Global periodicity conditions for maps and recurrences via Normal Forms

We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two and three dimensional classes of polynomial or rational maps. In particular we find the global periodic cases for several Lyness type recurrences.Comment: 25 page

Recent results in nuclear astrophysics at the n_TOF facility at CERN

The neutron time of flight (n_TOF) facility at CERN is a spallation source characterized by a white neutron spectrum. The innovative features of the facility, in the two experimental areas, (20 m and 185 m), allow for an accurate determination of the neutron cross section for radioactive samples or for isotopes with small neutron capture cross section, of interest for Nuclear Astrophysics. The recent results obtained at n_TOF facility are presented

Measurement of the α ratio and (n, γ) cross section of 235U from 0.2 to 200 eV at n_TOF

We measured the neutron capture-to-fission cross-section ratio (α ratio) and the capture cross section of 235U between 0.2 and 200 eV at the n_TOF facility at CERN. The simultaneous measurement of neutron-induced capture and fission rates was performed by means of the n_TOF BaF2 Total Absorption Calorimeter (TAC), used for detection of γ rays, in combination with a set of micromegas detectors used as fission tagging detectors. The energy dependence of the capture cross section was obtained with help of the 6 Li(n,t) standard reaction determining the n_TOF neutron fluence; the well-known integral of the 235U(n, f ) cross section between 7.8 and 11 eV was then used for its absolute normalization. The α ratio, obtained with slightly higher statistical fluctuations, was determined directly, without need for any reference cross section. To perform the analysis of this measurement we developed a new methodology to correct the experimentally observed effect that the probabilities of detecting a fission reaction in the TAC and the micromegas detectors are not independent. The results of this work have been used in a new evaluation of 235U performed within the scope of the Collaborative International Evaluated Library Organisation (CIELO) Project, and are consistent with the ENDF/B-VIII.0 and JEFF-3.3 capture cross sections below 4 eV and above 100 eV. However, the measured capture cross section is on average 10% larger between 4 and 100 eV.Ministerio de Economía, Industria y Competitividad de España. FPA2014-53290-C2-1, FPA2016-76765- P y FPA2017-82647-P7º Programa Marco CHANDA de la Comisión Europea. FP7-60520

UGT1A and TYMS genetic variants predict toxicity and response of colorectal cancer patients treated with first-line irinotecan and fluorouracil combination therapy

BACKGROUND: The impact of thymidylate synthase (TYMS) and UDP-glucoronosyltransferase 1A (UGT1A) germline polymorphisms on the outcome of colorectal cancer (CRC) patients treated with irinotecan plus 5-fluorouracil (irinotecan/5FU) is still controversial. Our objective was to define a genetic-based algorithm to select patients to be treated with irinotecan/5FU. METHODS: Genotyping of TYMS (5'TRP and 3'UTR), UGT1A1*28, UGT1A9*22 and UGT1A7*3 was performed in 149 metastatic CRC patients treated with irinotecan/5FU as first-line chemotherapy enrolled in a randomised phase 3 study. Their association with response, toxicity and survival was investigated by univariate and multivariate statistical analysis. RESULTS: TYMS 3TRP/3TRP genotype was the only independent predictor of tumour response (OR=5.87, 95% confidence interval (CI)=1.68-20.45; P=0.005). UGT1A1*28/*28 was predictive for haematologic toxicity (OR=6.27, 95% CI=1.09-36.12; P=0.04), specifically for neutropenia alone (OR=6.40, 95% CI=1.11-37.03; P=0.038) or together with diarrhoea (OR=18.87, 95% CI=2.14-166.67; P=0.008). UGT1A9*1/*1 was associated with non-haematologic toxicity (OR=2.70, 95% CI=1.07-6.82; P=0.035). Haplotype VII (all non-favourable alleles) was associated with non-haematologic toxicity (OR=2.11, 95% CI-1.12-3.98; P-0.02). CONCLUSION: TYMS and UGT1A polymorphisms influence on tumour response and toxicities derived from irinotecan/5FU treatment in CRC patients. A genetic-based algorithm to optimise treatment individualisation is proposed. British Journal of Cancer (2010) 103, 581-589. doi:10.1038/sj.bjc.6605776 www.bjcancer.com Published online 13 July 2010 (C) 2010 Cancer Research U

A pivotal role for starch in the reconfiguration of 14C-partitioning and allocation in Arabidopsis thaliana under short-term abiotic stress.

Plant carbon status is optimized for normal growth but is affected by abiotic stress. Here, we used 14C-labeling to provide the first holistic picture of carbon use changes during short-term osmotic, salinity, and cold stress in Arabidopsis thaliana. This could inform on the early mechanisms plants use to survive adverse environment, which is important for efficient agricultural production. We found that carbon allocation from source to sinks, and partitioning into major metabolite pools in the source leaf, sink leaves and roots showed both conserved and divergent responses to the stresses examined. Carbohydrates changed under all abiotic stresses applied; plants re-partitioned 14C to maintain sugar levels under stress, primarily by reducing 14C into the storage compounds in the source leaf, and decreasing 14C into the pools used for growth processes in the roots. Salinity and cold increased 14C-flux into protein, but as the stress progressed, protein degradation increased to produce amino acids, presumably for osmoprotection. Our work also emphasized that stress regulated the carbon channeled into starch, and its metabolic turnover. These stress-induced changes in starch metabolism and sugar export in the source were partly accompanied by transcriptional alteration in the T6P/SnRK1 regulatory pathway that are normally activated by carbon starvation

The n-TOF facility: Neutron beams for challenging future measurements at CERN

The CERN n_TOF neutron beam facility is characterized by a very high instantaneous neutron flux, excellent TOF resolution at the 185 m long flight path (EAR-1), low intrinsic background and coverage of a wide range of neutron energies, from thermal to a few GeV. These characteristics provide a unique possibility to perform high-accuracy measurements of neutron-induced reaction cross-sections and angular distributions of interest for fundamental and applied Nuclear Physics. Since 2001, the n_TOF Collaboration has collected a wealth of high quality nuclear data relevant for nuclear astrophysics, nuclear reactor technology, nuclear medicine, etc. The overall efficiency of the experimental program and the range of possible measurements has been expanded with the construction of a second experimental area (EAR-2), located 20 m on the vertical of the n_TOF spallation target. This upgrade, which benefits from a neutron flux 30 times higher than in EAR-1, provides a substantial extension in measurement capabilities, opening the possibility to collect data on neutron cross-section of isotopes with short half-lives or available in very small amounts. This contribution will outline the main characteristics of the n_TOF facility, with special emphasis on the new experimental area. In particular, we will discuss the innovative features of the EAR-2 neutron beam that make possible to perform very challenging measurements on short-lived radioisotopes or sub-mg samples, out of reach up to now at other neutron facilities around the world. Finally, the future perspectives of the facility will be presented

On the Lebesgue measure of Li-Yorke pairs for interval maps

We investigate the prevalence of Li-Yorke pairs for $C^2$ and $C^3$ multimodal maps $f$ with non-flat critical points. We show that every measurable scrambled set has zero Lebesgue measure and that all strongly wandering sets have zero Lebesgue measure, as does the set of pairs of asymptotic (but not asymptotically periodic) points. If $f$ is topologically mixing and has no Cantor attractor, then typical (w.r.t. two-dimensional Lebesgue measure) pairs are Li-Yorke; if additionally $f$ admits an absolutely continuous invariant probability measure (acip), then typical pairs have a dense orbit for $f \times f$. These results make use of so-called nice neighborhoods of the critical set of general multimodal maps, and hence uniformly expanding Markov induced maps, the existence of either is proved in this paper as well. For the setting where $f$ has a Cantor attractor, we present a trichotomy explaining when the set of Li-Yorke pairs and distal pairs have positive two-dimensional Lebesgue measure.Comment: 41 pages, 3 figure

The 33S(n,α)30Si cross section measurement at n-TOF-EAR2 (CERN) : From 0.01 eV to the resonance region

The 33S(n,α)30Si cross section measurement, using 10B(n,α) as reference, at the n-TOF Experimental Area 2 (EAR2) facility at CERN is presented. Data from 0.01 eV to 100 keV are provided and, for the first time, the cross section is measured in the range from 0.01 eV to 10 keV. These data may be used for a future evaluation of the cross section because present evaluations exhibit large discrepancies. The 33S(n,α)30Si reaction is of interest in medical physics because of its possible use as a cooperative target to boron in Neutron Capture Therapy (NCT)

Measurement of 73 Ge(n,γ) cross sections and implications for stellar nucleosynthesis

© 2019 The Author(s). Published by Elsevier B.V.73 Ge(n,γ) cross sections were measured at the neutron time-of-flight facility n_TOF at CERN up to neutron energies of 300 keV, providing for the first time experimental data above 8 keV. Results indicate that the stellar cross section at kT=30 keV is 1.5 to 1.7 times higher than most theoretical predictions. The new cross sections result in a substantial decrease of 73 Ge produced in stars, which would explain the low isotopic abundance of 73 Ge in the solar system.Peer reviewe