Empirical Behavior of a World Stock Index from Intra-Day to Monthly Time Scales

Most of the papers that study the distributional and fractal properties of financial instruments focus on stock prices or foreign exchange rates. This typically leads to mixed results concerning the distributions of log-returns and some multi-fractal properties of exchange rates, stock prices, and regional indices. This paper uses a well diversified world stock index as the central object of analysis. Such index approximates the growth optimal portfolio, which is demonstrated under the benchmark approach, it is the ideal reference unit for studying basic securities. When denominating this world index in units of a given currency, one measures the movements of the currency against the entire market. This provides a least disturbed observation of the currency dynamics. In this manner, one can expect to disentangle, e.g., the superposition of the two currencies involved in an exchange rate. This benchmark approach to the empirical analysis of financial data allows us to establish remarkable stylized facts. Most important is the observation that the repeatedly documented multi-fractal appearance of financial time series is very weak and much less pronounced than the deviation of the mono-scaling properties from Brownian-motion type scaling. The generalized Hurst exponent H(2) assumes typical values between 0.55 and 0.6. Accordingly, autocorrelations of log-returns decay according to a power law, and the quadratic variation vanishes when going to vanishing observation time step size. Furthermore, one can identify the Student t distribution as the log-return distribution of a well-diversified world stock index for long time horizons when a long enough data series is used for estimation. The study of dependence properties, finally, reveals that jumps at daily horizon originate primarily in the stock market while at 5 min horizon they originate in the foreign exchange market. These results are contrasted with the behavior of foreign exchange rates. The principal message of the empirical analysis is that there is evidence that a diffusion model without multi-scaling could reasonably well model the dynamics of a broadly diversified world stock index.

Finite element surface registration incorporating curvature, volume preservation, and statistical model information

We present a novel method for nonrigid registration of 3D surfaces and images. The method can be used to register surfaces by means of their distance images, or to register medical images directly. It is formulated as a minimization problem of a sum of several terms representing the desired properties of a registration result: smoothness, volume preservation, matching of the surface, its curvature, and possible other feature images, as well as consistency with previous registration results of similar objects, represented by a statistical deformation model. While most of these concepts are already known, we present a coherent continuous formulation of these constraints, including the statistical deformation model. This continuous formulation renders the registration method independent of its discretization. The finite element discretization we present is, while independent of the registration functional, the second main contribution of this paper. The local discontinuous Galerkin method has not previously been used in image registration, and it provides an efficient and general framework to discretize each of the terms of our functional. Computational efficiency and modest memory consumption are achieved thanks to parallelization and locally adaptive mesh refinement. This allows for the first time the use of otherwise prohibitively large 3D statistical deformation models

Posterior shape models

We present a method to compute the conditional distribution of a statistical shape model given partial data. The result is a "posterior shape model", which is again a statistical shape model of the same form as the original model. This allows its direct use in the variety of algorithms that include prior knowledge about the variability of a class of shapes with a statistical shape model. Posterior shape models then provide a statistically sound yet easy method to integrate partial data into these algorithms. Usually, shape models represent a complete organ, for instance in our experiments the femur bone, modeled by a multivariate normal distribution. But because in many application certain parts of the shape are known a priori, it is of great interest to model the posterior distribution of the whole shape given the known parts. These could be isolated landmark points or larger portions of the shape, like the healthy part of a pathological or damaged organ. However, because for most shape models the dimensionality of the data is much higher than the number of examples, the normal distribution is singular, and the conditional distribution not readily available. In this paper, we present two main contributions: First, we show how the posterior model can be efficiently computed as a statistical shape model in standard form and used in any shape model algorithm. We complement this paper with a freely available implementation of our algorithms. Second, we show that most common approaches put forth in the literature to overcome this are equivalent to probabilistic principal component analysis (PPCA), and Gaussian Process regression. To illustrate the use of posterior shape models, we apply them on two problems from medical image analysis: model-based image segmentation incorporating prior knowledge from landmarks, and the prediction of anatomically correct knee shapes for trochlear dysplasia patients, which constitutes a novel medical application. Our experiments confirm that the use of conditional shape models for image segmentation improves the overall segmentation accuracy and robustness

Gaussian Process Morphable Models

Statistical shape models (SSMs) represent a class of shapes as a normal distribution of point variations, whose parameters are estimated from example shapes. Principal component analysis (PCA) is applied to obtain a low-dimensional representation of the shape variation in terms of the leading principal components. In this paper, we propose a generalization of SSMs, called Gaussian Process Morphable Models (GPMMs). We model the shape variations with a Gaussian process, which we represent using the leading components of its Karhunen-Loeve expansion. To compute the expansion, we make use of an approximation scheme based on the Nystrom method. The resulting model can be seen as a continuous analogon of an SSM. However, while for SSMs the shape variation is restricted to the span of the example data, with GPMMs we can define the shape variation using any Gaussian process. For example, we can build shape models that correspond to classical spline models, and thus do not require any example data. Furthermore, Gaussian processes make it possible to combine different models. For example, an SSM can be extended with a spline model, to obtain a model that incorporates learned shape characteristics, but is flexible enough to explain shapes that cannot be represented by the SSM. We introduce a simple algorithm for fitting a GPMM to a surface or image. This results in a non-rigid registration approach, whose regularization properties are defined by a GPMM. We show how we can obtain different registration schemes,including methods for multi-scale, spatially-varying or hybrid registration, by constructing an appropriate GPMM. As our approach strictly separates modelling from the fitting process, this is all achieved without changes to the fitting algorithm. We show the applicability and versatility of GPMMs on a clinical use case, where the goal is the model-based segmentation of 3D forearm images

Perspectives on Security in Twentieth-Century Europe and the World

Despite the present-day attraction of ‘security' as an attention-grabbing word in politics and the public sphere, the study of security is a missing chapter in many state-of-the-art surveys of historical literature. Its central relevance for the modern statehood has been obvious for centuries in the European context. In Thomas Hobbes's mid-seventeenth-century Leviathan, written in the context of the devastating English civil war and previous religious wars, government was given the fundamental role in guaranteeing security. Over the course of the twentieth century, intellectuals have constantly debated Hobbes's ideas and concepts about security and societal peace. Especially after the second world war, security has found major attention in the fields of International Relations and its sub-discipline security studies. Security studies evolved during the nuclear age and were originally foremost about the study of the threat, use and control of military force, as one proponent of security studies, Stephen Walt, stated. They were mainly concerned with military strategy and giving policy advice to the military. Since the cold war, the study of security has come a long way. Most importantly, as Emma Rothschild has reminded us, during the past two decades or so, the concept was first extended downwards from states to individuals, upwards from the nation to the biosphere and horizontally from the military to the economic, social, political and environmental. It is the reflection of this dynamic change in theory, methodology and empirical research that connects most of the books under review in this articl

The adenosine story goes ionic: Ca(V)2.1-type Ca(2+) channels identified as effectors of adenosine's somnogenic actions.

The adenosine story goes ionic: Ca(V)2.1-type Ca(2+) channels identified as effectors of adenosine's somnogenic action

Sleep: Switching Off the Off-Switch.

What are the synaptic drives controlling the sleep-wake circuitry in the mammalian brain? In a new study it was found that GABAergic cells in posterior lateral hypothalamus inhibit sleep-promoting anterior hypothalamic cells to cause waking, whereas their inhibition augments sleep

A machine learning approach to statistical shape models with applications to medical image analysis

Statistical shape models have become an indispensable tool for image analysis. The use of shape models is especially popular in computer vision and medical image analysis, where they were incorporated as a prior into a wide range of different algorithms. In spite of their big success, the study of statistical shape models has not received much attention in recent years. Shape models are often seen as an isolated technique, which merely consists of applying Principal Component Analysis to a set of example data sets. In this thesis we revisit statistical shape models and discuss their construction and applications from the perspective of machine learning and kernel methods. The shapes that belong to an object class are modeled as a Gaussian Process whose parameters are estimated from example data. This formulation puts statistical shape models in a much wider context and makes the powerful inference tools from learning theory applicable to shape modeling. Furthermore, the formulation is continuous and thus helps to avoid discretization issues, which often arise with discrete models. An important step in building statistical shape models is to establish surface correspondence. We discuss an approach which is based on kernel methods. This formulation allows us to integrate the statistical shape model as an additional prior. It thus unifies the methods of registration and shape model fitting. Using Gaussian Process regression we can integrate shape constraints in our model. These constraints can be used to enforce landmark matching in the fitting or correspondence problem. The same technique also leads directly to a new solution for shape reconstruction from partial data. In addition to experiments on synthetic 2D data sets, we show the applicability of our methods on real 3D medical data of the human head. In particular, we build a 3D model of the human skull, and present its applications for the planning of cranio-facial surgeries

Molecular Dynamics Simulations of Dynamic Force Microscopy: Applications to the Si(111)-7x7 Surface

Molecular dynamics simulations have been performed to understand true atomic resolution, which has been observed on the Si(111)-7$\times$7 surface by dynamic force microscopy in ultra high vacuum(UHV). Stable atomic-scale contrast is reproduced in simulations at constant mean height above a critical tip-sample separation when monitoring the interaction force between tip and sample. Missing or additional adatoms can be recognized in such scans, although they are less well resolved than native adatoms. The resonance frequency shift, as well as arbitrary scans, e.g. at constant force can be computed from a series of force-distance characteristics. By means of dynamic simulations we show how energy losses induced by interaction with an oscillating tip can be monitored and that they occur even in the non-contact range.Comment: 5 pages, 5 figures, accepted publication in Applied Surface Scienc