Basic properties of nonsmooth Hormander's vector fields and Poincare's inequality

We consider a family of vector fields defined in some bounded domain of R^p, and we assume that they satisfy Hormander's rank condition of some step r, and that their coefficients have r-1 continuous derivatives. We extend to this nonsmooth context some results which are well-known for smooth Hormander's vector fields, namely: some basic properties of the distance induced by the vector fields, the doubling condition, Chow's connectivity theorem, and, under the stronger assumption that the coefficients belong to C^{r-1,1}, Poincare's inequality. By known results, these facts also imply a Sobolev embedding. All these tools allow to draw some consequences about second order differential operators modeled on these nonsmooth Hormander's vector fields.Comment: 60 pages, LaTeX; Section 6 added and Section 7 (6 in the previous version) changed. Some references adde

Long-range frustration in T=0 first-step replica-symmetry-broken solutions of finite-connectivity spin glasses

In a finite-connectivity spin-glass at the zero-temperature limit, long-range correlations exist among the unfrozen vertices (whose spin values being non-fixed). Such long-range frustrations are partially removed through the first-step replica-symmetry-broken (1RSB) cavity theory, but residual long-range frustrations may still persist in this mean-field solution. By way of population dynamics, here we perform a perturbation-percolation analysis to calculate the magnitude of long-range frustrations in the 1RSB solution of a given spin-glass system. We study two well-studied model systems, the minimal vertex-cover problem and the maximal 2-satisfiability problem. This work points to a possible way of improving the zero-temperature 1RSB mean-field theory of spin-glasses.Comment: 5 pages, two figures. To be published in JSTA

Cavity method for quantum spin glasses on the Bethe lattice

We propose a generalization of the cavity method to quantum spin glasses on fixed connectivity lattices. Our work is motivated by the recent refinements of the classical technique and its potential application to quantum computational problems. We numerically solve for the phase structure of a connectivity $q=3$ transverse field Ising model on a Bethe lattice with $\pm J$ couplings, and investigate the distribution of various classical and quantum observables.Comment: 27 pages, 9 figure

Cataract and optic disk drusen in a patient with glycogenosis and di George syndrome: clinical and molecular report

Background We report the ophthalmic findings of a patient with type Ia glycogen storage disease (GSD Ia), DiGeorge syndrome (DGS), cataract and optic nerve head drusen (ONHD). Case presentation A 26-year-old white woman, born at term by natural delivery presented with a post-natal diagnosis of GSD Ia. Genetic testing by array-comparative genomic hybridization (CGH) for DGS was required because of her low levels of serum calcium. The patient has been followed from birth, attending the day-hospital every six months at the San Paolo Hospital, Milan, outpatient clinic for metabolic diseases and previously at another eye center. During the last day-hospital visit, a complete eye examination showed ONHD and cataract in both eyes. Next Generation Sequencing (NGS) was subsequently done to check for any association between the eye problems and metabolic aspects. Conclusions This is the first description of ocular changes in a patient with GSD Ia and DGS. Mutations explaining GSD Ia and DGS were found but no specific causative mutation for cataract and ONHD. The metabolic etiology of her lens changes is known, whereas the pathogenesis of ONHD is not clear. Although the presence of cataract and ONHD could be a coincidence; the case reported could suggest that hypocalcemia due to DGS could be the common biochemical pathway

Optimization and characterization of tungsten thick coatings on copper based ally substrates

Tungsten is a promising armour material for plasma facing components of nuclear fusion reactors because of its low sputter rate and favourable thermo-mechanical properties. Among all the techniques able to realise W armours, plasma spray looks particularly attractive owing to its simplicity and low cost. The present work concerns the optimisation of spraying parameters aimed at 4–5 mm thickWcoating on copper–chromium–zirconium (Cu,Cr,Zr) alloy substrates. Characterisation of coatings was performed in order to assess microstructure, impurity content, density, tensile strength, adhesion strength, thermal conductivity and thermal expansion coefficient. The work performed has demonstrated the feasibility of thick W coatings on flat and curved geometries. These coatings appear as a reliable armour for medium heat flux plasma facing component

Random subcubes as a toy model for constraint satisfaction problems

We present an exactly solvable random-subcube model inspired by the structure of hard constraint satisfaction and optimization problems. Our model reproduces the structure of the solution space of the random k-satisfiability and k-coloring problems, and undergoes the same phase transitions as these problems. The comparison becomes quantitative in the large-k limit. Distance properties, as well the x-satisfiability threshold, are studied. The model is also generalized to define a continuous energy landscape useful for studying several aspects of glassy dynamics.Comment: 21 pages, 4 figure

Generalized Jacobi identities and ball-box theorem for horizontally regular vector fields

We consider a family of vector fields and we assume a horizontal regularity on their derivatives. We discuss the notion of commutator showing that different definitions agree. We apply our results to the proof of a ball-box theorem and Poincar\'e inequality for nonsmooth H\"ormander vector fields.Comment: arXiv admin note: material from arXiv:1106.2410v1, now three separate articles arXiv:1106.2410v2, arXiv:1201.5228, arXiv:1201.520

Shock wave lithotripsy for a renal stone in a tetraplegic patient as a trigger for life-threatening posterior reversible encephalopathy syndrome

Shock wave lithotripsy (SWL) is considered a non-invasive treatment for urinary stones and usually advocated for frail patients with spinal cord injury (SCI). We report a life-threatening complication, called posterior reversible encephalopathy syndrome (PRES), in a tetraplegic person who underwent SWL for a small renal stone. Based on our experience, we recommend performing SWL with caution in SCI patients and in tertiary referral hospitals that can promptly manage similar severe complications

Reconstruction on trees and spin glass transition

Consider an information source generating a symbol at the root of a tree network whose links correspond to noisy communication channels, and broadcasting it through the network. We study the problem of reconstructing the transmitted symbol from the information received at the leaves. In the large system limit, reconstruction is possible when the channel noise is smaller than a threshold. We show that this threshold coincides with the dynamical (replica symmetry breaking) glass transition for an associated statistical physics problem. Motivated by this correspondence, we derive a variational principle which implies new rigorous bounds on the reconstruction threshold. Finally, we apply a standard numerical procedure used in statistical physics, to predict the reconstruction thresholds in various channels. In particular, we prove a bound on the reconstruction problem for the antiferromagnetic ``Potts'' channels, which implies, in the noiseless limit, new results on random proper colorings of infinite regular trees. This relation to the reconstruction problem also offers interesting perspective for putting on a clean mathematical basis the theory of glasses on random graphs.Comment: 34 pages, 16 eps figure

Relational arenas in a regional Higher Education system: Insights from an empirical analysis

Extant indicators on research and higher education do not consider the complex relational structure in which universities are embedded and that influences their performance on one side, and the impact of policies on the other. This article investigates the overall pattern of universities' relational arenas in a Regional environment by considering their two main domains of activity, namely research and teaching. We study their structure, determinants, and existing interactions, in order to understand the possible consequences for policy making and management, and to identify synthetic indicators to represent the