Decay of correlations for maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors

We consider two dimensional maps preserving a foliation which is uniformly contracting and a one dimensional associated quotient map having exponential convergence to equilibrium (iterates of Lebesgue measure converge exponentially fast to physical measure). We prove that these maps have exponential decay of correlations over a large class of observables. We use this result to deduce exponential decay of correlations for the Poincare maps of a large class of singular hyperbolic flows. From this we deduce logarithm laws for these flows.Comment: 39 pages; 03 figures; proof of Theorem 1 corrected; many typos corrected; improvements on the statements and comments suggested by a referee. Keywords: singular flows, singular-hyperbolic attractor, exponential decay of correlations, exact dimensionality, logarithm la

Recurrence and algorithmic information

In this paper we initiate a somewhat detailed investigation of the relationships between quantitative recurrence indicators and algorithmic complexity of orbits in weakly chaotic dynamical systems. We mainly focus on examples.Comment: 26 pages, no figure

Khinchin theorem for integral points on quadratic varieties

We prove an analogue the Khinchin theorem for the Diophantine approximation by integer vectors lying on a quadratic variety. The proof is based on the study of a dynamical system on a homogeneous space of the orthogonal group. We show that in this system, generic trajectories visit a family of shrinking subsets infinitely often.Comment: 19 page

Statistical properties of Lorenz like flows, recent developments and perspectives

We comment on mathematical results about the statistical behavior of Lorenz equations an its attractor, and more generally to the class of singular hyperbolic systems. The mathematical theory of such kind of systems turned out to be surprisingly difficult. It is remarkable that a rigorous proof of the existence of the Lorenz attractor was presented only around the year 2000 with a computer assisted proof together with an extension of the hyperbolic theory developed to encompass attractors robustly containing equilibria. We present some of the main results on the statisitcal behavior of such systems. We show that for attractors of three-dimensional flows, robust chaotic behavior is equivalent to the existence of certain hyperbolic structures, known as singular-hyperbolicity. These structures, in turn, are associated to the existence of physical measures: \emph{in low dimensions, robust chaotic behavior for flows ensures the existence of a physical measure}. We then give more details on recent results on the dynamics of singular-hyperbolic (Lorenz-like) attractors.Comment: 40 pages; 10 figures; Keywords: sensitive dependence on initial conditions, physical measure, singular-hyperbolicity, expansiveness, robust attractor, robust chaotic flow, positive Lyapunov exponent, large deviations, hitting and recurrence times. Minor typos corrected and precise acknowledgments of financial support added. To appear in Int J of Bif and Chaos in App Sciences and Engineerin

Infinite ergodic theory and Non-extensive entropies

We bring into account a series of result in the infinite ergodic theory that we believe that they are relevant to the theory of non-extensive entropie

Robust exponential decay of correlations for singular-flows

We construct open sets of Ck (k bigger or equal to 2) vector fields with singularities that have robust exponential decay of correlations with respect to the unique physical measure. In particular we prove that the geometric Lorenz attractor has exponential decay of correlations with respect to the unique physical measure.Comment: Final version accepted for publication with added corrections (not in official published version) after O. Butterley pointed out to the authors that the last estimate in the argument in Subsection 4.2.3 of the previous version is not enough to guarantee the uniform non-integrability condition claimed. We have modified the argument and present it here in the same Subsection. 3 figures, 34 page

(Non)Invariance of dynamical quantities for orbit equivalent flows

We study how dynamical quantities such as Lyapunov exponents, metric entropy, topological pressure, recurrence rates, and dimension-like characteristics change under a time reparameterization of a dynamical system. These quantities are shown to either remain invariant, transform according to a multiplicative factor or transform through a convoluted dependence that may take the form of an integral over the initial local values. We discuss the significance of these results for the apparent non-invariance of chaos in general relativity and explore applications to the synchronization of equilibrium states and the elimination of expansions

A machine learning approach for mapping susceptibility to land subsidence caused by ground water extraction

Land subsidence is a worldwide threat that may cause irreversible damage to the environment and the infrastructures. Thus, identifying and mapping areas prone to land subsidence with accurate methods such as Land Subsidence Susceptibility Index (LSSI) mapping is crucial for mitigating the adverse impacts of this geohazard. Also, Machine Learning (ML) is now becoming a powerful tool to analyze vast and different datasets such as those necessary for LSSI mapping. In this study, we use the conventional Frequency Ratio (FR) method and ML models to generate LSSI maps of the region of Murcia (Spain) where land subsidence occurred in the past due to groundwater overdraft. A LSSI map was initially generated with known FR. Then, additional Conditioning Factors (CFs) with increased spatial resolution were used to train several ML models and generate a new LSSI map. The Extra-Trees Classifier (ETC) outperformed the other approaches, achieving the best performance with a weighted average precision and F1-Score of 0.96, after optimizing its hyperparameters. Then, a third LSSI map was calculated using the FR method and observations of land subsidence from InSAR (Interferometric Synthetic Aperture Radar). This study shows that the effectiveness of using several CFs depends on the added information of each layer. Moreover, the comparison between the different LSSI maps and InSAR data highlights the crucial role of the spatial resolution for accurate mapping, thus enhancing land subsidence risk assessment

Integrative organelle-based functional proteomics: in silico prediction of impaired functional annotations in SACS KO cell model

Autosomal recessive spastic ataxia of Charlevoix-Saguenay (ARSACS) is an inherited neurodegenerative disease characterized by early-onset spasticity in the lower limbs, axonal-demyelinating sensorimotor peripheral neuropathy, and cerebellar ataxia. Our understanding of ARSACS (genetic basis, protein function, and disease mechanisms) remains partial. The integrative use of organelle-based quantitative proteomics and whole-genome analysis proposed in the present study allowed identifying the affected disease-specific pathways, upstream regulators, and biological functions related to ARSACS, which exemplify a rationale for the development of improved early diagnostic strategies and alternative treatment options in this rare condition that currently lacks a cure. Our integrated results strengthen the evidence for disease-specific defects related to bioenergetics and protein quality control systems and reinforce the role of dysregulated cytoskeletal organization in the pathogenesis of ARSACS

Detection and Classification of Hysteroscopic Images Using Deep Learning

Background: Although hysteroscopy with endometrial biopsy is the gold standard in the diagnosis of endometrial pathology, the gynecologist experience is crucial for a correct diagnosis. Deep learning (DL), as an artificial intelligence method, might help to overcome this limitation. Unfortunately, only preliminary findings are available, with the absence of studies evaluating the performance of DL models in identifying intrauterine lesions and the possible aid related to the inclusion of clinical factors in the model. Aim: To develop a DL model as an automated tool for detecting and classifying endometrial pathologies from hysteroscopic images. Methods: A monocentric observational retrospective cohort study was performed by reviewing clinical records, electronic databases, and stored videos of hysteroscopies from consecutive patients with pathologically confirmed intrauterine lesions at our Center from January 2021 to May 2021. Retrieved hysteroscopic images were used to build a DL model for the classification and identification of intracavitary uterine lesions with or without the aid of clinical factors. Study outcomes were DL model diagnostic metrics in the classification and identification of intracavitary uterine lesions with and without the aid of clinical factors. Results: We reviewed 1500 images from 266 patients: 186 patients had benign focal lesions, 25 benign diffuse lesions, and 55 preneoplastic/neoplastic lesions. For both the classification and identification tasks, the best performance was achieved with the aid of clinical factors, with an overall precision of 80.11%, recall of 80.11%, specificity of 90.06%, F1 score of 80.11%, and accuracy of 86.74 for the classification task, and overall detection of 85.82%, precision of 93.12%, recall of 91.63%, and an F1 score of 92.37% for the identification task. Conclusion: Our DL model achieved a low diagnostic performance in the detection and classification of intracavitary uterine lesions from hysteroscopic images. Although the best diagnostic performance was obtained with the aid of clinical data, such an improvement was slight