A New Superconformal Mechanics

In this paper we propose a new supersymmetric extension of conformal mechanics. The Grassmannian variables that we introduce are the basis of the forms and of the vector-fields built over the symplectic space of the original system. Our supersymmetric Hamiltonian itself turns out to have a clear geometrical meaning being the Lie-derivative of the Hamiltonian flow of conformal mechanics. Using superfields we derive a constraint which gives the exact solution of the supersymmetric system in a way analogous to the constraint in configuration space which solved the original non-supersymmetric model. Besides the supersymmetric extension of the original Hamiltonian, we also provide the extension of the other conformal generators present in the original system. These extensions have also a supersymmetric character being the square of some Grassmannian charge. We build the whole superalgebra of these charges and analyze their closure. The representation of the even part of this superalgebra on the odd part turns out to be integer and not spinorial in character.Comment: Superfield re-define

Universal Hidden Supersymmetry in Classical Mechanics and its Local Extension

We review here a path-integral approach to classical mechanics and explore the geometrical meaning of this construction. In particular we bring to light a universal hidden BRS invariance and its geometrical relevance for the Cartan calculus on symplectic manifolds. Together with this BRS invariance we also show the presence of a universal hidden genuine non-relativistic supersymmetry. In an attempt to understand its geometry we make this susy local following the analogous construction done for the supersymmetric quantum mechanics of Witten.Comment: 6 pages, latex, Volkov Memorial Proceeding

Non equilibrium statistical physics with fictitious time

Problems in non equilibrium statistical physics are characterized by the absence of a fluctuation dissipation theorem. The usual analytic route for treating these vast class of problems is to use response fields in addition to the real fields that are pertinent to a given problem. This line of argument was introduced by Martin, Siggia and Rose. We show that instead of using the response field, one can, following the stochastic quantization of Parisi and Wu, introduce a fictitious time. In this extra dimension a fluctuation dissipation theorem is built in and provides a different outlook to problems in non equilibrium statistical physics.Comment: 4 page

Hamilton Jacobi Bellman equations in infinite dimensions with quadratic and superquadratic Hamiltonian

We consider Hamilton Jacobi Bellman equations in an inifinite dimensional Hilbert space, with quadratic (respectively superquadratic) hamiltonian and with continuous (respectively lipschitz continuous) final conditions. This allows to study stochastic optimal control problems for suitable controlled Ornstein Uhlenbeck process with unbounded control processes

Mechanical similarity as a generalization of scale symmetry

In this paper we study the symmetry known as mechanical similarity (LMS) and present for any monomial potential. We analyze it in the framework of the Koopman-von Neumann formulation of classical mechanics and prove that in this framework the LMS can be given a canonical implementation. We also show that the LMS is a generalization of the scale symmetry which is present only for the inverse square potential. Finally we study the main obstructions which one encounters in implementing the LMS at the quantum mechanical level.Comment: 9 pages, Latex, a new section adde

Neuroimaging Evidence of Major Morpho-Anatomical and Functional Abnormalities in the BTBR T+TF/J Mouse Model of Autism

BTBR T+tf/J (BTBR) mice display prominent behavioural deficits analogous to the defining symptoms of autism, a feature that has prompted a widespread use of the model in preclinical autism research. Because neuro-behavioural traits are described with respect to reference populations, multiple investigators have examined and described the behaviour of BTBR mice against that exhibited by C57BL/6J (B6), a mouse line characterised by high sociability and low self-grooming. In an attempt to probe the translational relevance of this comparison for autism research, we used Magnetic Resonance Imaging (MRI) to map in both strain multiple morpho-anatomical and functional neuroimaging readouts that have been extensively used in patient populations. Diffusion tensor tractography confirmed previous reports of callosal agenesis and lack of hippocampal commissure in BTBR mice, and revealed a concomitant rostro-caudal reorganisation of major cortical white matter bundles. Intact inter-hemispheric tracts were found in the anterior commissure, ventro-medial thalamus, and in a strain-specific white matter formation located above the third ventricle. BTBR also exhibited decreased fronto-cortical, occipital and thalamic gray matter volume and widespread reductions in cortical thickness with respect to control B6 mice. Foci of increased gray matter volume and thickness were observed in the medial prefrontal and insular cortex. Mapping of resting-state brain activity using cerebral blood volume weighted fMRI revealed reduced cortico-thalamic function together with foci of increased activity in the hypothalamus and dorsal hippocampus of BTBR mice. Collectively, our results show pronounced functional and structural abnormalities in the brain of BTBR mice with respect to control B6 mice. The large and widespread white and gray matter abnormalities observed do not appear to be representative of the neuroanatomical alterations typically observed in autistic patients. The presence of reduced fronto-cortical metabolism is of potential translational relevance, as this feature recapitulates previously-reported clinical observations

Thermalization of a Brownian particle via coupling to low-dimensional chaos

It is shown that a paradigm of classical statistical mechanics --- the thermalization of a Brownian particle --- has a low-dimensional, deterministic analogue: when a heavy, slow system is coupled to fast deterministic chaos, the resultant forces drive the slow degrees of freedom toward a state of statistical equilibrium with the fast degrees. This illustrates how concepts useful in statistical mechanics may apply in situations where low-dimensional chaos exists.Comment: Revtex, 11 pages, no figures

Hamiltonian dynamics and geometry of phase transitions in classical XY models

The Hamiltonian dynamics associated to classical, planar, Heisenberg XY models is investigated for two- and three-dimensional lattices. Besides the conventional signatures of phase transitions, here obtained through time averages of thermodynamical observables in place of ensemble averages, qualitatively new information is derived from the temperature dependence of Lyapunov exponents. A Riemannian geometrization of newtonian dynamics suggests to consider other observables of geometric meaning tightly related with the largest Lyapunov exponent. The numerical computation of these observables - unusual in the study of phase transitions - sheds a new light on the microscopic dynamical counterpart of thermodynamics also pointing to the existence of some major change in the geometry of the mechanical manifolds at the thermodynamical transition. Through the microcanonical definition of the entropy, a relationship between thermodynamics and the extrinsic geometry of the constant energy surfaces $\Sigma_E$ of phase space can be naturally established. In this framework, an approximate formula is worked out, determining a highly non-trivial relationship between temperature and topology of the $\Sigma_E$. Whence it can be understood that the appearance of a phase transition must be tightly related to a suitable major topology change of the $\Sigma_E$. This contributes to the understanding of the origin of phase transitions in the microcanonical ensemble.Comment: in press on Physical Review E, 43 pages, LaTeX (uses revtex), 22 PostScript figure

Promoter methylation and downregulated expression of the TBX15 gene in ovarian carcinoma.

TBX15 is a gene involved in the development of mesodermal derivatives. As the ovaries and the female reproductive system are of mesodermal origin, the aim of the present study was to determine the methylation status of the TBX15 gene promoter and the expression levels of TBX15 in ovarian carcinoma, which is the most lethal and aggressive type of gynecological tumor, in order to determine the role of TBX15 in the pathogenesis of ovarian carcinoma. This alteration could be used to predict tumor development, progression, recurrence and therapeutic effects. The study was conducted on 80 epithelial ovarian carcinoma and 17 control cases (normal ovarian and tubal tissues). TBX15 promoter methylation was first determined by pyrosequencing following bisulfite modification, then by cloning and sequencing, in order to obtain information about the epigenetic haplotype. Immunohistochemical analysis was performed to evaluate the correlation between the methylation and protein expression levels. Data revealed a statistically significant increase of the TBX15 promoter region methylation in 82% of the tumor samples and in various histological subtypes. Immunohistochemistry showed an inverse correlation between methylation levels and the expression of the TBX15 protein. Furthermore, numerous tumor samples displayed varying degrees of intratumor heterogeneity. Thus, the present study determined that ovarian carcinoma typically expresses low levels of TBX15 protein, predominantly due to an epigenetic mechanism. This may have a role in the pathogenesis of ovarian carcinoma independent of the histological subtype

Riemannian theory of Hamiltonian chaos and Lyapunov exponents

This paper deals with the problem of analytically computing the largest Lyapunov exponent for many degrees of freedom Hamiltonian systems. This aim is succesfully reached within a theoretical framework that makes use of a geometrization of newtonian dynamics in the language of Riemannian geometry. A new point of view about the origin of chaos in these systems is obtained independently of homoclinic intersections. Chaos is here related to curvature fluctuations of the manifolds whose geodesics are natural motions and is described by means of Jacobi equation for geodesic spread. Under general conditions ane effective stability equation is derived; an analytic formula for the growth-rate of its solutions is worked out and applied to the Fermi-Pasta-Ulam beta model and to a chain of coupled rotators. An excellent agreement is found the theoretical prediction and the values of the Lyapunov exponent obtained by numerical simulations for both models.Comment: RevTex, 40 pages, 8 PostScript figures, to be published in Phys. Rev. E (scheduled for November 1996