Equivalent forms of Dirac equations in curved spacetimes and generalized de Broglie relations

One may ask whether the relations between energy and frequency and between momentum and wave vector, introduced for matter waves by de Broglie, are rigorously valid in the presence of gravity. In this paper, we show this to be true for Dirac equations in a background of gravitational and electromagnetic fields. We first transform any Dirac equation into an equivalent canonical form, sometimes used in particular cases to solve Dirac equations in a curved spacetime. This canonical form is needed to apply the Whitham Lagrangian method. The latter method, unlike the WKB method, places no restriction on the magnitude of Planck's constant to obtain wave packets, and furthermore preserves the symmetries of the Dirac Lagrangian. We show using canonical Dirac fields in a curved spacetime, that the probability current has a Gordon decomposition into a convection current and a spin current, and that the spin current vanishes in the Whitham approximation, which explains the negligible effect of spin on wave packet solutions, independent of the size of Planck's constant. We further discuss the classical-quantum correspondence in a curved spacetime based on both Lagrangian and Hamiltonian formulations of the Whitham equations. We show that the generalized de Broglie relations in a curved spacetime are a direct consequence of Whitham's Lagrangian method, and not just a physical hypothesis as introduced by Einstein and de Broglie, and by many quantum mechanics textbooks.Comment: PDF, 32 pages in referee format. Added significant material on canonical forms of Dirac equations. Simplified Theorem 1 for normal Dirac equations. Added section on Gordon decomposition of the probability current. Encapsulated main results in the statement of Theorem

The relativistic Sagnac Effect: two derivations

The phase shift due to the Sagnac Effect, for relativistic matter and electromagnetic beams, counter-propagating in a rotating interferometer, is deduced using two different approaches. From one hand, we show that the relativistic law of velocity addition leads to the well known Sagnac time difference, which is the same independently of the physical nature of the interfering beams, evidencing in this way the universality of the effect. Another derivation is based on a formal analogy with the phase shift induced by the magnetic potential for charged particles travelling in a region where a constant vector potential is present: this is the so called Aharonov-Bohm effect. Both derivations are carried out in a fully relativistic context, using a suitable 1+3 splitting that allows us to recognize and define the space where electromagnetic and matter waves propagate: this is an extended 3-space, which we call "relative space". It is recognized as the only space having an actual physical meaning from an operational point of view, and it is identified as the 'physical space of the rotating platform': the geometry of this space turns out to be non Euclidean, according to Einstein's early intuition.Comment: 49 pages, LaTeX, 3 EPS figures. Revised (final) version, minor corrections; to appear in "Relativity in Rotating Frames", ed. G. Rizzi and M.L. Ruggiero, Kluwer Academic Publishers, Dordrecht, (2003). See also http://digilander.libero.it/solciclo

Examining Landscape Factors Influencing Relative Distribution of Mosquito Genera and Frequency of Virus Infection

Mosquito-borne infections cause some of the most debilitating human diseases, including yellow fever and malaria, yet we lack an understanding of how disease risk scales with human-driven habitat changes. We present an approach to study variation in mosquito distribution and concomitant viral infections on the landscape level. In a pilot study we analyzed mosquito distribution along a 10-km transect of a West African rainforest area, which included primary forest, secondary forest, plantations, and human settlements. Variation was observed in the abundance of Anopheles, Aedes,Culex, and Uranotaenia mosquitoes between the different habitat types. Screening of trapped mosquitoes from the different habitats led to the isolation of five uncharacterized viruses of the families Bunyaviridae, Coronaviridae, Flaviviridae, and Rhabdoviridae, as well as an unclassified virus. Polymerase chain reaction screening for these five viruses in individual mosquitoes indicated a trend toward infection with specific viruses in specific mosquito genera that differed by habitat. Based on these initial analyses, we believe that further work is indicated to investigate the impact of anthropogenic landscape changes on mosquito distribution and accompanying arbovirus infection

Primary biliary cirrhosis

Primary biliary cirrhosis (PBC) is an immune-mediated chronic cholestatic liver disease with a slowly progressive course. Without treatment, most patients eventually develop fibrosis and cirrhosis of the liver and may need liver transplantation in the late stage of disease. PBC primarily affects women (female preponderance 9–10:1) with a prevalence of up to 1 in 1,000 women over 40 years of age. Common symptoms of the disease are fatigue and pruritus, but most patients are asymptomatic at first presentation. The diagnosis is based on sustained elevation of serum markers of cholestasis, i.e., alkaline phosphatase and gamma-glutamyl transferase, and the presence of serum antimitochondrial antibodies directed against the E2 subunit of the pyruvate dehydrogenase complex. Histologically, PBC is characterized by florid bile duct lesions with damage to biliary epithelial cells, an often dense portal inflammatory infiltrate and progressive loss of small intrahepatic bile ducts. Although the insight into pathogenetic aspects of PBC has grown enormously during the recent decade and numerous genetic, environmental, and infectious factors have been disclosed which may contribute to the development of PBC, the precise pathogenesis remains enigmatic. Ursodeoxycholic acid (UDCA) is currently the only FDA-approved medical treatment for PBC. When administered at adequate doses of 13–15 mg/kg/day, up to two out of three patients with PBC may have a normal life expectancy without additional therapeutic measures. The mode of action of UDCA is still under discussion, but stimulation of impaired hepatocellular and cholangiocellular secretion, detoxification of bile, and antiapoptotic effects may represent key mechanisms. One out of three patients does not adequately respond to UDCA therapy and may need additional medical therapy and/or liver transplantation. This review summarizes current knowledge on the clinical, diagnostic, pathogenetic, and therapeutic aspects of PBC

International Consensus Statement on Rhinology and Allergy: Rhinosinusitis

Background: The 5 years since the publication of the first International Consensus Statement on Allergy and Rhinology: Rhinosinusitis (ICAR‐RS) has witnessed foundational progress in our understanding and treatment of rhinologic disease. These advances are reflected within the more than 40 new topics covered within the ICAR‐RS‐2021 as well as updates to the original 140 topics. This executive summary consolidates the evidence‐based findings of the document. Methods: ICAR‐RS presents over 180 topics in the forms of evidence‐based reviews with recommendations (EBRRs), evidence‐based reviews, and literature reviews. The highest grade structured recommendations of the EBRR sections are summarized in this executive summary. Results: ICAR‐RS‐2021 covers 22 topics regarding the medical management of RS, which are grade A/B and are presented in the executive summary. Additionally, 4 topics regarding the surgical management of RS are grade A/B and are presented in the executive summary. Finally, a comprehensive evidence‐based management algorithm is provided. Conclusion: This ICAR‐RS‐2021 executive summary provides a compilation of the evidence‐based recommendations for medical and surgical treatment of the most common forms of RS

Internal guide RNA interactions interfere with Cas9-mediated cleavage

The CRISPR/Cas system uses guide RNAs (gRNAs) to direct sequence-specific DNA cleavage. Not every gRNA elicits cleavage and the mechanisms that govern gRNA activity have not been resolved. Low activity could result from either failure to form a functional Cas9–gRNA complex or inability to recognize targets in vivo. Here we show that both phenomena influence Cas9 activity by comparing mutagenesis rates in zebrafish embryos with in vitro cleavage assays. In vivo, our results suggest that genomic factors such as CTCF inhibit mutagenesis. Comparing near-identical gRNA sequences with different in vitro activities reveals that internal gRNA interactions reduce cleavage. Even though gRNAs containing these structures do not yield cleavage-competent complexes, they can compete with active gRNAs for binding to Cas9. These results reveal that both genomic context and internal gRNA interactions can interfere with Cas9-mediated cleavage and illuminate previously uncharacterized features of Cas9–gRNA complex formation