On the solutions of universal differential equation by noncommutative Picard-Vessiot theory

Basing on Picard-Vessiot theory of noncommutative differential equations and algebraic combinatorics on noncommutative formal series with holomorphic coefficients, various recursive constructions of sequences of grouplike series converging to solutions of universal differential equation are proposed. Basing on monoidal factorizations, these constructions intensively use diagonal series and various pairs of bases in duality, in concatenation-shuffle bialgebra and in a Loday's generalized bialgebra. As applications, the unique solution, satisfying asymptotic conditions, of Knizhnik-Zamolodchikov equations is provided by d\'evissage

Families of eulerian functions involved in regularization of divergent polyzetas

Extending the Eulerian functions, we study their relationship with zeta function of several variables. In particular, starting with Weierstrass factorization theorem (and Newton-Girard identity) for the complex Gamma function, we are interested in the ratios of $\zeta(2k)/\pi^{2k}$ and their multiindexed generalization, we will obtain an analogue situation and draw some consequences about a structure of the algebra of polyzetas values, by means of some combinatorics of noncommutative rational series. The same combinatorial frameworks also allow to study the independence of a family of eulerian functions.Comment: preprin

On The Global Renormalization and Regularization of Several Complex Variable Zeta Functions by Computer

This review concerns the resolution of a special case of Knizhnik-Zamolodchikov equations ($KZ_3$) using our recent results on combinatorial aspects of zeta functions on several variables and software on noncommutative symbolic computations. In particular, we describe the actual solution of $(KZ_3)$ leading to the unique noncommutative series, $\Phi_{KZ}$, so-called Drinfel'd associator (or Drinfel'd series). Non-trivial expressions for series with rational coefficients, satisfying the same properties with $\Phi_{KZ}$, are also explicitly provided due to the algebraic structure and the singularity analysis of the polylogarithms and harmonic sums

Sound-Dr: Reliable Sound Dataset and Baseline Artificial Intelligence System for Respiratory Illnesses

As the burden of respiratory diseases continues to fall on society worldwide, this paper proposes a high-quality and reliable dataset of human sounds for studying respiratory illnesses, including pneumonia and COVID-19. It consists of coughing, mouth breathing, and nose breathing sounds together with metadata on related clinical characteristics. We also develop a proof-of-concept system for establishing baselines and benchmarking against multiple datasets, such as Coswara and COUGHVID. Our comprehensive experiments show that the Sound-Dr dataset has richer features, better performance, and is more robust to dataset shifts in various machine learning tasks. It is promising for a wide range of real-time applications on mobile devices. The proposed dataset and system will serve as practical tools to support healthcare professionals in diagnosing respiratory disorders. The dataset and code are publicly available here: https://github.com/ReML-AI/Sound-Dr/.Comment: 9 pages, PHMAP2023, PH

Late recurrence of myopic foveoschisis after successful repair with primary vitrectomy and incomplete membrane peeling

PURPOSE: To report three cases of late recurrence of myopic foveoschisis (MF) after initial successful repair with pars plana vitrectomy and membrane peeling to assess the importance of internal limiting membrane peeling. METHODS: A retrospective noncomparative case series was performed of patients who underwent a primary pars plana vitrectomy by a single surgeon with successful resolution of MF, but eventually underwent repeat pars plana vitrectomy for recurrent MF. Best-corrected visual acuity, fundus photography, and optical coherence tomography were obtained at each examination. RESULTS: Three eyes of three patients underwent pars plana vitrectomy for recurrent MF. Myopic foveoschisis recurrence occurred 6, 3.5, and 12 years after the primary vitrectomy, respectively. Repeat vitrectomy with staining and additional peeling of the internal limiting membrane resulted in good anatomical outcome and stabilization of visual acuity in all cases. CONCLUSION: Late recurrence of MF after successful primary vitrectomy is described. Fibrocellular proliferation on residual cortical vitreous or incomplete internal limiting membrane peeling during the initial vitrectomy may underlie recurrence

Coordinated Container Migration and Base Station Handover in Mobile Edge Computing

Offloading computationally intensive tasks from mobile users (MUs) to a virtualized environment such as containers on a nearby edge server, can significantly reduce processing time and hence end-to-end (E2E) delay. However, when users are mobile, such containers need to be migrated to other edge servers located closer to the MUs to keep the E2E delay low. Meanwhile, the mobility of MUs necessitates handover among base stations in order to keep the wireless connections between MUs and base stations uninterrupted. In this paper, we address the joint problem of container migration and base-station handover by proposing a coordinated migration-handover mechanism, with the objective of achieving low E2E delay and minimizing service interruption. The mechanism determines the optimal destinations and time for migration and handover in a coordinated manner, along with a delta checkpoint technique that we propose. We implement a testbed edge computing system with our proposed coordinated migration-handover mechanism, and evaluate the performance using real-world applications implemented with Docker container (an industry-standard). The results demonstrate that our mechanism achieves 30%-40% lower service downtime and 13%-22% lower E2E delay as compared to other mechanisms. Our work is instrumental in offering smooth user experience in mobile edge computing.Comment: 6 pages. Accepted for presentation at the IEEE Global Communications Conference (Globecom), Taipei, Taiwan, Dec. 202

Effect of polydispersity on the transport and sound absorbing properties of three-dimensional random fibrous structures

Sophisticated numerical approaches can predict the properties of composite nonwovens. However, for polydisperse random fibrous media, we need to identify microstructural descriptors for accurate predictions. We manufactured polydisperse composite felts with different fibrous structures and characterized them using scanning electron microscope images. The images showed a wide distribution of fiber diameters and a decreasing standard deviation of the azimuthal angle of fibers with increasing compression rate. Current models could not capture the evolution of their transport properties with compression rate. Therefore, we developed a fiber network model for the transport processes of transversely isotropic random fibrous media. The model relates the main visco-thermal dissipation mechanisms to the largest channels within the fluid phase, while the smallest channels lead the inertial behaviors. We estimated the viscous and thermal permeabilities from a representative elementary volume (REV) with a volume weighted average diameter, and the viscous and thermal characteristic lengths from a REV with inverse volume weighted average diameter. A unified empirical model was proposed. The model predictions agree with the experimental results.Comment: 29 pages, 19 figure