Cross sections for geodesic flows and \alpha-continued fractions

We adjust Arnoux's coding, in terms of regular continued fractions, of the geodesic flow on the modular surface to give a cross section on which the return map is a double cover of the natural extension for the \alpha-continued fractions, for each $\alpha$ in (0,1]. The argument is sufficiently robust to apply to the Rosen continued fractions and their recently introduced \alpha-variants.Comment: 20 pages, 2 figure

Toward a First High-quality Genome Draft for Marker-assisted Breeding in Leaf Chicory, Radicchio (Cichorium intybus L.)

Radicchio (Cichorium intybus subsp. intybus var. foliosum L.) is one of the most important leaf chicories, used mainly as a component for fresh salads. Recently, we sequenced and annotated the first draft of the leaf chicory genome, as we believe it will have an extraordinary impact from both scientific and economic points of view. Indeed, the availability of the first genome sequence for this plant species will provide a powerful tool to be exploited in the identification of markers associated with or genes responsible for relevant agronomic traits, influencing crop productivity and product quality. The plant material used for the sequencing of the leaf chicory genome belongs to the Radicchio of the Chioggia type. Genomic DNA was used for library preparation with the TruSeq DNA Sample Preparation chemistry (Illumina). Sequencing reactions were performed with the Illumina platforms HiSeq and MySeq, and sequence reads were then assembled and annotated. We are confident that our efforts will extend the current knowledge of the genome organization and gene composition of leaf chicory, which is crucial for developing new tools and diagnostic markers useful for our breeding strategies in Radicchio

The entropy of alpha-continued fractions: numerical results

We consider the one-parameter family of interval maps arising from generalized continued fraction expansions known as alpha-continued fractions. For such maps, we perform a numerical study of the behaviour of metric entropy as a function of the parameter. The behaviour of entropy is known to be quite regular for parameters for which a matching condition on the orbits of the endpoints holds. We give a detailed description of the set M where this condition is met: it consists of a countable union of open intervals, corresponding to different combinatorial data, which appear to be arranged in a hierarchical structure. Our experimental data suggest that the complement of M is a proper subset of the set of bounded-type numbers, hence it has measure zero. Furthermore, we give evidence that the entropy on matching intervals is smooth; on the other hand, we can construct points outside of M on which it is not even locally monotone.Comment: 33 pages, 14 figure

Survival and Neural Models for Private Equity Exit Prediction

Within the Private Equity (PE) market, the event of a private company undertaking an Initial Public Offering (IPO) is usually a very high-return one for the investors in the company. For this reason, an effective predictive model for the IPO event is considered as a valuable tool in the PE market, an endeavor in which publicly available quantitative information is generally scarce. In this paper, we describe a data-analytic procedure for predicting the probability with which a company will go public in a given forward period of time. The proposed method is based on the interplay of a neural network (NN) model for estimating the overall event probability, and Survival Analysis (SA) for further modeling the probability of the IPO event in any given interval of time. The proposed neuro-survival model is tuned and tested across nine industrial sectors using real data from the Thomson Reuters Eikon PE database

Natural extensions and entropy of α\alpha-continued fractions

We construct a natural extension for each of Nakada's $\alpha$-continued fractions and show the continuity as a function of $\alpha$ of both the entropy and the measure of the natural extension domain with respect to the density function $(1+xy)^{-2}$. In particular, we show that, for all $0 < \alpha \le 1$, the product of the entropy with the measure of the domain equals $\pi^2/6$. As a key step, we give the explicit relationship between the $\alpha$-expansion of $\alpha-1$ and of $\alpha$

Self-care in pediatric patients with chronic conditions: A systematic review of theoretical models

Background: To improve outcomes in children and young adults (CYAs) with chronic conditions, it is important to promote self-care through education and support. Aims: (1) to retrieve the literature describing theories or conceptual models of self-care in CYAs with chronic conditions and (2) to develop a comprehensive framework. Methods: A systematic literature search was conducted on nine databases, according to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. All peer-reviewed papers describing a theory or a conceptual model of self-care in CYAs (0-24 years) with chronic conditions were included. Results: Of 2674 records, 17 met the inclusion criteria. Six papers included a theory or a model of self-care, self-management, or a similar concept. Six papers developed or revised pre-existing models or theories, while five papers did not directly focus on a specific model or a theory. Patients were CYAs, mainly with type 1 diabetes mellitus and asthma. Some relevant findings about self-care in CYAs with neurocognitive impairment and in those living with cancer may have been missed. Conclusions: By aggregating the key elements of the 13 self-care conceptual models identified in the review, we developed a new overarching model emphasizing the shift of self-care agency from family to patients as main actors of their self-management process. The model describes influencing factors, self-care behaviors, and outcomes; the more patients engaged in self-care behaviors, the more the outcomes were favorable