Santiago Segarra

Humans are able to hear in a variety of complicated acoustic environments. This feat begins in the peripheral auditory system, where the cochlea collects and transmits thousands of individual bits of sound data to the brain. Here, we introduce GSP Cochlea: a graph signal processing-based framework to investigate and visualize sound encoding. We show that a cochlea graph with a mesh topology provides a mechanism of denoising, efficient information transfer, and modular processing. We demonstrate an application to assess hearing loss as more than just a decibel loss at particular frequencies of sound but also a significant change to the cochlea graph architecture. GSP Cochlea is a generalized approach that provides new insight into the higher-level functional activity of the inner ear.

Gene regulatory networks (GRNs) capture complex regulatory relationships that govern gene expression in cells. Inference of GRNs from single-cell RNA-seq (scRNA-seq) data has been an active topic of research in the past several years. However, despite the improvements in the data quality, the GRN inference problem remains a challenging task with many approaches showing variable performance dependent on the organism and cell type. To improve the quality of GRN inference and enable more comprehensive exploratory analyses of GRNs across various phenotypes of interest, we developed a two-stage meta-method called GRNITE. In the first step, GRNITE leverages LLM-based embeddings of plain text gene descriptions to create a prior gene interaction graph, which is then optimized with a graph neural network (GNN) to achieve a “universal” biological prior for GRN inference. In the second step, GRNITE uses a GNN to incorporate information from a GRN inferred from scRNA-seq data with any baseline inference method into our prior. The result of this two-step approach is a near-universal improvement in AUROC and recall of all evaluated methods, with minor trade-offs in precision. Furthermore, GRNITE is a lightweight meta-method, which adds a minimal amount of extra compute time on top of the original GRN inference performed. GRNITE and our pre-trained universal prior GRN are available on GitHub: https://github.com/aliaaz99/GRNITE .

Racism, discriminatory practices, institutional bias, and systematic exclusion can take lasting physical form in the built environment. There has been growing attention to the long-term consequences of housing policies and practices on social and economic outcomes, including residential segregation, but comparatively less attention to other aspects of the built environment, such as road networks and spatial (dis)connectivity. In this article, the authors introduce a novel method that constructs counterfactual road networks by identifying missing road segments that would be expected to exist in a city’s road network, given the surrounding infrastructure. The authors demonstrate the empirical application of the method by analyzing differences in racial composition and residential segregation for the observed and counterfactual road networks of five U.S. cities. The authors find that unexpected disconnectivity in a city’s road network is associated with greater differences in the racial composition of nearby areas and higher levels of segregation at the local and city levels. The present findings suggest that road networks warrant more attention as a factor that may contribute to the persistence of segregation.

We estimate fair graphs from graph-stationary nodal observations such that connections are not biased with respect to sensitive attributes. Edges in real-world graphs often exhibit preferences for connecting certain pairs of groups. Biased connections can not only exacerbate but even induce unfair treatment for downstream graph-based tasks. We therefore consider group and individual fairness for graphs corresponding to group- and node-level definitions, respectively. To evaluate the fairness of a given graph, we provide multiple bias metrics, including novel measurements in the spectral domain. Furthermore, we propose Fair Spectral Templates (FairSpecTemp), an optimization-based method with two variants for estimating fair graphs from stationary graph signals, a general model for graph data subsuming many existing ones. One variant of FairSpecTemp exploits commutativity properties of graph stationarity while directly constraining bias, while the other implicitly encourages fair estimates by restricting bias in the graph spectrum and is thus more flexible. Our methods enjoy high probability performance bounds, yielding a conditional tradeoff between fairness and accuracy. In particular, our analysis reveals that accuracy need not be sacrificed to recover fair graphs. We evaluate FairSpecTemp on synthetic and real-world data sets to illustrate its effectiveness and highlight the advantages of both variants of FairSpecTemp.

In wireless networks characterized by dense connectivity, the significant signaling overhead generated by distributed link scheduling algorithms can exacerbate issues like congestion, energy consumption, and radio footprint expansion. To mitigate these challenges, we propose a distributed link sparsification scheme employing graph neural networks (GNNs) to reduce scheduling overhead for delay-tolerant traffic while maintaining network capacity. A GNN module is trained to adjust contention thresholds for individual links based on traffic statistics and network topology, enabling links to withdraw from scheduling contention when they are unlikely to succeed. Our approach is facilitated by a novel offline constrained unsupervised learning algorithm capable of balancing two competing objectives: minimizing scheduling overhead while ensuring that total utility meets the required level. In simulated wireless multi-hop networks with up to 500 links, our link sparsification technique effectively alleviates network congestion and reduces radio footprints across four distinct distributed link scheduling protocols.

Graphons, as limit objects of dense graph sequences, play a central role in the statistical analysis of network data. However, existing graphon estimation methods often struggle with scalability to large networks and resolution-independent approximation, due to their reliance on estimating latent variables or costly metrics such as the Gromov-Wasserstein distance. In this work, we propose a novel, scalable graphon estimator that directly recovers the graphon via moment matching, leveraging implicit neural representations (INRs). Our approach avoids latent variable modeling by training an INR--mapping coordinates to graphon values--to match empirical subgraph counts (i.e., moments) from observed graphs. This direct estimation mechanism yields a polynomial-time solution and crucially sidesteps the combinatorial complexity of Gromov-Wasserstein optimization. Building on foundational results, we establish a theoretical guarantee: when the observed subgraph motifs sufficiently represent those of the true graphon (a condition met with sufficiently large or numerous graph samples), the estimated graphon achieves a provable upper bound in cut distance from the ground truth. Additionally, we introduce MomentMixup, a data augmentation technique that performs mixup in the moment space to enhance graphon-based learning. Our graphon estimation method achieves strong empirical performance--demonstrating high accuracy on small graphs and superior computational efficiency on large graphs--outperforming state-of-the-art scalable estimators in 75\% of benchmark settings and matching them in the remaining cases. Furthermore, MomentMixup demonstrated improved graph classification accuracy on the majority of our benchmarks.

Diffusion models have emerged as powerful generative models for graph generation, yet their use for conditional graph generation remains a fundamental challenge. In particular, guiding diffusion models on graphs under arbitrary reward signals is difficult: gradient-based methods, while powerful, are often unsuitable due to the discrete and combinatorial nature of graphs, and non-differentiable rewards further complicate gradient-based guidance. We propose Graph Guided Diffusion (GGDiff), a novel guidance framework that interprets conditional diffusion on graphs as a stochastic control problem to address this challenge. GGDiff unifies multiple guidance strategies, including gradient-based guidance (for differentiable rewards), control-based guidance (using control signals from forward reward evaluations), and zero-order approximations (bridging gradient-based and gradient-free optimization). This comprehensive, plug-and-play framework enables zero-shot guidance of pre-trained diffusion models under both differentiable and non-differentiable reward functions, adapting well-established guidance techniques to graph generation--a direction largely unexplored. Our formulation balances computational efficiency, reward alignment, and sample quality, enabling practical conditional generation across diverse reward types. We demonstrate the efficacy of GGDiff in various tasks, including constraints on graph motifs, fairness, and link prediction, achieving superior alignment with target rewards while maintaining diversity and fidelity.