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The aim of this paper is to introduce the notion of (α,β)-Zb-Geraghty type contraction via b-simulation function and use this contraction to establish a common fixed point theorem for a pair of self-mappings in the context of a b-metric-like space. Our result extends and generalizes the result of Matthews [21], Khojasteh et al. [20], Demma et al. [15], Chandok [12] and some others also. We deduce some corollaries from our main result and provide examples to illustrate our results. Moreover, we apply our result to obtain a solution of second order differential equation. [ABSTRACT FROM AUTHOR]

Background: Migraine has been associated with functional brain changes including altered connectivity and activity both during and between headache attacks. Recent studies established that the variability of the blood-oxygen-level-dependent (BOLD) signal is an important attribute of brain activity, which has so far been understudied in migraine. In this study, we investigate how time-varying measures of BOLD variability change interictally in episodic migraine patients., Methods: Two independent resting state functional MRI datasets acquired on 3T (discovery cohort) and 1.5T MRI scanners (replication cohort) including 99 episodic migraine patients (n 3T  = 42, n 1.5T =57) and 78 healthy controls (n 3T  = 46, n 1.5T =32) were analyzed in this cross-sectional study. A framework using time-varying measures of BOLD variability was applied to derive BOLD variability states. Descriptors of BOLD variability states such as dwell time and fractional occupancy were calculated, then compared between migraine patients and healthy controls using Mann-Whitney U-tests. Spearman's rank correlation was calculated to test associations with clinical parameters., Results: Resting-state activity was characterized by states of high and low BOLD signal variability. Migraine patients in the discovery cohort spent more time in the low variability state (mean dwell time: p = 0.014, median dwell time: p = 0.022, maximum dwell time: p = 0.013, fractional occupancy: p = 0.013) and less time in the high variability state (mean dwell time: p = 0.021, median dwell time: p = 0.021, maximum dwell time: p = 0.025, fractional occupancy: p = 0.013). Higher uptime of the low variability state was associated with greater disability as measured by MIDAS scores (maximum dwell time: R = 0.45, p = 0.007; fractional occupancy: R = 0.36, p = 0.035). Similar results were observed in the replication cohort., Conclusion: Episodic migraine patients spend more time in a state of low BOLD variability during rest in headache-free periods, which is associated with greater disability. BOLD variability states show potential as a replicable functional imaging marker in episodic migraine., (© 2024. The Author(s).)

Visual dysfunction is a recognized early symptom of Parkinson's disease (PD) that partly scales motor symptoms, yet its background is heterogeneous. With additional deficits in visuospatial attention, the two systems are hard to disentangle and it is not known whether impaired functional connectivity in the visual cortex is translative in nature or disrupted attentional modulation also contributes. In this study, we investigate functional connectivity modulation during a visuospatial attention task in patients with PD. In total, 15 PD and 16 age-matched healthy controls performed a visuospatial attention task while undergoing fMRI, in addition to a resting-state fMRI scan. Tensorial independent component analysis was used to investigate task-related network activity patterns. Independently, an atlas-based connectivity modulation analysis was performed using the task potency method. Spearman's rank correlation was calculated between task-related network expression, connectivity modulation, and clinical characteristics. Task-related networks including mostly visual, parietal, and prefrontal cortices were expressed to a significantly lesser degree in patients with PD ( p < 0.027). Resting-state functional connectivity did not differ between the healthy and diseased cohorts. Connectivity between the precuneus and ventromedial prefrontal cortex was modulated to a higher degree in patients with PD ( p < 0.004), while connections between the posterior parietal cortex and primary visual cortex, and also the superior frontal gyrus and opercular cortex were modulated to a lesser degree ( p < 0.001 and p < 0.011). Task-related network expression and superior frontal gyrus-opercular cortex connectivity modulation were significantly associated with UPDRSIII motor scores and the Hoehn-Yahr stages ( R = -0.72, p < 0.006 and R = -0.90, p < 0.001; R = -0.68, p < 0.01 and R = -0.71, p < 0.007). Task-related networks function differently in patients with PD in association with motor symptoms, whereas impaired modulation of visual and default-mode network connectivity was not correlated with motor function., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Veréb, Kovács, Antal, Kocsis, Szabó, Kincses, Bozsik, Faragó, Tóth, Király, Klivényi, Zádori and Kincses.)