### 1st semester (Sept 2008-Jan 2009)

##### October, 9

Speakers:

Mobile ad hoc networks are rapidly emerging in a variety of application areas such as wild life monitoring, road-traffic information dissemination and disaster relief situations. A key characteristic of such networks is that connections between stations are intermittently rather than stationary. In this presentation, we propose a modelling framework for a class of mobile ad hoc networks. This class comprises single-channel networks with mobile stations that move only in a local neighbourhood. The proposed model is in fact a single-server polling system which operates under a specific time-limited service discipline. The analysis of this model provides us insight in the transfer delays and required buffer levels of the stations in the network. We will give some examples of networks that fit into our framework, and indicate several directions for future work.

Viktor Lukocius on Statistical analysis of dependencies withing insurance portfolios

What is the distribution of the sum of individual claims of large insurance portfolios? Typically it is assumed that insurance claims are independent, although it is clearly recognized that dependencies do occur in practice: man and wife both insured in the same portfolio, carpoolers using a collective company insurance, catastrophes like hurricanes or floods hitting numerous insured at the same time.
Studies demonstrate that the effects of dependence can be astronomical, so there is ample cause to take small dependence effects seriously. In my work a general model is developed, which covers what happens in practice in a realistic way. Approximations are presented which are both accurate and transparent and the results obtained are illustrated through some explicit examples.

##### November, 13

Speakers:

Tim Op 't Root on One-way wave propagation through smoothly varying media

As part of the application called migration or reflection seismic imaging, we model wave propagation through the earth, governed by the acoustic wave equation. Downward continuation is a technique to describe or to estimate the seismic wave field at a point beneath a surface where the seismic field is known due to measurements or knowledge of the source. For several reasons this downward continuation is often governed by the so called one-way wave equation. The difficulty of deriving and understanding this equation is due to the fact that the velocity is spatially varying. We assume the velocity to be a smooth function and derive the one-way wave equation, using the theory of pseudo-differential operators. One of the challenges is to derive the one-way wave equation such that it descibes wave amplitudes correctly. It relies on an asymptotic approximation of rational powers of the partial differential operator

$\frac{-1}{c(x,z)^2}\partial_t^2+\partial_x^2$, for example its square root. Another challenge is to numerically compute the downward propagation using an implementation of the involved pseudo-differential operators.

MicroCHP is a home device, which turns gas into heat and electricity. This means that people can heat their home, and meanwhile generate electricity. If heat is stored temporarily in the home, production and consumption of both heat and electricity can be decoupled. If microCHP is applied on a large scale (say, in all houses in The Netherlands), a large part of the electricity production is distributed over the country. To prevent high peak loads in the electricity grid, we need to control this distributed production. In this colloquium I present this control problem as an ILP formulation.

##### December, 11

Speakers:

Driven by public opinion, increased health expenditures, an ageing population, and long waiting lists, a flood of changes in the healthcare system has been set in motion to try to make the Dutch hospitals more efficient. In this project we apply techniques from Operations Research and Operations Management to improve operational processes in health care. Using a problem-driven approach, our aim is to provide solutions for current problems at Leiden University Medical Center, which are also of interest to other hospitals.

Vehicle routing problems (VRP) have been extensively studied in the past decades. Since transportation costs constitute a significant part (4 to 10 percent) of a product selling price, efficient vehicle routing methods are highly valuable in practice. On the other hand, due to its computational complexity the VRP has drawn a lot of attention from the scientific community. In order to cope with many additional real life restrictions, the traditional vehicle routing model has been extended to several generalizations of the VRP. Local search methods have proven to be very successful in solving these different variants of the VRP.
However, a major drawback of local search methods is that they require careful tailoring for each specific variant of the VRP in order to obtain high quality solutions. Therefore, it is very hard to generalize one local search method to solve different variants of the VRP. We present a flexible framework for solving VRPs based on restricted dynamic programming. We demonstrate the flexibility of this framework by showing how it can handle a wide range of different variants of the VRP, including some hard real-life constraints which have been generally ignored in the VRP-literature. The quality of the restricted dynamic programming method is demonstrated by solving a set of benchmark instances for the capacitated vehicle routing problem (CVRP).

#### 2nd semester (Feb 2010-July 2010)

##### February, 12

Speakers:

All linear, time-invariant, ordinary and partial differential equations can be written in the abstract form x'(t) = Ax(t), x(0) = x0, where x(·) is the state trajectory which is assumed to lie in the (linear) finite or infinite-dimensional state space X, for instance Rn, L2(0, 1) or L1(0, 1). The solutions of the differential equation are given via the semigroup (eAt) t >= 0 ; i.e. x(t) = eAtx0.
A standard numerical way of solving such a differential equation is the Crank-Nicolson method. In this method the differential equation is replaced by the difference equation
xd(n + 1) = (A + I) (A − I)−1 xd(n) := Adxd(n), xd(0) = x0,
the operator Ad is known as the Cayley transform.
We are interested in understanding how the Cayley transform affects the semigroup properties. For instance, what happens to stability and stable solutions.

Readers of the Physics World magazine voted in 2006 for the Maxwell equations as the greatest equation(s) of all times. It topped a list that included much better-known competitors such as Newton's second law or Einstein's famous E = mc^2. But is the high standing justified?
Probably yes. The Maxwell equations describe electromagnetic waves and their propagative properties. They gave rise to radiotechnology from which information technology later evolved. Indeed, it would be very difficult to imagine the world today without all the fancy devices that make our lives so much more convenient. However, solving the Maxwell equations is no trivial task. An exact solution is usually unattainable except for the simplest cases, so one has to resort to approximating the solution by using a numerical discretisation method.
Out of the several existing such techniques, in my talk I will focus on what's called the discontinuous Galerkin finite element method (DG-FEM). This is a relatively new technology that for certain applications offers a number of advantages over other numerical methods.

##### March, 12

Speakers:

Saikat Saha on Particle Filter : the Monte Carlo approach to signal processing
Extracting the underlying information optimally from noisy observation data is a major challenge in signal processing. After the seminal works of Wiener and Kalman, the problem got a major breakthrough with the idea of Particle Filter. We explain this line of development with application to the target tracking problem.

Debris flows are flows of water-saturated slurry mixtures. Examples are mud slides initiated by heavy rainfall on eroded mountain sides consisting of mixtures of rock, sand and mud; and volcanic debris flows in which the flow may be a mixture of volcanic debris and water. These flows often cause major destruction to buildings and infrastructure, with accompanying loss of human lives. In this presentation we discuss some aspects of a model used for simulating debris flows. We furthermore validate the model against a laboratory experiment and show the abilities of the model to capture physical phenomena.

Poster

##### April, 9

Speakers:

In classical models the risk of option pricing can be eliminated by a perfect hedging portfolio. In real markets there are risks that cannot be hedged by trading. The value of an option will thus consist of two parts: the cost of the hedging strategy plus a risk premium, required by the option seller to cover her residual risk.

The talk will focus on axiomatically based risk measures and how these risk measures can be implemented to price options.

Within this project we try to construct new numerical schemes that aim to improve current ensemble forecasting models for climate. Most contemporary climate models conserve energy and potential vorticity in the case of no forcing and dissipation. What's missing in most cases, however, is a consistent discretization of the phase space structure for unforced and dissipation-free flow. Constructing such schemes is nontrivial. One may argue that this feature, in principle, should not have an effect in the simulation of the real climate, since it is ultimately driven by (nonuniform) solar heating and damped by (eddy) viscosity. However, we have good reasons to believe that such a consistent discretization, which is closer to the governing equations in the sense that it reproduces the correct flow even if the forcing and friction is set to zero, will lead to better climate predictions.

Poster

##### May, 14

Speakers:

In our work we construct the stability analysis for a class of switched linear systems, modelled by hybrid automaton. A switched
linear system is a dynamical system consisting of a finite number of different continuous time linear systems. With each continuous time system we associate a discrete state or location. The dynamics of the system has a discrete component that describes the switches from one discrete state to another and a continuous component corresponding to the dynamics within discrete state. We assume that dynamics in a location is linear and asymptotically stable; the guard on the transition is hyperplane in the state space. We define necessary and sufficient conditions for stability of the linear switched system with fixed and arbitrary dynamics in a location. We formulate the stability criteria for the linear switched system using an approximation of solution via a quadratic Lyapunov function.

Ivan Lakhturov on Dispersion in 1-D Variational Boussinesq Model

The Variational Boussinesq Model for waves over ideal fluid conserves mass, momentum, energy, and contains decreased dimensionality compared to the full initial problem. It is derived from the Hamiltonian formulation via an approximation of the kinetic energy, and can provide approximate dispersion characteristics. Having in mind a signalling problem, we search for optimal dispersive properties of the 1-D linear Variational Boussinesq Model over flat bottom and, using the finite element numerical code, investigate its robustness against the exact dispersion in a spectral code.

Poster

##### June, 11

Speakers:

The modeling of flow through porous media is hampered by the geometrical complexities of their internal solid surfaces. Finding an adequate mathematical description of the solid boundaries proves to be extremely difficult. To avoid this problem, an averaged description of the field variables can be adopted. However, this averaging technique introduces new and unknown transport coefficients, such as: the permeability. In this talk we set out to solve the permeability coefficient by fully resolving the flow field through a spatially periodic array of staggered squares. The numerical method of choice for approximating the flow is the versatile 'immersed boundary method.'

We present a model to influx waves in a water basin. Waves in hydrodynamics laboratories are generated by giving a certain motion that
is related to the desired prescribed time signal. The measurements of the waves height then be made at some positions. Each measurement is a function of time. For a dispersive model it turns out to be a challenge how one should translate such a motion into the dynamic evolution equation. We consider unidirectional dispersive waves described by the so called AB-equation.

Poster