Maxwell equations in matrix form, squaring procedure, separating the variables, and structure of electromagnetic solutions

The Riemann -- Silberstein -- Majorana -- Oppenheimer approach to the Maxwell electrodynamics in vacuum is investigated within the matrix formalism. The matrix form of electrodynamics includes three real 4 \times 4 matrices. Within the squaring procedure we construct four formal solutions of the Maxwell equations on the base of scalar Klein -- Fock -- Gordon solutions. The problem of separating physical electromagnetic waves in the linear space \lambda_{0}\Psi^{0}+\lambda_{1}\Psi^{1}+\lambda_{2}\Psi^{2}+ lambda_{3}\Psi^{3} is investigated, several particular cases, plane waves and cylindrical waves, are considered in detail.Comment: 26 pages 16 International Seminar NCPC, May 19-22, 2009, Minsk, Belaru

On the density of periodic configurations in strongly irreducible subshifts

Let $G$ be a residually finite group and let $A$ be a finite set. We prove that if $X \subset A^G$ is a strongly irreducible subshift of finite type containing a periodic configuration then periodic configurations are dense in $X$. The density of periodic configurations implies in particular that every injective endomorphism of $X$ is surjective and that the group of automorphisms of $X$ is residually finite. We also introduce a class of subshifts $X \subset A^\Z$, including all strongly irreducible subshifts and all irreducible sofic subshifts, in which periodic configurations are dense

Generalized Gravi-Electromagnetism

A self consistant and manifestly covariant theory for the dynamics of four charges (masses) (namely electric, magnetic, gravitational, Heavisidian) has been developed in simple, compact and consistent manner. Starting with an invariant Lagrangian density and its quaternionic representation, we have obtained the consistent field equation for the dynamics of four charges. It has been shown that the present reformulation reproduces the dynamics of individual charges (masses) in the absence of other charge (masses) as well as the generalized theory of dyons (gravito - dyons) in the absence gravito - dyons (dyons). key words: dyons, gravito - dyons, quaternion PACS NO: 14.80H

A note on a local ergodic theorem for an infinite tower of coverings

This is a note on a local ergodic theorem for a symmetric exclusion process defined on an infinite tower of coverings, which is associated with a finitely generated residually finite amenable group.Comment: Final version to appear in Springer Proceedings in Mathematics and Statistic

Droplet digital PCR assay as an innovative and promising highly sensitive assay to unveil residual and cryptic HBV replication in peripheral compartment

: Droplet digital PCR is an innovative and promising approach for highly sensitive quantification of nucleic acids that is being increasingly used in the field of clinical virology, including the setting of hepatitis B virus (HBV). Here, we comprehensively report a robust and reproducible ddPCR assay for the highly sensitive quantification of serum HBV-DNA. The assay showed a limit of detection of 4 copies/ml (<1IU/ml) by Probit analysis, showed a good linearity (R2 = 0.94) and a high intra- and inter-run reproducibility with differences between the values obtained in the same run or in two independent runs never exceeding 0.14logcopies/mL and 0.21logcopies/mL, respectively. By analysing serum samples from chronically HBV infected patients (mostly under antiviral treatment), ddPCR successfully quantified serum HBV-DNA in 89.8% of patients with detectable serum HBV-DNA < 20 IU/mL [equivalent to <112copies/ml] by classical Real-Time PCR assay, with a median (IQR) of 8(5-14)IU/mL [45(28-78)copies/ml], and in 66.7% of patients with undetectable serum HBV-DNA, with a median (IQR) of 5(4-9)IU/mL [28(20-50)copies/ml]. Similarly, by analysing serum samples from patients with a serological profile compatible with occult HBV infection (anti-HBc+/HBsAg-), ddPCR successfully quantified serum HBV-DNA in 40% of patients with a median (IQR) value of 1(1-2)IU/mL [5(5-11)copies/ml], in line with the extremely limited viral replication typically observed in occult HBV infection. Overall, the availability of assays for the highly sensitive quantification of serum HBV-DNA can provide an added value in optimizing the diagnosis of occult hepatitis B infection, improving the therapeutic management of chronically HBV infected patients, also in the light of innovative drugs (upcoming in clinical practise) aimed at achieving HBV functional cure

Favorable outcome of early treatment of new onset child and adolescent migraine-implications for disease modification.

There is evidence that the prevalence of migraine in children and adolescents may be increasing. Current theories of migraine pathophysiology in adults suggest activation of central cortical and brainstem pathways in conjunction with the peripheral trigeminovascular system, which ultimately results in release of neuropeptides, facilitation of central pain pathways, neurogenic inflammation surrounding peripheral vessels, and vasodilatation. Although several risk factors for frequent episodic, chronic, and refractory migraine have been identified, the causes of migraine progression are not known. Migraine pathophysiology has not been fully evaluated in children. In this review, we will first discuss the evidence that early therapeutic interventions in the child or adolescent new onset migraineur, may halt or limit progression and disability. We will then review the evidence suggesting that many adults with chronic or refractory migraine developed their migraine as children or adolescents and may not have been treated adequately with migraine-specific therapy. Finally, we will show that early, appropriate and optimal treatment of migraine during childhood and adolescence may result in disease modification and prevent progression of this disease

Quaternion Analysis for Generalized Electromagnetic Fields of Dyons in Isotropic Medium

Quaternion analysis of time dependent Maxwell's equations in presence of electric and magnetic charges has been developed and the solutions for the classical problem of moving charges (electric and magnetic) are obtained in unique, simple and consistent manner

Spherical harmonic decomposition applied to spatial-temporal analysis of human high-density EEG

We demonstrate an application of spherical harmonic decomposition to analysis of the human electroencephalogram (EEG). We implement two methods and discuss issues specific to analysis of hemispherical, irregularly sampled data. Performance of the methods and spatial sampling requirements are quantified using simulated data. The analysis is applied to experimental EEG data, confirming earlier reports of an approximate frequency-wavenumber relationship in some bands.Comment: 12 pages, 8 figures, submitted to Phys. Rev. E, uses APS RevTeX style

SARS-CoV-2 variants and their relevant mutational profiles: update summer 2021

: Since the beginning of the coronavirus disease 2019 (COVID-19) pandemic caused by it, severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has been undergoing a genetic diversification leading to the emergence of new variants. Nevertheless, a clear definition of the genetic signatures underlying the circulating variants is still missing. Here, we provide a comprehensive insight into mutational profiles characterizing each SARS-CoV-2 variant, focusing on spike mutations known to modulate viral infectivity and/or antigenicity. We focused on variants and on specific relevant mutations reported by GISAID, Nextstrain, Outbreak.info, Pango, and Stanford database websites that were associated with any clinical/diagnostic impact, according to published manuscripts. Furthermore, 1,223,338 full-length high-quality SARS-CoV-2 genome sequences were retrieved from GISAID and used to accurately define the specific mutational patterns in each variant. Finally, mutations were mapped on the three-dimensional structure of the SARS-CoV-2 spike protein to assess their localization in the different spike domains. Overall, this review sheds light and assists in defining the genetic signatures characterizing the currently circulating variants and their clinical relevance. IMPORTANCE Since the emergence of SARS-CoV-2, several recurrent mutations, particularly in the spike protein, arose during human-to-human transmission or spillover events between humans and animals, generating distinct worrisome variants of concern (VOCs) or of interest (VOIs), designated as such due to their clinical and diagnostic impacts. Characterizing these variants and their related mutations is important in tracking SAR-CoV-2 evolution and understanding the efficacy of vaccines and therapeutics based on monoclonal antibodies, convalescent-phase sera, and direct antivirals. Our study provides a comprehensive survey of the mutational profiles characterizing the important SARS-CoV-2 variants, focusing on spike mutations and highlighting other protein mutations