Ingve Simonsen

Determination of the Hurst exponent by use of wavelet transforms

We propose a new method for (global) Hurst exponent determination based on wavelets. Using this method, we analyze synthetic data with predefined Hurst exponents, fracture surfaces and data from economy. The results are compared with those obtained from Fourier spectral analysis. When many samples are available, the wavelet and Fourier methods are comparable in accuracy. However, when one or only a few samples are available, the wavelet method outperforms the Fourier method by a large margin.

Transient dynamics increasing network vulnerability to cascading failures.

We study cascading failures in networks using a dynamical flow model based on simple conservation and distribution laws. It is found that considering the flow dynamics may imply reduced network robustness compared to previous static overload failure models. This is due to the transient oscillations or overshooting in the loads, when the flow dynamics adjusts to the new (remaining) network structure. The robustness of networks showing cascading failures is generally given by a complex interplay between the network topology and flow dynamics.

Modularity and extreme edges of the internet.

We study the spectral properties of a diffusion process taking place on the Internet network focusing on the slowest decaying modes. These modes identify an underlying modular structure roughly corresponding to individual countries. For instance, in the slowest decaying mode the diffusion current flows from Russia to U.S. military sites. Quantitatively the modular structure manifests itself in a 10 times larger participation ratio of its slow decaying modes compared to a random scale-free network. We propose to use the fraction of nodes participating in slow decaying modes as a general measure of the modularity of a network. For the 100 slowest decaying modes of the Internet this fraction is approximately 30%. Finally, we suggest that the degree of isolation of an individual module can be assessed by comparing its participation in different diffusion modes.

Measuring anti-correlations in the nordic electricity spot market by wavelets

We consider the Nordic electricity spot market from mid-1992 to the end of year 2000. This market is found to be well approximated by an anti-persistent self-affine (mean-reverting) walk. It is characterized by a Hurst exponent of H≃0.41 over three orders of magnitude in time ranging from days to years. We argue that in order to see such a good scaling behavior, and to locate cross-overs, it is crucial that an analyzing technique is used that decouples scales. This is in our case achieved by utilizing a (multi-scale) wavelet approach. The shortcomings of methods that do not decouple scales are illustrated by applying, to the same data set, the classic R/S- and Fourier techniques, for which scaling regimes and/or positions of cross-overs are hard to define.

Modeling highly volatile and seasonal markets: evidence from the Nord Pool electricity market

In this paper we address the issue of modeling spot electricity prices. After analyzing factors leading to the unobservable in other financial or commodity markets price dynamics we propose a mean reverting jump diffusion model. We fit the model to data from the Nord Pool power exchange and find that it nearly duplicates the spot price’s main characteristics. The model can thus be used for risk management and pricing derivatives written on the spot electricity price.

Optimal investment horizons

Abstract:In stochastic finance, one traditionally considers the return as a competitive measure of an asset, i.e., the profit generated by that asset after some fixed time span Δt, say one week or one year. This measures how well (or how bad) the asset performs over that given period of time. It has been established that the distribution of returns exhibits “fat tails” indicating that large returns occur more frequently than what is expected from standard Gaussian stochastic processes [1-3]. Instead of estimating this “fat tail” distribution of returns, we propose here an alternative approach, which is outlined by addressing the following question: What is the smallest time interval needed for an asset to cross a fixed return level of say 10%? For a particular asset, we refer to this time as the investment horizon and the corresponding distribution as the investment horizon distribution. This latter distribution complements that of returns and provides new and possibly crucial information for portfolio design and risk-management, as well as for pricing of more exotic options. By considering historical financial data, exemplified by the Dow Jones Industrial Average, we obtain a novel set of probability distributions for the investment horizons which can be used to estimate the optimal investment horizon for a stock or a future contract.

Diffusion on complex networks: A way to probe their large-scale topological structures

A diffusion process on complex networks is introduced in order to uncover their large-scale topological structures. This is achieved by focusing on the slowest decaying diffusive modes of the network. The proposed procedure is applied to real-world networks like a friendship network of known modular structure, and an Internet routing network. For the friendship network, its known structure is well reproduced. In case of the Internet, where the structure is far less well known, one indeed finds a modular structure, and modules can roughly be associated with individual countries. Quantitatively, the modular structure of the Internet manifests itself in an approximately 10 times larger participation ratio of its slowest decaying modes as compared to the null model—a random scale-free network. The extreme edges of the Internet are found to correspond to Russian and US military sites.

GRANFILM: a software for calculating thin-layer dielectric properties and Fresnel coefficients

Abstract This paper describes new software—called GranFilm —for computing linear optical coefficients for surfaces and thin layers. The underlying theory relies on the treatment of the electromagnetic boundary conditions at the surface using the notions of integrated electromagnetic excess fields and surface susceptibilities. Any type of Fresnel quantities (reflection, transmission, absorption or ellipsometric coefficients) and dielectric coefficients (energy electron loss cross-section) can be computed by this software for various kinds of surface morphology: thin continuous films, island layers made of truncated spheres or spheroids, or rough surfaces. The only restriction on the morphology is that the thickness of the surface perturbed layer is much smaller than the optical wavelength. G ran F ilm covers most of the material developed by Bedeaux and Vlieger in the recently published book ‘Optical Properties of Surfaces’ (Imperial College Press, London, 2001).

Scattering of electromagnetic waves from two-dimensional randomly rough perfectly conducting surfaces: The full angular intensity distribution

Author(s): Simonsen, I; Maradudin, AA; Leskova, TA | Abstract: By a computer simulation approach we study the scattering of p- or s-polarized light from a two-dimensional, randomly rough, perfectly conducting surface. The pair of coupled inhomogeneous integral equations for two independent tangential components of the magnetic field on the surface are converted into matrix equations by the method of moments, which are then solved by the biconjugate gradient stabilized method. The solutions are used to calculate the mean differential reflection coefficient for given angles of incidence and specified polarizations of the incident and scattered fields. The full angular distribution of the intensity of the scattered light is obtained for strongly randomly rough surfaces by a rigorous computer simulation approach.

Numerical modeling of the optical response of supported metallic particles

The present work reports a general method for the calculation of t he polarizability of a truncated sphere on a substrate. A multipole ex pansion is used, where the multipoles are not necessarily localized in the center of the sphere but can freely move on the revolution axis. From the weak formulation of the boundary conditions, an infinite set of linear equations for the multipole coefficients is derived. To obta in this set, the interaction between the island and the substrate is t aken into account by the technique of image multipoles. For numerical implementation, this set is truncated at an arbitrary mu ltipole order. The accuracy of the method is jugded through the stabil ity of the truncated sphere polarizability and the the fulfilment of t he boundary conditions which are demonstrated to be satisfied in large regions of the parameter space. This method brings an improvement wit h respect to the Bedeauxs case \cite{Wind87a,Wind87b} where the multi poles are located in the center of the sphere.