Cauchy distributions for the integrable standard map

We consider the integrable (zero perturbation) two--dimensional standard map, in light of current developments on ergodic sums of irrational rotations, and recent numerical evidence that it might possess non-trivial q-Gaussian statistics. Using both classical and recent results, we show that the phase average of the sum of centered positions of an orbit, for long times and after normalization, obeys the Cauchy distribution (a q-Gaussian with q=2), while for almost all individual orbits such a sum does not obey any distribution at all. We discuss the question of existence of distributions for KAM tori.Comment: 6 pages, 2 figure

Zebrafish patient-derived xenografts identify chemo-response in pancreatic ductal adenocarcinoma patients

It is increasingly evident the necessity of new predictive tools for the treatment of pancreatic ductal adenocarcinoma in a personalized manner. We present a co-clinical trial testing the predic-tiveness of zPDX (zebrafish patient-derived xenograft) for assessing if patients could benefit from a therapeutic strategy (ClinicalTrials.gov: XenoZ, NCT03668418). zPDX are generated xenografting tumor tissues in zebrafish embryos. zPDX were exposed to chemotherapy regimens commonly used. We considered a zPDX a responder (R) when a decrease ≥50% in the relative tumor area was reported; otherwise, we considered them a non-responder (NR). Patients were classified as Responder if their own zPDX was classified as an R for the chemotherapy scheme she/he received an adjuvant treatment; otherwise, we considered them a Non-Responder. We compared the cancer recurrence rate at 1 year after surgery and the disease-free survival (DFS) of patients of both groups. We reported a statistically significant higher recurrence rate in the Non-Responder group: 66.7% vs. 14.3% (p = 0.036), anticipating relapse/no relapse within 1 year after surgery in 12/16 patients. The mean DFS was longer in the R-group than the NR-group, even if not statistically significant: 19.2 months vs. 12.7 months, (p = 0.123). The proposed strategy could potentially improve preclinical evaluation of treatment modalities and may enable prospective therapeutic selection in everyday clinical practice

Habitat-related birdsong divergence: a multi-level study on the influence of territory density and ambient noise in European blackbirds

Song plays an important role in avian communication and acoustic variation is important at both the individual and population level. Habitat-related variation between populations in particular can reflect adaptations to the environment accumulated over generations, but this may not always be the case. In this study, we test whether variation between individuals matches local conditions with respect to noise level and territory density to examine whether short-term flexibility could contribute to song divergence at the population level. We conducted a case study on an urban and forest population of the European blackbird and show divergence at the population level (i.e. across habitats) in blackbird song, anthropogenic noise level and territory density. Unlike in several other species, we found a lack of any correlation at the individual level (i.e. across individuals) between song features and ambient noise. This suggests species-specific causal explanations for noise-dependent song differentiation which are likely associated with variation in song-copying behaviour or feedback constraints related to variable singing styles. On the other hand, we found that at the level of individual territories, temporal features, but not spectral ones, are correlated to territory density and seasonality. This suggests that short-term individual variation can indeed contribute to habitat-dependent divergence at the population level. As this may undermine the potential role for song as a population marker, we conclude that more investigations on individual song flexibility are required for a better understanding of the impact of population-level song divergence on hybridisation and speciation

Real-Life Clinical Data of Cabozantinib for Unresectable Hepatocellular Carcinoma

Introduction: Cabozantinib has been approved by the European Medicine Agency (EMA) for hepatocellular carcinoma (HCC) previously treated with sorafenib. Cabozantinib is also being tested in combination with immune checkpoint inhibitors in the frontline setting. Real-life clinical data of cabozantinib for HCC are still lacking. Moreover, the prognostic factors for HCC treated with cabozantinib have not been investigated. Methods: We evaluated clinical data and outcome of HCC patients who received cabozantinib in the legal context of named patient use in Italy. Results: Ninety-six patients from 15 centres received cabozantinib. All patients had preserved liver function (Child-Pugh A), mostly with an advanced HCC (77.1%) in a third-line setting (75.0%). The prevalence of performance status (PS) > 0, macrovascular invasion (MVI), extrahepatic spread, and alpha-fetoprotein (AFP) >400 ng/mL was 50.0, 30.2, 67.7, and 44.8%, respectively. Median overall survival (OS) and progression-free survival were 12.1 (95% confidence interval 9.4–14.8) and 5.1 (3.3–6.9) months, respectively. Most common treatment-related adverse events (AEs) were fatigue (67.7%), diarrhoea (54.2%), anorexia (45.8%), HFSR (43.8%), weight loss (24.0%), and hypertension (24.0%). Most common treatment-related Grade 3–4 AEs were fatigue (6.3%), HFSR (6.3%), and increased aminotransferases (6.3%). MVI, ECOG-PS > 0, and AFP >400 ng/mL predicted a worse OS. Discontinuation for intolerance and no new extrahepatic lesions at the progression were associated with better outcomes. Conclusions: In a real-life Western scenario (mostly in a third-line setting), cabozantinib efficacy and safety data were comparable with those reported in its registration trial. Data regarding the prognostic factors might help in patient selection and design of clinical trials

Periodicity and Transport from Round-Off Errors

this paper we consider the effects of discretizing the phase space of a smooth area-preserving planar mapping that supports quasi-periodic motions, and we study the statistical properties of the resulting discrete representations of invariant tori. Discretization of the phase space can be achieved in many ways, and the most natural ones amount to restricting the dynamics to discrete subsets of the phase space, most notably those containing periodic orbits. For instance, in the case of the Anosov diffeomorphisms of the torus---a class of strongly chaotic systems---the periodic orbits correspond to points with rational coordinates, which can be effectively represented as algebraic numbers in the field generated over the rationals by the eigenvalues of the mapping [Percival and Vivaldi 1987; Bartuccelli and Vivaldi 1989; Keating c fl A K Peters, Ltd. 1058-6458/96 $0.50 per page 304 Experimental Mathematics, Vol. 3 (1994), No. 4 1991]. In the case of polynomial mappings over the complex field, the relevant discrete sets are towers of algebraic number fields containing the periodic and eventually periodic orbits [Vivaldi and Hatjispyros 1992; Bousch 1992; Morton and Patel 1994]. The thermodynamical formalism and the apparatus of dynamical zeta functions provide a link between the dynamics over these discrete sets and the statistics of their continuous counterpart (see [Ruelle 1978; Artuso et al. 1990; Artuso 1991] and references therein). The discretization introduced by round-off is significantly more difficult to deal with. In this case the discrete and continuous systems are related only weakly, the discrete phase space does not have any useful algebraic structure, there is no framework for relating periodicity to the statistics of fluctuations, and the limit of fine di..