improve cost effectiveness of CT. Recent findings : Advances in next generation sequencing have both speeded up the time taken for a genetic diagnosis and reduced costs. Also, it is now clear that, in the majority of patients with a clinical diagnosis of FH where no mutation can be found, the most likely cause of their elevated LDL-cholesterol (LDL-C) is because they have inherited a greater number than average of common LDL-C raising variants in many different genes. The major cost driver for CT is not DNA testing but of treatment over the remaining lifetime of the identified relative. With potent statins now off-patent, the overall cost has reduced considerably, and combining these three factors, a FH service based around DNA-CT is now less than 25% of that estimated by NICE in 2009. Summary : While all patients with a clinical diagnosis of FH need to have their LDL-C lowered, CT should be focused on those with the monogenic form and not the polygenic form

Development of an improved protective cover/light block for multilayer insulation

The feasibility of using a scrim-reinforced, single metallized, 4-mil Tedlar film as a replacement for the Teflon coated Beta-cloth/single metallized 3-mil Kapton film presently used as the protective cover/light block for multilayer insulation (MLI) on the Orbiter, Spacelab, and other space applications was demonstrated. The proposed Tedlar concept is lighter and potentially lower in cost. Thermal analysis with the proper concept was much simpler than with the present system. Tests have already demonstrated that white Tedlar has low alpha (adsorption) degradation in space from U.V. The proposed concept was 4400 percent cheaper with nominal weight savings of 50 percent

The Essential Stability of Local Error Control for Dynamical Systems

Although most adaptive software for initial value problems is designed with an accuracy requirement—control of the local error—it is frequently observed that stability is imparted by the adaptation. This relationship between local error control and numerical stability is given a firm theoretical underpinning. The dynamics of numerical methods with local error control are studied for three classes of ordinary differential equations: dissipative, contractive, and gradient systems. Dissipative dynamical systems are characterised by having a bounded absorbing set B which all trajectories eventually enter and remain inside. The exponentially contractive problems studied have a unique, globally exponentially attracting equilibrium point and thus they are also dissipative since the absorbing set B may be chosen to be a ball of arbitrarily small radius around the equilibrium point. The gradient systems studied are those for which the set of equilibria comprises isolated points and all trajectories are bounded so that each trajectory converges to an equilibrium point as t → ∞. If the set of equilibria is bounded then the gradient systems are also dissipative. Conditions under which numerical methods with local error control replicate these large-time dynamical features are described. The results are proved without recourse to asymptotic expansions for the truncation error. Standard embedded Runge–Kutta pairs are analysed together with several nonstandard error control strategies. Both error per step and error per unit step strategies are considered. Certain embedded pairs are identified for which the sequence generated can be viewed as coming from a small perturbation of an algebraically stable scheme, with the size of the perturbation proportional to the tolerance τ. Such embedded pairs are defined to be essentially algebraically stable and explicit essentially stable pairs are identified. Conditions on the tolerance τ are identified under which appropriate discrete analogues of the properties of the underlying differential equation may be proved for certain essentially stable embedded pairs. In particular, it is shown that for dissipative problems the discrete dynamical system has an absorbing set B_τ and is hence dissipative. For exponentially contractive problems the radius of B_τ is proved to be proportional to τ. For gradient systems the numerical solution enters and remains in a small ball about one of the equilibria and the radius of the ball is proportional to τ. Thus the local error control mechanisms confer desirable global properties on the numerical solution. It is shown that for error per unit step strategies the conditions on the tolerance τ are independent of initial data while for error per step strategies the conditions are initial-data dependent. Thus error per unit step strategies are considerably more robust

Runge–Kutta Methods for Dissipative and Gradient Dynamical Systems

The numerical approximation of dissipative initial value problems by fixed time-stepping Runge–Kutta methods is considered and the asymptotic features of the numerical and exact solutions are compared. A general class of ordinary differential equations, for which dissipativity is induced through an inner product, is studied throughout. This class arises naturally in many finite dimensional applications (such as the Lorenz equations) and also from the spatial discretization of a variety of partial differential equations arising in applied mathematics. It is shown that the numerical solution defined by an algebraically stable method has an absorbing set and is hence dissipative for any fixed step-size h > 0. The numerical solution is shown to define a dynamical system on the absorbing set if h is sufficiently small and hence a global attractor A_h exists; upper-semicontinuity of A_h at h = 0 is established, which shows that, for h small, every point on the numerical attractor is close to a point on the true global attractor A. Under the additional assumption that the problem is globally Lipschitz, it is shown that if h is sufficiently small any method with positive weights defines a dissipative dynamical system on the whole space and upper semicontinuity of A_h at h = 0 is again established. For gradient systems with globally Lipschitz vector fields it is shown that any Runge–Kutta method preserves the gradient structure for h sufficiently small. For general dissipative gradient systems it is shown that algebraically stable methods preserve the gradient structure within the absorbing set for h sufficiently small. Convergence of the numerical attractor is studied and, for a dissipative gradient system with hyperbolic equilibria, lower semicontinuity at h = 0 is established. Thus, for such a system, A_h converges to A in the Hausdorff metric as h → 0

Model Problems in Numerical Stability Theory for Initial Value Problems

In the past numerical stability theory for initial value problems in ordinary differential equations has been dominated by the study of problems with simple dynamics; this has been motivated by the need to study error propagation mechanisms in stiff problems, a question modeled effectively by contractive linear or nonlinear problems. While this has resulted in a coherent and self-contained body of knowledge, it has never been entirely clear to what extent this theory is relevant for problems exhibiting more complicated dynamics. Recently there have been a number of studies of numerical stability for wider classes of problems admitting more complicated dynamics. This on-going work is unified and, in particular, striking similarities between this new developing stability theory and the classical linear and nonlinear stability theories are emphasized. The classical theories of A, B and algebraic stability for Runge–Kutta methods are briefly reviewed; the dynamics of solutions within the classes of equations to which these theories apply—linear decay and contractive problems—are studied. Four other categories of equations—gradient, dissipative, conservative and Hamiltonian systems—are considered. Relationships and differences between the possible dynamics in each category, which range from multiple competing equilibria to chaotic solutions, are highlighted. Runge-Kutta schemes that preserve the dynamical structure of the underlying problem are sought, and indications of a strong relationship between the developing stability theory for these new categories and the classical existing stability theory for the older problems are given. Algebraic stability, in particular, is seen to play a central role. It should be emphasized that in all cases the class of methods for which a coherent and complete numerical stability theory exists, given a structural assumption on the initial value problem, is often considerably smaller than the class of methods found to be effective in practice. Nonetheless it is arguable that it is valuable to develop such stability theories to provide a firm theoretical framework in which to interpret existing methods and to formulate goals in the construction of new methods. Furthermore, there are indications that the theory of algebraic stability may sometimes be useful in the analysis of error control codes which are not stable in a fixed step implementation; this work is described

Pressure Relief Tunnel System at US22/SR7 Interchange, OH

Construction of the US22/SR7 interchange in Steubenville, OH resulted in the need to excavate the toe of the steep 350 ft. high slope overlooking the Ohio River. To maintain the stability of the slope, the Ohio Department of Transportation (ODOT) chose to construct a 4 tier, 130- ft. high, 2,200 ft. long tieback anchor retaining wall. During the design phase, it became apparent that reductions in both the tieback loading and cost could be realized by lowering the groundwater levels in the hillside. A Pressure Relief Tunnel System (PRTS) was selected from several drainage options. The PRTS consists of a 1,945 ft. long tunnel, excavated parallel to, and 200 ft. behind, the retaining wall, and a series 85 ft. long, sub-vertical drainage holes drilled upward from inside the tunnel. This paper presents the design of the PRTS, an outline of the instrumentation program and a comparison of the observed and expected drawdowns

Empirical model for quasi direct current interruption with a convoluted arc

This contribution considers various aspects of a quasi direct current, convoluted arc produced by a magnetic field (B-field) connected in parallel with an RLC circuit that have not been considered in combination. These aspects are the arc current limitation due to the arc convolution, changes in arc resistance due to the B-field and material ablation, and the relative significance of the RLC circuit in producing an artificial current zero. As a result, it has been possible to produce an empirical equation for predicting the current interruption capability in terms of the B-field magnitude and RLC components