arXiv subjects

Mehdi Naima

Publications and source records attributed to Mehdi Naima.

10 recordsLinked to original sources

arXiv2026

Modern Structure-Aware Simplicial Spatiotemporal Neural Network

Spatiotemporal modeling has evolved beyond simple time series analysis to become fundamental in structural time series analysis. While current research extensively employs graph neural networks (GNNs) for spatial feature extraction with notable success, these networks are limited to capturing only pairwise relationships, despite real-world networks containing richer topological relationships. Additionally, GNN-based models face computational challenges that scale with graph complexity, limiting their applicability to large networks. To address these limitations, we present Modern Structure-Aware Simplicial SpatioTemporal neural network (ModernSASST), the first approach to leverage simplicial complex structures for spatiotemporal modeling. Our method employs spatiotemporal random walks on high-dimensional simplicial complexes and integrates parallelizable Temporal Convolutional Networks to capture high-order topological structures while maintaining computational efficiency. Our source code is publicly available on GitHub\footnote{Code is available at: https://github.com/ComplexNetTSP/ST_RUM.

cs.LG↗

arXiv2026

Reversible Residual Normalization Alleviates Spatio-Temporal Distribution Shift

Distribution shift severely degrades the performance of deep forecasting models. While this issue is well-studied for individual time series, it remains a significant challenge in the spatio-temporal domain. Effective solutions like instance normalization and its variants can mitigate temporal shifts by standardizing statistics. However, distribution shift on a graph is far more complex, involving not only the drift of individual node series but also heterogeneity across the spatial network where different nodes exhibit distinct statistical properties. To tackle this problem, we propose Reversible Residual Normalization (RRN), a novel framework that performs spatially-aware invertible transformations to address distribution shift in both spatial and temporal dimensions. Our approach integrates graph convolutional operations within invertible residual blocks, enabling adaptive normalization that respects the underlying graph structure while maintaining reversibility. By combining Center Normalization with spectral-constrained graph neural networks, our method captures and normalizes complex Spatio-Temporal relationships in a data-driven manner. The bidirectional nature of our framework allows models to learn in a normalized latent space and recover original distributional properties through inverse transformation, offering a robust and model-agnostic solution for forecasting on dynamic spatio-temporal systems.

cs.LG↗

arXiv2026

Beyond the Laplacian: Doubly Stochastic Matrices for Graph Neural Networks

Graph Neural Networks (GNNs) conventionally rely on standard Laplacian or adjacency matrices for structural message passing. In this work, we substitute the traditional Laplacian with a Doubly Stochastic graph Matrix (DSM), derived from the inverse of the modified Laplacian, to naturally encode continuous multi-hop proximity and strict local centrality. To overcome the intractable $O(n^3)$ complexity of exact matrix inversion, we first utilize a truncated Neumann series to scalably approximate the DSM, which serves as the foundation for our proposed DsmNet. Furthermore, because algebraic truncation inherently causes probability mass leakage, we introduce DsmNet-compensate. This variant features a mathematically rigorous Residual Mass Compensation mechanism that analytically re-injects the truncated tail mass into self-loops, strictly restoring row-stochasticity and structural dominance. Extensive theoretical and empirical analyses demonstrate that our decoupled architectures operate efficiently in $O(K|E|)$ time and effectively mitigate over-smoothing by bounding Dirichlet energy decay, providing robust empirical validation on homophilic benchmarks. Finally, we establish the theoretical boundaries of the DSM on heterophilic topologies and demonstrate its versatility as a continuous structural encoding for Graph Transformers.

cs.LG↗

arXiv2025

Efficient Sampling of Temporal Networks with Preserved Causality Structure

In this paper, we extend the classical Color Refinement algorithm for static networks to temporal (undirected and directed) networks. This enables us to design an algorithm to sample synthetic networks that preserves the $d$-hop neighborhood structure of a given temporal network. The higher $d$ is chosen, the better the temporal neighborhood structure of the original network is preserved. Specifically, we provide efficient algorithms that preserve time-respecting ("causal") paths in the networks up to length $d$, and scale to real-world network sizes. We validate our approach theoretically (for Degree and Katz centrality) and experimentally (for edge persistence, causal triangles, and burstiness). An experimental comparison shows that our method retains these key temporal characteristics more effectively than existing randomization methods.

cs.SI↗

arXiv2024

The ascent lattice on Dyck paths

In the Stanley lattice defined on Dyck paths of size $n$, cover relations are obtained by replacing a valley $DU$ by a peak $UD$. We investigate a greedy version of this lattice, first introduced by Chenevi\`ere, where cover relations replace a factor $DU^k D$ by $U^kD^2$. By relating this poset to another poset recently defined by Nadeau and Tewari, we prove that this still yields a lattice, which we call the ascent lattice, $L_n$. We then count intervals in $L_n$. Their generating function is found to be algebraic of degree $3$. The proof is based on a recursive decomposition of intervals involving two catalytic parameters. The solution of the corresponding functional equation is inspired by recent work on the enumeration of walks confined to a quadrant. We also consider the order induced in $L_{mn}$ on $m$-Dyck paths, that is, paths in which all ascent lengths are multiples of $m$, and on mirrored $m$-Dyck paths, in which all descent lengths are multiples of $m$. The first poset $L_{m,n}$ is still a lattice for any $m$, while the second poset $L'_{m,n}$ is only a join semilattice when $m>1$. In both cases, the enumeration of intervals is still described by an equation in two catalytic variables. Interesting connections arise with the sylvester congruence of Hivert, Novelli and Thibon, and again with walks confined to a quadrant. We combine the latter connection with probabilistic results to give asymptotic estimates of the number of intervals in both $L_{m,n}$ and $L'_{m,n}$. Their form implies that the generating functions of intervals are no longer algebraic, nor even D-finite, when $m>1$.

math.CO↗

arXiv2023

A lattice on Dyck paths close to the Tamari lattice

We introduce a new poset structure on Dyck paths where the covering relation is a particular case of the relation inducing the Tamari lattice. We prove that the transitive closure of this relation endows Dyck paths with a lattice structure. We provide a trivariate generating function counting the number of Dyck paths with respect to the semilength, the numbers of outgoing and incoming edges in the Hasse diagram. We deduce the numbers of coverings, meet and join irreducible elements. As a byproduct, we present a new involution on Dyck paths that transports the bistatistic of the numbers of outgoing and incoming edges into its reverse. Finally, we give a generating function for the number of intervals, and we compare this number with the number of intervals in the Tamari lattice.

math.CO↗

arXiv2023

Temporal Betweenness Centrality on Shortest Walks Variants

Betweenness centrality has been extensively studied since its introduction in 1977 as a measure of node importance in graphs. This measure has found use in various applications and has been extended to temporal graphs with time-labeled edges. Recent research by Buss et al. and Rymar et al. has shown that it is possible to compute the shortest path betweenness centrality of all nodes in a temporal graph in $O(n^3\,T^2)$ and $O(n^2\,m\,T^2)$ time, respectively, where $T$ is the maximum time, $m$ is the number of temporal edges, and $n$ is the number of nodes. These approaches considered paths that do not take into account contributions from intermediate temporal nodes. In this paper, we study the classical temporal betweenness centrality paths that we call \textit{passive} shortest paths, as well as an alternative variant that we call \textit{active} shortest paths, which takes into account contributions from all temporal nodes. We present an improved analysis of the running time of the classical algorithm for computing betweenness centrality of all nodes, reducing the time complexity to $O(n\,m\,T+ n^2\,T)$. Furthermore, for active paths, we show that the betweenness centrality can be computed in $O(n\,m\,T+ n^2\,T^2)$. We also show that our results hold for different shortest paths variants. Finally, we provide an open-source implementation of our algorithms and conduct experiments on several real-world datasets. We compare the results of the two variants on both the node and time dimensions of the temporal graph, and we also compare the temporal betweenness centrality to its static counterpart. Our experiments suggest that for the shortest foremost variant looking only at the first $10\%$ of the temporal interaction is a very good approximation for the overall top ranked nodes.

cs.DS↗

arXiv2023

Temporal Betweenness Centrality on Shortest Paths

Betweenness centrality measure assesses the importance of nodes in a graph and has been used in a variety of contexts. Betweenness centrality has also been extended to temporal graphs. Temporal graphs have edges that bear labels according to the time of the interactions between the nodes. Betweenness centrality has been extended to the temporal graph settings, and the notion of paths has been extended to temporal paths. Recent results by Bu{\ss} et al. and Rymar et al. showed that the betweenness centrality of all nodes in a temporal graph can be computed in O(n^3 T^2) or O(n^2 m T^2 ), where T is the number of time units, m the number of temporal edges and n the number of nodes. In this paper, we improve the running time analysis of these previous approaches to compute the betweenness centrality of all nodes in a temporal graph. We give an algorithm that runs in O(n m T + n^2 T ).

cs.DS↗

arXiv2020

Compaction for two models of logarithmic-depth trees: Analysis and Experiments

We are interested in the quantitative analysis of the compaction ratio for two classical families of trees: recursive trees and plane binary increasing trees. These families are typical representatives of tree models with a small depth. Once a tree of size $n$ is compacted by keeping only one occurrence of all fringe subtrees appearing in the tree the resulting graph contains only $O(n / \ln n)$ nodes. This result must be compared to classical results of compaction in the families of simply generated trees, where the analogous result states that the compacted structure is of size of order $n / \sqrt{\ln n}$. The result about the plane binary increasing trees has already been proved, but we propose a new and generic approach to get the result. Finally, an experimental study is presented, based on a prototype implementation of compacted binary search trees that are modeled by plane binary increasing trees.

math.CO↗

arXiv2019

Ranked Schröder Trees

In biology, a phylogenetic tree is a tool to represent the evolutionary relationship between species. Unfortunately, the classical Schröder tree model is not adapted to take into account the chronology between the branching nodes. In particular, it does not answer the question: how many different phylogenetic stories lead to the creation of n species and what is the average time to get there? In this paper, we enrich this model in two distinct ways in order to obtain two ranked tree models for phylogenetics, i.e. models coding chronology. For that purpose, we first develop a model of (strongly) increasing Schröder trees, symbolically described in the classical context of increasing labeling. Then we introduce a generalization for the labeling with some unusual order constraint in Analytic Combinatorics (namely the weakly increasing trees). Although these models are direct extensions of the Schröder tree model, it appears that they are also in one-to-one correspondence with several classical combinatorial objects. Through the paper, we present these links, exhibit some parameters in typical large trees and conclude the studies with efficient uniform samplers.

cs.DS↗