Online variance minimization

We consider the following type of online variance minimization problem: In every trial t our algorithms get a covariance matrix C ^t and try to select a parameter vector w ^t−1 such that the total variance over a sequence of trials ?_t=1^T (w^t-1)^T C^tw^t-1\sum_{t=1}^{T} (\boldsymbol {w}^{t-1})^{\top} \boldsymbol {C}^{t}\boldsymbol {w}^{t-1} is not much larger than the total variance of the best parameter vector u chosen in hindsight. Two parameter spaces in ℝ ⁿ are considered—the probability simplex and the unit sphere. The first space is associated with the problem of minimizing risk in stock portfolios and the second space leads to an online calculation of the eigenvector with minimum eigenvalue of the total covariance matrix ?_t=1^T C^t\sum_{t=1}^{T} \boldsymbol {C}^{t}. For the first parameter space we apply the Exponentiated Gradient algorithm which is motivated with a relative entropy regularization. In the second case, the algorithm has to maintain uncertainty information over all unit directions u. For this purpose, directions are represented as dyads uu ^⊤ and the uncertainty over all directions as a mixture of dyads which is a density matrix. The motivating divergence for density matrices is the quantum version of the relative entropy and the resulting algorithm is a special case of the Matrix Exponentiated Gradient algorithm. In each of the two cases we prove bounds on the additional total variance incurred by the online algorithm over the best offline parameter.     

Deep Drawing of Friction Stir Welded Thin Sheet Aluminium Steel Tailored Hybrids

Friction stir welding undergoes a steep evolution in industrial applications since the invention in the early 1990s. Especially for aluminium alloys in sheet thicknesses over 2 mm a lot of applications are established, whereas a lack in knowledge about friction stir welding of thin sheets with sheet thickness less than 2 mm exists. This article deals with friction stir welding of thin sheet aluminium steel tailored hybrids and their formability. These investigations tend to close the gap of availability of friction stir welded blanks in the range of 1 mm sheet thickness and to offer new applications of this joining technology. For production of aluminium steel tailored hybrids AA5182 with a thickness of 1.2 mm and DC04 in 1.0 mm are used, the joining partners are friction stir welded in a lap joint. Different tool geometries and process parameters are performed to achieve the highest strength and elongation at fracture of the tailored hybrids. The influence of the stirring on the arrangement and distribution of both materials in the welding zone and its microstructure is analysed using light optical and scanning electron microscopy. In addition to tensile tests planar microhardness measurements help to detect the local changes of the mechanical properties in the characteristic zones of the weld seam. Tailored hybrids, which were friction stir welded with the best welding parameters in accordance to the mechanical properties of the weld seams, were used for deep drawing tests of friction stir welded thin sheet aluminium steel tailored hybrids. The maximum drawing ratio of these tailored hybrids coincides with the one of the parent material of AA5182.     

Impurity effect on Kramer-Pesch core shrinkage ins-wave vortex and chiralp-wave vortex

The low-temperature shrinking of the vortex core (Kramer-Pesch effect) is studied for an isolated single vortex for chiral p-wave and s-wave superconducting phases. The effect of nonmagnetic impurities on the vortex core radius is numerically investigated in the Born limit by means of a quasiclassical approach. It is shown that in the chiral p-wave phase the Kramer-Pesch effect displays a certain robustness against impurities owing to a specific quantum effect, while the s-wave phase reacts more sensitively to impurity scattering. This suggests chiral p-wave superconductors as promising candidates for the experimental observation of the Kramer-Pesch effect.     

Securing Passive Objects in Mobile Ad-Hoc Peer-to-Peer Networks

Security and privacy in mobile ad-hoc peer-to-peer environments are hard to attain, especially when working with passive objects (without own processing power, e.g. RFID tags). This paper introduces a method for integrating such objects into a peer-to-peer environment without infrastructure components while providing a high level of privacy and security for peers interacting with objects. The integration is done by associating public keys to passive objects, which can be used by peers to validate proxies (peers additionally acting on behalf of objects). To overcome the problem of limited storage capacity on small embedded objects, ECC keys are used.     

A Functional Rephrasing of the Assumption/Commitment Specification Style

The assumption/commitment (also called rely/guarantee) style has been advocated for the specification of interactive components of distributed systems. It suggests the structuring of specifications into assumptions about the behavior of the component's environment and into commitments that are fulfilled by the component, provided the environment fulfills these assumptions. One of its motivations is to achieve modularity (also called compositionality) for state transition specifications of system components. Another reason for writing specifications in this format lies in proof rules that refer to this format. We define the assumption/commitment formats for functional system specifications. In particular, we work out a canonical decomposition of system specifications following the assumption/commitment format into safety and liveness aspects. We demonstrate the format of assumption/commitment specifications by a number of examples. Finally, we discuss the methodological significance of the assumption/commitment format in the stepwise development of specifications.     

An analysis of the parametrization by data driven local coordinates for multivariable linear systems

In this paper, we study a novel parametrization for state-space systems, namely data driven local coordinates (DDLC) which have recently been introduced and applied. Even though DDLC has meanwhile become the default parametrization used in the system identification toolbox of the software package MATLAB, an analysis of properties of DDLC, which are relevant to identification, has not been performed up to now. In this paper, we provide insights into the geometry and topology of the DDLC construction and show a number of results which are important for actual identification such as maximum likelihood-type estimation.     

TIME'S ARROW IN PARTICLE PHYSICS

This article gives an introduction into the current understanding of time invariance and evidence of its violation in experimental particle physics. The connection between time invariance and other discrete symmetries, particularly, CP-invariance, is explained. The first experimental determination of CP-violation is explained, and recent experiments on CP-violation and on T-violation are discussed.     

The Internal Pressure Test in Experiment and Simulation—Influence of the Wall Thickness Variation and the Change of the Packaging Behavior after the Impact of Standard Liquids

The effect of the wall thickness variation of blow‐moulded bodies made of high‐density polyethylene on an internal pressure test after prestoring the packaging with standard liquids was evaluated in experiments and simulations. The objects of the investigation were jerrycans used for the transportation and storage of dangerous goods. The wall thickness was determined using two alternative methods to the magnetostatic measurement. These alternative methods are used for research purpose to get a volumetric model of the jerrycan wall as a geometric model for the simulation. The comparison of the experiments and the simulations of the internal pressure test were performed using the digital image correlation method. The integral strain and deformation of the whole jerrycan was detected by measuring the total mass of the jerrycan being filled with water during the internal pressure test. This is a suitable alternative to the optical measurements of local deformation by the digital image correlation method. Prestorage at 40 °C without the influence of chemicals strengthens the jerrycan, whereas the swelling effect of butyl acetate and hydrocarbon mixture softens the jerrycan. The comparison with the experiment is necessary to verify the accuracy of the simulation. It shows that the deformation can be simulated more precisely by using the actual measured geometry. The weakening of the high‐density polyethylene caused by a hydrocarbon mixture can be simulated using the Arrhenius equation. The aim of the simulation was to discover whether it is possible to use specimens to predict the behaviour of a packaging both after the influence of standard liquids. Copyright © 2012 John Wiley & Sons, Ltd.