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We find sufficient conditions for a self-map of the unit ball to converge uniformly under iteration to a fixed point or idempotent on the entire ball. Using these tools, we establish spectral containments for weighted composition operators on Hardy and Bergman spaces of the ball. When the compositional symbol is in the Schur–Agler class, we establish the spectral radii of these weighted composition operators. 

Artificial Intelligence (AI) bots receive much attention and usage in industry manufacturing and even store cashier applications. Our research is to train AI bots to be software engineering assistants, specifically to detect biases and errors inside AI software applications. An example application is an AI machine learning system that sorts and classifies people according to various attributes, such as the algorithms involved in criminal sentencing, hiring, and admission practices. Biases, unfair decisions, and flaws in terms of the equity, diversity, and justice presence, in such systems could have severe consequences. As a Hispanic-Serving Institution, we are concerned about underrepresented groups and devoted an extended amount of our time to implementing “An Assure AI” (AAAI) Bot to detect biases and errors in AI applications. Our state-of-the-art AI Bot was developed based on our previous accumulated research in AI and Deep Learning (DL). The key differentiator is that we are taking a unique approach: instead of cleaning the input data, filtering it out and minimizing its biases, we trained our deep Neural Networks (NN) to detect and mitigate biases of existing AI models. The backend of our bot uses the Detection Transformer (DETR) framework, developed by Facebook, 

Abstract Previously, spectra of certain weighted composition operators W ѱ, φ on H 2 were determined under one of two hypotheses: either φ converges under iteration to the Denjoy-Wolff point uniformly on all of 𝔻 rather than simply on compact subsets, or φ is “essentially linear fractional.” We show that if φ is a quadratic self-map of 𝔻 of parabolic type, then the spectrum of W ѱ, φ can be found when these maps exhibit both of the aforementioned properties, and we determine which symbols do so. 

The fast-paced, volatile nature of hockey makes it a challenging sport to analyze and predict the final outcome. This paper presents two continuous-time Markov process models that predict the probability that a team will win a hockey game given particular states during the game. These states incorporate shot and goal differential relative to the opposing team and are used to approximate the probability that the home team would win depending on the state they are currently 

Hepatitis B (HBV) is one of the most common infectious diseases, with a worldwide annual incidence of over 250 million people. About one-third of the cases are in China. While China made significant efforts to implement a nationwide HBV vaccination program for newborns, a significant number of susceptible adults and teens remain. In this paper, we analyze a game-theoretical model of HBV dynamics that incorporates government-provided vaccination at birth coupled with voluntary vaccinations of susceptible adults and teens. We show that the optimal voluntary vaccination brings the disease incidence to very low levels. This result is robust and, in particular, due to a high HBV treatment cost, essentially independent from the vaccine cost. 

Abstract In 2016, more than 11 million Americans abused prescription opioids. The National Institute on Drug Abuse considers the opioid crisis a national addiction epidemic, as an increasing number of people are affected each year. Using the framework developed in mathematical modelling of infectious diseases, we create and analyse a compartmental opioid-abuse model consisting of a system of ordinary differential equations. Since $$40\%$$ of opioid overdoses are caused by prescription opioids, our model includes prescription compartments for the four most commonly prescribed opioids, as well as for the susceptible, addicted and recovered populations. While existing research has focused on drug abuse models in general and opioid models with one prescription compartment, no previous work has been done comparing the roles that the most commonly prescribed opioids have had on the crisis. By combining data from the Substance Abuse and Mental Health Services Administration (which tracked the proportion of people who used or misused one of the four individual opioids) with data from the Centers of Disease Control and Prevention (which counted the total number of prescriptions), we estimate prescription rates and probabilities of addiction for the four most commonly prescribed opioids. Additionally, we perform a sensitivity analysis and reallocate prescriptions to determine which opioid has the largest impact on the epidemic. Our results indicate that oxycodone prescriptions are both the most likely to lead to addiction and have the largest impact on the size of the epidemic, while hydrocodone prescriptions had the smallest impact.