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- ItemStatistical inference on the local dependence condition of extreme values in a stationary sequence(Springer, 2025-07-28) Holešovský, Jan; Fusek, MichalThe extremal index is an important characteristic measuring dependence of extreme values in a stationary series. Several new estimators that are mostly based on interexceedance times within the Peaks-over-Threshold model have been recently published. Nevertheless, in many cases these estimators rely on suitable choice of auxiliary parameters and/or are derived under assumptions that are related to validity of the local dependence condition $D^{(k)}(u_n)$. Although the determination of the correct order $k$ in the $D^{(k)}(u_n)$ condition can have major effect on the extremal index estimates, there are not many reliable methods available for this task. In this paper, we present various approaches to assessing validity of the $D^{(k)}(u_n)$ condition including a graphical diagnostics and propose several statistical tests. A simulation study is carried out to determine performance of the statistical tests, particularly the type I and type II errors.
- ItemExistence results for non-coercive problems(De Gruyter, 2025-01-01) Diblík, Josef; Galewski, Marek; Šmarda, ZdeněkIn this article, we investigate non-coercive variational equations under assumptions related to generalized monotonicity. We present some general abstract tools regarding the existence of bounded solutions and their multiplicity, which we then apply to the Dirichlet boundary value problem driven by the perturbed (negative) p p -Laplacian. As a by-product of our findings, we provide a version of the Browder-Minty theorem in the potential case that does not involve the Brouwer fixed-point theorem but utilizes optimization techniques.
- ItemStatic solutions for Choquard equations with Coulomb potential and upper critical growth(Springer Nature, 2025-06-02) Chen, Sitong; Radulescu, Vicentiu; Shu, Muhua; Wei, JiuyangThis paper focuses on static solutions for the following Choquard equation with zero mass and Coulomb potential (Formula presented.) where >0, 1870 when 4Const. when 3
- ItemRegularity for a class of degenerate fully nonlinear nonlocal elliptic equations(Springer Nature, 2025-06-06) Fang, Yuzhou; Radulescu, Vicentiu; Zhang, ChaoWe consider a wide class of fully nonlinear integro-differential equations that degenerate when the gradient of the solution vanishes. By using compactness and perturbation arguments, we give a complete characterization of the regularity of viscosity solutions according to different diffusion orders. More precisely, when the order of the fractional diffusion is sufficiently close to 2, we obtain Hölder continuity for the gradient of any viscosity solutions and further derive an improved gradient regularity estimate at the origin. For the order of the fractional diffusion in the interval (1, 2), we prove that there is at least one solution of class Cloc1,. Additionally, if the order of the fractional diffusion is in the interval (0, 1], the local Hölder continuity of solutions is inferred.
- ItemToward a Tailored Acoustic-Based Approach in Music Neuromodulation in Epilepsy(Wiley, 2025-07-05) Strýček, Ondřej; Mekyska, Jiří; Miklánek, Štěpán; Fusek, Michal; Štillová, Klára; Mazánek, Martin; Rektor, IvanBackground Music-based neuromodulation has garnered interest as a potential therapeutic approach for drug-resistant epilepsy. This study expands on prior research by examining the effects of different musical features on interictal epileptiform discharges (IEDs) within intracerebral EEG (iEEG). Methods Twenty-five patients with drug-resistant epilepsy undergoing presurgical iEEG evaluation participated in the study. Over 2days, patients listened to various musical compositions characterized by distinct acoustic properties. EEG measurements were recorded before and after each listening session to evaluate IED changes. Results The study identified individualized patterns in IED reduction, with certain acoustic properties showing consistent effects across musical genres. Mozart's “Piano Concerto No. 27” K 595c globally reduced IEDs by 28% while listening to music (p=0.0191) and 19% in the postmusic resting state (p=0.0111); relaxation music increased IEDs by 55% (p=0.0197). Based on the acoustic analysis of individuals, we identified compositions that significantly reduced IEDs, with reductions ranging from 32% to 44% (p=0.0001). In contrast, compositions with differing acoustic properties did not result in significant changes in IEDs. These results suggest that specific acoustic properties, rather than genre, primarily influence IEDs. Conclusions The findings suggest that specific acoustic properties can influence brain activity in a reproducible manner at the individual level, modulating IEDs based on personalized testing and selection across a spectrum of musical genres. These results suggest the potential for music-based neuromodulation as a personalized therapeutic approach in epilepsy management, emphasizing the importance of acoustic features over musical genre. Further research is needed to explore individual aspects of music-based interventions.