Finger extensor variability in TMS parameters among chronic stroke patients

BACKGROUND: This study determined the reliability of topographic motor cortical maps and MEP characteristics in the extensor digitorum communis (EDC) evoked by single-pulse TMS among patients with chronic stroke. METHODS: Each of ten patients was studied on three occasions. Measures included location of the EDC hotspot and center of gravity (COG), threshold of activation and average amplitude of the hotspot, number of active sites, map volume, and recruitment curve (RC) slope. RESULTS: Consistent intrahemispheric measurements were obtained for the three TMS mapping sessions for all measured variables. No statistically significant difference was observed between hemispheres for the number of active sites, COG distance or the RC slope. The magnitude and range of COG movement between sessions were similar to those reported previously with this muscle in able-bodied individuals. The average COG movement over three sessions in both hemispheres was 0.90 cm. The average COG movement in the affected hemisphere was 1.13 (± 0.08) cm, and 0.68 (± 0.04) cm) for the less affected hemisphere. However, significant interhemispheric variability was seen for the average MEP amplitude, normalized map volume, and resting motor threshold. CONCLUSION: The physiologic variability in some TMS measurements of EDC suggest that interpretation of TMS mapping data derived from hemiparetic patients in the chronic stage following stroke should be undertaken cautiously. Irrespective of the muscle, potential causes of variability should be resolved to accurately assess the impact of pharmacological or physical interventions on cortical organization as measured by TMS among patients with stroke

Magnetic Fields Recorded by Chondrules Formed in Nebular Shocks

Recent laboratory efforts (Fu et al., 2014) have constrained the remanent magnetizations of chondrules and the magnetic field strengths at which the chondrules were exposed to as they cooled below their Curie points. An outstanding question is whether the inferred paleofields represent the background magnetic field of the solar nebula or were unique to the chondrule-forming environment. We investigate the amplification of the magnetic field above background values for two proposed chondrule formation mechanisms, large-scale nebular shocks and planetary bow shocks. Behind large-scale shocks, the magnetic field parallel to the shock front is amplified by factors $\sim 10-30$, regardless of the magnetic diffusivity. Therefore, chondrules melted in these shocks probably recorded an amplified magnetic field. Behind planetary bow shocks, the field amplification is sensitive to the magnetic diffusivity. We compute the gas properties behind a bow shock around a 3000 km-radius planetary embryo, with and without atmospheres, using hydrodynamics models. We calculate the ionization state of the hot, shocked gas, including thermionic emission from dust, and thermal ionization of gas-phase potassium atoms, and the magnetic diffusivity due to Ohmic dissipation and ambipolar diffusion. We find that the diffusivity is sufficiently large that magnetic fields have already relaxed to background values in the shock downstream where chondrules acquire magnetizations, and that these locations are sufficiently far from the planetary embryos that chondrules should not have recorded a significant putative dynamo field generated on these bodies. We conclude that, if melted in planetary bow shocks, chondrules probably recorded the background nebular field.Comment: 17 pages, 11 figures, accepted for publication in Ap

The EU deal to avoid Brexit: Take it or leave. CEPS Special Report No. 131/February 2016

Beyond the drama of the European Council summit of 18-19 February 2016, what became clear was the fundamental desire on the part of the leaders of all 28 EU member states to agree a deal on the British government’s demands for a renegotiated settlement on the UK’s relationship within the European Union. The deal has provided David Cameron with the political capital he needed to call a date for the in/out referendum and to lead a campaign for the UK to stay in the EU. Yet, for all the technical reforms packed into it, the deal is neither a crowd pleaser nor a vote winner. It does, however, mark a watershed acknowledgement that EU integration is not a one-directional process of ‘ever closer union’. In this CEPS Special Report, Stefani Weiss and Steven Blockmans analyse the substance of the “Decision of the Heads of State or Government, meeting within the European Council, concerning a New Settlement for the United Kingdom within the European Union” and shed light on its legal character. They contextualise this EU deal to avoid Brexit, and draw on the conclusions reached in a simulation of European Council negotiations between representatives of think tanks in the European Policy Institutes Network (EPIN), conducted by CEPS and the Bertelsmann Stiftung in October 2015

Will Cameron get what he wants? Anticipating reactions to Britain’s EU reform proposals. CEPS Commentary, 29 October 2015

After months of speculation about the British Prime Minister’s specific demands in terms of the “renegotiation” of the UK’s relationship with the EU, David Cameron has bowed to pressure from the heads of state or government of the other EU member states and committed himself to setting out the UK’s specific “concerns” in writing by early November. While we cannot be certain of the contents of David Cameron’s missive to the EU, his recent pronouncements before Parliament set out an agenda whose contours have become quite clear. In this Commentary the authors consider how far the other EU member states might be willing to accommodate Cameron’s demands and provide him with the political capital he seeks to lead the ‘in’ campaign. They distinguish four different attitudes among EU countries, and advocate a constructive approach that sets the scene for a Convention after 2017 – one that opens the treaty for a revision that could accommodate both the British demands for an ‘opt-out’ from ever closer union and gives leeway to those who wish to integrate further. Putting emphasis on strengthening the single market in the more immediate term would allow the Prime Minister to show his home audience that he is a leading reformer and that the EU gives oxygen to the British economy.This is an obvious area where he might be able to seal deals during the UK’s Presidency of the Council of the EU in the second half of 2017. The authors also consider what the European Council Conclusions on the UK’s wish list for EU reform might look like, given that any treaty revision before the time set for the UK referendum is unattainable. They present the results of a two-day simulation exercise involving a cross-section of national experts and present mock European Council Conclusions on the areas of ever closer union; the role of national parliaments; competitiveness; economic and monetary integration; and the free movement of labour

The emergence of 4-cycles in polynomial maps over the extended integers

Let $f(x) \in \mathbb{Z}[x]$; for each integer $\alpha$ it is interesting to consider the number of iterates $n_{\alpha}$, if possible, needed to satisfy $f^{n_{\alpha}}(\alpha) = \alpha$. The sets $\{\alpha, f(\alpha), \ldots, f^{n_{\alpha} - 1}(\alpha), \alpha\}$ generated by the iterates of $f$ are called cycles. For $\mathbb{Z}[x]$ it is known that cycles of length 1 and 2 occur, and no others. While much is known for extensions to number fields, we concentrate on extending $\mathbb{Z}$ by adjoining reciprocals of primes. Let $\mathbb{Z}[1/p_1, \ldots, 1/p_n]$ denote $\mathbb{Z}$ extended by adding in the reciprocals of the $n$ primes $p_1, \ldots, p_n$ and all their products and powers with each other and the elements of $\mathbb{Z}$. Interestingly, cycles of length 4, called 4-cycles, emerge for polynomials in $\mathbb{Z}\left[1/p_1, \ldots, 1/p_n\right][x]$ under the appropriate conditions. The problem of finding criteria under which 4-cycles emerge is equivalent to determining how often a sum of four terms is zero, where the terms are $\pm 1$ times a product of elements from the list of $n$ primes. We investigate conditions on sets of primes under which 4-cycles emerge. We characterize when 4-cycles emerge if the set has one or two primes, and (assuming a generalization of the ABC conjecture) find conditions on sets of primes guaranteed not to cause 4-cycles to emerge.Comment: 14 pages, 1 figur

Global model of differential rotation in the Sun

The isorotation contours of the solar convective zone (SCZ) show three distinct morphologies, corresponding to two boundary layers (inner and outer), and the bulk of the interior. Previous work has shown that the thermal wind equation together with informal arguments on the nature of convection in a rotating fluid could be used to deduce the shape of the isorotation surfaces in the bulk of the SCZ with great fidelity, and that the tachocline contours could also be described by relatively simple phenomenology. In this paper, we show that the form of these surfaces can be understood more broadly as a mathematical consequence of the thermal wind equation and a narrow convective shell. The analysis does not yield the angular velocity function directly, an additional surface boundary condition is required. But much can already be deduced without constructing the entire rotation profile. The mathematics may be combined with dynamical arguments put forth in previous works to the mutual benefit of each. An important element of our approach is to regard the constant angular velocity surfaces as an independent coordinate variable for what is termed the "residual entropy," a quantity that plays a key role in the equation of thermal wind balance. The difference between the dynamics of the bulk of the SCZ and the tachocline is due to a different functional form of the residual entropy in each region. We develop a unified theory for the rotational behavior of both the SCZ and the tachocline, using the solutions for the characteristics of the thermal wind equation. These characteristics are identical to the isorotation contours in the bulk of the SCZ, but the two deviate in the tachocline. The outer layer may be treated, at least descriptively, by similar mathematical techniques, but this region probably does not obey thermal wind balance.Comment: 26 pages, 7 figures, accepted to MNRA