Arnold maps with noise: Differentiability and non-monotonicity of the rotation number

Arnold's standard circle maps are widely used to study the quasi-periodic route to chaos and other phenomena associated with nonlinear dynamics in the presence of two rationally unrelated periodicities. In particular, the El Nino-Southern Oscillation (ENSO) phenomenon is a crucial component of climate variability on interannual time scales and it is dominated by the seasonal cycle, on the one hand, and an intrinsic oscillatory instability with a period of a few years, on the other. The role of meteorological phenomena on much shorter time scales, such as westerly wind bursts, has also been recognized and modeled as additive noise. We consider herein Arnold maps with additive, uniformly distributed noise. When the map's nonlinear term, scaled by the parameter $\epsilon$, is sufficiently small, i.e. $\epsilon < 1$, the map is known to be a diffeomorphism and the rotation number $\rho_{\omega}$ is a differentiable function of the driving frequency $\omega$. We concentrate on the rotation number's behavior as the nonlinearity becomes large, and show rigorously that $\rho _{\omega }$ is a differentiable function of $\omega$, even for $\epsilon \geq 1$, at every point at which the noise-perturbed map is mixing. We also provide a formula for the derivative of the rotation number. The reasoning relies on linear-response theory and a computer-aided proof. In the diffeomorphism case of $\epsilon <1$, the rotation number $\rho_{\omega }$ behaves monotonically with respect to $\omega$. We show, using again a computer-aided proof, that this is not the case when $\epsilon \geq 1$ and the map is not a diffeomorphism.Comment: Electronic copy of final peer-reviewed manuscript accepted for publication in the Journal of Statistical Physic

Variable renewal rate and growth properties of cell populations in colon crypts

A nonlinear mathematical model is used to investigate the time evolution of the cell populations in colon crypts (stem, semidifferentiated and fully differentiated cells). To mimic pathological alteration of the biochemical pathways leading to abnormal proliferative activity of the population of semidifferentiated cells their renewal rate is assumed to be dependent on the population size. Then, the effects of such perturbation on the population dynamics are investigated theoretically. Using both theoretical methods and numerical simulations it is shown that the increase in the renewal rate of semidifferentiated cells strongly impacts the dynamical behavior of the cell populations

Neuroplastic Changes Following Brain Ischemia and their Contribution to Stroke Recovery: Novel Approaches in Neurorehabilitation

Ischemic damage to the brain triggers substantial reorganization of spared areas and pathways, which is associated with limited, spontaneous restoration of function. A better understanding of this plastic remodeling is crucial to develop more effective strategies for stroke rehabilitation. In this review article, we discuss advances in the comprehension of post-stroke network reorganization in patients and animal models. We first focus on rodent studies that have shed light on the mechanisms underlying neuronal remodeling in the perilesional area and contralesional hemisphere after motor cortex infarcts. Analysis of electrophysiological data has demonstrated brain-wide alterations in functional connectivity in both hemispheres, well beyond the infarcted area. We then illustrate the potential use of non-invasive brain stimulation (NIBS) techniques to boost recovery. We finally discuss rehabilitative protocols based on robotic devices as a tool to promote endogenous plasticity and functional restoration

Delayed Self-Synchronization in Homoclinic Chaos

The chaotic spike train of a homoclinic dynamical system is self-synchronized by re-inserting a small fraction of the delayed output. Due to the sensitive nature of the homoclinic chaos to external perturbations, stabilization of very long periodic orbits is possible. On these orbits, the dynamics appears chaotic over a finite time, but then it repeats with a recurrence time that is slightly longer than the delay time. The effect, called delayed self-synchronization (DSS), displays analogies with neurodynamic events which occur in the build-up of long term memories.Comment: Submitted to Phys. Rev. Lett., 13 pages, 7 figure

Granulicatella spp., a Causative Agent of Infective Endocarditis in Children

Granulicatella spp. are non-motile, non-sporulating, facultatively anaerobic Gram-positive cocci. Throughout the literature, these organisms have been referred to by several names, such as “nutritionally deficient streptococci”, “vitamin-B dependent streptococci” and “pyridoxal-dependent streptococci”, because of their fastidious nutritional requirements, which can often make culture isolation challenging. Known to be a member of the normal microbiota of the human oral cavity and urogenital and intestinal tracts, similar to other streptococci, Granulicatella spp. can cause bacteremia, sepsis and infective endocarditis. Considering the difficulty in growing this organism on culture medium, the fact that it is now included among the bacteria known to be responsible for culture-negative infective endocarditis suggests that its pathogenic role could be highly underestimated. Moreover, being considered such a rare causative agent, it is not a target of standard antibiotic empiric treatment. We present a rare case of G. elegans endocarditis in a young child and review the medical literature on Granulicatella endocarditis in the pediatric population, with the aim of sharing knowledge about this microorganism, which can be challenging for a clinician who is not familiar with it

Grammatical gender and linguistic complexity I: General issues and specific studies

The many facets of grammatical gender remain one of the most fruitful areas of linguistic research, and pose fascinating questions about the origins and development of complexity in language. The present work is a two-volume collection of 13 chapters on the topic of grammatical gender seen through the prism of linguistic complexity. The contributions discuss what counts as complex and/or simple in grammatical gender systems, whether the distribution of gender systems across the world’s languages relates to the language ecology and social history of speech communities. Contributors demonstrate how the complexity of gender systems can be studied synchronically, both in individual languages and over large cross-linguistic samples, and diachronically, by exploring how gender systems change over time. In addition to three chapters on the theoretical foundations of gender complexity, volume one contains six chapters on grammatical gender and complexity in individual languages and language families of Africa, New Guinea, and South Asia. This volume is complemented by volume two, which consists of three chapters providing diachronic and typological case studies, followed by a final chapter discussing old and new theoretical and empirical challenges in the study of the dynamics of gender complexity

Grammatical gender and linguistic complexity I: General issues and specific studies

The many facets of grammatical gender remain one of the most fruitful areas of linguistic research, and pose fascinating questions about the origins and development of complexity in language. The present work is a two-volume collection of 13 chapters on the topic of grammatical gender seen through the prism of linguistic complexity. The contributions discuss what counts as complex and/or simple in grammatical gender systems, whether the distribution of gender systems across the world’s languages relates to the language ecology and social history of speech communities. Contributors demonstrate how the complexity of gender systems can be studied synchronically, both in individual languages and over large cross-linguistic samples, and diachronically, by exploring how gender systems change over time. In addition to three chapters on the theoretical foundations of gender complexity, volume one contains six chapters on grammatical gender and complexity in individual languages and language families of Africa, New Guinea, and South Asia. This volume is complemented by volume two, which consists of three chapters providing diachronic and typological case studies, followed by a final chapter discussing old and new theoretical and empirical challenges in the study of the dynamics of gender complexity

Grammatical gender and linguistic complexity I: General issues and specific studies

The many facets of grammatical gender remain one of the most fruitful areas of linguistic research, and pose fascinating questions about the origins and development of complexity in language. The present work is a two-volume collection of 13 chapters on the topic of grammatical gender seen through the prism of linguistic complexity. The contributions discuss what counts as complex and/or simple in grammatical gender systems, whether the distribution of gender systems across the world’s languages relates to the language ecology and social history of speech communities. Contributors demonstrate how the complexity of gender systems can be studied synchronically, both in individual languages and over large cross-linguistic samples, and diachronically, by exploring how gender systems change over time. In addition to three chapters on the theoretical foundations of gender complexity, volume one contains six chapters on grammatical gender and complexity in individual languages and language families of Africa, New Guinea, and South Asia. This volume is complemented by volume two, which consists of three chapters providing diachronic and typological case studies, followed by a final chapter discussing old and new theoretical and empirical challenges in the study of the dynamics of gender complexity

Grammatical gender and linguistic complexity I: General issues and specific studies

The many facets of grammatical gender remain one of the most fruitful areas of linguistic research, and pose fascinating questions about the origins and development of complexity in language. The present work is a two-volume collection of 13 chapters on the topic of grammatical gender seen through the prism of linguistic complexity. The contributions discuss what counts as complex and/or simple in grammatical gender systems, whether the distribution of gender systems across the world’s languages relates to the language ecology and social history of speech communities. Contributors demonstrate how the complexity of gender systems can be studied synchronically, both in individual languages and over large cross-linguistic samples, and diachronically, by exploring how gender systems change over time. In addition to three chapters on the theoretical foundations of gender complexity, volume one contains six chapters on grammatical gender and complexity in individual languages and language families of Africa, New Guinea, and South Asia. This volume is complemented by volume two, which consists of three chapters providing diachronic and typological case studies, followed by a final chapter discussing old and new theoretical and empirical challenges in the study of the dynamics of gender complexity