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Social media contains useful information about people and the society that could help advance research in many different areas (e.g. by applying opinion mining, emotion/sentiment analysis, and statistical analysis) such as business and finance, health, socio-economic inequality and gender vulnerability. User demographics provide rich information that could help study the subject further. However, user demographics such as gender are considered private and are not freely available. In this study, we propose a model based on transformers to predict the user's gender from their images and tweets. We fine-tune a model based on Vision Transformers (ViT) to stratify female and male images. Next, we fine-tune another model based on Bidirectional Encoders Representations from Transformers (BERT) to recognize the user's gender by their tweets. This is highly beneficial, because not all users provide an image that indicates their gender. The gender of such users could be detected form their tweets. The combination model improves the accuracy of image and text classification models by 6.98% and 4.43%, respectively. This shows that the image and text classification models are capable of complementing each other by providing additional information to one another. We apply our method to the PAN-2018 dataset, and obtain an accuracy of 85.52%.

Structured epidemic models can be formulated as first-order hyperbolic PDEs, where the "spatial" variables represent individual traits, called structures. For models with two structures, we propose a numerical technique to approximate $R_{0}$, which measures the transmissibility of an infectious disease and, rigorously, is defined as the dominant eigenvalue of a next-generation operator. Via bivariate collocation and cubature on tensor grids, the latter is approximated with a finite-dimensional matrix, so that its dominant eigenvalue can easily be computed with standard techniques. We use test examples to investigate experimentally the behavior of the approximation: the convergence order appears to be infinite when the corresponding eigenfunction is smooth, and finite for less regular eigenfunctions. To demonstrate the effectiveness of the technique for more realistic applications, we present a new epidemic model structured by demographic age and immunity, and study the approximation of $R_{0}$ in some particular cases of interest., Comment: 24 pages, 5 figures, submitted for publication

Despite the unprecedented success in the rapid development of several effective vaccines against the Cov-SARS-2, global vaccination rollout efforts suffer from vaccine distribution inequality and vaccine acceptance, leading to insufficient public immunity provided by the vaccine products. While a major current focus in vaccine acceptance research is how to model and inform vaccine acceptance based on social-demographic parameters, characteristics of vaccine acceptance are not well understood and in particular, it is not known whether and how information diffusion influences vaccine acceptance. This study examines how information diffusion can change vaccine acceptance by developing a comprehensive computational model with an agent-based simulation technique to overcome the modeling and quantification complexity associated with socio-demographics, vaccine types, population statistics, and information diffusion. Our analyses, calibrated by the vaccine acceptance survey data from the provinces and territories of Canada, provide clear evidence that the propagation of information can greatly influence vaccine acceptance rates. The results illustrate that spread of negative messages about the COVID-19 vaccines can cause significant vaccine hesitancy that challenges the goal of a high public immunity provided by the vaccines. Our findings might help solve the vaccine hesitancy problem by focusing more on individuals' opinions and behavior.

In a fast evolving major public health crisis such as the COVID-19 pandemic, multiple pieces of relevant information can be posted sequentially in a social media platform. The interval between subsequent posting times may have different impact on the transmission and cross-propagation of the old and new information to result in different peak value and final size of forwarding users of the new information, depending on the content correlation and whether the new information is posted during the outbreak or quasi steady state phase of the old information. To help in designing effective communication strategies to ensure information is delivered to the maximal number of users, we develop and analyze two classes of susceptible-forwarding-immune information propagation models with delay in transmission, to describe the cross-propagation process of relevant information. We parametrize these models using real data from the Sina-Microblog and use the parametrized models to define and evaluate mutual attractiveness indices, and we use these indices and parameter sensitivity analyses to inform strategies to ensure optimal strategies for a new information to be effectively propagated in the microblog., Comment: 29 pages, 22 figures

Expansion and reduction of a neural network's width has well known properties in terms of the entropy of the propagating information. When carefully stacked on top of one another, an encoder network and a decoder network produce an autoencoder, often used in compression. Using this architecture, we develop an efficient method of encoding and decoding 4D Light Field data, with a substantial compression factor at a minimal loss in quality. Our best results managed to achieve a compression of 48.6x, with a PSNR of 29.46 dB and a SSIM of 0.8104. Computations of the encoder and decoder can be run in real time, with average computation times of 1.62s and 1.81s respectively, and the entire network occupies a reasonable 584MB by today's storage standards., Comment: 11 pages, 8 figures

In the paper, the pricing of Quanto options is studied, where the underlying foreign asset and the exchange rate are correlated with each other. Firstly, we adopt Bayesian methods to estimate unknown parameters entering the pricing formula of Quanto options, including the volatility of stock, the volatility of exchange rate and the correlation. Secondly, we compute and predict prices of different four types of Quanto options based on Bayesian posterior prediction techniques and Monte Carlo methods. Finally, we provide numerical simulations to demonstrate the advantage of Bayesian method used in this paper comparing with some other existing methods. This paper is a new application of the Bayesian methods in the pricing of multi-asset options., Comment: 31 pages, 5 figures and 2 tables

We consider a $C^{1,\alpha}$ smooth flow in $\mathbb{R}^n$ which is "strongly monotone" with respect to a cone $C$ of rank $k$, a closed set that contains a linear subspace of dimension $k$ and no linear subspaces of higher dimension. We prove that orbits with initial data from an open and dense subset of the phase space are either pseudo-ordered or convergent to equilibria. This covers the celebrated Hirsch's Generic Convergence Theorem in the case $k=1$, yields a generic Poincar\'{e}-Bendixson Theorem for the case $k=2$, and holds true with arbitrary dimension $k$. Our approach involves the ergodic argument using the $k$-exponential separation and the associated $k$-Lyapunov exponent (that reduces to the first Lyapunov exponent if $k=1$).

We consider semiflows in general Banach spaces motivated by monotone cyclic feedback systems or differential equations with integer-valued Lyapunov functionals. These semiflows enjoy strong monotonicity properties with respect to cones of high ranks, which imply order-related structures on the $\omega$-limit sets of precompact semi-orbits. We show that for a pseudo-ordered precompact semi-orbit the $\omega$-limit set $\Omega$ is either ordered, or is contained in the set of equilibria, or possesses a certain ordered homoclinic property. In particular, we show that if $\Omega$ contains no equilibrium, then $\Omega$ itself is ordered and hence the dynamics of the semiflow on $\Omega$ is topologically conjugate to a compact flow on $\mathbb{R}^k$ with $k$ being the rank. We also establish a Poincar\'{e}-Bendixson type Theorem in the case where $k=2$. All our results are established without the smoothness condition on the semiflow, allowing applications to such cellular or physiological feedback systems with piecewise linear vector fields and to such infinite dimensional systems where the $C^1$-Closing Lemma or smooth manifold theory has not been developed.