MFN status and the choice of tariff regime

The gradualist approach to trade liberalization views the uniform tariffs implied by MFN status as an important step on the path to free trade. We investigate whether a regime of uniform tariffs will be preferable to discriminatory tariffs when countries engage in non-cooperative interaction in multilateral trade. The analysis includes product differentiation and asymmetric costs. We show that with the cost asymmetry the countries will disagree on the choice of tariff regime. When the choice of import tariffs and export subsidies is made sequentially the uniform tariff regime may not be sustainable, because of an incentive to deviate to a discriminatory regime. Hence, an international body is needed to ensure compliance with tariff agreement

EXPRESS: Differences in outcomes following an intensive upper-limb rehabilitation programme for patients with common CNS-acting drug prescriptions

Difficulty using the upper-limb is a major barrier to independence for many patients post-stroke or brain injury. High dose rehabilitation can result in clinically significant improvements in function even years after the incident, however there is still high variability in patient responsiveness to such interventions that cannot be explained by age, sex or time since stroke. This retrospective study investigated whether patients prescribed certain classes of CNS-acting drugs - GABA agonists, antiepileptics and antidepressants-differed in their outcomes on the 3 week intensive Queen Square Upper-Limb (QSUL) programme. For 277 stroke or brain injury patients (167 male, median age 52 years (IQR 21), median time since incident 20 months (IQR 26)) upper-limb impairment and activity was assessed at admission to the programme and at 6 months post-discharge, using the upper limb component of the Fugl-Meyer (FM), Action Research Arm Test (ARAT), and Chedoke Arm and Hand Activity Inventory (CAHAI). Drug prescriptions were obtained from primary care physicians at referral. Specification curve analysis (SCA) was used to protect against selective reporting results and add robustness to the conclusions of this retrospective study. Patients with GABA agonist prescriptions had significantly worse upper-limb scores at admission but no evidence for a significant difference in programme-induced improvements was found. Additionally, no evidence of significant differences in patients with or without antiepileptic drug prescriptions on either admission to, or improvement on, the programme was found in this study. Whereas, though no evidence was found for differences in admission scores, patients with antidepressant prescriptions experienced reduced improvement in upper-limb function, even when accounting for anxiety and depression scores.These results demonstrate that, when prescribed typically, there was no evidence that patients prescribed GABA agonists performed worse on this high-intensity rehabilitation programme. Patients prescribed antidepressants, however, performed poorer than expected on the QSUL rehabilitation programme. While the reasons for these differences are unclear, identifying these patients prior to admission may allow for better accommodation of differences in their rehabilitation needs

Generalized DPW method and an application to isometric immersions of space forms

Let $G$ be a complex Lie group and $\Lambda G$ denote the group of maps from the unit circle ${\mathbb S}^1$ into $G$, of a suitable class. A differentiable map $F$ from a manifold $M$ into $\Lambda G$, is said to be of \emph{connection order $(_a^b)$} if the Fourier expansion in the loop parameter $\lambda$ of the ${\mathbb S}^1$-family of Maurer-Cartan forms for $F$, namely F_\lambda^{-1} \dd F_\lambda, is of the form $\sum_{i=a}^b \alpha_i \lambda^i$. Most integrable systems in geometry are associated to such a map. Roughly speaking, the DPW method used a Birkhoff type splitting to reduce a harmonic map into a symmetric space, which can be represented by a certain order $(_{-1}^1)$ map, into a pair of simpler maps of order $(_{-1}^{-1})$ and $(_1^1)$ respectively. Conversely, one could construct such a harmonic map from any pair of $(_{-1}^{-1})$ and $(_1^1)$ maps. This allowed a Weierstrass type description of harmonic maps into symmetric spaces. We extend this method to show that, for a large class of loop groups, a connection order $(_a^b)$ map, for $a<0<b$, splits uniquely into a pair of $(_a^{-1})$ and $(_1^b)$ maps. As an application, we show that constant non-zero curvature submanifolds with flat normal bundle of a sphere or hyperbolic space split into pairs of flat submanifolds, reducing the problem (at least locally) to the flat case. To extend the DPW method sufficiently to handle this problem requires a more general Iwasawa type splitting of the loop group, which we prove always holds at least locally.Comment: Some typographical correction

Intensive upper limb neurorehabilitation in chronic stroke: outcomes from the Queen Square programme

OBJECTIVE: Persistent difficulty in using the upper limb remains a major contributor to physical disability post-stroke. There is a nihilistic view about what clinically relevant changes are possible after the early post-stroke phase. The Queen Square Upper Limb Neurorehabilitation programme delivers high-quality, high-dose, high-intensity upper limb neurorehabilitation during a 3-week (90 hours) programme. Here, we report clinical changes made by the chronic stroke patients treated on the programme, factors that might predict responsiveness to therapy and the relationship between changes in impairment and activity. METHODS: Upper limb impairment and activity were assessed on admission, discharge, 6 weeks and 6 months after treatment, with modified upper limb Fugl-Meyer (FM-UL, max-54), Action Research Arm Test (ARAT, max-57) and Chedoke Arm and Hand Activity Inventory (CAHAI, max-91). Patient-reported outcome measures were recorded with the Arm Activity Measure (ArmA) parts A (0-32) and B (0-52), where lower scores are better. RESULTS: 224 patients (median time post-stroke 18 months) completed the 6-month programme. Median scores on admission were as follows: FM-UL = 26 (IQR 16-37), ARAT=18 (IQR 7-33), CAHAI=40 (28-55), ArmA-A=8 (IQR 4.5-12) and ArmA-B=38 (IQR 24-46). The median scores 6 months after the programme were as follows: FM-UL=37 (IQR 24-48), ARAT=27 (IQR 12-45), CAHAI=52 (IQR 35-77), ArmA-A=3 (IQR 1-6.5) and ArmA-B=19 (IQR 8.5-32). We found no predictors of treatment response beyond admission scores. CONCLUSION: With intensive upper limb rehabilitation, chronic stroke patients can change by clinically important differences in measures of impairment and activity. Crucially, clinical gains continued during the 6-month follow-up period

Curved Flats, Pluriharmonic Maps and Constant Curvature Immersions into Pseudo-Riemannian Space Forms

We study two aspects of the loop group formulation for isometric immersions with flat normal bundle of space forms. The first aspect is to examine the loop group maps along different ranges of the loop parameter. This leads to various equivalences between global isometric immersion problems among different space forms and pseudo-Riemannian space forms. As a corollary, we obtain a non-immersibility theorem for spheres into certain pseudo-Riemannian spheres and hyperbolic spaces. The second aspect pursued is to clarify the relationship between the loop group formulation of isometric immersions of space forms and that of pluriharmonic maps into symmetric spaces. We show that the objects in the first class are, in the real analytic case, extended pluriharmonic maps into certain symmetric spaces which satisfy an extra reality condition along a totally real submanifold. We show how to construct such pluriharmonic maps for general symmetric spaces from curved flats, using a generalised DPW method.Comment: 21 Pages, reference adde

Bailouts in a common market: a strategic approach

Governments in the EU grant Rescue and Restructure Subsidies to bail out ailing firms. In an international asymmetric Cournot duopoly we study effects of such subsidies on market structure and welfare. We adopt a common market setting, where consumers from the two countries form one market. We show that the subsidy is positive also when it fails to prevent the exit. The reason is a strategic effect, which forces the more efficient firm to make additional cost-reducing effort. When the exit is prevented, allocative and productive efficiencies are lower and the only gaining player is the rescued firm

Constructing solutions to the Bj\"orling problem for isothermic surfaces by structure preserving discretization

In this article, we study an analog of the Bj\"orling problem for isothermic surfaces (that are more general than minimal surfaces): given a real analytic curve $\gamma$ in ${\mathbb R}^3$, and two analytic non-vanishing orthogonal vector fields $v$ and $w$ along $\gamma$, find an isothermic surface that is tangent to $\gamma$ and that has $v$ and $w$ as principal directions of curvature. We prove that solutions to that problem can be obtained by constructing a family of discrete isothermic surfaces (in the sense of Bobenko and Pinkall) from data that is sampled along $\gamma$, and passing to the limit of vanishing mesh size. The proof relies on a rephrasing of the Gauss-Codazzi-system as analytic Cauchy problem and an in-depth-analysis of its discretization which is induced from the geometry of discrete isothermic surfaces. The discrete-to-continuous limit is carried out for the Christoffel and the Darboux transformations as well.Comment: 29 pages, some figure