Chromatic symmetric functions and combinatorial polynomials are central constructs in modern algebraic combinatorics, extending classical graph invariants into rich algebraic frameworks. Originating ...
Polynomials and power functions are the foundation for modelling non-linear relationships. Polynomial functions such as quadratic, cubic and quartic model variables raised to exponents of different ...
Inspired by Rearick's work on logarithm and exponential functions of arithmetic functions, we introduce two new operators, LOG and EXP. The LOG operates on generalized Fibonacci polynomials giving ...
General graph neural networks (GNNs) implement convolution operations on graphs based on polynomial spectral filters. Existing filters with high-order polynomial approximations can detect more ...
There are a number of situations in which it is useful to graduate fertility distributions; for example when the data are obtained from small samples of the population, or when it is desired to ...
Abstract: Understanding the underlying graph structure of a nonlinear map over a particular domain is essential in evaluating its potential for real applications. In this paper, we investigate the ...
Improved Modeling and Generalization Capabilities of Graph Neural Networks With Legendre Polynomials
Abstract: LegendreNet is a novel graph neural network (GNNs) model that addresses stability issues present in traditional GNN models such as ChebNet, while also more effectively capturing higher-order ...
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