arXiv subjects

Guo Lin

Publications and source records attributed to Guo Lin.

6 recordsLinked to original sources

arXiv2023

Sparks of Artificial General Recommender (AGR): Early Experiments with ChatGPT

This study investigates the feasibility of developing an Artificial General Recommender (AGR), facilitated by recent advancements in Large Language Models (LLMs). An AGR comprises both conversationality and universality to engage in natural dialogues and generate recommendations across various domains. We propose ten fundamental principles that an AGR should adhere to, each with its corresponding testing protocols. We proceed to assess whether ChatGPT, a sophisticated LLM, can comply with the proposed principles by engaging in recommendation-oriented dialogues with the model while observing its behavior. Our findings demonstrate the potential for ChatGPT to serve as an AGR, though several limitations and areas for improvement are identified.

cs.IR↗

arXiv2014

Traveling Wave Solutions of a Reaction-Diffusion Equation with State-Dependent Delay

This paper is concerned with the traveling wave solutions of a reaction-diffusion equation with state-dependent delay. When the birth function is monotone, the existence and nonexistence of monotone traveling wave solutions are established. When the birth function is not monotone, the minimal wave speed of nontrivial traveling wave solutions is obtained. The results are proved by the construction of upper and lower solutions and application of the fixed point theorem.

math.DS↗

arXiv2013

Coinvasion-Coexistence Traveling Wave Solutions of an Integro-Difference Competition System

This paper is concerned with the traveling wave solutions of an integro-difference competition system, of which the purpose is to model the coinvasion-coexistence process of two competitors with age structure. The existence of nontrivial traveling wave solutions is obtained by constructing generalized upper and lower solutions. The asymptotic and nonexistence of traveling wave solutions are proved by combining the theory of asymptotic spreading with the idea of contracting rectangle.

math.DS↗

arXiv2013

Traveling Wave Solutions for Delayed Reaction-Diffusion Systems and Applications to Lotka-Volterra Competition-Diffusion Models with Distributed Delays

This paper is concerned with the traveling wave solutions of delayed reaction-diffusion systems. By using Schauder's fixed point theorem, the existence of traveling wave solutions is reduced to the existence of generalized upper and lower solutions. Using the technique of contracting rectangles, the asymptotic behavior of traveling wave solutions for delayed diffusive systems is obtained. To illustrate our main results, the existence, nonexistence and asymptotic behavior of positive traveling wave solutions of diffusive Lotka-Volterra competition systems with distributed delays are established. The existence of nonmonotone traveling wave solutions of diffusive Lotka-Volterra competition systems is also discussed. In particular, it is proved that if there exists instantaneous self-limitation effect, then the large delays appearing in the intra-specific competitive terms may not affect the existence and asymptotic behavior of traveling wave solutions.

math.DS↗

arXiv2013

Traveling Wave Solutions for Integro-Difference Systems

This paper is concerned with the traveling wave solutions for integro-difference systems of higher order. By using Schauder fixed point theorem, the existence of traveling wave solutions is reduced to the existence of generalized upper and lower solutions. Then the asymptotic behavior of traveling wave solutions is studied by the idea of contracting rectangles. To illustrate our results, the traveling wave solutions of three systems are considered, which completes some known results.

math.DS↗

arXiv2010

Asymptotic Spreading Fastened by Inter-Specific Coupled Nonlinearities: a Cooperative System

This paper is concerned with the asymptotic spreading of a Lotka-Volterra cooperative system. By using the theory of asymptotic spreading of nonautonomous equations, the asymptotic speeds of spreading of unknown functions formulated by a coupled system are estimated. Our results imply that the asymptotic spreading of one species can be significantly fastened by introducing a mutual species, which indicates the role of cooperation described by the coupled nonlinearities.

math.DS↗