Alternative linear structures for classical and quantum systems

The possibility of deforming the (associative or Lie) product to obtain alternative descriptions for a given classical or quantum system has been considered in many papers. Here we discuss the possibility of obtaining some novel alternative descriptions by changing the linear structure instead. In particular we show how it is possible to construct alternative linear structures on the tangent bundle TQ of some classical configuration space Q that can be considered as "adapted" to the given dynamical system. This fact opens the possibility to use the Weyl scheme to quantize the system in different non equivalent ways, "evading", so to speak, the von Neumann uniqueness theorem.Comment: 32 pages, two figures, to be published in IJMP

The local structure of n-Poisson and n-Jacobi manifolds

N-Lie algebra structures on smooth function algebras given by means of multi-differential operators, are studied. Necessary and sufficient conditions for the sum and the wedge product of two $n$-Poisson sructures to be again a multi-Poisson are found. It is proven that the canonical $n$-vector on the dual of an n-Lie algebra g is n-Poisson iff dim(g) are not greater than n+1. The problem of compatibility of two n-Lie algebra structures is analyzed and the compatibility relations connecting hereditary structures of a given n-Lie algebra are obtained. (n+1)-dimensional n-Lie algebras are classified and their "elementary particle-like" structure is discovered. Some simple applications to dynamics are discussed.Comment: 45 pages, latex, no figure

Microscopic construction of the chiral Luttinger liquid theory of the quantum Hall edge

We give a microscopic derivation of the chiral Luttinger liquid theory for the Laughlin states. Starting from the wave function describing an arbitrary incompressibly deformed Laughlin state (IDLS) we quantize these deformations. In this way we obtain the low-energy projections of local microscopic operators and derive the quantum field theory of edge excitations directly from quantum mechanics of electrons. This shows that to describe experimental and numeric deviations from chiral Luttinger liquid theory one needs to go beyond Laughlin's approximation. We show that in the large N limit the IDLS is described by the dispersionless Toda hierarchy.Comment: 5 pages, revtex, several clarifying comments adde

WNT4 deficiency—a clinical phenotype distinct from the classic Mayer-Rokitansky-Kuster-Hauser syndrome: A Case Report

The pathways leading to female sexual determination in mammals are incompletely defined. Loss-of-function mutations in the WNT4 gene appear to cause developmental abnormalities of sexual differentiation in women and mice. We recruited six patients with different degrees of Müllerian abnormalities, with or without renal aberrations and a normal female 46,XX karyotype. A clear androgen excess was found only in one patient. This 19-year-old woman was affected by primary amenorrhoea, absence of Müllerian ducts derivatives, clinical (acne and hirsutism) and biochemical (repeatedly high levels of testosterone) signs of androgen excess. Direct sequencing of her WNT4 gene followed by functional studies in human ovarian cells (OVCAR3) was performed. This patient carried the novel R83C loss-of-function dominant negative mutation in her WNT4, confirming the role of WNT4 in the development and maintenance of the female phenotype in women. Our study can also help refine the phenotype of WNT4 deficiency in humans. In fact, it appears that at least in this limited casuistic small group of patients, the absence of a uterus (and not other Müllerian abnormalities) and the androgen excess are the pathognomonic signs of WNT4 defects, suggesting that this might be a clinical entity distinct from the classic Mayer-Rokitansky-Kuster-Hauser syndrom

Alpha-particle clustering in excited expanding self-conjugate nuclei

The fragmentation of quasi-projectiles from the nuclear reaction 40Ca + 12C at 25 MeV/nucleon was used to produce alpha-emission sources. From a careful selection of these sources provided by a complete detection and from comparisons with models of sequential and simultaneous decays, strong indications in favour of $\alpha$-particle clustering in excited 16O, 20Ne and 24}Mg are reported.Comment: 8 pages, 4 figures, 12th International Conference on Nucleus-Nucleus collisions (NN2015), 21-26 June 2015, Catania, Ital

On a class of dynamical systems both quasi-bi-Hamiltonian and bi-Hamiltonian

It is shown that a class of dynamical systems (encompassing the one recently considered by F. Calogero [J. Math. Phys. 37 (1996) 1735]) is both quasi-bi-Hamiltonian and bi-Hamiltonian. The first formulation entails the separability of these systems; the second one is obtained trough a non canonical map whose form is directly suggested by the associated Nijenhuis tensor.Comment: 11 pages, AMS-LaTex 1.

Feature- versus rule-based generalization in rats, pigeons and humans

Humans can spontaneously create rules that allow them to efficiently generalize what they have learned to novel situations. An enduring question is whether rule-based generalization is uniquely human or whether other animals can also abstract rules and apply them to novel situations. In recent years, there have been a number of high-profile claims that animals such as rats can learn rules. Most of those claims are quite weak because it is possible to demonstrate that simple associative systems (which do not learn rules) can account for the behavior in those tasks. Using a procedure that allows us to clearly distinguish feature-based from rule-based generalization (the Shanks-Darby procedure), we demonstrate that adult humans show rule-based generalization in this task, while generalization in rats and pigeons was based on featural overlap between stimuli. In brief, when learning that a stimulus made of two components ("AB") predicts a different outcome than its elements ("A" and "B"), people spontaneously abstract an opposites rule and apply it to new stimuli (e.g., knowing that "C" and "D" predict one outcome, they will predict that "CD" predicts the opposite outcome). Rats and pigeons show the reverse behavior-they generalize what they have learned, but on the basis of similarity (e.g., "CD" is similar to "C" and "D", so the same outcome is predicted for the compound stimulus as for the components). Genuinely rule-based behavior is observed in humans, but not in rats and pigeons, in the current procedure