On the identifiability of ternary forms

We describe a new method to determine the minimality and identifiability of a Waring decomposition $A$ of a specific form (symmetric tensor) $T$ in three variables. Our method, which is based on the Hilbert function of $A$, can distinguish between forms in the span of the Veronese image of $A$, which in general contains both identifiable and not identifiable points, depending on the choice of coefficients in the decomposition. This makes our method applicable for all values of the length $r$ of the decomposition, from $2$ up to the generic rank, a range which was not achievable before. Though the method in principle can handle all cases of specific ternary forms, we introduce and describe it in details for forms of degree $8$

New insights on Anthracotherium monsvialense De Zigno, 1888 (Mammalia, Cetartiodactyla) from the lower Oligocene of Monteviale (Vicenza, northeastern Italy)

In Italy, anthracotheres are represented by a few fossils, most of them described during the XIX century and without a standardized scientific method. Anthracotherium monsvialense De Zigno, 1888 was originally erected from a fossil discovered in the site of Monteviale (Vicenza, northeastern Italy), whose Rupelian (MP21) lignitic beds yielded the richest lower Oligocene evidence of the genus Anthracotherium in Europe. A. monsvialense ranges from MP21 to MP23 and its small size has been interpreted as a consequence of the insular environment, at least at Monteviale. In this study, we summarize the long history of Italian findings providing new descriptions of dental and postcranial morphological features of A. monsvialense, and comparing such small anthracothere with its Asian and European relatives. Morphometric analyses are also performed on teeth, in order to verify the presence of evolutionary trends of the genus Anthracotherium

Modelling optical emission of Ultra-luminous X-ray Sources accreting above the Eddington limit

We study the evolution of binary systems of Ultra-luminous X-ray sources and compute their optical emission assuming accretion onto a black hole via a non standard, advection-dominated slim disc with an outflow. We consider systems with black holes of $20M_{\odot}$ and $100M_{\odot}$, and donor masses between $8M_{\odot}$ and $25M_{\odot}$. Super-critical accretion has considerable effects on the optical emission. The irradiating flux in presence of an outflow remains considerably stronger than that produced by a standard disc. However, at very high accretion rates the contribution of X-ray irradiation becomes progressively less important in comparison with the intrinsic flux emitted from the disc. After Main Sequence the evolutionary tracks of the optical counterpart on the colour-magnitude diagram are markely different from those computed for Eddington-limited accretion. Systems with stellar-mass black holes and $12-20 M_{\odot}$ donors accreting supercritically are characterized by blue colors (F450W -- F555W $\simeq - 0.2 : +0.1$) and high luminosity ($M_{V} \simeq - 4 : - 6.5$). Systems with more massive black holes accreting supercritically from evolved donors of similar mass have comparable colours but can reach $M_V \simeq - 8$. We apply our model to NGC 1313 X-2 and NGC 4559 X-7. Both sources are well represented by a system accreting above Eddington from a massive evolved donor. For NGC 1313 X-2 the agreement is for a $\sim 20M_{\odot}$ black hole, while NGC4559 X-7 requires a significantly more massive black hole.Comment: 13 pages, 15 figures, Accepted for publication in MNRAS; Acknowledgments adde

Genetic diagnosis as a tool for personalized treatment of Duchenne muscular dystrophy

Accurate definition of genetic mutations causing Duchenne muscular dystrophy (DMD) has always been relevant in order to provide genetic counseling to patients and families, and helps to establish the prognosis in the case where the distinction between Duchenne, Becker, or intermediate muscular dystrophy is not obvious. As molecular treatments aimed at dystrophin restoration in DMD are increasingly available as commercialized drugs or within clinical trials, genetic diagnosis has become an indispensable tool in order to determine eligibility for these treatments. DMD patients in which multiplex ligation-dependent probe amplification (MLPA) or similar techniques show a deletion suitable to exon skipping of exons 44, 45, 51, or 53, may be currently treated with AONs targeting these exons, in the context of clinical trials, or, as is the case for exon 51 skipping in the United States, with the first commercialized drug (eteplirsen). Patients who test negative at MLPA, but in whom DMD gene sequencing shows a nonsense mutation, may be amenable for treatment with stop codon readthrough compounds such as ataluren. Novel molecular approaches such as CRISPR-Cas9 targeting of specific DMD mutations are still in the preclinical stages, but appear promising. In conclusion, an accurate genetic diagnosis represents the entrance into a new scenario of personalized medicine in DMD

A Coloring Problem for Infinite Words

In this paper we consider the following question in the spirit of Ramsey theory: Given $x\in A^\omega,$ where $A$ is a finite non-empty set, does there exist a finite coloring of the non-empty factors of $x$ with the property that no factorization of $x$ is monochromatic? We prove that this question has a positive answer using two colors for almost all words relative to the standard Bernoulli measure on $A^\omega.$ We also show that it has a positive answer for various classes of uniformly recurrent words, including all aperiodic balanced words, and all words $x\in A^\omega$ satisfying $\lambda_x(n+1)-\lambda_x(n)=1$ for all $n$ sufficiently large, where $\lambda_x(n)$ denotes the number of distinct factors of $x$ of length $n.$Comment: arXiv admin note: incorporates 1301.526

Optical turbulence forecast in the Adaptive Optics realm

(35-words maximum) In this talk I present the scientific drivers related to the optical turbulence forecast applied to the ground-based astronomy supported by Adaptive Optics, the state of the art of the achieved results and the most relevant challenges for future progresses.Comment: 1 figure, Orlando, Florida United States, 25 - 28 June 2018, ISBN: 978-1-943580-44-6,Turbulence & Propagation, JW5I.1 Adaptive Optics: Analysis, Methods and System

Identifiability for a class of symmetric tensors

We use methods of algebraic geometry to find new, effective methods for detecting the identifiability of symmetric tensors. In particular, for ternary symmetric tensors T of degree 7, we use the analysis of the Hilbert function of a finite projective set, and the Cayley-Bacharach property, to prove that, when the Kruskal's rank of a decomposition of T are maximal (a condition which holds outside a Zariski closed set of measure 0), then the tensor T is identifiable, i.e. the decomposition is unique, even if the rank lies beyond the range of application of both the Kruskal's and the reshaped Kruskal's criteria

Single and cross-generation natural hedging of longevity and financial risk

The paper provides natural hedging strategies among death benefits and annuities written on a single and on different generations. It obtains closed-form Delta and Gamma hedges, in the presence of both longevity and interest rate risk. We present an application to UK data on survivorship and bond dynamics. We first compare longevity and financial risk exposures: Deltas and Gammas for longevity risk are greater in absolute value than the corresponding sensitivities for interest rate risk. We then calculate the optimal hedges, both within and across generations. Our results apply to both asset and asset-liability management