A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance

We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately, many intuitive (e.g. finite difference based) discretisations can be shown to converge. However, especially when using fully implicit time stepping schemes with their desirable stability properties, one is still faced with the considerable task of solving the resulting nonlinear discrete system. In this paper, we introduce a penalty method which approximates the nonlinear discrete system to first order in the penalty parameter, and we show that an iterative scheme can be used to solve the penalised discrete problem in finitely many steps. We include a number of examples from mathematical finance for which the described approach yields a rigorous numerical scheme and present numerical results.Comment: 18 Pages, 4 Figures. This updated version has a slightly more detailed introduction. In the current form, the paper will appear in SIAM Journal on Numerical Analysi

Clustering Memes in Social Media

The increasing pervasiveness of social media creates new opportunities to study human social behavior, while challenging our capability to analyze their massive data streams. One of the emerging tasks is to distinguish between different kinds of activities, for example engineered misinformation campaigns versus spontaneous communication. Such detection problems require a formal definition of meme, or unit of information that can spread from person to person through the social network. Once a meme is identified, supervised learning methods can be applied to classify different types of communication. The appropriate granularity of a meme, however, is hardly captured from existing entities such as tags and keywords. Here we present a framework for the novel task of detecting memes by clustering messages from large streams of social data. We evaluate various similarity measures that leverage content, metadata, network features, and their combinations. We also explore the idea of pre-clustering on the basis of existing entities. A systematic evaluation is carried out using a manually curated dataset as ground truth. Our analysis shows that pre-clustering and a combination of heterogeneous features yield the best trade-off between number of clusters and their quality, demonstrating that a simple combination based on pairwise maximization of similarity is as effective as a non-trivial optimization of parameters. Our approach is fully automatic, unsupervised, and scalable for real-time detection of memes in streaming data.Comment: Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM'13), 201

Sub-unit cell layer-by-layer growth of Fe3O4, MgO, and Sr2RuO4 thin films

The use of oxide materials in oxide electronics requires their controlled epitaxial growth. Recently, it was shown that Reflection High Energy Electron Diffraction (RHEED) allows to monitor the growth of oxide thin films even at high oxygen pressure. Here, we report the sub-unit cell molecular or block layer growth of the oxide materials Sr2RuO4, MgO, and magnetite using Pulsed Laser Deposition (PLD) from stoichiometric targets. Whereas for perovskites such as SrTiO3 or doped LaMnO3 a single RHEED intensity oscillation is found to correspond to the growth of a single unit cell, in materials where the unit cell is composed of several molecular layers or blocks with identical stoichiometry, a sub-unit cell molecular or block layer growth is established resulting in several RHEED intensity oscillations during the growth of a single unit-cell

Evaluating Terrain for Harvesting Equipment Selection

A terrain evaluation model, utilizing a geographic information system, has been developed as a tool for planning large-scale industrial timber harvesting operations. The model combines terrain descriptions with machine operating criteria to produce maps delineating operable areas. The integration of the model with a harvest planning decision support system is discussed and an example is presented

Penalty Methods for the Solution of Discrete HJB Equations -- Continuous Control and Obstacle Problems

In this paper, we present a novel penalty approach for the numerical solution of continuously controlled HJB equations and HJB obstacle problems. Our results include estimates of the penalisation error for a class of penalty terms, and we show that variations of Newton's method can be used to obtain globally convergent iterative solvers for the penalised equations. Furthermore, we discuss under what conditions local quadratic convergence of the iterative solvers can be expected. We include numerical results demonstrating the competitiveness of our methods.Comment: 31 Pages, 7 Figure

Modelling of air resistance during drying of wood-chips

The objective of this study was to investigate the parameters that affect the drying process of wood chips at low air flow conditions. This objective was determined by measuring the air pressure resistance being produced by wood chips by examining different variables such as: air flow rate, air velocity, wood chip size, bulk density, bulk height and porosity. The air flow resistance was measured inside a 3 meter high cylindrical air duct constructed at University of Hohenheim. Physical properties of two different Spruce wood chip fractions were analyzed and their characteristics were considered on fitting the model expression. The analysed model expresses the physical behaviour of air flow resistance. Statistical analyses show high correlation of air speed versus air flow resistance. The model could be used for determination of drying conditions with low air mass flow. The height of bulk density according air mass flow generated or the necessary air mass flow needed for transporting air through the bulk height

In-trap conversion electron spectroscopy

The Penning trap REXTRAP at ISOLDE was used to test the feasibility of in-trap conversion electron spectroscopy. The results of simulations, experiments with solid conversion electron sources as well as first on-line and tests with trapped radioactive ions are presented. In addition to obtaining high-resolution spectroscopic data, the detection of conversion electrons was found to be a useful tool for the diagnostics of the trap operation. The tests proved the feasibility of in-trap spectroscopy but also revealed some potential problems to be addressed in the future

Projected changes in the Asian-Australian monsoon region in 1.5°C and 2.0°C global-warming scenarios

In light of the Paris Agreement, it is essential to identify regional impacts of half a degree additional global warming to inform climate adaptation and mitigation strategies. We investigate the effects of 1.5°C and 2.0°C global warming above pre-industrial conditions, relative to present day (2006-2015), over the Asian-Australian monsoon region (AAMR) using five models from the Half a degree Additional warming, Prognosis and Projected Impacts (HAPPI) project. There is considerable inter-model variability in projected changes to mean climate and extreme events in 2.0°C and 1.5°C scenarios. There is high confidence in projected increases to mean and extreme surface temperatures over AAMR, as well as more-frequent persistent daily temperature extremes over East Asia, Australia and northern India with an additional 0.5°C warming, which are likely to occur. Mean and extreme monsoon precipitation amplify over AAMR, except over Australia at 1.5°C where there is uncertainty in the sign of the change. Persistent daily extreme precipitation events are likely to become more frequent over parts of East Asia and India with an additional 0.5°C warming. There is lower confidence in projections of precipitation change than in projections of surface temperature change. These results highlight the benefits of limiting the global-mean temperature change to 1.5°C above pre-industrial, as the severity of the above effects increases with an extra 0.5°C warming