Numerical Methods for Integral Equations

We first propose a multiscale Galerkin method for solving the Volterra integral equations of the second kind with a weakly singular kernel. Due to the special structure of Volterra integral equations and the ``shrinking support property of multiscale basis functions, a large number of entries of the coefficient matrix appearing in the resulting discrete linear system are zeros. This result, combined with a truncation scheme of the coefficient matrix, leads to a fast numerical solution of the integral equation. A quadrature method is designed especially for the weakly singular kernel involved inside the integral operator to compute the nonzero entries of the compressed matrix so that the quadrature errors will not ruin the overall convergence order of the approximate solution of the integral equation. We estimate the computational cost of this numerical method and its approximate accuracy. Numerical experiments are presented to demonstrate the performance of the proposed method. We also exploit two methods based on neural network models and the collocation method in solving the linear Fredholm integral equations of the second kind. For the first neural network (NN) model, we cast the problem of solving an integral equation as a data fitting problem on a finite set, which gives rise to an optimization problem. In the second method, which is referred to as the NN-Collocation model, we first choose the polynomial space as the projection space of the Collocation method, then approximate the solution of the integral equation by a linear combination of polynomials in that space. The coefficients of the linear combination are served as the weights between the hidden layer and the output layer of the neural network. We train both neural network models using gradient descent with Adam optimizer. Finally, we compare the performances of the two methods and find that the NN-Collocation model offers a more stable, accurate, and efficient solution

A Study on the Impact of Short-Video Product Placement Advertising on Viewers Ad Adoption Intention: A Perspective of ELM and Social Learning Theory

[Purpose/Meaning]Short-video platform is currently a new mainstream social media entertainment platform. The way of placing product advertisements in short videos is increasingly accepted by more people. Exploring the influencing factors of viewers’ intention to adopt short video product placement ads is of great significance for further mining the commercial value of short-video advertising and promoting the maturity of the e-commerce module in short-video platforms. [Method/Process] Based on ELM and social learning theory and combined with the characteristics of short-video product placement ads, this study constructs a model about the impact of product placement ads on viewers’ ads adopt intention. The empirical research obtained 304 samples through way of questionnaire, and verified the model with SmartPLS 3. [Results/Conclusions] First, product-celebrity matching degree and plot-realistic matching degree positively affect the usefulness of perceived advertising information, and perceived usefulness positively affects viewers’ advertising adoption intentions. Second, viewers may ignore discount their own beliefs and imitate others through observational learning, and both discount own beliefs and imitating others positively affect the intention of advertising adoption. Based on the research conclusions, this research provides corresponding marketing suggestions for short video makers and short-video platforms

An Improved Apriori Algorithm Based on an Evolution-Communication Tissue-Like P System with Promoters and Inhibitors

Apriori algorithm, as a typical frequent itemsets mining method, can help researchers and practitioners discover implicit associations from large amounts of data. In this work, a fast Apriori algorithm, called ECTPPI-Apriori, for processing large datasets, is proposed, which is based on an evolution-communication tissue-like P system with promoters and inhibitors. The structure of the ECTPPI-Apriori algorithm is tissue-like and the evolution rules of the algorithm are object rewriting rules. The time complexity of ECTPPI-Apriori is substantially improved from that of the conventional Apriori algorithms. The results give some hints to improve conventional algorithms by using membrane computing models

Social4Rec: Distilling User Preference from Social Graph for Video Recommendation in Tencent

Despite recommender systems play a key role in network content platforms, mining the user's interests is still a significant challenge. Existing works predict the user interest by utilizing user behaviors, i.e., clicks, views, etc., but current solutions are ineffective when users perform unsettled activities. The latter ones involve new users, which have few activities of any kind, and sparse users who have low-frequency behaviors. We uniformly describe both these user-types as "cold users", which are very common but often neglected in network content platforms. To address this issue, we enhance the representation of the user interest by combining his social interest, e.g., friendship, following bloggers, interest groups, etc., with the activity behaviors. Thus, in this work, we present a novel algorithm entitled SocialNet, which adopts a two-stage method to progressively extract the coarse-grained and fine-grained social interest. Our technique then concatenates SocialNet's output with the original user representation to get the final user representation that combines behavior interests and social interests. Offline experiments on Tencent video's recommender system demonstrate the superiority over the baseline behavior-based model. The online experiment also shows a significant performance improvement in clicks and view time in the real-world recommendation system. The source code is available at https://github.com/Social4Rec/SocialNet

New oscillation criteria for second-order delay differential equations with mixed nonlinearities

We establish new oscillation criteria for second-order delay differential equations with mixed nonlinearities of the form p t x t n i 1 p i t x t−τ i n i 1 q i t |x t−τ i | αi sgn x t−τ i e t , t ≥ 0, where p t , p i t , q i t , and e t are continuous functions defined on 0, ∞ , and p t > 0, p t ≥ 0, and No restriction is imposed on the potentials p i t , q i t , and e t to be nonnegative. These oscillation criteria extend and improve the results given in the recent papers. An interesting example illustrating the sharpness of our results is also provided