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

Migraine Prevention through Ketogenic Diet: More than Body Mass Composition Changes

The ketogenic diet (KD) is gaining attention as a preventive treatment for migraine, which is sustained by many pre-clinical and clinical data. KD is also used for weight loss, and there is a relation between migraine and weight excess, but it is speculated that KD efficacy on migraine may go beyond this effect. We conducted a retrospective observational study on 23 migraine patients who received a KD and were evaluated at the baseline and then after 3 months both from a neurological and a nutritional point of view, including body mass composition analysis. We observed a reduction in monthly headache days (12.5 ± 9.5 vs. 6.7 ± 8.6; p < 0.001) and in days of acute medication intake (11.06 ± 9.37 vs. 4.93 ± 7.99; p = 0.008). We also observed a reduction in patients’ weight (73.8 ± 15.2 vs. 68.4 ± 14.6; p < 0.001) and BMI (26.9 ± 6.2 vs. 23.7 ± 8.1; p < 0.001) with a decrement of the fat mass (28.6 ± 12.5 vs. 20.6 ± 9.8; p < 0.001). Patients who responded to KD and those who did not had no differences with respect to weight or fat mass loss. These data corroborate the utilization of KD as a preventive treatment for migraine and suggest that the efficacy of such an intervention is not only due to weight or fat mass loss but probably relies on other mechanisms specific to KD

2:1 ketogenic diet and low-glycemic-index diet for the treatment of chronic and episodic migraine: a single-center real-life retrospective study

Aims: The evidence supporting the efficacy of dietary preventive therapy in migraine is rising, particularly regarding the ketogenic diet. However, less evidence exists for the Low-Glycemic Index Diet and the 2:1 KD. This retrospective single-center real-life study aims to evaluate the efficacy of a 2:1 ketogenic diet and a Low-Glycemic-index Diet in chronic and high-frequency episodic migraine. Methods: Sixty patients with high-frequency episodic and chronic migraine were treated with either a Low-Glycemic-index diet (39 patients) or a 2:1 (21 patients) ketogenic diet for three months. We collected data on the migraine frequency and intensity and the MIDAS and HIT-6 scores through the headache diary. Anthropometric measurements (BMI, fat mass, free fat mass, and weight) were also collected and analyzed similarly. Data obtained at the baseline and after three months of each diet were compared. Results: Migraine intensity, frequency, MIDAS and HIT-6 scores, fat mass, weight, and BMI improved in both diet groups. Conclusions: Both diets are effective in reducing migraine symptoms and migraine-related disability

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

Effects of Transmitters and Amyloid-Beta Peptide on Calcium Signals in Rat Cortical Astrocytes: Fura-2AM Measurements and Stochastic Model Simulations

BACKGROUND: To better understand the complex molecular level interactions seen in the pathogenesis of Alzheimer's disease, the results of the wet-lab and clinical studies can be complemented by mathematical models. Astrocytes are known to become reactive in Alzheimer's disease and their ionic equilibrium can be disturbed by interaction of the released and accumulated transmitters, such as serotonin, and peptides, including amyloid- peptides (A). We have here studied the effects of small amounts of A25-35 fragments on the transmitter-induced calcium signals in astrocytes by Fura-2AM fluorescence measurements and running simulations of the detected calcium signals. METHODOLOGY/PRINCIPAL FINDINGS: Intracellular calcium signals were measured in cultured rat cortical astrocytes following additions of serotonin and glutamate, or either of these transmitters together with A25-35. A25-35 increased the number of astrocytes responding to glutamate and exceedingly increased the magnitude of the serotonin-induced calcium signals. In addition to A25-35-induced effects, the contribution of intracellular calcium stores to calcium signaling was tested. When using higher stimulus frequency, the subsequent calcium peaks after the initial peak were of lower amplitude. This may indicate inadequate filling of the intracellular calcium stores between the stimuli. In order to reproduce the experimental findings, a stochastic computational model was introduced. The model takes into account the major mechanisms known to be involved in calcium signaling in astrocytes. Model simulations confirm the principal experimental findings and show the variability typical for experimental measurements. CONCLUSIONS/SIGNIFICANCE: Nanomolar A25-35 alone does not cause persistent change in the basal level of calcium in astrocytes. However, even small amounts of A25-35, together with transmitters, can have substantial synergistic effects on intracellular calcium signals. Computational modeling further helps in understanding the mechanisms associated with intracellular calcium oscillations. Modeling the mechanisms is important, as astrocytes have an essential role in regulating the neuronal microenvironment of the central nervous system

Global Chronic Total Occlusion Crossing Algorithm: JACC State-of-the-Art Review

The authors developed a global chronic total occlusion crossing algorithm following 10 steps: 1) dual angiography; 2) careful angiographic review focusing on proximal cap morphology, occlusion segment, distal vessel quality, and collateral circulation; 3) approaching proximal cap ambiguity using intravascular ultrasound, retrograde, and move-the-cap techniques; 4) approaching poor distal vessel quality using the retrograde approach and bifurcation at the distal cap by use of a dual-lumen catheter and intravascular ultrasound; 5) feasibility of retrograde crossing through grafts and septal and epicardial collateral vessels; 6) antegrade wiring strategies; 7) retrograde approach; 8) changing strategy when failing to achieve progress; 9) considering performing an investment procedure if crossing attempts fail; and 10) stopping when reaching high radiation or contrast dose or in case of long procedural time, occurrence of a serious complication, operator and patient fatigue, or lack of expertise or equipment. This algorithm can improve outcomes and expand discussion, research, and collaboration