Construction of Selection Indexes with Restrictions

In this paper the problem of unistage selection with inequality constraints is formulated. If the predictor and criterion variables are all normally distributed, this problem can be written as a convex programming problem, with a linear objective function and with linear constraints and a quadratic constraint. Using the duality theory, for convex nonlinear programming it is proved, that its dual problem can be transformed into a convex minimization problem with non-negativity conditions. Good computational methods are known for solving this problem. By the help of the dual problem sufficient conditions for a solution of the original primal problem are derived and illustrated by an example of practical interest.     

Structuring policy problems for plastics,the environment and human health: reflections from the UK

How can we strengthen the science–policy interface for plastics, the environment and human health? In a complex policy area with multiple stakeholders, it is important to clarify the nature of the particular plastics-related issue before trying to understand how to reconcile the supply and demand for evidence in policy. This article proposes a simple problem typology to assess the fundamental characteristics of a policy issue and thus identify appropriate processes for science–policy interactions. This is illustrated with two case studies from one UK Government Department, showing how policy and science meet over the environmental problems of plastics waste in the marine environment and on land. A problem-structuring methodology helps us understand why some policy issues can be addressed through relatively linear flows of science from experts to policymakers but why others demand a more reflexive approach to brokering the knowledge between science and policy. Suggestions are given at the end of the article for practical actions that can be taken on both sides.     

The paradox of magnetobiology: Analysis and prospects for solution

The formulation, content, and corollaries of the so-called kT problem are considered. The problem points to a paradox in the biological effect of weak low-frequency magnetic fields. The conventional formulation of the problem contains implicit assumptions that prove not fully valid according to the results of analysis.     

Extracting the time-dependent transmission rate from infection data via solution of an inverse ODE problem

The transmission rate of many acute infectious diseases varies significantly in time, but the underlying mechanisms are usually uncertain. They may include seasonal changes in the environment, contact rate, immune system response, etc. The transmission rate has been thought difficult to measure directly. We present a new algorithm to compute the time-dependent transmission rate directly from prevalence data, which makes no assumptions about the number of susceptible or vital rates. The algorithm follows our complete and explicit solution of a mathematical inverse problem for SIR-type transmission models. We prove that almost any infection profile can be perfectly fitted by an SIR model with variable transmission rate. This clearly shows a serious danger of overfitting such transmission models. We illustrate the algorithm with historic UK measles data and our observations support the common belief that measles transmission was predominantly driven by school contacts.     

Acoustic reflectometry for an in vitro model of a human upper airway using sinusoidal wave packets and the Ware–Aki algorithm

Acoustic reflectometry is often used for estimating the cross-sectional area of a cylindrical cavity when used in combination with an acoustic pulse. The objective of this research is to sweep a spectral bandwidth from 50 Hz to 10 kHz at steps of 50 Hz, with Gaussian sinusoidal wave packets, and to apply the Ware–Aki algorithm. In practice, not only it is difficult to generate a broad spectral bandwidth, but also robust methods are required to compensate for attenuation in the propagating wave and to eliminate a DC offset component generated in its impulse response. This paper looks at using numerical techniques to compute the impulse response and estimate the cross-sectional area as a function of an increment in the frequency response. Preliminary results show that both simulated and reconstructed cross-sectional areas for an in vitro model of a human upper airway may be estimated with an appropriate resolution, suggesting that this method is suitable for such applications.     

A 3d-fem Simulation of Highest Stress Lines in Mandible Fractures by Elastic Impact

Abstract

In this article, the more usual mandible fracture areas are located by identifying the highest stress lines using a three-dimensional (tetrahedral) finite element method. By taking into account the temporomandibular contact and the inertia effects, the mathematical model is considered to be a dynamic Signorini's problem, that is, a dynamic variational inequality which is discretized in time following Newmark's method. So, in each time step a stationary variational inequality is solved by a penalty-duality algorithm. Finally, some numerical results obtained by simulating the more usual fractures in the human mandible are presented and compared with clinical experimental information.