The bisymplectomorphism group of a bounded symmetric domain

An Hermitian bounded symmetric domain in a complex vector space, given in its circled realization, is endowed with two natural symplectic forms: the flat form and the hyperbolic form. In a similar way, the ambient vector space is also endowed with two natural symplectic forms: the Fubini-Study form and the flat form. It has been shown in arXiv:math.DG/0603141 that there exists a diffeomorphism from the domain to the ambient vector space which puts in correspondence the above pair of forms. This phenomenon is called symplectic duality for Hermitian non compact symmetric spaces. In this article, we first give a different and simpler proof of this fact. Then, in order to measure the non uniqueness of this symplectic duality map, we determine the group of bisymplectomorphisms of a bounded symmetric domain, that is, the group of diffeomorphisms which preserve simultaneously the hyperbolic and the flat symplectic form. This group is the direct product of the compact Lie group of linear automorphisms with an infinite-dimensional Abelian group. This result appears as a kind of Schwarz lemma.Comment: 19 pages. Version 2: minor correction

Riemannian geometry of Hartogs domains

Let D_F = \{(z_0, z) \in {\C}^{n} | |z_0|^2 < b, \|z\|^2 < F(|z_0|^2) \} be a strongly pseudoconvex Hartogs domain endowed with the \K metric $g_F$ associated to the \K form $\omega_F = -\frac{i}{2} \partial \bar{\partial} \log (F(|z_0|^2) - \|z\|^2)$. This paper contains several results on the Riemannian geometry of these domains. In the first one we prove that if $D_F$ admits a non special geodesic (see definition below) through the origin whose trace is a straight line then $D_F$ is holomorphically isometric to an open subset of the complex hyperbolic space. In the second theorem we prove that all the geodesics through the origin of $D_F$ do not self-intersect, we find necessary and sufficient conditions on $F$ for $D_F$ to be geodesically complete and we prove that $D_F$ is locally irreducible as a Riemannian manifold. Finally, we compare the Bergman metric $g_B$ and the metric $g_F$ in a bounded Hartogs domain and we prove that if $g_B$ is a multiple of $g_F$, namely $g_B=\lambda g_F$, for some $\lambda\in \R^+$, then $D_F$ is holomorphically isometric to an open subset of the complex hyperbolic space.Comment: to appear in International Journal of Mathematic

GABA and Muscimol as Reversible Inactivation Tools in Learning and Memory

Reversible inactivation of brain areas is a useful method for inferring brain-behavior relationships. Infusion of GABA or of the GABA receptor agonist muscimol is considered one interesting reversible inactivation method because it may not affect fibers of passage and may therefore be compared to axon-sparing types of lesions. This article reviews the data obtained with this method in learning and memory experiments. A critical analysis of data, collected in collaboration with Simon Brailowsky, with chronic GABA infusion is presented, together with an illustration of data obtained with muscimol-induced inactivation

Quasi-saddles as relevant points of the potential energy surface in the dynamics of supercooled liquids

The supercooled dynamics of a Lennard-Jones model liquid is numerically investigated studying relevant points of the potential energy surface, i.e. the minima of the square gradient of total potential energy $V$. The main findings are: ({\it i}) the number of negative curvatures $n$ of these sampled points appears to extrapolate to zero at the mode coupling critical temperature $T_c$; ({\it ii}) the temperature behavior of $n(T)$ has a close relationship with the temperature behavior of the diffusivity; ({\it iii}) the potential energy landscape shows an high regularity in the distances among the relevant points and in their energy location. Finally we discuss a model of the landscape, previously introduced by Madan and Keyes [J. Chem. Phys. {\bf 98}, 3342 (1993)], able to reproduce the previous findings.Comment: To be published in J. Chem. Phy

The faster the better: On the shortest paths role for near real-time decision making of water utilities

Near real-time monitoring and control of critical infrastructure is essential for the operation and management of cities in a world that is, today, more complex and interconnected than ever. Such an infrastructure can be represented as complex networks an some of their related indices and statistics, many of them based on the shortest paths, play a pivotal role in the decision making for public services such as internet, energy or water. Particularly, the literature has shown that shortest paths are key for resilience and criticality assessment in a water distribution systems (WDS). This paper proposes a procedure to speed-up the computation of shortest paths in a WDS, as it can straightforwardly benefit any critical infrastructure. The proposal is based on a reduced dimension of a complex network representing any critical infrastructure. Despite the consequent decrease in the number of all possible paths in the network, the main advantage and novelty of this proposal is to continue finding the exact solution for the shortest paths. Experimental results show that the procedure brings a computational-time reduction consistently over 50% and up to 90% in some cases. In addition, the paper reveals how the use of shortest paths benefits WDS operation and management, as well as playing a key role in near real-time contamination detection and leakage control

On weak r-Helix submanifolds

In this paper, we investigate special curves on a weak r-helix submanifold in Euclidean n-space E^{n}. Also, we give the important relations between weak r-helix submanifolds and the special curves such as line of curvature, asymptotic curve and helix line.Comment: arXiv admin note: text overlap with arXiv:1203.160

Taste Perception And Food Choices

OBJECTIVES: The extent to which variation in taste perception influences food preferences is, to date, controversial. Bitterness in food triggers an innate aversion that is responsible for dietary restriction in children. We investigated the association among genetic variations in bitter receptor TAS2R38 and food choices in healthy children in the Mediterranean area, to develop appropriate tools to evaluate the relation among genetic predisposition, dietary habits, and feeding disorders. The aims of the study were to get a first baseline picture of taste sensitivity in healthy adults and their children and to explore taste sensitivity in a preliminary sample of obese children and in samples affected by functional gastrointestinal diseases. METHODS: Individuals (98 children, 87 parents, 120 adults) were recruited from the general population in southern Italy. Bitterness sensitivity was assessed by means of a suprathreshold method with 6-propyl-2-thiouracil. Genomic DNA from saliva was used to genotype individuals for 3 polymorphisms of TAS2R38 receptor, A49P, A262 V, and V296I. Food intake was assessed by a food frequency questionnaire. RESULTS: Children's taste sensation differed from that of adults: we observed a higher frequency of supertasters among children even in the mother-child dyads with the same diplotypes. Among adults, supertaster status was related with proline-alanine-valine (taster allele) homozygous haplotype, whereas supertaster children were mainly heterozygous. Regarding the food choices, we found that a higher percentage of taster children avoided bitter vegetables or greens altogether compared with taster adults. Taster status was also associated with body mass index in boys. CONCLUSIONS: Greater sensitivity to 6-propyl-2-thiouracil predicts lower preferences for vegetables in children, showing an appreciable effect of the genetic predisposition on food choices. None of the obese boys was a supertaster

Targeting Food Allergy with Probiotics.

The dramatic increase in food allergy prevalence and severity globally is demanding effective strategies. Food allergy derives from a defect in immune tolerance mechanisms. Immune tolerance is modulated by gut microbiota composition and function, and gut microbiota dysbiosis has been associated with the development of food allergy. Selected probiotic strains could act on immune tolerance mechanisms. The mechanisms are multiple and still not completely defined. Increasing evidence is providing useful information on the choice of optimal bacterial species/strains, dosage, and timing for intervention. The increased knowledge on the crucial role played by gut microbiota-derived metabolites, such as butyrate, is also opening the way to a postbiotic approach in the stimulation of immune tolerance

A Berger type normal holonomy theorem for complex submanifolds

We prove a kind of Berger-Simons' Theorem for the normal holonomy group of a complex submanifold of the projective spac