Abstract basins of attraction

Abstract basins appear naturally in different areas of several complex variables. In this survey we want to describe three different topics in which they play an important role, leading to interesting open problems

A counterexample to parabolic dichotomies in holomorphic iteration

We give an example of a parabolic holomorphic self-map $f$ of the unit ball $\mathbb B^2\subset \mathbb C^2$ whose canonical Kobayashi hyperbolic semi-model is given by an elliptic automorphism of the disc $\mathbb D\subset \mathbb C$, which can be chosen to be different from the identity. As a consequence, in contrast to the one dimensional case, this provides a first example of a holomorphic self-map of the unit ball which has points with zero hyperbolic step and points with nonzero hyperbolic step, solving an open question and showing that parabolic dynamics in the ball $\\mathbb B^2$ is radically different from parabolic dynamics in the disc. The example is obtained via a geometric method, embedding the ball $\mathbb B^2$ as a domain $\Omega$ in the bidisc $\\mathbb D\times \mathbb{H}$ that is forward invariant and absorbing for the map $(z,w)\mapsto (e^{i\theta}z,w+1)$, where $\mathbb H\subset \mathbb C$ denotes the right half-plane. We also show that a complete Kobayashi hyperbolic domain $\Omega$ with such properties cannot be Gromov hyperbolic w.r.t. the Kobayashi distance (hence, it cannot be biholomorphic to $\\mathbb B^2$) if an additional quantitative geometric condition is satisfied

Dynamics of transcendental Hénon maps-II

Transcendental Hénon maps are the natural extensions of the well investigated complex polynomial Hénon maps to the much larger class of holomorphic automorphisms. We prove here that transcendental Hénon maps always have non-trivial dynamical behavior, namely that they always admit both periodic and escaping orbits, and that their Julia sets are non-empty and perfect

NMR and μ+\mu^{+}SR detection of unconventional spin dynamics in Er(trensal) and Dy(trensal) molecular magnets

Measurements of proton Nuclear Magnetic Resonance (1H NMR) spectra and relaxation and of Muon Spin Relaxation ($\mu^{+}$SR) have been performed as a function of temperature and external magnetic field on two isostructural lanthanide complexes, Er(trensal) and Dy(trensal) featuring crystallographically imposed trigonal symmetry. Both the nuclear 1/T1 and muon $\lambda$ longitudinal relaxation rates, LRR, exhibit a peak for temperatures T lower than 30K, associated to the slowing down of the spin dynamics, and the width of the NMR absorption spectra starts to increase significantly at T ca. 50K, a temperature sizably higher than the one of the LRR peaks. The LRR peaks have a field and temperature dependence different from those previously reported for all Molecular Nanomagnets. They do not follow the Bloembergen-Purcell-Pound scaling of the amplitude and position in temperature and field and thus cannot be explained in terms of a single dominating correlation time $\tau$c determined by the spin slowing down at low temperature. Further, for T lower than 50K the spectral width does not follow the temperature behavior of the magnetic susceptibility chi. We suggest, using simple qualitative considerations, that the observed behavior is due to a combination of two different relaxation processes characterized by the correlation times $\tau$LT and $\tau$HT, dominating for T lower than 30K and T higher than 50K, respectively. Finally, the observed flattening of LRR for T lower than 5K is suggested to have a quantum origin

Dynamics of transcendental hÉnon maps III: Infinite entropy

Very little is currently known about the dynamics of non-polynomial entire maps in several complex variables. The family of transcendental Hénon maps offers the potential of combining ideas from transcendental dynamics in one variable and the dynamics of polynomial Hénon maps in two. Here we show that these maps all have infinite topological and measure theoretic entropy. The proof also implies the existence of infinitely many periodic orbits of any order greater than two

Cabergoline Withdrawal Before and After Menopause : Outcomes in Microprolactinomas

Natural course of prolactinomas after menopause is not fully elucidated. The aim of this study was to compare recurrence rate after cabergoline withdrawal in premenopausal vs. postmenopausal women with microprolactinoma. Sixty-two women with microprolactinoma treated with cabergoline for at least 1 year and followed for 2 years after drug withdrawal were retrospectively selected. Patients were divided into two groups: 48 patients stopped cabergoline before menopause ("PRE" group), while 14 after menopause ("POST" group). Recurrence was defined by prolactin levels above normal, confirmed on two occasions. Overall, 39/62 women relapsed. Patients who relapsed apparently had higher prolactin before withdrawal (median 216.2, range 21.2-464.3 mIU/L) compared with those in long-term remission (94.3, 29.7-402.8 mIU/L; p < 0.05), and the risk of recurrence seemed lower in POST women (4/14, 29%) than in PRE ones (35/48, 73%, p < 0.005, OR 0.149, 95% CI 0.040-0.558). However, none of the factors (prolactin before withdrawal, menopausal status, treatment duration, complete adenoma regression) showed a correlation with recurrence risk in multivariate analysis. The best strategy able to optimize CBG treatment and withdrawal's outcomes is still to be defined in microprolactinomas. Postmenopausal status cannot reliably predict long-term remission, and follow-up is needed also in women of this age

Hepatic heparan sulfate is a master regulator of hepcidin expression and iron homeostasis in human hepatocytes and mice.

Hepcidin is a liver-derived peptide hormone that controls systemic iron homeostasis. Its expression is regulated by the bone morphogenetic protein 6 (BMP6)/SMAD1/5/8 pathway and by the proinflammatory cytokine interleukin 6 (IL6). Proteoglycans that function as receptors of these signaling proteins in the liver are commonly decorated by heparan sulfate, but the potential role of hepatic heparan sulfate in hepcidin expression and iron homeostasis is unclear. Here, we show that modulation of hepatic heparan sulfate significantly alters hepcidin expression and iron metabolism both in vitro and in vivo Specifically, enzymatic removal of heparan sulfate from primary human hepatocytes, CRISPR/Cas9 manipulation of heparan sulfate biosynthesis in human hepatoma cells, or pharmacological manipulation of heparan sulfate-protein interactions using sodium chlorate or surfen dramatically reduced baseline and BMP6/SMAD1/5/8-dependent hepcidin expression. Moreover inactivation of the heparan sulfate biosynthetic gene N-deacetylase and N-sulfotransferase 1 (Ndst1) in murine hepatocytes (Ndst1 f/f AlbCre +) reduced hepatic hepcidin expression and caused a redistribution of systemic iron, leading to iron accumulation in the liver and serum of mice. Manipulation of heparan sulfate had a similar effect on IL6-dependent hepcidin expression in vitro and suppressed IL6-mediated iron redistribution induced by lipopolysaccharide in vivo These results provide compelling evidence that hepatocyte heparan sulfate plays a key role in regulating hepcidin expression and iron homeostasis in mice and in human hepatocytes

AEROBIC TRAINING WITH LIMBS INTERMITTENT ISCHEMIA IMPROVES MYOCARDIAL FUNCTION AND WALL STRETCH IN PATIENTS WITH CLAUDICATION

Background: peripheral arterial disease (PAD) is a chronic disease determining functional impairment and increased risk of cardiovascular events. Physical training improves cardiac performance and reduces NTproBNP concentration, marker of risk of cardiovascular events, in cardiac patients. Aim: we aimed to examine the effects training conducted till ischemic pain at the leg of PAD patients on myocardial function and peripheral flux.Methods: we enrolled 22 patients affected by peripheral arterial disease without cardiac disease. All patients undergone a physical training of 15 days, with treadmill test at the begin and at the end of training. Results: at the end of training patients increased walking distance (450\ub1180 m vs 250\ub1108 m; p<0.05). We documented at rest, at the end of physical training, an increase in flow volume of common femoral artery of the symptomatic leg (2,55\ub12,13 L/min vs 1,86\ub11,30 L/min; p<0.05); NTproBNP concentration at rest was lower al the end of training (210\ub1130 pg/mL vs 188\ub1108 pg/mL; p<0.005), an increase of NTproBNP concentration after maximal exercise on treadmill before treatment, with a reduced increase at the end of training period (24\ub121 vs 12\ub110 pg/mL; p<0.0005); a reduction of end-diastolic diameter of left ventricle at rest (48\ub14 mm vs 50\ub15 mm; p<0.05). The ejection fraction did not changed, while heart rate reduced after training (66\ub19 bpm vs 71\ub112 bpm; p<0.05). Conclusions: this study documented an improvement of hemodynamic and cardiac performance in response of physical training in peripheral arterial disease patients not affected by cardiac disease. Further trials will be necessary to evaluate the use of NTproBNP as a marker of good response to physical training in these patients

Augmented Reality to Engage Visitors of Science Museums through Interactive Experiences

In the last years, interactive exhibitions based on digital technologies have become widely common, thanks to their flexibility and effectiveness in engaging visitors and creating memorable experiences. One of the topics in which digital technologies can be particularly effective is the communication of abstract concepts that are difficult for the human mind to imagine. An emblematic example is the astronomy discipline, which requires us to imagine and understand phenomena far away from our everyday life. In this paper, the authors present a research project, MARSS, in which digital technologies are used effectively to enhance the Users' Experience of the Museo Astronomico di Brera located in Milan. Specifically, the MARSS project aims at designing and developing a new digital journey inside the museum to allow different categories of visitors to enjoy the exhibition in an engaging and interactive way. The paper presents the design and development phases of the experience and its evaluation with users. The results of the evaluation indicate that the digital interactive experience is appreciated by users and is successful in translating the content of high scientific value into more engaging and easily understandable elements

Quantitative mitochondrial DNA copy number determination using droplet digital PCR with single cell resolution

Mitochondria are involved in a number of diverse cellular functions, including energy production, metabolic regulation, apoptosis, calcium homeostasis, cell proliferation, and motility, as well as free radical generation. Mitochondrial DNA (mtDNA) is present at hundreds to thousands of copies per cell in a tissue-specific manner. mtDNA copy number also varies during aging and disease progression and therefore might be considered as a biomarker that mirrors alterations within the human body. Here, we present a new quantitative, highly sensitive droplet digital PCR (ddPCR) method, droplet digital mitochondrial DNA measurement (ddMDM), to measure mtDNA copy number not only from cell populations but also from single cells. Our developed assay can generate data in as little as 3 h, is optimized for 96-well plates, and also allows the direct use of cell lysates without the need for DNA purification or nuclear reference genes. We show that ddMDM is able to detect differences between samples whose mtDNA copy number was close enough as to be indistinguishable by other commonly used mtDNA quantitation methods. By utilizing ddMDM, we show quantitative changes in mtDNA content per cell across a wide variety of physiological contexts including cancer progression, cell cycle progression, human T cell activation, and human aging