The lid method for exhaustive exploration of metastable states of complex systems

The `lid' algorithm performs an exhaustive exploration of neighborhoods of local energy minima of energy landscapes. This paper describes an implementation of the algorithm, including issues of parallel performance and scalability. To illustrate the versatility of the approach and to stress the common features present in landscapes of quite different systems, we present selected results for 1) a spin glass, 2) a ferromagnet, 3) a covalent network model for glassy systems, and 4) a polymer. The exponential nature of the local density of states found in these systems and its relation to the ordering transition is briefly commented upon.Comment: RevTeX, 11 pages, 1 figur

The Rate Structure

Världen står inför en av de kanske största utmaningarna någonsin, att begränsa mängden växthusgaser i atmosfären till hållbara nivåer. För att uppnå detta måste alla delar av samhället effektivisera och begränsa sin energi och resursanvändning. I detta kandidatexamensarbete har ett av Åsbacka Trädgårds växthus i Söderhamn studerats för att undersöka möjliga investeringar till reduktion av den energianvändning som idag råder. De energireducerande åtgärderna har simulerats med programvaran IDA ICE 4.6 och därefter analyserats och jämförts med varandra. Då anläggningen idag värms med olja är det intressant att ersätta denna med en förnybar energiresurs. Resultatet visar att vid installation av energiväv kan en reduktion av energibehovet göras med upp till 20 procent. Betydande besparingar i uppvärmningskostnad kan ske om energiväven kombineras med uppvärmning från träpellets eller bergvärme, där besparingar mellan 70 000 och 85 000 kronor årligen kan uppnås för den aktuella perioden Åsbacka Trädgård bedriver verksamhet i växthuset. Detta kan jämföras med de 100 000 kronor som driften kostar idag. Av denna anledning rekommenderas installation av energiväv och ett utbyte till förnybar energiresurs. De presenterade investeringarna har valts utifrån produkter som finns tillgängliga på marknaden. Investeringskostnader för de presenterade alternativen har inte beaktats, endast den årliga driftskostnaden för uppvärmning har tagits hänsyn till.

On the exponential convergence of the Kaczmarz algorithm

The Kaczmarz algorithm (KA) is a popular method for solving a system of linear equations. In this note we derive a new exponential convergence result for the KA. The key allowing us to establish the new result is to rewrite the KA in such a way that its solution path can be interpreted as the output from a particular dynamical system. The asymptotic stability results of the corresponding dynamical system can then be leveraged to prove exponential convergence of the KA. The new bound is also compared to existing bounds

Foreword

Magnetometers and inertial sensors (accelerometers and gyroscopes) are widely used to estimate 3D orientation. For the orientation estimates to be accurate, the sensor axes need to be aligned and the magnetometer needs to be calibrated for sensor errors and for the presence of magnetic disturbances. In this work we use a grey-box system identification approach to compute maximum likelihood estimates of the calibration parameters. An experiment where the magnetometer data is highly disturbed shows that the algorithm works well on real data, providing good calibration results and improved heading estimates. We also provide an identifiability analysis to understand how much rotation is needed to be able to solve the calibration problem.MC ImpulseCADIC

Properties of the energy landscape of network models for covalent glasses

We investigate the energy landscape of two dimensional network models for covalent glasses by means of the lid algorithm. For three different particle densities and for a range of network sizes, we exhaustively analyse many configuration space regions enclosing deep-lying energy minima. We extract the local densities of states and of minima, and the number of states and minima accessible below a certain energy barrier, the 'lid'. These quantities show on average a close to exponential growth as a function of their respective arguments. We calculate the configurational entropy for these pockets of states and find that the excess specific heat exhibits a peak at a critical temperature associated with the exponential growth in the local density of states, a feature of the specific heat also observed in real glasses at the glass transition.Comment: RevTeX, 19 pages, 7 figure

Getting Started with Particle Metropolis-Hastings for Inference in Nonlinear Dynamical Models

This tutorial provides a gentle introduction to the particle Metropolis-Hastings (PMH) algorithm for parameter inference in nonlinear state-space models together with a software implementation in the statistical programming language R. We employ a step-by-step approach to develop an implementation of the PMH algorithm (and the particle filter within) together with the reader. This final implementation is also available as the package pmhtutorial in the CRAN repository. Throughout the tutorial, we provide some intuition as to how the algorithm operates and discuss some solutions to problems that might occur in practice. To illustrate the use of PMH, we consider parameter inference in a linear Gaussian state-space model with synthetic data and a nonlinear stochastic volatility model with real-world data.Comment: 41 pages, 7 figures. In press for Journal of Statistical Software. Source code for R, Python and MATLAB available at: https://github.com/compops/pmh-tutoria