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

Hot-water treatment of dormant grape cuttings: Its effects on Agrobacterium tumefaciens and on grafting and growth of vine

Hot-water treatment (50°C for 20-30 min) was carried out to confirm its efficacy in eradicating Agrobacterium tumefaciens biovar 3 (AT3) in symptomless grape cuttings.After the forcing period, analyses of callus from cuttings of grape cvs Albana, Lambrusco Grasparossa, Rulander and Fortana, and from their graft combinations with the rootstocks 420A, 41B, 5BB and 1103P, revealed the low infection level in the grape material used. Dormant scion and rootstock cuttings treated identically in the U.S. gave similar results. Despite this, it was possible to confirm the efficacy of thermotherapy in eradicating the pathogen.An assessment was also made of the effect of treatment on growth parameters of grafted vines in the greenhouse and after 8 months in a field nursery. The effect of hot-water treatment on the vitality and growth of vines varied with the different scion-rootstock combinations. Treatment did not generally have detrimental effects on vitality; there were some negative effects on graft-take. The number and length of canes, as well as the diameter of the trunks, increased in most instances.The treatments and times usually did not affect bud survival and, in most cases, increased the level of callus formation at the base of cuttings.

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

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

Thermodynamic formalism for systems with Markov dynamics

The thermodynamic formalism allows one to access the chaotic properties of equilibrium and out-of-equilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function within the framework of discrete time Markov chains was not suitable for continuous time Markov dynamics. Here we propose another interpretation of the definition that allows us to apply the thermodynamic formalism to continuous time. We also generalize the formalism --a dynamical Gibbs ensemble construction-- to a whole family of observables and their associated large deviation functions. This allows us to make the connection between the thermodynamic formalism and the observable involved in the much-studied fluctuation theorem. We illustrate our approach on various physical systems: random walks, exclusion processes, an Ising model and the contact process. In the latter cases, we identify a signature of the occurrence of dynamical phase transitions. We show that this signature can already be unravelled using the simplest dynamical ensemble one could define, based on the number of configuration changes a system has undergone over an asymptotically large time window.Comment: 64 pages, LaTeX; version accepted for publication in Journal of Statistical Physic

Difference Operator Approach to the Moyal Quantization and Its Application to Integrable Systems

Inspired by the fact that the Moyal quantization is related with nonlocal operation, I define a difference analogue of vector fields and rephrase quantum description on the phase space. Applying this prescription to the theory of the KP-hierarchy, I show that their integrability follows to the nature of their Wigner distribution. Furthermore the definition of the ``expectation value'' clarifies the relation between our approach and the Hamiltonian structure of the KP-hierarchy. A trial of the explicit construction of the Moyal bracket structure in the integrable system is also made.Comment: 19 pages, to appear in J. Phys. Soc. Jp

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

Intrinsic excitation-inhibition imbalance affects medial prefrontal cortex differently in autistic men versus women

Excitation-inhibition (E:I) imbalance is theorized as an important pathophysiological mechanism in autism. Autism affects males more frequently than females and sex-related mechanisms (e.g., X-linked genes, androgen hormones) can influence E:I balance. This suggests that E:I imbalance may affect autism differently in males versus females. With a combination of in-silico modeling and in-vivo chemogenetic manipulations in mice, we first show that a time-series metric estimated from fMRI BOLD signal, the Hurst exponent (H), can be an index for underlying change in the synaptic E:I ratio. In autism we find that H is reduced, indicating increased excitation, in the medial prefrontal cortex (MPFC) of autistic males but not females. Increasingly intact MPFC H is also associated with heightened ability to behaviorally camouflage social-communicative difficulties, but only in autistic females. This work suggests that H in BOLD can index synaptic E:I ratio and that E:I imbalance affects autistic males and females differently

Expansion of plasmablasts and loss of memory B cells in peripheral blood from COVID-19 patients with pneumonia

Studies on the interactions between SARS-CoV-2 and humoral immunity are fundamental to elaborate effective therapies including vaccines. We used polychromatic flow cytometry, coupled with unsupervised data analysis and principal component analysis (PCA), to interrogate B cells in untreated patients with COVID-19 pneumonia. COVID-19 patients displayed normal plasma levels of the main immunoglobulin classes, of antibodies against common antigens or against antigens present in common vaccines. However, we found a decreased number of total and na\uefve B cells, along with decreased percentages and numbers of memory switched and unswitched B cells. On the contrary, IgM+ and IgM 12 plasmablasts were significantly increased. In vitro cell activation revealed that B lymphocytes showed a normal proliferation index and number of dividing cells per cycle. PCA indicated that B-cell number, naive and memory B cells but not plasmablasts clustered with patients who were discharged, while plasma IgM level, C-reactive protein, D-dimer, and SOFA score with those who died. In patients with pneumonia, the derangement of the B-cell compartment could be one of the causes of the immunological failure to control SARS-Cov2, have a relevant influence on several pathways, organs and systems, and must be considered to develop vaccine strategies