Supersymmetry for integrable hierarchies on loop superalgebras

The algebraic approach is employed to formulate N=2 supersymmetry transformations in the context of integrable systems based on loop superalgebras $\hat{\rm sl}(p+1,p), p \ge 1$ with homogeneous gradation. We work with extended integrable hierarchies, which contain supersymmetric AKNS and Lund-Regge sectors. We derive the one-soliton solution for $p=1$ which solves positive and negative evolution equations of the N=2 supersymmetric model.Comment: Latex, 21 page

On negative flows of the AKNS hierarchy and a class of deformations of bihamiltonian structure of hydrodynamic type

A deformation parameter of a bihamiltonian structure of hydrodynamic type is shown to parameterize different extensions of the AKNS hierarchy to include negative flows. This construction establishes a purely algebraic link between, on the one hand, two realizations of the first negative flow of the AKNS model and, on the other, two-component generalizations of Camassa-Holm and Dym type equations. The two-component generalizations of Camassa-Holm and Dym type equations can be obtained from the negative order Hamiltonians constructed from the Lenard relations recursively applied on the Casimir of the first Poisson bracket of hydrodynamic type. The positive order Hamiltonians, which follow from Lenard scheme applied on the Casimir of the second Poisson bracket of hydrodynamic type, are shown to coincide with the Hamiltonians of the AKNS model. The AKNS Hamiltonians give rise to charges conserved with respect to equations of motion of two-component Camassa-Holm and two-component Dym type equations.Comment: 20 pages, Late

Darboux-Egoroff Metrics, Rational Landau-Ginzburg Potentials and the Painleve VI Equation

We present a class of three-dimensional integrable structures associated with the Darboux-Egoroff metric and classical Euler equations of free rotations of a rigid body. They are obtained as canonical structures of rational Landau-Ginzburg potentials and provide solutions to the Painleve VI equation.Comment: 20 page

The complex Sine-Gordon equation as a symmetry flow of the AKNS Hierarchy

It is shown how the complex sine-Gordon equation arises as a symmetry flow of the AKNS hierarchy. The AKNS hierarchy is extended by the ``negative'' symmetry flows forming the Borel loop algebra. The complex sine-Gordon and the vector Nonlinear Schrodinger equations appear as lowest negative and second positive flows within the extended hierarchy. This is fully analogous to the well-known connection between the sine-Gordon and mKdV equations within the extended mKdV hierarchy. A general formalism for a Toda-like symmetry occupying the ``negative'' sector of sl(N) constrained KP hierarchy and giving rise to the negative Borel sl(N) loop algebra is indicated.Comment: 8 pages, LaTeX, typos corrected, references update

The neural underpinning of religious beliefs: Evidence from brain lesions

International audienc

Brain networks involved in the influence of religion on empathy in male Vietnam War veterans

Humans all over the world believe in spirits and deities, yet how the brain supports religious cognition remains unclear. Drawing on a unique sample of patients with penetrating traumatic brain injuries (pTBI) and matched healthy controls (HCs) we investigate dependencies of religious cognition on neural networks that represent (1) others agents’ intentions (Theory of Mind, ToM) and (2) other agents’ feelings (Empathy). Extending previous observations that ToM networks are recruited during prayer, we find that people with vmPFC damage report higher scores on the personal relationship with God inventory even when they are not praying. This result offers evidence that it is the modulation of ToM networks that support beliefs in supernatural agents. With respect to empathetic processing, we observed that vmPFC and pSTS/TPJ lesions mediated by the strength of the personal relationship with God affect empathetic responses. We suggest that the neurological networks underpinning God representations amplify human empathetic responses. The cultural evolutionary study of religion has argued that supernatural beliefs evoke pro-social responses because people fear the wrath of Gods. Our findings imply greater attention should be paid to the mechanisms by which religious cognition may regulate empathetic responses to others.Results - Descriptive statistic results. - Group analysis. - Correlation analyses. - Mediation analysis. Discussion Materials and methods - Participants. - CT acquisition and analysis. - Neuropsychological testing. - Statistical analyses

Cause of Death and Predictors of All-Cause Mortality in Anticoagulated Patients With Nonvalvular Atrial Fibrillation : Data From ROCKET AF

M. Kaste on työryhmän ROCKET AF Steering Comm jäsen.Background-Atrial fibrillation is associated with higher mortality. Identification of causes of death and contemporary risk factors for all-cause mortality may guide interventions. Methods and Results-In the Rivaroxaban Once Daily Oral Direct Factor Xa Inhibition Compared with Vitamin K Antagonism for Prevention of Stroke and Embolism Trial in Atrial Fibrillation (ROCKET AF) study, patients with nonvalvular atrial fibrillation were randomized to rivaroxaban or dose-adjusted warfarin. Cox proportional hazards regression with backward elimination identified factors at randomization that were independently associated with all-cause mortality in the 14 171 participants in the intention-to-treat population. The median age was 73 years, and the mean CHADS(2) score was 3.5. Over 1.9 years of median follow-up, 1214 (8.6%) patients died. Kaplan-Meier mortality rates were 4.2% at 1 year and 8.9% at 2 years. The majority of classified deaths (1081) were cardiovascular (72%), whereas only 6% were nonhemorrhagic stroke or systemic embolism. No significant difference in all-cause mortality was observed between the rivaroxaban and warfarin arms (P=0.15). Heart failure (hazard ratio 1.51, 95% CI 1.33-1.70, P= 75 years (hazard ratio 1.69, 95% CI 1.51-1.90, P Conclusions-In a large population of patients anticoagulated for nonvalvular atrial fibrillation, approximate to 7 in 10 deaths were cardiovascular, whereasPeer reviewe

Deformations of N=2 super-conformal algebra and supersymmetric two-component Camassa-Holm equation

This paper is concerned with a link between central extensions of N=2 superconformal algebra and a supersymmetric two-component generalization of the Camassa--Holm equation. Deformations of superconformal algebra give rise to two compatible bracket structures. One of the bracket structures is derived from the central extension and admits a momentum operator which agrees with the Sobolev norm of a coadjoint orbit element. The momentum operator induces via Lenard relations a chain of conserved hamiltonians of the resulting supersymmetric Camassa-Holm hierarchy.Comment: Latex, 21 pages, version to appear in J. Phys.

Antithrombotic therapy in atrial fibrillation associated with valvular heart disease: A joint consensus document from the European Heart Rhythm Association (EHRA) and European Society of Cardiology Working Group on Thrombosis, endorsed by the ESC Working Group on Valvular Heart Disease, Cardiac Arrhythmia Society of Southern Africa (CASSA), Heart Rhythm Society (HRS), Asia Pacific Heart Rhythm Society (APHRS), South African Heart (SA Heart) Association and Sociedad Latinoamericana de Estimulación Cardíaca y Electrofisiología (SOLEACE)

Atrial fibrillation (AF) is a major public health problem1 with global prevalence rates (per 1000000 population) in 2010 being 596.2 (95% uncertainty interval (UI), 558.4-636.7) in men and 373.1 (95% UI, 347.9-402.2) in women; the incidence rates increased to 77.5 (95% UI, 65.2-95.4) in men and 59.5 (95% UI, 49.9-74.9) in women.2 Worldwide, AF in association with valvular heart disease (VHD) is also common, and management strategies for this group of patients have been less addressed by randomized trials. The latter have largely focused on 'non-valvular AF' patients leading to major uncertainties over how to define (and treat) such patients. There is also an important heterogeneity in the definition of valvular and non-valvular AF.3 Some physicians assume that any valve disease should be considered as 'valvular' AF. Others consider that only mechanical valve prosthesis and rheumatic mitral stenosis should be defined as 'valvular' AF. The term valvular AF has been arbitrarily applied and the 2016 ESC guidelines have avoided the term 'valvular AF' and refer simply to 'AF related to hemodynamically significant mitral stenosis or prosthetic mechanical heart valves'.4 AF clearly leads to an incremental risk for thromboembolism in patients with mitral valve stenosis, but there are limited data for other valvular diseases. Another proposal is to use the acronym MARM-AF as a simple acronym to designate 'Mechanical and Rheumatic Mitral AF' as an alternative to term 'valvular AF' to designate the clinical scenarios for which at the non-vitamin K antagonist oral anticoagulants (NOACs) are not indicated.5 For this document we recognize the uncertainty in terminology, and our scope largely relates to AF related to 'hemodynamically significant' rheumatic VHD (ie. severe enough to impact on patient's survival or necessitates an intervention or surgery) or prosthetic mechanical heart valves. Nonetheless, thrombo-embolic (TE) risk varies according to valve lesion and may be associated with CHA2DS2VASc score risk factor components, rather than the valve disease per se being causal.6,7 TE risk may also be influenced not only by type but also the severity of the lesion. For example, the degree of mitral regurgitation may matter when it comes to risk of TE as some studies suggest that mild (Grade 1) mitral regurgitation is associated with a 2.7-fold increased risk of stroke/TE, while severe forms may possibly have a 'protective' effect (HR = 0.45 for stroke and 0.27 for LA stasis.8 An appropriate definition of 'valvular AF' would need to identify a subgroup of patients with similar pathophysiology of thrombo-embolism, TE risk, and treatment strategies6,9; however, this would be challenging given the major heterogeneity of the condition. This consensus document proposes that the term 'valvular AF' is outdated and given that any definition ultimately relates to the evaluated practical use of oral anticoagulation (OAC) type, we propose a functional EHRA (EvaluatedHeartvalves, Rheumatic orArtificial) categorization in relation to the type of OAC use in patients with AF, as follows:Evaluated Heartvalves, Rheumatic or Artificial (EHRA) Type 1,which refers to AF patients with 'VHD needing therapy with a Vitamin K antagonist (VKA)

Soliton Spectrum of Integrable Models with Local Symmetries

The soliton spectrum (massive and massless) of a family of integrable models with local U(1) and U(1)\otimes U(1) symmetries is studied. These models represent relevant integrable deformations of SL(2,R) \otimes U(1)^{n-1} - WZW and SL(2,R) \otimes SL(2,R)\otimes U(1)^{n-2} - WZW models. Their massless solitons appears as specific topological solutions of the U(1) (or U(1)\otimes U(1)) - CFTs. The nonconformal analog of the GKO-coset formula is derived and used in the construction of the composite massive solitons of the ungauged integrable models.Comment: 44 pages, Latex, 1 eps fig, few misprints corrected. to appear in JHE