Farshad Navah

Shaina Raza, Mizanur Rahman, Safiullah Kamawal et al.

Recommender Systems (RS) play an integral role in enhancing user experiences by providing personalized item suggestions. This survey reviews the progress in RS inclusively from 2017 to 2024, effectively connecting theoretical advances with practical applications. We explore the development from traditional RS techniques like content-based and collaborative filtering to advanced methods involving deep learning, graph-based models, reinforcement learning, and large language models. We also discuss specialized systems such as context-aware, review-based, and fairness-aware RS. The primary goal of this survey is to bridge theory with practice. It addresses challenges across various sectors, including e-commerce, healthcare, and finance, emphasizing the need for scalable, real-time, and trustworthy solutions. Through this survey, we promote stronger partnerships between academic research and industry practices. The insights offered by this survey aim to guide industry professionals in optimizing RS deployment and to inspire future research directions, especially in addressing emerging technological and societal trends\footnote. The survey resources are available in the public GitHub repository https://github.com/VectorInstitute/Recommender-Systems-Survey. (Recommender systems, large language models, chatgpt, responsible AI)

Samuel Quaegebeur, Siva Nadarajah, Farshad Navah et al.

Recovering some prominent high-order approaches such as the discontinuous Galerkin (DG) or the spectral difference (SD) methods, the flux reconstruction (FR) approach has been adopted by many individuals in the research community and is now commonly used to solve problems on unstructured grids over complex geometries. This approach relies on the use of correction functions to obtain a differential form for the discrete problem. A class of correction functions, named energy stable flux reconstruction (ESFR) functions, has been proven stable for the linear advection problem. This proof has then been extended for the diffusion equation using the local discontinuous Galerkin (LDG) scheme to compute the numerical fluxes. Although the LDG scheme is commonly used, many prefer the interior penalty (IP), as well as the Bassi and Rebay II (BR2) schemes. Similarly to the LDG proof, this article provides a stability analysis for the IP and the BR2 numerical fluxes. In fact, we obtain a theoretical condition on the penalty term to ensure stability. This result is then verified through numerical simulations. To complete this study, a von Neumann analysis is conducted to provide a combination of parameters producing the maximal time step while converging at the correct order. All things considered, this article has for purpose to provide the community with a stability condition while using the IP and the BR2 schemes.