Efficient Higher Order Derivatives of Objective Functions Composed of Matrix Operations

This paper is concerned with the efficient evaluation of higher-order derivatives of functions $f$ that are composed of matrix operations. I.e., we want to compute the $D$-th derivative tensor $\nabla^D f(X) \in \mathbb R^{N^D}$, where $f:\mathbb R^{N} \to \mathbb R$ is given as an algorithm that consists of many matrix operations. We propose a method that is a combination of two well-known techniques from Algorithmic Differentiation (AD): univariate Taylor propagation on scalars (UTPS) and first-order forward and reverse on matrices. The combination leads to a technique that we would like to call univariate Taylor propagation on matrices (UTPM). The method inherits many desirable properties: It is easy to implement, it is very efficient and it returns not only $\nabla^D f$ but yields in the process also the derivatives $\nabla^d f$ for $d \leq D$. As performance test we compute the gradient $\nabla f(X)$ % and the Hessian $\nabla_A^2 f(A)$ by a combination of forward and reverse mode of f(X) = \trace (X^{-1}) in the reverse mode of AD for $X \in \mathbb R^{n \times n}$. We observe a speedup of about 100 compared to UTPS. Due to the nature of the method, the memory footprint is also small and therefore can be used to differentiate functions that are not accessible by standard methods due to limited physical memory

Large-Scale Disasters and the Insurance Industry

We investigate the impact of the 20 largest – in terms of insured losses – man-made or natural disasters on various insurance industry stock indices. We show via an event study that insurance sectors worldwide are quite resilient, in a market–value sense, to unexpected losses to capital: our data provide evidence that equity market investors believe that insurance companies will on average be able to make losses back over the foreseeable future, i.e. that the adverse shocks to equity which have resulted from these catastrophes will be compensated by either an outward shift of the demand curve or an ability to raise premiums, or both.disaster, insurance industry, event-study

Large-scale disasters and the insurance industry

We investigate the effect of the 20 largest – in terms of insured losses – man-made or natural disasters on the insurance industry. We show via an event study that insurance markets worldwide are quite resilient to unexpected losses to capital and are even outperforming the general market subsequent to great disasters. --disaster,insurance industry,event-study

CP Violating Asymmetry in Stop Decay into Bottom and Chargino

In the MSSM with complex parameters, loop corrections to the decay of a stop into a bottom quark and a chargino can lead to a CP violating decay rate asymmetry. We calculate this asymmetry at full one-loop level and perform a detailed numerical study, analyzing the dependence on the parameters and complex phases involved. In addition, we take the Yukawa couplings of the top and bottom quark running. We account for the constraints on the parameters coming from several experimental limits. Asymmetries of several percent are obtained. We also comment on the feasibility of measuring this asymmetry at the LHC.Comment: Contributed talk given by Sebastian Frank in June 2009 at SUSY09 - 17th International Conference on Supersymmetry and the Unification of Fundamental Interactions, Northeastern University, Boston, USA. To appear in the AIP conference proceedings, 4 pages, 7 figures (fixed links in references

Shortcomings of the Bond Orientational Order Parameters for the Analysis of Disordered Particulate Matter

Local structure characterization with the bond-orientational order parameters q4, q6, ... introduced by Steinhardt et al. has become a standard tool in condensed matter physics, with applications including glass, jamming, melting or crystallization transitions and cluster formation. Here we discuss two fundamental flaws in the definition of these parameters that significantly affect their interpretation for studies of disordered systems, and offer a remedy. First, the definition of the bond-orientational order parameters considers the geometrical arrangement of a set of neighboring spheres NN(p) around a given central particle p; we show that procedure to select the spheres constituting the neighborhood NN(p) can have greater influence on both the numerical values and qualitative trend of ql than a change of the physical parameters, such as packing fraction. Second, the discrete nature of neighborhood implies that NN(p) is not a continuous function of the particle coordinates; this discontinuity, inherited by ql, leads to a lack of robustness of the ql as structure metrics. Both issues can be avoided by a morphometric approach leading to the robust Minkowski structure metrics ql'. These ql' are of a similar mathematical form as the conventional bond-orientational order parameters and are mathematically equivalent to the recently introduced Minkowski tensors [Europhys. Lett. 90, 34001 (2010); Phys. Rev. E. 85, 030301 (2012)]

Super-resolution microscopy reveals specific recruitment of HIV-1 envelope proteins to viral assembly sites dependent on the envelope C-terminal tail

The inner structural Gag proteins and the envelope (Env) glycoproteins of human immunodeficiency virus (HIV-1) traffic independently to the plasma membrane, where they assemble the nascent virion. HIV-1 carries a relatively low number of glycoproteins in its membrane, and the mechanism of Env recruitment and virus incorporation is incompletely understood. We employed dual-color super-resolution microscopy visualizing Gag assembly sites and HIV-1 Env proteins in virus-producing and in Env expressing cells. Distinctive HIV-1 Gag assembly sites were readily detected and were associated with Env clusters that always extended beyond the actual Gag assembly site and often showed enrichment at the periphery and surrounding the assembly site. Formation of these Env clusters depended on the presence of other HIV-1 proteins and on the long cytoplasmic tail (CT) of Env. CT deletion, a matrix mutation affecting Env incorporation or Env expression in the absence of other HIV-1 proteins led to much smaller Env clusters, which were not enriched at viral assembly sites. These results show that Env is recruited to HIV-1 assembly sites in a CT-dependent manner, while Env(ΔCT) appears to be randomly incorporated. The observed Env accumulation surrounding Gag assemblies, with a lower density on the actual bud, could facilitate viral spread . Keeping Env molecules on the nascent virus low may be important for escape from the humoral immune response, while cell-cell contacts mediated by surrounding Env molecules could promote HIV-1 transmission through the virological synapse

What active labour market programmes work for immigrants in Europe? : a meta-analysis of the evaluation literature

A growing body of programme evaluation literature recognises immigrants as a disadvantaged group on European labour markets and investigates the employment effects of Active Labour Market Pro-grammes (ALMPs) on this subgroup. Using a meta-analysis, we condense 93 estimates from 33 empir-ical studies of the effectiveness of four types of ALMPs employed across Europe to combat immigrant unemployment: training, job search assistance, and subsidised public and private sector employment. We find that only wage subsidies in the private sector can be confidently recommended to European policy-makers