Kernels and Designs for Modelling Invariant Functions: From Group Invariance to Additivity

We focus on kernels incorporating different kinds of prior knowledge on functions to be approximated by Kriging. A recent result on random fields with paths invariant under a group action is generalised to combinations of composition operators, and a characterisation of kernels leading to random fields with additive paths is obtained as a corollary. A discussion follows on some implications on design of experiments, and it is shown in the case of additive kernels that the so-called class of “axis designs” outperforms Latin hypercubes in terms of the IMSE criterion.

Triality, periodicity and stability of SO(8) gauged supergravity

While electromagnetic duality is a symmetry of many supergravity theories, this is not the case for the N = 8 gauged theory. It was recently shown that this rotation leads to a one-parameter family of SO(8) supergravities. It is an open question what the period of this parameter is. This issue is investigated in the SO(4) invariant sectors of the theory. We classify such critical points and find a novel branch of non-supersymmetric and unstable solutions, whose embedding is related via triality to the two known ones. Secondly, we show that the three branches of solutions lead to a π/4 periodicity of the vacuum structure. The general interrelations between triality and periodicity are discussed. Finally, we comment on the connection to other gauge groups as well as the possibility to achieve (non-)perturbative stability around AdS/Mkw/dS transitions.

The SU(3)-invariant sector of new maximal supergravity

We investigate the SU(3)-invariant sector of the one-parameter family of SO(8) gauged maximal supergravities that has been recently discovered. To this end, we construct the N=2 truncation of this theory and analyse its full vacuum structure. The number of critical point is doubled and includes new N=0 and N=1 branches. We numerically exhibit the parameter dependence of the location and cosmological constant of all extrema. Moreover, we provide their analytic expressions for cases of special interest. Finally, while the mass spectra are found to be parameter independent in most cases, we show that the novel non-supersymmetric branch with SU(3) invariance provides the first counterexample to this.

The Coin Rotation Task: A Valid Test for Manual Dexterity in Multiple Sclerosis

BACKGROUND: Impaired manual dexterity is frequent and disabling in patients with multiple sclerosis (MS). Therefore, convenient, quick and validated tests for manual dexterity in MS patients are needed. OBJECTIVE: The aim of this study was to validate the Coin Rotation task (CRT) to examine manual dexterity in patients with MS. DESIGN: Cross-sectional study. METHODS: 101 outpatients with MS were assessed with the CRT, the Expanded Disability Status Scale (EDSS), the Scale for the assessment and rating of ataxia (SARA), the Modified Ashworth Scale (MAS), and their muscle strength and sensory deficits of the hands were noted. Concurrent validity and diagnostic accuracy of the CRT were determined by comparison with the Nine Hole Peg Test (9HPT). Construct validity was determined by comparison with a valid dexterity questionnaire. Multiple regression analysis was done to explore correlations of the CRT with the EDSS, SARA, MAS, muscle strength and sensory deficits. RESULTS: The CRT correlated significantly with the 9HPT (r=.73, p<.0001) indicating good concurrent validity. The cut-off values for the CRT relative to the 9HPT were 18.75 seconds for the dominant (sensitivity: 81.5%; specificity 80.0%) and 19.25 seconds for the non-dominant hand (sensitivity: 90.3%; specificity: 81.8%) demonstrating good diagnostic accuracy. Furthermore, the CRT correlated significantly with the dexterity questionnaire (r=-.49, p<.0001) indicating moderate construct validity. Multiple regression analyses revealed that the EDSS was the strongest predictor for impaired dexterity. LIMITATIONS: Mostly relapsing-remitting MS patients with an EDSS up to 7 were examined. CONCLUSIONS: This study validates the CRT as a test that can be used easily and quickly to evaluate manual dexterity in patients with MS.

CAP Reform vs WTO: Crop Diversification or Crop Rotation? : Legal opinion prepared by Dr. Christian Häberli at the request of APRODEV, the Association of World Council of Churches related Development Organisations in Europe

The European Commission’s proposals for the Legislative Framework of the Common Agricultural Policy (CAP) in the period 2014-2020 include, inter alia, the introduction of a “strong greening component”. For the first time, all EU farmers in receipt of support are to “go beyond the requirements of cross compliance and deliver environmental and climate benefits as part of their everyday activities crop diversification as a contribution to all EU farmers in receipt of support go beyond the requirements of cross compliance and deliver environmental and climate benefits as part of their everyday activities.” In a legal opinion prepared at the request of APRODEV, the Association of World Council of Churches related Development Organisations in Europe (www.aprodev.eu), Christian Häberli examines the WTO implications of this proposal, as compared with an alternative proposal to rather link direct payments to crop rotation. The conclusions are twofold: 1. Crop rotation is at least as likely to be found Green Box-compatible as crop diversification. Moreover, it will be more difficult to argue that crop diversification is “not more than minimally production-distorting” because it entails for most farmers less cost and work. 2. Even if (either of the two cropping schemes) were to be found “amber”, the EU would not have to relinquish this conditionality. This is because the direct payments involved would in all likelihood not, together with the other price support instruments, exceed the amount available under the presently scheduled maximum.

Search for Quantum Black Hole Production in High-Invariant-Mass Lepton plus Jet Final States Using pp Collisions at root s=8 TeV and the ATLAS Detector

This Letter presents a search for quantum black-hole production using 20.3 fb(-1) of data collected with the ATLAS detector in pp collisions at the LHC at root s = 8 TeV. The quantum black holes are assumed to decay into a final state characterized by a lepton (electron or muon) and a jet. In either channel, no event with a lepton-jet invariant mass of 3.5 TeV or more is observed, consistent with the expected background. Limits are set on the product of cross sections and branching fractions for the lepton + jet final states of quantum black holes produced in a search region for invariant masses above 1 TeV. The combined 95% confidence level upper limit on this product for quantum black holes with threshold mass above 3.5 TeV is 0.18 fb. This limit constrains the threshold quantum black-hole mass to be above 5.3 TeV in the model considered.