Simultaneous Joint Lower and Upper record values Probability Laws for Absolutely Continuous or Discrete Data

This paper investigates the probability density function (pdf) of the \((2n-1)\)-vector \((n\geq 1)\) of both lower and upper record values for a sequence of independent random variables with common \textit{pdf} \(f\) defined on the same probability space, provided that the lower and upper record times are finite up to \(n\). A lot is known about the lower or the upper record values when they are studied separately. When put together, the challenges are far complicated. The rare results in the literature still present some flaws. This paper begins a new and complete investigation with a few number of records: (n=2\) and \(n=3\). Lessons from these simple cases will allow addressing the general formulation of simultaneous joint lower-upper records.

The dilemma of COVID-19 vaccination among Health Care Workers (HCWs) of Uttar Pradesh

Background: Immediately after the outbreak of COVID-19 pandemic, with an unprecedented cooperation between biomedical, pharmaceutical, technological, and political sectors, new vaccines were developed and approved in record times. However, doubts were raised on their efficacy and adverse effects. Globally, it was agreed that the first recipients for vaccines would be the health care workers (HCWs). Logically, it was bound to raise some concerns and result in hesitancy among the HCWs. Aims: The current study was planned to study the proportion of HCWs having hesitancy towards COVID-19 vaccination and factors effecting it. Settings and Design: Cross-sectional study conducted among HCWs of Uttar Pradesh. Methods and Material: The survey was conducted both in online and offline mode and attempted by 254 HCWs eligible for receiving COVID-19 vaccine. Statistical analysis used: t-test, chi-square test, proportion, mean, SD Results: Vaccine hesitancy was present in 35.8% HCWs. Only social factors like caste (p=0.023) and religion (p<0.001) were found to be significantly associated with vaccine hesitancy. Gender, type of health worker, fear of COVID-19 infection, fear of lethality or pre-existing diseases did not affect vaccine hesitancy. The maximum number of HCWs (71.4%) were hesitant because they were unsure of the side-effects followed by the reason of being unsure about its effect on their own health (53.8%). When asked about their attitude towards compulsory COVID-19 vaccination for HCWs, should it be made mandatory by the government, 42.9% were in favour and 40.6% were against any such mandate. Conclusions: The study concluded that social factors like religion and caste are more deterministic for vaccine hesitancy.

Predicting Breaststroke and Butterfly Stroke Results in Swimming Based on Olympics History

Here we describe historic variations in Olympic breaststroke and butterfly performance and predict swimming results for the 2021 Olympic Games in Tokyo. The results of the finalists, winners, and last participants in the women’s and men’s finals were analyzed, and a mathematical predictive model was created. The predicted times for the future Olympics were presented. Swimming performance among Olympians has been steadily improving, with record times of 18.51 s for female finalists in the 100 m butterfly (a 24.63% improvement) and 31.33 s for male finalists in the 200 m butterfly (21.44%). The results in all analyzed groups showed improvement in athletic performance, and the gap between the finalists has narrowed. Women Olympians’ performances have improved faster than men’s, reducing the gap between genders. We conclude that swimming performance among Olympians is continuing to improve.

Finiteness of Record values and Alternative Asymptotic Theory of Records with Atom Endpoints

Asymptotic theories on record values and times, including central limit theorems, make sense only if the sequence of records values (and of record times) is infinite. If not, such theories could not even be an option. In this paper, we give necessary and/or sufficient conditions for the finiteness of the number of records. We prove, for example for iid real valued random variable, that strong upper record values are finite if and only if the upper endpoint is finite and is an atom of the common cumulative distribution function. The only asymptotic study left to us concerns the infinite sequence of hitting times of that upper endpoints, which by the way, is the sequence of weak record times. The asymptotic characterizations are made using negative binomial random variables and the dimensional multinomial random variables. Asymptotic comparison in terms of consistency bounds and confidence intervals on the different sequences of hitting times are provided. The example of a binomial random variable is given.

The Stratigraphy of Mass Extinctions and Recoveries

Interpretations of the tempo of mass extinctions and recoveries often rely on the distribution of fossils in a stratigraphic column. These interpretations are generally compromised when they are not based on a knowledge of marine ecological gradients and sequence-stratigraphic architecture. Crucially, last and first occurrences of species do not record times of extinction and origination. A face-value interpretation of the stratigraphic record leads to incorrect inferences of pulsed extinction, underestimates of the duration of mass extinction, and overestimates of local recovery times. An understanding of the processes of extinction and recovery is substantially improved by knowledge of the distribution of species along marine environmental gradients, interpreting sequence-stratigraphic architecture to show how those gradients are sampled through time, and sampling along regional transects along depositional dip. Doing so suggests that most ancient mass extinctions were substantially longer and local recoveries substantially shorter than generally thought. ▪ The concepts that let geologists find petroleum allow paleontologists to reinterpret ancient mass extinctions and their recoveries. ▪ Most ancient mass extinctions were longer than the fossil record suggests, lasting hundreds of thousands of years to a few million years. ▪ Ancient recoveries from mass extinctions were shorter than thought and likely overlapped with extinction during a period of turnover.

Inefficiency of K-FAC for Large Batch Size Training

There have been several recent work claiming record times for ImageNet training. This is achieved by using large batch sizes during training to leverage parallel resources to produce faster wall-clock training times per training epoch. However, often these solutions require massive hyper-parameter tuning, which is an important cost that is often ignored. In this work, we perform an extensive analysis of large batch size training for two popular methods that is Stochastic Gradient Descent (SGD) as well as Kronecker-Factored Approximate Curvature (K-FAC) method. We evaluate the performance of these methods in terms of both wall-clock time and aggregate computational cost, and study the hyper-parameter sensitivity by performing more than 512 experiments per batch size for each of these methods. We perform experiments on multiple different models on two datasets of CIFAR-10 and SVHN. The results show that beyond a critical batch size both K-FAC and SGD significantly deviate from ideal strong scaling behaviour, and that despite common belief K-FAC does not exhibit improved large-batch scalability behavior, as compared to SGD.

How to build a new athletic track to break records

We introduce a new optimal control model which encompasses pace optimization and motor control effort for a runner on a fixed distance. The system couples mechanics, energetics, neural drive to an economic decision theory of cost and benefit. We find how effort is minimized to produce the best running strategy, in particular, in the bend. This allows us to discriminate between different types of tracks and estimate the discrepancy between lanes. Relating this model to the optimal path problem called the Dubins path, we are able to determine the geometry of the optimal track and estimate record times.