420 research outputs found
Quasi-classical Lie algebras and their contractions
After classifying indecomposable quasi-classical Lie algebras in low
dimension, and showing the existence of non-reductive stable quasi-classical
Lie algebras, we focus on the problem of obtaining sufficient conditions for a
quasi-classical Lie algebras to be the contraction of another quasi-classical
algebra. It is illustrated how this allows to recover the Yang-Mills equations
of a contraction by a limiting process, and how the contractions of an algebra
may generate a parameterized families of Lagrangians for pairwise
non-isomorphic Lie algebras.Comment: 17 pages, 2 Table
Vlasov moment flows and geodesics on the Jacobi group
By using the moment algebra of the Vlasov kinetic equation, we characterize
the integrable Bloch-Iserles system on symmetric matrices
(arXiv:math-ph/0512093) as a geodesic flow on the Jacobi group. We analyze the
corresponding Lie-Poisson structure by presenting a momentum map, which both
untangles the bracket structure and produces particle-type solutions that are
inherited from the Vlasov-like interpretation. Moreover, we show how the Vlasov
moments associated to Bloch-Iserles dynamics correspond to particular subgroup
inclusions into a group central extension (first discovered in
arXiv:math/0410100), which in turn underlies Vlasov kinetic theory. In the most
general case of Bloch-Iserles dynamics, a generalization of the Jacobi group
also emerges naturally.Comment: 45 page
Extensions, expansions, Lie algebra cohomology and enlarged superspaces
After briefly reviewing the methods that allow us to derive consistently new
Lie (super)algebras from given ones, we consider enlarged superspaces and
superalgebras, their relevance and some possible applications.Comment: 9 pages. Invited talk delivered at the EU RTN Workshop, Copenhagen,
Sep. 15-19 and at the Argonne Workshop on Branes and Generalized Dynamics,
Oct. 20-24, 2003. Only change: wrong number of a reference correcte
Contractions and deformations of quasi-classical Lie algebras preserving a non-degenerate quadratic Casimir operator
By means of contractions of Lie algebras, we obtain new classes of
indecomposable quasi-classical Lie algebras that satisfy the Yang-Baxter
equations in its reformulation in terms of triple products. These algebras are
shown to arise naturally from non-compact real simple algebras with non-simple
complexification, where we impose that a non-degenerate quadratic Casimir
operator is preserved by the limiting process. We further consider the converse
problem, and obtain sufficient conditions on integrable cocycles of
quasi-classical Lie algebras in order to preserve non-degenerate quadratic
Casimir operators by the associated linear deformations.Comment: 12 pages. LATEX with revtex4; Proceedings of the XII International
Conference on Symmetry Methods in Physics, (Yerevan, 2006) eds. G.S. Pogosyan
et al
Expansions of algebras and superalgebras and some applications
After reviewing the three well-known methods to obtain Lie algebras and
superalgebras from given ones, namely, contractions, deformations and
extensions, we describe a fourth method recently introduced, the expansion of
Lie (super)algebras. Expanded (super)algebras have, in general, larger
dimensions than the original algebra, but also include the Inonu-Wigner and
generalized IW contractions as a particular case. As an example of a physical
application of expansions, we discuss the relation between the possible
underlying gauge symmetry of eleven-dimensional supergravity and the
superalgebra osp(1|32).Comment: Invited lecture delivered at the 'Deformations and Contractions in
Mathematics and Physics Workshop', 15-21 January 2006, Mathematisches
Forschungsinstitut Oberwolfach, German
Predicting the safety and efficacy of butter therapy to raise tumour pHe: an integrative modelling study
Background: Clinical positron emission tomography imaging has demonstrated the vast majority of human cancers exhibit significantly increased glucose metabolism when compared with adjacent normal tissue, resulting in an acidic tumour microenvironment. Recent studies demonstrated reducing this acidity through systemic buffers significantly inhibits development and growth of metastases in mouse xenografts.\ud
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Methods: We apply and extend a previously developed mathematical model of blood and tumour buffering to examine the impact of oral administration of bicarbonate buffer in mice, and the potential impact in humans. We recapitulate the experimentally observed tumour pHe effect of buffer therapy, testing a model prediction in vivo in mice. We parameterise the model to humans to determine the translational safety and efficacy, and predict patient subgroups who could have enhanced treatment response, and the most promising combination or alternative buffer therapies.\ud
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Results: The model predicts a previously unseen potentially dangerous elevation in blood pHe resulting from bicarbonate therapy in mice, which is confirmed by our in vivo experiments. Simulations predict limited efficacy of bicarbonate, especially in humans with more aggressive cancers. We predict buffer therapy would be most effectual: in elderly patients or individuals with renal impairments; in combination with proton production inhibitors (such as dichloroacetate), renal glomular filtration rate inhibitors (such as non-steroidal anti-inflammatory drugs and angiotensin-converting enzyme inhibitors), or with an alternative buffer reagent possessing an optimal pK of 7.1–7.2.\ud
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Conclusion: Our mathematical model confirms bicarbonate acts as an effective agent to raise tumour pHe, but potentially induces metabolic alkalosis at the high doses necessary for tumour pHe normalisation. We predict use in elderly patients or in combination with proton production inhibitors or buffers with a pK of 7.1–7.2 is most promising
Projective dynamics and first integrals
We present the theory of tensors with Young tableau symmetry as an efficient
computational tool in dealing with the polynomial first integrals of a natural
system in classical mechanics. We relate a special kind of such first
integrals, already studied by Lundmark, to Beltrami's theorem about
projectively flat Riemannian manifolds. We set the ground for a new and simple
theory of the integrable systems having only quadratic first integrals. This
theory begins with two centered quadrics related by central projection, each
quadric being a model of a space of constant curvature. Finally, we present an
extension of these models to the case of degenerate quadratic forms.Comment: 39 pages, 2 figure
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
Projective dynamics and classical gravitation
Given a real vector space V of finite dimension, together with a particular
homogeneous field of bivectors that we call a "field of projective forces", we
define a law of dynamics such that the position of the particle is a "ray" i.e.
a half-line drawn from the origin of V. The impulsion is a bivector whose
support is a 2-plane containing the ray. Throwing the particle with a given
initial impulsion defines a projective trajectory. It is a curve in the space
of rays S(V), together with an impulsion attached to each ray. In the simplest
example where the force is identically zero, the curve is a straight line and
the impulsion a constant bivector. A striking feature of projective dynamics
appears: the trajectories are not parameterized.
Among the projective force fields corresponding to a central force, the one
defining the Kepler problem is simpler than those corresponding to other
homogeneities. Here the thrown ray describes a quadratic cone whose section by
a hyperplane corresponds to a Keplerian conic. An original point of view on the
hidden symmetries of the Kepler problem emerges, and clarifies some remarks due
to Halphen and Appell. We also get the unexpected conclusion that there exists
a notion of divergence-free field of projective forces if and only if dim V=4.
No metric is involved in the axioms of projective dynamics.Comment: 20 pages, 4 figure
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