Model selection in fracture mapping from elastostatic data

AbstractIn this paper, the inverse problem of imaging internally pressurized cracks from elastostatic measurements is investigated with special attention to the question of model choice. The selection of the most probable model from among a finite set of fracture geometry and loading model is carried out using Bayes factors. The modelling error variance is also estimated during the inversion procedure. This Bayesian model selection method also produces a known limit for the resolution of fracture dimensions, which depends on the configuration of the measurements. Both synthetic and real field examples in hydraulic fracture mapping applications are presented

I nostri figli, le nostre scuole, il nostro futuro: la scuola del futuro parte dall’Aquila

Policy paper La scuola è luogo di cittadinanza, soprattutto in una città che ha bisogno di cittadini “nuovi”, consapevoli del passato e portatori di futuro. Le nuove generazioni hanno il diritto di formarsi in spazi sicuri e ben organizzati, che consentano lo sviluppo dei migliori processi di apprendimento ed insegnamento, di partecipazione, di socializzazione e di acquisizione di sensibilità, valori da spendere positivamente nella costruzione della città futura

The Complex Langevin method: When can it be trusted?

We analyze to what extent the complex Langevin method, which is in principle capable of solving the so-called sign problems, can be considered as reliable. We give a formal derivation of the correctness and then point out various mathematical loopholes. The detailed study of some simple examples leads to practical suggestions about the application of the method.Comment: 14 pages, including several eps figures and tables; clarification and minor corrections added, to appear in PR

Non-teratogenic vitamin A preparation for women of child-bearing age

For treatment of acne the glucuronide of retinoic acid (retinoyl β-glucuronide) is orally administered to women of child-bearing age who are capable of conception. This therapy is safer than the oral administration of retinoic acid because retinoic acid glucuronide is essentially non-teratogenic at dose levels effective for the acne treatment. The retinoic acid glucuronide can be in all-trans or 13-cis form

Retinoic acid glucuronide preparations for application to the skin

A method and preparation are described for treating human skin with retinoic acid glucuronide (RAG) in a topical carrier. For treatment of acne or wrinkled skin, RAG can be applied in an effective amount which is nonirritating to the skin. Retinoid dermatitis, an objectionable side effect of topical application of retinoid compounds, can thereby be avoided

Motor timing deficits in community and clinical boys with hyperactive behaviour: The effect of methylphenidate on motor timing.

In a previous paper we showed that community children with hyperactive behavior were more inconsistent than controls in the temporal organization of their motor output. In this study we investigated: (1) various aspects of motor timing processes in 13 clinically diagnosed boys with attention deficit hyperactivity disorder (ADHD) who were compared to 11 community boys with hyperactive behavior and to a control group and (2) the effect of methylphenidate on the motor timing processes in the clinical group with ADHD in a double blind, cross-over, medication-placebo design, including 4 weeks of medication. The clinical group with ADHD, like the community group with hyperactivity, showed greater variability in sensorimotor synchronization and in sensorimotor anticipation relative to controls. The clinical group was also impaired in time perception, which was spared in the community group with hyperactivity. The persistent, but not the acute dose, of methylphenidate reduced the variability of sensorimotor synchronization and anticipation, but had no effect on time perception. This study shows that motor timing functions are impaired in both clinical and community children with hyperactivity. It is the first study to show the effectiveness of persistent administration of methylphenidate on deficits in motor timing in ADHD children and extends the use of methylphenidate from the domain of attentional and inhibitory functions to the domain of executive motor timing

Determinantal Characterization of Canonical Curves and Combinatorial Theta Identities

We characterize genus g canonical curves by the vanishing of combinatorial products of g+1 determinants of Brill-Noether matrices. This also implies the characterization of canonical curves in terms of (g-2)(g-3)/2 theta identities. A remarkable mechanism, based on a basis of H^0(K_C) expressed in terms of Szego kernels, reduces such identities to a simple rank condition for matrices whose entries are logarithmic derivatives of theta functions. Such a basis, together with the Fay trisecant identity, also leads to the solution of the question of expressing the determinant of Brill-Noether matrices in terms of theta functions, without using the problematic Klein-Fay section sigma.Comment: 35 pages. New results, presentation improved, clarifications added. Accepted for publication in Math. An

Strong asymptotics for Cauchy biorthogonal polynomials with application to the Cauchy two--matrix model

We apply the nonlinear steepest descent method to a class of 3x3 Riemann-Hilbert problems introduced in connection with the Cauchy two-matrix random model. The general case of two equilibrium measures supported on an arbitrary number of intervals is considered. In this case, we solve the Riemann-Hilbert problem for the outer parametrix in terms of sections of a spinorial line bundle on a three-sheeted Riemann surface of arbitrary genus and establish strong asymptotic results for the Cauchy biorthogonal polynomials.Comment: 31 pages, 12 figures. V2; typos corrected, added reference

Menelaus relation and Fay's trisecant formula are associativity equations

It is shown that the celebrated Menelaus relation and Fay's trisecant formula similar to the WDVV equation are associativity conditions for structure constants of certain three-dimensional algebra.Comment: Talk given at the Conference " Mathematics and Physics of Solitons and Integrable Systems", Dijon, 28.6-2.7, 2009. Minor misprints correcte