The emergence of SARS-CoV-2 variants of concern is driven by acceleration of the evolutionary rate

The ongoing SARS-CoV-2 pandemic has seen an unprecedented amount of rapidly generated genome data. These data have revealed the emergence of lineages with mutations associated to transmissibility and antigenicity, known as variants of concern (VOCs). A striking aspect of VOCs is that many of them involve an unusually large number of defining mutations. Current phylogenetic estimates of the evolutionary rate of SARS-CoV-2 suggest that its genome accrues around 2 mutations per month. However, VOCs can have around 15 defining mutations and it is hypothesised that they emerged over the course of a few months, implying that they must have evolved faster for a period of time. We analysed genome sequence data from the GISAID database to assess whether the emergence of VOCs can be attributed to changes in the evolutionary rate of the virus and whether this pattern can be detected at a phylogenetic level using genome data. We fit a range of molecular clock models and assessed their statistical fit. Our analyses indicate that the emergence of VOCs is driven by an episodic increase in the evolutionary rate of around 4-fold the background phylogenetic rate estimate that may have lasted several weeks or months. These results underscore the importance of monitoring the molecular evolution of the virus as a means of understanding the circumstances under which VOCs may emerge.

Newton-type methods near critical solutions of piecewise smooth nonlinear equations

It is well-recognized that in the presence of singular (and in particular nonisolated) solutions of unconstrained or constrained smooth nonlinear equations, the existence of critical solutions has a crucial impact on the behavior of various Newton-type methods. On the one hand, it has been demonstrated that such solutions turn out to be attractors for sequences generated by these methods, for wide domains of starting points, and with a linear convergence rate estimate. On the other hand, the pattern of convergence to such solutions is quite special, and allows for a sharp characterization which serves, in particular, as a basis for some known acceleration techniques, and for the proof of an asymptotic acceptance of the unit stepsize. The latter is an essential property for the success of these techniques when combined with a linesearch strategy for globalization of convergence. This paper aims at extensions of these results to piecewise smooth equations, with applications to corresponding reformulations of nonlinear complementarity problems.

Prevalence of fibrodysplasia ossificans progressiva (FOP) in the United States: estimate from three treatment centers and a patient organization

Background Fibrodysplasia ossificans progressiva (FOP), an ultra-rare, progressive, and permanently disabling disorder of extraskeletal ossification, is characterized by episodic and painful flare-ups and irreversible heterotopic ossification in muscles, tendons, and ligaments. Prevalence estimates have been hindered by the rarity of FOP and the heterogeneity of disease presentation. This study aimed to provide a baseline prevalence of FOP in the United States, based on contact with one of 3 leading treatment centers for FOP (University of Pennsylvania, Mayo Clinic, or University of California San Francisco), the International Fibrodysplasia Ossificans Progressiva Association (IFOPA) membership list, or the IFOPA FOP Registry through July 22, 2020. Results Patient records were reviewed, collected, and deduplicated using first and last name initials, sex, state, and year of birth. A Kaplan–Meier survival curve was applied to each individual patient to estimate the probability that he or she was still alive, and a probability-weighted net prevalence estimate was calculated. After deduplication, 373 unique patients were identified in the United States, 294 of whom who were not listed as deceased in any list. The average time since last contact for 284 patients was 1.5 years. Based on the application of the survival probability, it is estimated that 279 of these patients were alive on the prevalence date (22 July 2020). An adjusted prevalence of 0.88 per million US residents was calculated using either an average survival rate estimate of 98.4% or a conservative survival rate estimate of 92.3% (based on the Kaplan–Meier survival curve from a previous study) and the US Census 2020 estimate of 329,992,681 on prevalence day. Conclusions This study suggests that the prevalence of FOP is higher than the often-cited value of 0.5 per million. Even so, because inclusion in this study was contingent upon treatment by the authors, IFOPA membership with confirmed clinical diagnosis, and the FOP Registry, the prevalence of FOP in the US may be higher than that identified here. Thus, it is imperative that efforts be made to identify and provide expert care for patients with this ultra-rare, significantly debilitating disease.

Thermohaline structure and circulation beneath the Langhovde Glacier ice shelf in East Antarctica

Basal melting of ice shelves is considered to be the principal driver of recent ice mass loss in Antarctica. Nevertheless, in-situ oceanic data covering the extensive areas of a subshelf cavity are sparse. Here we show comprehensive structures of temperature, salinity and current measured in January 2018 through four boreholes drilled at a ~3-km-long ice shelf of Langhovde Glacier in East Antarctica. The measurements were performed in 302–12 m-thick ocean cavity beneath 234–412 m-thick ice shelf. The data indicate that Modified Warm Deep Water is transported into the grounding zone beneath a stratified buoyant plume. Water at the ice-ocean interface was warmer than the in-situ freezing point by 0.65–0.95°C, leading to a mean basal melt rate estimate of 1.42 m a−1. Our measurements indicate the existence of a density-driven water circulation in the cavity beneath the ice shelf of Langhovde Glacier, similar to that proposed for warm-ocean cavities of larger Antarctic ice shelves.

Global existence and energy decay of solutions for a wave equation with a time-varying delay term

We consider, in a bounded domain, a certain wave equation with a weak internal time-varying delay term. Under appropriate conditions, we prove global existence of solutions by the Faedo-Galerkin method and establish a decay rate estimate for the energy using the multiplier method.

The True Infection Mortality Rate of COVID-19 During the Spring 2020 Wave

Estimations of the infection mortality rate of COVID-19, the disease caused by the SARS-CoV-2 virus, are prone to biases due to underdiagnosis, false positives, false negatives, and time lag between diagnosis and death. With a systematic analysis that combines epidemiological modeling of COVID-19 in Spain and in the state of New York, and results of random immunological testing in the spring of 2020 in both locations, most of the bias is eliminated and any remaining bias is evaluated and reported as an uncertainty estimate. A true infection mortality rate of 1.45 ± 0.45 % is obtained, representing an average for the two locations, and obtained with a different technique to minimize the effect of potential biases. In the absence of specific local data, this number can be used for the first wave of COVID-19 in OECD countries. This mortality rate estimate of the new coronavirus is sufficiently accurate to be used as a basis for policy decisions. When differences in age distribution between Spain and the state of New York are accounted for, tentative infection mortality rates of 1.18 ± 0.26 % and 1.94 ± 0.43 % are put forward for New York and Spain, respectively.

The True Infection Mortality Rate of COVID-19 During the Spring 2020 Wave

Estimations of the infection mortality rate of COVID-19, the disease caused by the SARS-CoV-2 virus, are prone to biases due to underdiagnosis, false positives, false negatives, and time lag between diagnosis and death. With a systematic analysis that combines epidemiological modeling of COVID-19 in Spain and in the state of New York, and results of random immunological testing in the spring of 2020 in both locations, most of the bias is eliminated and any remaining bias is evaluated and reported as an uncertainty estimate. A true infection mortality rate of 1.45 ± 0.45 % is obtained, representing an average for the two locations, and obtained with a different technique to minimize the effect of potential biases. In the absence of specific local data, this number can be used for the first wave of COVID-19 in OECD countries. This mortality rate estimate of the new coronavirus is sufficiently accurate to be used as a basis for policy decisions. When differences in age distribution between Spain and the state of New York are accounted for, tentative infection mortality rates of 1.18 ± 0.26 % and 1.94 ± 0.43 % are put forward for New York and Spain, respectively.

DEEP REINFORCEMENT LEARNING WITH SPARSE DISTRIBUTED MEMORY FOR “WATER WORLD” PROBLEM SOLVING

Context. Machine learning is one of the actively developing areas of data processing. Reinforcement learning is a class of machine learning methods where the problem involves mapping the sequence of environmental states to agent’s actions. Significant progress in this area has been achieved using DQN-algorithms, which became one of the first classes of stable algorithms for learning using deep neural networks. The main disadvantage of this approach is the rapid growth of RAM in real-world tasks. The approach proposed in this paper can partially solve this problem. Objective. The aim is to develop a method of forming the structure and nature of access to the sparse distributed memory with increased information content to improve reinforcement learning without additional memory. Method. A method of forming the structure and modification of sparse distributed memory for storing previous transitions of the actor in the form of prototypes is proposed. The method allows increasing the informativeness of the stored data and, as a result, to improve the process of creating a model of the studied process by intensifying the learning of the deep neural network. Increasing the informativeness of the stored data is the result of this sequence of actions. First, we compare the new transition and the last saved transition. To perform this comparison, this method introduces a rate estimate for the distance between transitions. If the distance between the new transition and the last saved transition is smaller than the specified threshold, the new transition is written in place of the previous one without increasing the amount of memory. Otherwise, we create a new prototype in memory while deleting the prototype that has been stored in memory the longest. Results. The work of the proposed method was studied during the solution of the popular “Water World” test problem. The results showed a 1.5-times increase in the actor’s survival time in a hostile environment. This result was achieved by increasing the informativeness of the stored data without increasing the amount of RAM. Conclusions. The proposed method of forming and modifying the structure of sparse distributed memory allowed to increase the informativeness of the stored data. As a result of this approach, improved reinforcement learning parameters on the example of the “Water World” problem by increasing the accuracy of the model of the physical process represented by a deep neural network.

Fractional order convergence rate estimate of finite-difference method for the heat equation with concentrated capacity

The convergence of difference scheme for initial-boundary value problem for the heat equation with concentrated capacity and time-dependent coefficient of the space derivatives, is considered. Fractional order convergence rate estimate in a special discrete Sobolev norms, compatible with the smoothness of the coefficient and solution, is proved.