consisting of 35 risky assets. The first one uses periodically updated optimal weights from standard Markowitz/Sharpe portfolio theory. The second strategy removes a fixed number of assets that have highest positive correlation with the rest of the portfolio. Both approaches perform better (have larger Sharpe ratio) than the existing strategies.

1. Minimize the total number of deaths due to influenza.

2. Minimize the total number of infections with influenza.

3. Reduce the spread of resistance to antivirals.

It is understood that not all the objectives above might be satisfied at the same time, and the purpose of the work is to consider the outcome in the different scenarios. The aim of the present project is to see if optimal control theory can contribute to a better formulation of the treatment intensity, in order to bring the epidemic under control while avoiding wide-spread resistance in the population.

Other aspects of the modelling such as rainfall, run-off, overflow/flooding, evaporation, absorption/seepage, bed-slopes, bed friction have not been incorporated in the model due to their specific nature.

Four problems are considered, namely, the geometry of the labelling process, the formation of wrinkles related to physical qualities of the paper, the spreading of the glue and removal of the labels.

An optimal speed was found for the labelling process. The group evaluated the importance of the distance between the glue strips both for wrinkle constraint and removal of the labels. The group also investigated the influence of the angle between the preferential expansion direction of the paper and the glue strips and showed that the glue strips should be perpendicular to the fibres in the paper.

For the first, we used the method of multiple scales to homogenize this model over the microstructure, formed by the small lithium particles in the electrodes.

For the second, we gave rigorous bounds for the effective electrochemical conductivity for a linearized case.

We expect similar results and bounds for the "full nonlinear problem" because variational results are generally not adversely affected by a sinh term.

Finally we used the asymptotic methods, based on parameters estimated from the literature, to attain a greatly simplified one-dimensional version of the original homogenized model. This simplified model accounts for the fact that diffusion of lithium atoms within individual electrode particles is relatively much faster than that of lithium ions across the whole cell so that lithium ion diffusion is what limits the performance of the battery. However, since most of the potential drop occurs across the Debye layers surrounding each electrode particle, lithium ion diffusion only significantly affects cell performance if there is more or less complete depletion of lithium ions in some region of the electrolyte which causes a break in the current flowing across the cell. This causes catastrophic failure. Providing such failure does not occur the potential drop across the cell is determined by the concentration of lithium atoms in the electrode particles. Within each electrode lithium atom concentration is, to leading order, a function of time only and not of position within the electrode. The depletion of electrode lithium atom concentration is directly proportional to the current being drawn off the cell. This leads one to expect that the potential of the cell gradually drops as current is drawn of it.

We would like to emphasize that all the homogenization methods employed in this work give a systematic approach for investigating the effect that changes in the microstructure have on the behaviour of the battery. However, due to lack of time, we have not used this method to investigate particular particle geometries.

The starting point for the mathematical modeling was the equations presented in [1] for a glass fiber with a hole undergoing extensional flow. These equations were reconsidered here with the additional reduction that the hole, i.e. the gas bubble, was thin as compared to the radius of the fiber and of finite extent. The primary model considered was one in which the mass of the gas inside the bubble was fixed. This fixed-mass model involved equations for the axial velocity and fiber radius, and equations for the radius of the bubble and the gas pressure inside the bubble. The model equations assumed that the temperature of the furnace of the drawing tower was known.

The governing equations of the bubble are hyperbolic and predict that the bubble cannot extend beyond the limiting characteristics specified by the ends of the initial bubble shape. An analysis of pinch-off was performed, and it was found that pinch-off can occur, depending on the parameters of the model, due to surface tension when the bubble radius is small.

In order to determine the evolution of a bubble, a numerical method of solution was presented. The method was used to study the evolution of two different initial bubble shapes, one convex and the other non-convex. Both initial bubble shapes had fore-aft symmetry, and it was found that the bubbles stretched and elongated severely during the drawing process. For the convex shape, fore-aft symmetry was lost in the middle of the drawing process, but the symmetry was re-gained by the end of the drawing tower. A small amount of pinch-off was observed at each end for this case, so that the final bubble length was slightly shorter than its theoretical maximum length. For the non-convex initial shape, pinch-off occurred in the middle of the bubble resulting in two bubbles by the end of the fiber draw.

The two bubbles had different final pressures and did not have fore-aft symmetry.

An extension of the fixed-mass model was considered in which the gas in the bubble was allowed to diffuse into the surrounding glass. The governing equations for this leaky-mass model were developed and manipulated into a form suitable for a numerical treatment.

For a restricted version of this problem an ILP approach has been presented in the literature. In this paper, we consider the general shunting problem and derive a greedy heuristic approach and an exact solution method based on dynamic programming. Both methods are flexible in the sense that they allow the incorporation of practical planning rules and may be extended to cover additional requirements from practice.

In this paper, we consider the problem of mechanical deformation of electrodes in RF MEMS switch due to the electrostatic forces caused by the difference in voltage between the electrodes. It is known from previous studies of this problem, that the solution exhibits multiple deformation states for a given electrostatic force. Subsequently, the capacity of the switch that depends on the deformation of electrodes displays a hysteresis behaviour against the voltage in the switch.

We investigate the present problem along two lines of attack.

First, we solve for the deformation states of electrodes using numerical methods such as finite difference and shooting methods. Subsequently, a relationship between capacity and voltage of the RF MEMS switch is constructed. The solutions obtained are exemplified using the continuation and bifurcation package AUTO.

Second, we focus on the analytical methods for a simplified version of the problem and on the stability analysis for the solutions of deformation states. The stability analysis shows that there exists a continuous path of equilibrium deformation states between the open and closed state.

We study the effect of the increasing intensity of peaks of precipitation events on the water system managed by “het Waterschap Regge en Dinkel”. Some explanation of the nature of this problem owner is in order.

In the present paper, we address two problems concerning the design and performance of an SWSN: optimal sensor placement and algorithms for object detection in the presence of false alarms. For both problems, we propose explicit decision rules and efficient algorithmic solutions. Further, we provide several numerical examples and present a simulation model that combines our placement and detection methods.

1. immersion in a polishing tank containing acid;

2. rinsing in a tank containing water; and

3. settlement of the solid reaction products in a settlement tank.

The manufacturer hopes to optimise its polishing process to

• minimise the health/environmental impact of the process;

• maximise throughput;

• maintain the sharpness of the cut edges while still polishing to an acceptable level of transparency.

The study group was asked to focus on modelling three aspects of the process:

• the chemical reactions involved in the etching at the glass-acid solution interface;

• the removal of reaction products in the settlement tank;

• flow within the polishing tank.

The tank water has a large thermal capacity and National Grid wishes to investigate whether circulation of the tank water without external heating could provide sufficient energy input to avoid freezing. Only tanks in which the tank water is below ground are investigated in the report. The soil temperature under the reservoir at depth of 10m and lower is almost constant.

Currently many actuaries may assume that the volatility of property assets is between those of equities and bonds, but without quantifying it from real data. The challenge for the Study Group is to produce a model for estimating the volatility or uncertainty in property asset values, for use in portfolio planning. The Study Group examined contexts for the use of volatility estimates, particularly in relation to solvency calculations as required by the Financial Services Authority, fund trustees and corporate boards, and it proposed a number of possible approaches. This report summarises that work, and it suggests directions for further investigation.

The Study Group found clusters in 'signal space,' that is, handsets reporting similar signal strengths with the same base stations and explored methods of locating these clusters geographically.

Study Group suggested to use the approach of bipartite networks to construct a similarity matrix that would allow the recommendation scores for different products to be computed. Given a current basket and a customer ID, this approach gives recommendation scores for each available item and recommends the item with the highest score that is not already in the basket. The similarity matrix can be computed offline, while recommendation score calculations can be performed live. This report contains the summary of Study Group findings together with the insights into properties of the similarity matrix and other related issues, such as recommendation for the data collection.

The Study Group was asked to investigate ways of putting bounds on the accuracy of such a system, and to suggest any improvements that might be made.

The work performed in the week followed three strands:

(a) an understanding of how deviations from the camera’s calibrated position lead to errors in the train’s calculated position and velocity;

(b) development of models for the train suspension, designed to place bounds on these deviations;

and (c) the performance of the associated image processing algorithms.

At the workshop, the Barker code group split into four non-disjoint subgroups:

- An "algebra group", who explored symmetries of the search space that preserve the autocorrelations' magnitude.

- A "computing group", who explored methods for quickly finding binary codes with very good autocorrelation properties.

- A "statistics group", who explored ways to quantify what has been empirically observed about autocorrelation in the search space S_2^N.

- A "continuous group", who explored a non-discrete analogue of the problem of finding sequences with good autocorrelations.

This will lower the horizontal friction, but may also bring about surface contact in high load situations.

Each group is operated by one worker (two in one case), and an operation cycle corresponds to injection, cooling, and removal of the sole. The time taken at each step varies from one order to another, and when starting a new task a machine needs to be tuned, which takes some extra time. Machines are working in parallel. At the moment the assignment is carried out empirically, and the problem proposed is to optimize the procedure.

At New Zealand Steel the process takes place inside a batch annealing furnace. The MISG group considered the problem of where the cold point lies within the steel coils, i.e. what is the last part of the coil to reach the required temperature, and how long does it take to reach this temperature? Challenges include deciding what the boundary conditions are on a coil, and dealing with the nonlinearity and anisotropy caused by height-dependent gaps within coils.

We focussed on making contributions in two main areas, namely:

1. Identification of sensitive cells in a table,

2. Maximizing data utility and minimising information loss - ensuring the table provides useful information.

One of the critical requirements for reliable inundation modelling is an accurate model of the earth's surface that extends from the open ocean through the inter-tidal zone into the onshore areas to be studied. Production of a sufficiently accurate elevation model is a complex and difficult process made more difficult because the available elevation data inevitably will come from a number of different sources and will have a range of vintages, resolutions and reliability.

There are two questions that arise when data is requested. The first deals with the true variability of the topography. Obviously, a flat surface needn’t be sampled nearly as finely as a highly convoluted surface. The second question relates to sensitivity; how are error bars derived for the impact results if the error bars on each elevation point is known? ANUGA solves the 2D nonlinear shallow water wave equations using a finite volume method and typical models can take days of computational time, so proper sensitivity analyses are often prohibitively expensive in terms of computational resources.

The main aim of this project was therefore to understand the uncertainties in the outputs of the inundation model based on possible uncertainty in the input data.

The company wishes to understand the fuse blow process mathematically in order to develop a model that can accurately simulate the blowing of the fuses. This report records the thermal, electrical, solid and fluid mechanics of the blowing process that was discussed at the Study Group, with remarks on possible future research for modelling the process.

Also of considerable interest is the chemical process of phase-separation and self-assembly of the diblock copolymer. Existing models in the literature rely heavily on computationally expensive Monte-Carlo simulation methods.

The modelling work performed during the study group in summarized in this report. The report is split into four main sections, with discussion and suggestions for experiments in the concluding section. The content of the sections is as follows:

Section 0.2: Mathematical modelling of spin-coating onto a flat substrate; no annealing considered.

Section 0.3: Modelling of spin-coating onto a substrate with topography (i.e. trenches); no annealing considered.

Section 0.4: Flow of polymer during annealing.

Section 0.5: Models for self-assembly of polymers into nanostructures.

Sections 0.2 to 0.4 are focussed on the fluid flow problems for the polymer, and go some way to providing useful answers to Problem 1. On the other hand, Problem 2 was found to be extremely challenging, and the efforts described in section 0.5 represent only a relatively modest impact on this problem.

We give to both problems formulations that fit in the framework of combinatorial optimization.