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

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

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

Reclassification of CTO Crossing Strategies in the ERCTO Registry According to the CTO-ARC Consensus Recommendations

Background: The CTO-ARC (Chronic Total Occlusion Academic Research Consortium) recognized that a nonstandardized definition of chronic total occlusion (CTO) percutaneous coronary intervention approaches can bias the complications' attribution to each crossing strategy. Objectives: The study sought to describe the numbers, efficacy, and safety of each final CTO crossing strategy according to CTO-ARC recommendations. Methods: In this cross-sectional study, data were retrieved from the European Registry of Chronic Total Occlusions between 2021 and&nbsp;2022. Results: Out of 8,673 patients, antegrade and retrograde approach were performed in 79.2% and 20.8% of cases, respectively. The antegrade approach included antegrade wiring and antegrade dissection and re-entry, both performed with or without retrograde contribution (antegrade wiring without retrograde contribution: n = 5,929 [68.4%]; antegrade wiring with retrograde contribution: n&nbsp;=&nbsp;446 [5.1%]; antegrade dissection and re-entry without retrograde contribution: n&nbsp;=&nbsp;353 [4.1%]; antegrade dissection and re-entry with retrograde contribution: n&nbsp;=&nbsp;137 [1.6%]). The retrograde approach included retrograde wiring (n&nbsp;=&nbsp;735 [8.4%]) and retrograde dissection and re-entry (n&nbsp;=&nbsp;1,073 [12.4%]). Alternative antegrade crossing was associated with lower technical success (70% vs 86% vs 93.1%, respectively; P &lt; 0.001) and higher complication rates (4.6% vs 2.9% vs 1%, respectively; P &lt; 0.001) as compared with retrograde and true antegrade crossing. However, alternative antegrade crossing was applied mostly as a rescue strategy (96.1%). Conclusions: The application of CTO-ARC definitions allowed the reclassification of 6.7% of procedures as alternative antegrade crossing with retrograde or antegrade contribution which showed higher MACCE and lower technical success rates, as compared with true antegrade and retrograde crossing

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

Procedural Impact of Advanced Calcific Plaque Modification Devices Within Percutaneous Revascularization of Chronic Total Occlusions.

Background: Significant calcifications within a coronary chronic total occlusion (CTO) increase procedural complexity and the risk for complications. Expert consensus documents recommend the use of advanced calcific plaque modification devices (ACPMDs) for calcified CTO percutaneous coronary intervention (PCI), whereas data on their procedural impact are limited. Objectives: The aim of this study was to describe trends, settings, and outcomes of PCI of severely calcified CTO performed with and without ACPMDs. Methods: Data from 15,329 CTO PCIs enrolled in the ERCTO (European Registry of Chronic Total Occlusion) between 2021 and 2023 were analyzed. On the basis of the presence of severe calcifications within the CTO, the study population was divided into 2 groups: nonsevere (n = 12,289) and severe (n = 3,040) calcium. Then, the severe group was divided into non-ACPMD (n = 2,253) and ACPMD (n = 787), according to the use of ACPMDs. Results: Compared with the non-ACPMD group, the ACPMD group had higher rates of antegrade wiring (77.9% vs 49.2%; P &lt; 0.001) and technical success (97.6% vs 79.1%; P = 0.001) and lower rates of periprocedural and in-hospital major adverse cardiac and cerebrovascular events (MACCE) (1.8% vs 3.5%; P = 0.001). A severe amount of calcium was independently associated with technical failure (OR: 3.13; 95% CI: 2.43-4.09; P &lt; 0.001) but not with MACCE (OR: 0.88; 95% CI: 0.58-1.35; P = 0.15). Furthermore, extraplaque crossing was independently associated with MACCE (antegrade dissection and re-entry without retrograde contribution: OR: 3.12; 95% CI: 1.79-4.20; P &lt; 0.001; antegrade dissection and re-entry with retrograde contribution: OR: 3.12; 95% CI: 1.67-4.11; P = 0.049; retrograde dissection and re-entry: OR: 1.90; 95% CI: 1.25-2.86; P = 0.002). Conclusions: Applying ACPMDs in severely calcified CTO to PCI was associated with higher technical success and lower MACCE rates. The presence of severe coronary calcification on coronary angiography was a marker of clinical and procedural complexity and was associated with technical failure but not with MACCE