COVID-19 is a respiratory illness caused by an RNA virus prone to mutations. In December 2020, variants with different characteristics that could affect transmissibility emerged around the world. To address this new dynamic of the disease, we formulate and analyze a mathematical model of a two-strain COVID- 19 transmission dynamics with strain 1 vaccination. The model is theoretically analyzed and sufficient conditions for the stability of its equilibria are derived. In addition to the disease-free and endemic equilibria, the model also has single-strain 1 and strain 2 endemic equilibria. Using the center manifold theory, it is shown that the model does not exhibit the phenomenon of backward bifurcation, and global stability of the model equilibria when the basic reproduction number R 0 is either less or greater than unity as the case maybe are proved using various approaches. Simulations to support the model theoretical results are provided. We calculate the basic reproductive number for both strains R 1 and R 2 independently. Results indicate that - both strains will persist when R 1 > 1 and R 2 > 1 - Stain 2 could establish itself as the dominant strain if R 1 < 1 and R 2 > 1, or when R 2 is at least two times greater than R 1 . However, with the current knowledge of the epidemiology of the COVID-19 pandemic and the availability of treatment and an effective vaccine against strain 1, it is expected that eventually, strain 2 will likely be eradicated in the population due to de novo herd immunity provided the threshold parameter R 2 is controlled to remain below unity.
￼￼￼￼￼￼￼The free propagation in time of a normalisable wave packet is the oldest problem of continuum quantum mechanics. Its motion from microscopic to macroscopic distance is the way in which most quantum systems are detected experimentally. Although much studied and analysed since 1927 and presented in many text books, here the problem is re-appraised from the standpoint of semi-classical mechanics. Particular aspects are the emergence of deterministic trajectories of particles emanating from a region of atomic dimensions and the interpretation of the wave function as describing a single particle or an ensemble of identical particles. Of possible wave packets, that of gaussian form is most studied due to the simple exact form of the time-dependent solution in real and in momentum space. Furthermore, this form is important in laser optics. Here the equivalence of the time-dependent Schroedinger equation to the paraxial equation for the propagation of light is demonstrated explicitly. This parallel helps to understand the relevance of trajectory concepts and the conditions necessary for the perception of motion as classical.
Objective To document longitudinal changes in brain development in fetuses with congenital diaphragmatic hernia (CDH). Design Retrospective cohort study Setting Single tertiary fetal surgery center Population Fetuses with isolated CDH and at least two MRI-examinations (n=42 fetuses). Fifty-six fetuses who underwent MRI for a condition not interfering with fetal brain development or fetuses from healthy volunteers served as controls. Methods Biometry included biparietal and fronto-occipital diameter, ventricular atrial width, transcerebellar diameter, head circumference and width of the extra-axial space. Cortical maturation was assessed using a qualitative and quantitative grading system. 3D volumes were segmented for white matter, intra-axial and extra-axial cerebrospinal fluid and cerebellum. Main outcome measures Brain development on MRI with subjective and objective assessment. Results The mean GA at first MRI was 28.0 ± 2.1 wks and at the second 33.2 ± 1.3 wks. The mean GA in controls was 30.7 ± 4.2 wks. At 28 weeks CDH fetuses displayed abnormal maturation grading (p<0.003) and fissure depth (p<0.05). By 33 wks, the brain grading indices were still abnormal (p<0.01), but fissure depth measurements were in the normal range (p>0.05). Also, the extra-axial fluid and the ventricular volume were increased (resp. p 0.0054 and p 0.0243). There was no difference in white matter or cerebellum volume (p>0.05). Conclusions Brain development in CDH fetuses around 28 weeks appears to be delayed. This is less prominent at 33 weeks. In addition, there was an increase in ventricular and extra-axial space volume in the third trimester.
Using whole genome shotgun sequences from 92 white-tailed eagles (Haliaeetus albicilla) sampled from Greenland, Iceland, Norway, Denmark, Estonia, and Turkey between 1885-1950 and after 1990, we investigate the genomic variation within countries over time, and between countries. Clear genetic differentiation is observed between samples from the different countries, with the largest differences between the island and mainland populations, and indications that the island populations share the most recent ancestry with the Norwegian population. We find signs of strong inbreeding in the island populations. Further, temporal differences are observed in some populations, for example, replacement of the Danish gene pool following its population’s extinction in the early 20th century, as well as a change in the genetic diversity of the Icelandic population following a severe bottleneck during the last century, all of which could warrant a further conservation effort in Iceland. More generally, all populations show a decline in effective population size, which may have been shaped by I) distinct refugia during the last glacial period, II) population divergence following the colonization of the deglaciated areas ~10,000 years ago, III) human population expansion and e.g., settlement in Iceland ~1,100 years ago, and IV) human persecution and toxic pollutants during the last two centuries.
Background Since the introduction of the E-Vita Open NEO aortic prosthesis in 2020, several incidences of post-anastomotic oozing from the polyester portion of the graft have emerged. The use of BioGlue to prime E-Vita Open NEO to prevent this has been suggested as a way to mitigate this worrying complication. We investigate the extent of graft oozing in E-Vita Open NEO and evaluate the use of BioGlue in preventing oozing, both experimentally and in terms of potential clinical complications. Methods and materials E-Vita Open NEO (in straight and branched configurations) was implanted in a perfused model. The distal stent-graft and side branches were clamped, and the graft pressurised with blood to 120 mmHg. The volume of blood (ml) oozing from the graft within 60 seconds was measured. Non-pressurised grafts were coated with BioGlue up to a thickness 1-, 2-, and 3 mm, and the volume (mm3) of BioGlue required to do so was recorded. Results Within 60 seconds, 250.0 ml of blood oozed from the grafts tested. 43.694 mm3, 87.389 mm3, and 174.778 mm3 of BioGlue was required to coat the device with 1-, 2-, and 3 mm of BioGlue. Conclusion Graft oozing from E-Vita Open NEO represents an omnipresent and worrying risk. The use of BioGlue herein is likely associated with several adverse consequences, which are an additional risk on top of that posed by graft oozing. These risks call into question the suitability of E-Vita Open NEO, especially when compared to alternative devices not affected by oozing.
There is increasing understanding, globally, that climate change and increased pollution will have a profound and mostly harmful effect on human health. This review brings together international experts to describe both the direct (such as heat waves) and indirect (such as vector-borne disease incidence) impacts of climate change depending on their vulnerability (i.e., diseases) on an international, economic, political and environmental context. This unique review also expands on these issues to address a third category of potential longer-term impacts on global health: famine, population dislocation, and environmental justice and education. This scholarly resource explores these issues fully, linking them to global health in urban and rural settings in developed and developing countries. The review finishes with a practical discussion of action that health professionals around the world in our field can yet take.
In this paper, the fixed-time projective synchronization issue for a class of delayed memristive neural networks is studied via aperiodically intermittent switching control. Firstly, according to the existing aperiodically intermittent switching strategy, a novel theorem for aperiodically intermittent switching fixed-time stability is proposed and proved through mathematical induction. Subsequently, an aperiodically intermittent switching controller is designed to reach fixed-time projective synchronization for drive-response systems. The power exponent is a function of error system state rather than one or two fixed constants. With the help of the extended differential inclusion framework, the inequality technique and the analysis method, some novel sufficient conditions are derived to ensure fixed-time projective synchronization for the considered systems. The settling time is closely related to the number of neurons and the maximum ratio of the rest width to the aperiodic time span, but independent of the initial value conditions. Furthermore, the fixed-time complete synchronization, fixed-time anti-synchronization and fixed-time stability obtained are special cases of the main theorem. Meanwhile, the conclusions of this paper improve some previous relevant works. Finally, a numerical example is given to verify the effectiveness and feasibility of the obtained results
Patients with pleural effusion are mostly presenting with shortness of breath and pleuritic chest pain. This report describes a case of PE who presented with left shoulder pain and was found to have rapidly accumulating massive effusion within 24 hours of presentation. Thoracocentesis was performed a showed an exudative picture
Cardiac myxoma is the most common benign cardiac tumor. Its tremendous size and fragile character severely bother the surgeons. Several minimal invasive approaches had been applied for radical tumor excision. The wound was forcibly enlarged for en-bloc specimen removal and prevention of debris sputtering. We reported a case of huge tricuspid valve (TV) myxoma managed by robot-assisted endoscopic tumor resection and TV repair. The tumor was downsized with a morcellator and removed through a keyhole wound (1.1 cm in diameter). The patient recovered uneventfully and was discharged after four days.
In the era of “fast-track’ liver transplantation (LT), neuromuscular blockade (NMB) antagonists such as neostigmine or sugammadex are used to achieve the restoration of neuromuscular function. While sugammadex reverses NMB faster than neostigmine, it has been shown to prolong prothrombin time (PT) and activated thromboplastin time (aPTT). However, this agent’s impact on coagulation during LT is not understood. We compare bleeding risk associated with sugammadex versus neostigmine during liver transplantation. This is a single-center, retrospective review of LT patients who received NMB antagonists intraoperatively between 01/01/2015 to 05/31/2018 at Mayo Clinic in Florida. The primary outcomes were postoperative day (POD) 0-1 bleeding events and POD 0 values of aPTT and INR. Total 241 patients were included, with 135 patients in the neostigmine group (NG) and 106 in the sugammadex group (SG). POD 0-1 postoperative bleeding requiring transfusion occurred in 20% of NG versus 10.4% in SG. POD 0-1 re-operation for bleeding occurred in 1.5% in NG vs. 0% in SG. POD 0 mean INR was 2.0±0.4 in both groups. POD 0 mean aPTT was 45.5±7.9 in NG vs. 49.3±9.0 in SG. Our retrospective study suggests that sugammadex is not associated with an increased risk of bleeding compared to neostigmine use.
Understanding mathematical topics is important for both educators and students to capture latent concepts of questions, evaluate study performance, and recommend content in online learning systems. Compared to traditional text classification, mathematical topic classification has several main challenges: (1) the length of mathematical questions is relatively short; (2) there are various representations of the same mathematical concept(i.e., calculations and application); (3) the content of question is complex including algebra, geometry, and calculus. In order to overcome these problems, we propose a framework that combines content tokens and mathematical knowledge concepts in whole procedures. We embed entities from mathematics knowledge graphs, integrate entities into tokens in a masked language model, set up semantic similarity-based tasks for next-sentence prediction, and fuse knowledge vectors and token vectors during the fine-tuning procedure. We also build a Chinese mathematical topic prediction dataset consisting of more than 70,000 mathematical questions with topics. Our experiments using real data demonstrate that our knowledge graph-based mathematical topic prediction model outperforms other state-of-the-art methods.
In this paper, we study the existence and nonexistence of nontrivial solutions to the following critical biharmonic problem with the Steklov boundary conditions Δ2=+Δ+||2**-2 in , =Δ+=0 on , where ,, ∈ , ⊂ N( ≥ 5) is a unit ball, 2** = 2/N-4 denotes the critical Sobolev exponent for the embedding 2() →2** () and is the outer normal derivative of on . Under some assumptions on , and , we prove the existence of nontrivial solutions to the above biharmonic problem by the Mountain pass theorem and show the nonexistence of nontrivial solutions to it by the Pohozaev identity.
Environmental DNA (eDNA) analysis is a promising tool for non-disruptive and cost-efficient estimation of species abundance. However, its practical applicability in natural environments is limited because it is unclear whether eDNA concentrations actually represent species abundance in the field. Although the importance of accounting for eDNA dynamics, such as transport and degradation, has been discussed, the influences of eDNA characteristics, including production source and state, and methodology, including collection and quantification strategy and abundance metrics, on the accuracy of eDNA-based abundance estimation were entirely overlooked. We conducted a meta-analysis using 56 previous eDNA literature and investigated the relationships between the accuracy (R2) of eDNA-based abundance estimation and eDNA characteristics and methodology. Our meta-regression analysis found that R2 values were significantly lower for crustaceans than fish, suggesting that less frequent eDNA production owing to their external morphology and physiology may impede accurate estimation of their abundance via eDNA. Moreover, R2 values were positively associated with filter pore size, indicating that selective collection of larger-sized eDNA, which is typically fresher, could improve the estimation accuracy of species abundance. Furthermore, R2 values were significantly lower for natural than laboratory conditions, while there was no difference in the estimation accuracy among natural environments. Our findings shed a new light on the importance of what characteristics of eDNA should be targeted for more accurate estimation of species abundance. Further empirical studies are required to validate our findings and fully elucidate the relationship between eDNA characteristics and eDNA-based abundance estimation.
For the first time we built a correlative model for predicting the distribution of H. marginatum, one of the main vector of Crimean-Congo Haemorrhagic fever virus (CCHFV), at high resolution in a recently colonized area, namely south of France. Field tick collections were conducted on horses from 2016 to 2021 in 14 French southern departments, which resulted in a first map of H. marginatum on the national territory. Such updated presence/absence data, as well as the mean number of H. marginatum per examined animal (mean parasitic load) as a proxy of the tick abundance, were correlated to multiple parameters that described the climate and habitats characterizing each collection site, as well as movements of horses as a possible source of tick diffusion and new establishment. Our model highlighted the importance of warm temperatures all along the year, as well as dry conditions during summer and moderate annual humidity for the establishment of H. marginatum. A predominance of open natural habitats in the environment was also identified as a supporting factor, in opposition to artificial and humid habitats that were determined as unsuitable. Based on this model, we predicted the current suitable areas for the establishment of the tick H. marginatum in South of France, with a relatively good accuracy using internal and external validation methods. Concerning tick abundance, some correlative relationships were similar than in the occurrence model but the type of horse movements were also pointed out as an important factor explaining the mean parasitic load, leading to differential exposure to ticks. The limitations of estimating and modelling H. marginatum abundance in a correlative model are discussed.
This Research Highlight provides context for the report of Gope et al. on experimental and computational probes of the decay of doubly-ionized methanol to H3+ and HCO+/COH+. The formation of the H3+ ionic product is shown to occur through the agency of a roaming H2 molecule generated from the carboxyl moiety that undergoes prompt proton transfer from the carbon atom, or, delayed proton transfer from the oxygen atom. This novel method for H3+ formation is contrasted with the conventional ion-molecule pathway, known for over a century, that forms the basis for interstellar molecule formation.
Is a classical description of nuclear motion sufficient when describing chemical reactions? The present paper investigates some phenomena that were previously attributed to nuclear quantum effects. The aim is to show that these phenomena can be modelled with traditional Car-Parrinello molecular dynamics, that is, with a method which treats nuclear motion classically. We find that no additional paradigm is needed for describing chemical reactions. The special reactivity observed for carbenes can be attributed to the special environment represented by a noble gas matrix. Also the infrared spectrum of porphycene is perfectly modelled by traditional Car-Parrinello molecular dynamics. If no more convincing examples are produced, one will stick to deterministic quantum mechanics, as it is the simpler theory which, in addition, is free of paradoxa.
We present a rare case of an elderly man with degenerated bioprosthetic aortic valve complicated by infectious endocarditis 6 months after Covid-19 infection, who was treated successfully with valve-in valve after antibiotic therapy for the acute phase of infection, with excellent result and no complication early after the procedure and in follow-up visits.