Coronavirus disease 2019 (COVID-19) has triggered an enormous number of discussion topics on social media Twitter. It has an impact on the global health system and citizen responses to the pandemic. Multiple responses (replies, favorites, and retweets) reflect the followers’ attitudes and emotions towards these tweets. Twitter data such as these have inspired substantial research interest in sentiment and social trend analyses. To date, studies on Twitter data have focused on the associational relationships between variables in a population. There is a need for further discovery of causality, such as the influence of sentiment polarity of tweet response on further discussion topics. These topics often reflect the human perception of COVID-19. This study addresses this exact topic. It aims to develop a new method to unveil the causal relationships between the sentiment polarity and responses in social media data. We employed sentiment polarity, i.e., positive or negative sentiment, as the treatment variable in this quasi-experimental study. The data is the tweets posted by nine authoritative public organizations in four countries and the World Health Organization from December 1, 2019, to May 10, 2020. Employing the inverse probability weighting model, we identified the treatment effect of sentiment polarity on the multiple responses of tweets. The topics with negative sentiment polarity on COVID-19 attracted significantly more replies (69±49) and favorites (688±677) than the positive tweets. However, no significant difference in the number of retweets was found between the negative and positive tweets. This study contributes a new method for social media analysis. It generates new insight into the influence of sentiment polarity of tweets about COVID-19 on tweet responses.

Dimensional analysis transforms a dimensionally homogeneous model into its simplest form; the number of input variables can be reduced. Such a reduction is very helpful in statistical design and analysis. Although the Buckingham π theorem provides a method of transforming the model based on the basis quantities (BQ’s), the choice of the BQ’s in general is not unique. In practice, a different choice of the BQ’s may lead to a different performance in statistical analysis. A new criterion, based on the BQ’s with a small coefficient of variation, is proposed to choose the optimal BQ’s. It is anticipated that such a criterion will be popularly used in practice. The distribution of the newly proposed criterion is derived to statistically differentiate the performance via different choices of the BQ’s. Three case studies are provided for illustration.

Lead time plays an important role in many areas, including supply chain, economics, and marketing. A conventional assumption in most stochastic lead-time inventory models is that the lead times are independent and identically distributed (i.i.d.). However, it can be shown that applying such an assumption on practical lead time may not be valid in case of order crossover. An order crossover occurs when a later order received earlier. This becomes a common phenomenon in many business applications. Any inventory policy based on identically distributed practical lead times needs to be re-investigated. Although the crossover issue has been noticed in the literature, the exact solution for lead-time distribution under crossover remains primitive. Inventory model generally can be separated into two classes, periodic and continuous review. Our paper focuses on continuous-review models. When the lead-time sequence is stationary, some common techniques might be useful to estimate the statistics of the distribution, such as the autocorrelation function and partial autocorrelation function. However, the practical lead time in case of order crossover is not stationary. The proposed method reveals the joint distribution of the practical lead time instead. Any statistics, such as mean and correlation, can be estimated from the joint distribution directly. Subsequently, the optimal inventory police can be obtained in case of order crossover. An exponential distributed lead-time case study is used to demonstrate the use of the proposed method and the risk of mis-use i.i.d. practical lead times. Other phenomena can be studied by similar derivation.

We consider a general framework for constructing non-linear generators by adding a (32-bit or larger) pseudo-random number generator (PRNG) as a baseline generator to the basic RC4 design, in which an index-selection scheme similar to RC4 is used. We refer to the proposed design as the eRC (enhanced/extended RC4) design. We discuss several advantages of adding a good baseline generator to the RC4 design, including new updating schemes for the auxiliary table. We consider some popular PRNGs with the nice properties of high-dimensional equi-distribution, efficiency, long period, and portability as the baseline generator. We demonstrate that eRC generators are very efficient via extensive empirical testing on some eRC generators. We also show that eRC is flexible enough to choose minimal design parameters for eRC generators and yet the resulting eRC generators still pass stringent empirical tests, which makes them suitable for both software and hardware implementations.