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In this article, we model and study the spread of COVID-19 in Germany, Japan, India and highly impacted states in India, i.e., in Delhi, Maharashtra, West Bengal, Kerala and Karnataka. We consider recorded data published in Worldometers and COVID-19 India websites from April 2020 to July 2021, including periods of interest where these countries and states were hit severely by the pandemic. Our methodology is based on the classic susceptible-infected-removed (SIR) model and can track the evolution of infections in communities, where we (a) allow for the susceptible and infected populations to be reset at times where surges, outbreaks or secondary waves appear in the recorded data sets, (b) consider the parameters in the SIR model that represent the effective transmission and recovery rates to be functions of time and (c) estimate the number of deaths by combining the model solutions with the recorded data sets to approximate them between consecutive surges, outbreaks or secondary waves, providing a more accurate estimate. We report on the status of the current infections in these countries and states, and the infections and deaths in India and Japan. Our model can adapt to the recorded data and can be used to explain them and importantly, to forecast the number of infected, recovered, removed and dead individuals, as well as it can estimate the effective infection and recovery rates as functions of time, assuming an outbreak occurs at a given time. The latter can be used to forecast the future reproduction number and together with the forecast on the number of infected and dead individuals, our approach can be used to suggest the implementation of intervention strategies and mitigation policies to keep at bay the number of infected and dead individuals. This can help reduce the impact of the spread around the world and improve the wellbeing of people., Comment: 16 pages, 6 figures, 1 table

In this paper, a susceptible-infected-removed (SIR) model has been used to track the evolution of the spread of the COVID-19 virus in four countries of interest. In particular, the epidemic model, that depends on some basic characteristics, has been applied to model the time evolution of the disease in Italy, India, South Korea and Iran. The economic, social and health consequences of the spread of the virus have been cataclysmic. Hence, it is essential that available mathematical models can be developed and used for the comparison to be made between published data sets and model predictions. The predictions estimated from the SIR model here, can be used in both the qualitative and quantitative analysis of the spread. It gives an insight into the spread of the virus that the published data alone cannot do by updating them and the model on a daily basis. For example, it is possible to detect the early onset of a spike in infections or the development of a second wave using our modeling approach. We considered data from March to June, 2020, when different communities are severely affected. We demonstrate predictions depending on the model's parameters related to the spread of COVID-19 until September 2020. By comparing the published data and model results, we conclude that in this way, it may be possible to better reflect the success or failure of the adequate measures implemented by governments and individuals to mitigate and control the current pandemic., Comment: 17 pages, 13 figures

In this paper, we study the effectiveness of the modelling approach on the pandemic due to the spreading of the novel COVID-19 disease and develop a susceptible-infected-removed (SIR) model that provides a theoretical framework to investigate its spread within a community. Here, the model is based upon the well-known susceptible-infected-removed (SIR) model with the difference that a total population is not defined or kept constant per se and the number of susceptible individuals does not decline monotonically. To the contrary, as we show herein, it can be increased in surge periods! In particular, we investigate the time evolution of different populations and monitor diverse significant parameters for the spread of the disease in various communities, represented by countries and the state of Texas in the USA. The SIR model can provide us with insights and predictions of the spread of the virus in communities that the recorded data alone cannot. Our work shows the importance of modelling the spread of COVID-19 by the SIR model that we propose here, as it can help to assess the impact of the disease by offering valuable predictions. Our analysis takes into account data from January to June, 2020, the period that contains the data before and during the implementation of strict and control measures. We propose predictions on various parameters related to the spread of COVID-19 and on the number of susceptible, infected and removed populations until September 2020. By comparing the recorded data with the data from our modelling approaches, we deduce that the spread of COVID-19 can be under control in all communities considered, if proper restrictions and strong policies are implemented to control the infection rates early from the spread of the disease., Comment: 18 pages, 17 figures

The Data Activated Liu Graph Engine - DALiuGE - is an execution framework for processing large astronomical datasets at a scale required by the Square Kilometre Array Phase 1 (SKA1). It includes an interface for expressing complex data reduction pipelines consisting of both data sets and algorithmic components and an implementation run-time to execute such pipelines on distributed resources. By mapping the logical view of a pipeline to its physical realisation, DALiuGE separates the concerns of multiple stakeholders, allowing them to collectively optimise large-scale data processing solutions in a coherent manner. The execution in DALiuGE is data-activated, where each individual data item autonomously triggers the processing on itself. Such decentralisation also makes the execution framework very scalable and flexible, supporting pipeline sizes ranging from less than ten tasks running on a laptop to tens of millions of concurrent tasks on the second fastest supercomputer in the world. DALiuGE has been used in production for reducing interferometry data sets from the Karl E. Jansky Very Large Array and the Mingantu Ultrawide Spectral Radioheliograph; and is being developed as the execution framework prototype for the Science Data Processor (SDP) consortium of the Square Kilometre Array (SKA) telescope. This paper presents a technical overview of DALiuGE and discusses case studies from the CHILES and MUSER projects that use DALiuGE to execute production pipelines. In a companion paper, we provide in-depth analysis of DALiuGE's scalability to very large numbers of tasks on two supercomputing facilities., Comment: 31 pages, 12 figures, currently under review by Astronomy and Computing

The `excised ensemble', a random matrix model for the zeros of quadratic twist families of elliptic curve $L$-functions, was introduced by Due\~nez, Huynh, Keating, Miller and Snaith. The excised model is motivated by a formula for central values of these $L$-functions in a paper by Kohnen and Zagier. This formula indicates that for a finite set of $L$-functions from a family of quadratic twists, the central values are all either zero or are greater than some positive cutoff. The excised model imposes this same condition on the central values of characteristic polynomials of matrices from $SO(2N)$. Strangely, the cutoff on the characteristic polynomials that results in a convincing model for the $L$-function zeros is significantly smaller than that which we would obtain by naively transferring Kohnen and Zagier's cutoff to the $SO(2N)$ ensemble. In this current paper we investigate a modification to the excised model. It lacks the simplicity of the original excised ensemble, but it serves to explain the reason for the unexpectedly low cutoff in the original excised model. Additionally, the distribution of central $L$-values is `choppier' than the distribution of characteristic polynomials, in the sense that it is a superposition of a series of peaks: the characteristic polynomial distribution is a smooth approximation to this. The excised model didn't attempt to incorporate these successive peaks, only the initial cutoff. Here we experiment with including some of the structure of the $L$-value distribution. The conclusion is that a critical feature of a good model is to associate the correct mass to the first peak of the $L$-value distribution.