A numerical study of infinitely renormalizable area-preserving maps

It has been shown in (Gaidashev et al, 2010) and (Gaidashev et al, 2011) that infinitely renormalizable area-preserving maps admit invariant Cantor sets with a maximal Lyapunov exponent equal to zero. Furthermore, the dynamics on these Cantor sets for any two infinitely renormalizable maps is conjugated by a transformation that extends to a differentiable function whose derivative is Holder continuous of exponent alpha>0. In this paper we investigate numerically the specific value of alpha. We also present numerical evidence that the normalized derivative cocycle with the base dynamics in the Cantor set is ergodic. Finally, we compute renormalization eigenvalues to a high accuracy to support a conjecture that the renormalization spectrum is real

Dynamics of the Universal Area-Preserving Map Associated with Period Doubling: Hyperbolic Sets

It is known that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of {\fR}^2. A renormalization approach has been used in \cite{EKW1} and \cite{EKW2} in a computer-assisted proof of existence of a "universal" area-preserving map $F_*$ -- a map with orbits of all binary periods 2^k, k \in \fN. In this paper, we consider maps in some neighbourhood of $F_*$ and study their dynamics. We first demonstrate that the map $F_*$ admits a "bi-infinite heteroclinic tangle": a sequence of periodic points $\{z_k\}$, k \in \fZ, |z_k| \converge{{k \to \infty}} 0, \quad |z_k| \converge{{k \to -\infty}} \infty, whose stable and unstable manifolds intersect transversally; and, for any N \in \fN, a compact invariant set on which $F_*$ is homeomorphic to a topological Markov chain on the space of all two-sided sequences composed of $N$ symbols. A corollary of these results is the existence of {\it unbounded} and {\it oscillating} orbits. We also show that the third iterate for all maps close to $F_*$ admits a horseshoe. We use distortion tools to provide rigorous bounds on the Hausdorff dimension of the associated locally maximal invariant hyperbolic set: $$ 0.7673 \ge {\rm dim}_H(\cC_F) \ge \varepsilon \approx 0.00044 e^{-1797}.$

Absence of VHL gene alteration and high VEGF expression are associated with tumour aggressiveness and poor survival of renal-cell carcinoma

International audienceBACKGROUND: The von Hippel-Lindau gene (VHL) alteration, a common event in sporadic clear-cell renal-cell carcinoma (CCRCC), leads to highly vascularised tumours. Vascular endothelial growth factor (VEGF) is the major factor involved in angiogenesis, but the prognostic significance of both VHL inactivation and VEGF expression remain controversial. The aims of this study were to analyse the relationship between VHL genetic and epigenetic alterations, VHL expression and VEGF tumour or plasma expression, and to analyse their respective prognostic value in patients with CCRCC. METHODS: A total of 102 patients with CCRCC were prospectively analysed. Alterations in VHL were determined by sequencing, Multiplex Ligation-dependent Probe Amplification (MLPA) and methylation-specific MLPA. Expression of pVHL and VEGF was determined by immunohistochemistry. Plasma VEGF was measured by enzyme-linked immunosorbent assay (ELISA). RESULTS: VHL mutation, deletion and promoter methylation were identified in 70, 76 and 14 cases, respectively. Overall, at least one VHL-gene alteration occurred in 91 cases (89.2%). Both VEGF tumour and plasma expression appeared to be decreased in case of VHL alteration. Median progression-free survival and CCRCC-specific survival were significantly reduced in patients with wild-type VHL or altered VHL and high VEGF expression, which, therefore, represent two markers of tumour aggressiveness in CCRCC. CONCLUSION: Stratifying CCRCCs according to VHL and VEGF status may help tailor therapeutic strategy

The influence of early aging on eye movements during motor simulation

Movement based interventions such as imagery and action observation are used increasingly to support physical rehabilitation of adults during early aging. The efficacy of these more covert approaches is based on an intuitively appealing assumption that movement execution, imagery and observation share neural substrate; alteration of one influences directly the function of the other two. Using eye movement metrics this paper reports findings that question the congruency of the three conditions. The data reveal that simulating movement through imagery and action observation may offer older adults movement practice conditions that are not constrained by the age-related decline observed in physical conditions. In addition, the findings provide support for action observation as a more effective technique for movement reproduction in comparison to imagery. This concern for imagery was also seen in the less congruent temporal relationship in movement time between imagery and movement execution suggesting imagery inaccuracy in early aging

Trials

BACKGROUND: Postoperative upper gastrointestinal fistula (PUGIF) is a devastating complication, leading to high mortality (reaching up to 80%), increased length of hospital stay, reduced health-related quality of life and increased health costs. Nutritional support is a key component of therapy in such cases, which is related to the high prevalence of malnutrition. In the prophylactic setting, enteral nutrition (EN) is associated with a shorter hospital stay, a lower incidence of severe infectious complications, lower severity of complications and decreased cost compared to total parenteral nutrition (TPN) following major upper gastrointestinal (GI) surgery. There is little evidence available for the curative setting after fistula occurrence. We hypothesize that EN increases the 30-day fistula closure rate in PUGIF, allowing better health-related quality of life without increasing the morbidity or mortality. METHODS/DESIGN: The NUTRILEAK trial is a multicenter, randomized, parallel-group, open-label phase III trial to assess the efficacy of EN (the experimental group) compared with TPN (the control group) in patients with PUGIF. The primary objective of the study is to compare EN versus TPN in the treatment of PUGIF (after esophagogastric resection including bariatric surgery, duodenojejunal resection or pancreatic resection with digestive tract violation) in terms of the 30-day fistula closure rate. Secondary objectives are to evaluate the 6-month postrandomization fistula closure rate, time of first fistula closure (in days), the medical- and surgical treatment-related complication rate at 6 months after randomization, the fistula-related complication rate at 6 months after randomization, the type and severity of early (30 days after randomization) and late fistula-related complications (over 30 days after randomization), 30-day and 6-month postrandomization mortality rate, nutritional status at day 30, day 60, day 90 and day 180 postrandomization, the mean length of hospital stay, the patient's health-related quality of life (by self-assessment questionnaire), oral feeding time and direct costs of treatment. A total of 321 patients will be enrolled. DISCUSSION: The two nutritional supports are already used in daily practice, but most surgeons are reluctant to use the enteral route in case of PUGIF. This study will be the first randomized trial testing the role of EN versus TPN in PUGIF. TRIAL REGISTRATION: ClinicalTrials.gov: NCT03742752. Registered on 14 November 2018.This research program is funded by the French Ministry of Health through Programme Hospitalier de Recherche Clinique 2016