Do Killing-Yano tensors form a Lie Algebra?

Killing-Yano tensors are natural generalizations of Killing vectors. We investigate whether Killing-Yano tensors form a graded Lie algebra with respect to the Schouten-Nijenhuis bracket. We find that this proposition does not hold in general, but that it does hold for constant curvature spacetimes. We also show that Minkowski and (anti)-deSitter spacetimes have the maximal number of Killing-Yano tensors of each rank and that the algebras of these tensors under the SN bracket are relatively simple extensions of the Poincare and (A)dS symmetry algebras.Comment: 17 page

A Wish for More Archers: Archers at the Battle of Agincourt, 1415

A knight expressed the desire to his king that he would add to their small army ten thousand of the best archers in England. This thesis utilizes archaeology evidence, financial records, iconographic depictions, literary and chronicle sources to understand the men who fought at the battle of Agincourt within the larger context and traditions of archery in England, the interconnections between archers and men-at-arms and the particular actions of those men in the battle itself

Commuting symmetry operators of the Dirac equation, Killing-Yano and Schouten-Nijenhuis brackets

In this paper we derive the most general first-order symmetry operator commuting with the Dirac operator in all dimensions and signatures. Such an operator splits into Clifford even and Clifford odd parts which are given in terms of odd Killing-Yano and even closed conformal Killing-Yano inhomogeneous forms respectively. We study commutators of these symmetry operators and give necessary and sufficient conditions under which they remain of the first-order. In this specific setting we can introduce a Killing-Yano bracket, a bilinear operation acting on odd Killing-Yano and even closed conformal Killing-Yano forms, and demonstrate that it is closely related to the Schouten-Nijenhuis bracket. An important non-trivial example of vanishing Killing-Yano brackets is given by Dirac symmetry operators generated from the principal conformal Killing-Yano tensor [hep-th/0612029]. We show that among these operators one can find a complete subset of mutually commuting operators. These operators underlie separability of the Dirac equation in Kerr-NUT-(A)dS spacetimes in all dimensions [arXiv:0711.0078].Comment: 37 pages, no figure

Invariant classification of orthogonally separable Hamiltonian systems in Euclidean space

The problem of the invariant classification of the orthogonal coordinate webs defined in Euclidean space is solved within the framework of Felix Klein's Erlangen Program. The results are applied to the problem of integrability of the Calogero-Moser model

Jacobi structures revisited

Jacobi algebroids, that is graded Lie brackets on the Grassmann algebra associated with a vector bundle which satisfy a property similar to that of the Jacobi brackets, are introduced. They turn out to be equivalent to generalized Lie algebroids in the sense of Iglesias and Marrero and can be viewed also as odd Jacobi brackets on the supermanifolds associated with the vector bundles. Jacobi bialgebroids are defined in the same manner. A lifting procedure of elements of this Grassmann algebra to multivector fields on the total space of the vector bundle which preserves the corresponding brackets is developed. This gives the possibility of associating canonically a Lie algebroid with any local Lie algebra in the sense of Kirillov.Comment: 20 page

The Psychobiology of Authentic and Simulated Dissociative Personality States:The Full Monty

The etiology of dissociative identity disorder (DID) remains a topic of debate. Proponents of the fantasy model and the trauma model of DID have both called for more empirical research. To this end, the current study presents new and extended data analyses of a previously published (H2O)-O-15 positron emission tomography imaging study. This study included 29 subjects: 11 patients with DID and 10 high- and 8 low-fantasy-prone DID-simulating mentally healthy control subjects. All subjects underwent an autobiographical memory script-driven (neutral and trauma related) imagery paradigm in 2 (simulated) dissociative personality states (neutral and trauma related). Psychobiological and psychophysiological data were obtained. Results of the new post-hoc tests on the psychophysiological responses support the trauma model. New results of the brain imaging data did not support the fantasy model. This study extends previously published results by offering important new supporting data for the trauma model of DID.</p

Inter-muscular coherence in speed skaters with skater's cramp

Introduction: Skater's cramp is a career-ending movement disorder in expert speed skaters noted to be a likely task-specific dystonia. In other movement disorders, including task-specific dystonia, studies have found evidence of central dysregulation expressed as higher inter-muscular coherence. We looked at whether inter-muscular coherence was higher in affected skaters as a possible indicator that it is centrally driven, and by extension further evidence it is a task-specific dystonia.Methods: In 14 affected and 14 control skaters we calculated inter-muscular coherence in the theta-band in a stationary task where tonic muscle activation was measured at 10%, 20% and 50% of maximum voluntary contraction. Additionally, we calculated wavelet coherence while skating at key moments in the stroke cycle.Results: Coherence did not differ in the stationary activation task. While skating, coherence was higher in the impacted leg of affected skaters compared to their non-impacted leg, p = .05, η2 = 0.031, and amplitude of electromyography correlated with coherence in the impacted leg, p = .009, R2adjusted = 0.41. A sub-group of severely affected skaters (n = 6) had higher coherence in the impacted leg compared to the left and right leg of controls, p = .02, Cohen's d = 1.59 and p = .01, Cohen's d = 1.63 respectively. Results were less clear across the entire affected cohort probably due to a diverse case-mix.Conclusion: Our results of higher coherence in certain severe cases of skater's cramp is preliminary evidence of a central dysregulation, making the likelihood it is a task-specific dystonia higher.</p

Double bracket dissipation in kinetic theory for particles with anisotropic interactions

We derive equations of motion for the dynamics of anisotropic particles directly from the dissipative Vlasov kinetic equations, with the dissipation given by the double bracket approach (Double Bracket Vlasov, or DBV). The moments of the DBV equation lead to a nonlocal form of Darcy's law for the mass density. Next, kinetic equations for particles with anisotropic interaction are considered and also cast into the DBV form. The moment dynamics for these double bracket kinetic equations is expressed as Lie-Darcy continuum equations for densities of mass and orientation. We also show how to obtain a Smoluchowski model from a cold plasma-like moment closure of DBV. Thus, the double bracket kinetic framework serves as a unifying method for deriving different types of dynamics, from density--orientation to Smoluchowski equations. Extensions for more general physical systems are also discussed.Comment: 19 pages; no figures. Submitted to Proc. Roy. Soc.

Fact or Factitious? A Psychobiological Study of Authentic and Simulated Dissociative Identity States

BACKGROUND: Dissociative identity disorder (DID) is a disputed psychiatric disorder. Research findings and clinical observations suggest that DID involves an authentic mental disorder related to factors such as traumatization and disrupted attachment. A competing view indicates that DID is due to fantasy proneness, suggestibility, suggestion, and role-playing. Here we examine whether dissociative identity state-dependent psychobiological features in DID can be induced in high or low fantasy prone individuals by instructed and motivated role-playing, and suggestion. METHODOLOGY/PRINCIPAL FINDINGS: DID patients, high fantasy prone and low fantasy prone controls were studied in two different types of identity states (neutral and trauma-related) in an autobiographical memory script-driven (neutral or trauma-related) imagery paradigm. The controls were instructed to enact the two DID identity states. Twenty-nine subjects participated in the study: 11 patients with DID, 10 high fantasy prone DID simulating controls, and 8 low fantasy prone DID simulating controls. Autonomic and subjective reactions were obtained. Differences in psychophysiological and neural activation patterns were found between the DID patients and both high and low fantasy prone controls. That is, the identity states in DID were not convincingly enacted by DID simulating controls. Thus, important differences regarding regional cerebral bloodflow and psychophysiological responses for different types of identity states in patients with DID were upheld after controlling for DID simulation. CONCLUSIONS/SIGNIFICANCE: The findings are at odds with the idea that differences among different types of dissociative identity states in DID can be explained by high fantasy proneness, motivated role-enactment, and suggestion. They indicate that DID does not have a sociocultural (e.g., iatrogenic) origin