GKW representation theorem and linear BSDEs under restricted information. An application to risk-minimization

In this paper we provide Galtchouk-Kunita-Watanabe representation results in the case where there are restrictions on the available information. This allows to prove existence and uniqueness for linear backward stochastic differential equations driven by a general c\`adl\`ag martingale under partial information. Furthermore, we discuss an application to risk-minimization where we extend the results of F\"ollmer and Sondermann (1986) to the partial information framework and we show how our result fits in the approach of Schweizer (1994).Comment: 22 page

Looking for a new panacea in ALK-rearranged NSCLC: may be Ceritinib?

In the past decade, the advent of targeted therapy led to a silent revolution in the war against lung cancer and a significant evolution on the concept of Phase I clinical trials design. Thanks to the specificity of their target, the new drugs have radically changed NSCLC treatment, leading to the development of personalized strategies. The accelerated approval of the first ALK-inhibitor, Crizotinib and more recently Ceritinib, without a Phase III randomized, clinical trial, has been an amazing success story in lung cancer research, marking the beginning of a new decade of targeted drugs development, characterized by modern, biomarker-driven, early clinical trial design and shorter times for clinical approval. Is Ceritinib a new panacea for the treatment of ALK-rearranged NSCLC? We aimed to discuss the reasons of such success, including the new emerging questions, regarding mechanisms of acquired resistance, and the best treatment algorithm for ALK-rearranged NSCLC patients

Bounds for the relative n-th nilpotency degree in compact groups

The line of investigation of the present paper goes back to a classical work of W. H. Gustafson of the 1973, in which it is described the probability that two randomly chosen group elements commute. In the same work, he gave some bounds for this kind of probability, providing information on the group structure. We have recently obtained some generalizations of his results for finite groups. Here we improve them in the context of the compact groups.Comment: 9 pages; to appear in Asian-European Journal of Mathematics with several improvement

Design strategies for the self-assembly of polyhedral shells

The control over the self-assembly of complex structures is a long-standing challenge of material science, especially at the colloidal scale, as the desired assembly pathway is often kinetically derailed by the formation of amorphous aggregates. Here we investigate in detail the problem of the self-assembly of the three Archimedean shells with five contact points per vertex, i.e. the icosahedron, the snub cube, and the snub dodecahedron. We use patchy particles with five interaction sites (or patches) as model for the building blocks, and recast the assembly problem as a Boolean satisfiability problem (SAT) for the patch-patch interactions. This allows us to find effective designs for all targets, and to selectively suppress unwanted structures. By tuning the geometrical arrangement and the specific interactions of the patches, we demonstrate that lowering the symmetry of the building blocks reduces the number of competing structures, which in turn can considerably increase the yield of the target structure. These results cement SAT-assembly as an invaluable tool to solve inverse design problems.Comment: 21 pages, 10 figure

Negative symptoms as key features of depression among cannabis users: a preliminary report.

OBJECTIVE: Cannabis use is frequent among depressed patients and may lead to the so-called "amotivational syndrome", which combines symptoms of affective flattening and loss of emotional reactivity (i.e. the so-called "negative" symptomatology). The aim of this study was to investigate the negative symptomatology in depressed patients with concomitant cannabis use disorders (CUDs) in comparison with depressed patients without CUDs. PATIENTS AND METHODS: Fifty-one patients with a diagnosis of Major Depressive Disorder (MDD) and concomitant CUD and fifty-one MDD patients were enrolled in the study. The 21-Item Hamilton Depression Rating Scale (HDRS) and the negative symptoms subscales of the Positive and Negative Syndrome Scale (PANSS) were used to assess depressive and negative symptomatology. RESULTS: Patients with cannabis use disorders presented significantly more severe negative symptoms in comparison with patients without cannabis use (15.18 ± 2.25 vs 13.75 ± 2.44; t100 = 3.25 p = 0.002). DISCUSSION: A deeper knowledge of the "negative" psychopathological profile of MDD patients who use cannabis may lead to novel etiopathogenetic models of MDD and to more appropriate treatment approaches

Two-step nucleation in a binary mixture of patchy particles

Nucleation in systems with a metastable liquid–gas critical point is the prototypical example of a two-step nucleation process in which the appearance of the critical nucleus is preceded by the formation of a liquid-like density fluctuation. So far, the majority of studies on colloidal and protein crystallization have focused on one-component systems, and we are lacking a clear description of two-step nucleation processes in multicomponent systems, where critical fluctuations involve coupled density and concentration inhomogeneities. Here, we examine the nucleation process of a binary mixture of patchy particles designed to nucleate into a diamond lattice. By combining Gibbs-ensemble simulations and direct nucleation simulations over a wide range of thermodynamic conditions, we are able to pin down the role of the liquid–gas metastable phase diagram on the nucleation process. In particular, we show that the strongest enhancement of crystallization occurs at an azeotropic point with the same stoichiometric composition of the crystal

Lattice Gas Analogue Of SK Model: A paradigm for the glass transition

We investigate the connection between the well known Sherrington-Kirkpatrick Ising Spin Glass and the corresponding Lattice Gas model by analyzing the relation between their thermodynamical functions. We present results of replica approach in the Replica Symmetric approximation and discuss its stability as a function of temperature and external source. Next we examine the effects of first order Replica Symmetry Breaking at zero temperature. We finally compare SK results with ours and suggest how the latter could be relevant to a description of the structural glass transition.Comment: 33 Pages, LaTeX file; 15 Figures added, some grammatical corrections. To appear in Journal of Physics

On the classification of OADP varieties

The main purpose of this paper is to show that OADP varieties stand at an important crossroad of various main streets in different disciplines like projective geometry, birational geometry and algebra. This is a good reason for studying and classifying them. Main specific results are: (a) the classification of all OADP surfaces (regardless to their smoothness); (b) the classification of a relevant class of normal OADP varieties of any dimension, which includes interesting examples like lagrangian grassmannians. Following [PR], the equivalence of the classification in (b) with the one of quadro-quadric Cremona transformations and of complex, unitary, cubic Jordan algebras are explained.Comment: 13 pages. Dedicated to Fabrizio Catanese on the occasion of his 60th birthday. To appear in a special issue of Science in China Series A: Mathematic

Classical Solutions in Two-Dimensional String Theory and Gravitational Collapse

A general solution to the $D=2$ 1-loop beta functions equations including tachyonic back reaction on the metric is presented. Dynamical black hole (classical) solutions representing gravitational collapse of tachyons are constructed. A discussion on the correspondence with the matrix-model approach is given.Comment: 7 pages, UTTG-31-9

Lines on projective varieties and applications

The first part of this note contains a review of basic properties of the variety of lines contained in an embedded projective variety and passing through a general point. In particular we provide a detailed proof that for varieties defined by quadratic equations the base locus of the projective second fundamental form at a general point coincides, as a scheme, with the variety of lines. The second part concerns the problem of extending embedded projective manifolds, using the geometry of the variety of lines. Some applications to the case of homogeneous manifolds are included.Comment: 15 pages. One example removed; one remark and some references added; typos correcte