The proof of infeasibility condition (Theorem 3.2) is provided in Section B. Explanations on conditions derived in Theorem 3.2 are included in Section C. The proof of properties of the proposed model (r)LogSpecT (Proposition 3.4 The truncated Hausdorff distance based proof details of Theorem 4.1 and Corollary 4.4 are Details of L-ADMM and its convergence analysis are in Section F. Additional experiments and discussions on synthetic data are included in Section G. ( m 1) Again, from Farkas' lemma, this implies that the following linear system does not have a solution: Example 3.1 we know δ = 2|h Since the constraint set S is a cone, it follows that for all γ > 0, γ S = S . Opt(C, α) = α Opt(C, 1), which completes the proof. The proof will be conducted by constructing a feasible solution for rLogSpecT. Since the LogSpecT is a convex problem and Slater's condition holds, the KKT conditions We show that it is feasible for rLogSpecT. R, its epigraph is defined as epi f: = {( x, y) | y f ( x) }. Before presenting the proof, we first introduce the following lemma.

Theoretically, feedback-looped filters can guarantee convergence w.r.t. a specified error bound, and be applied

By definition, P is an independent between-class random walk matrix. Compare equations 5 and 6. Therefore, the necessary condition for the spectral gap to be 0 is g (0) = g (2). For GPRGNN, GCNII, GNNGuard and ProGNN, we rely on the officially released code. The URL and commit number are presented in Table 2).

Recently, convolutional filters have been increasingly adopted in sequential recommendation for their ability to capture local sequential patterns. However, most of these models complement convolutional filters with self-attention. This is because convolutional filters alone, generally fixed filters, struggle to capture global interactions necessary for accurate recommendation. We propose Time-Variant Convolutional Filters for Sequential Recommendation (TV-Rec), a model inspired by graph signal processing, where time-variant graph filters capture position-dependent temporal variations in user sequences. By replacing both fixed kernels and self-attention with time-variant filters, TV-Rec achieves higher expressive power and better captures complex interaction patterns in user behavior. This design not only eliminates the need for self-attention but also reduces computation while accelerating inference. Extensive experiments on six public benchmarks show that TV-Rec outperforms state-of-the-art baselines by an average of 7.49%.

Neurodegeneration, characterized by the progressive loss of neuronal structure or function, is commonly assessed in clinical practice through reductions in cortical thickness or brain volume, as visualized by structural MRI. While informative, these conventional approaches lack the statistical sophistication required to fully capture the spatially correlated and heterogeneous nature of neurodegeneration, which manifests both in healthy aging and in neurological disorders. To address these limitations, brain age gap has emerged as a promising data-driven biomarker of brain health. The brain age gap prediction (BAGP) models estimate the difference between a person's predicted brain age from neuroimaging data and their chronological age. The resulting brain age gap serves as a compact biomarker of brain health, with recent studies demonstrating its predictive utility for disease progression and severity. However, practical adoption of BAGP models is hindered by their methodological obscurities and limited generalizability across diverse clinical populations. This tutorial article provides an overview of BAGP and introduces a principled framework for this application based on recent advancements in graph signal processing (GSP). In particular, we focus on graph neural networks (GNNs) and introduce the coVariance neural network (VNN), which leverages the anatomical covariance matrices derived from structural MRI. VNNs offer strong theoretical grounding and operational interpretability, enabling robust estimation of brain age gap predictions. By integrating perspectives from GSP, machine learning, and network neuroscience, this work clarifies the path forward for reliable and interpretable BAGP models and outlines future research directions in personalized medicine.

Details and more visualizations are in Appendices C and D.

The proof of infeasibility condition (Theorem 3.2) is provided in Section B. Explanations on conditions derived in Theorem 3.2 are included in Section C. The proof of properties of the proposed model (r)LogSpecT (Proposition 3.4 The truncated Hausdorff distance based proof details of Theorem 4.1 and Corollary 4.4 are Details of L-ADMM and its convergence analysis are in Section F. Additional experiments and discussions on synthetic data are included in Section G. ( m 1) Again, from Farkas' lemma, this implies that the following linear system does not have a solution: Example 3.1 we know δ = 2|h Since the constraint set S is a cone, it follows that for all γ > 0, γ S = S . Opt(C, α) = α Opt(C, 1), which completes the proof. The proof will be conducted by constructing a feasible solution for rLogSpecT. Since the LogSpecT is a convex problem and Slater's condition holds, the KKT conditions We show that it is feasible for rLogSpecT. R, its epigraph is defined as epi f: = {( x, y) | y f ( x) }. Before presenting the proof, we first introduce the following lemma.