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Traditional cancer rate estimations are often limited in spatial resolutions and lack considerations of environmental factors. Satellite imagery has become a vital data source for monitoring diverse urban environments, supporting applications across environmental, socio-demographic, and public health domains. However, while deep learning (DL) tools, particularly convolutional neural networks, have demonstrated strong performance in extracting features from high-resolution imagery, their reliance on local spatial cues often limits their ability to capture complex, non-local, and higher-order structural information. To overcome this limitation, we propose a novel LLM-based multi-agent coordination system for satellite image analysis, which integrates visual and contextual reasoning through a simplicial contrastive learning framework (Agent- SNN). Our Agent-SNN contains two augmented superpixel-based graphs and maximizes mutual information between their latent simplicial complex representations, thereby enabling the system to learn both local and global topological features. The LLM-based agents generate structured prompts that guide the alignment of these representations across modalities. Experiments with satellite imagery of Los Angeles and San Diego demonstrate that Agent-SNN achieves signi cant improvements over state-of-the-art baselines in regional cancer prevalence estimation tasks. 

Pre-training has emerged as a dominant paradigm in graph representation learning to address data scarcity and generalization challenges. The majority of existing methods primarily focus on refining fine-tuning and prompting techniques to extract information from pre-trained models. However, the effectiveness of these approaches is contingent upon the quality of the pre-trained knowledge (i.e., latent representations). Inspired by the recent success in topological representation learning, we propose a novel pre-training strategy to capture and learn topological information of graphs. The key to the success of our strategy is to pre-train expressive Graph Neural Networks (GNNs) at the levels of individual nodes while accounting for the key topological characteristics of a graph so that GNNs become sufficiently powerful to effectively encode input graph information. The proposed model is designed to be seamlessly integrated with various downstream graph representation learning tasks. 

Each year wildfires result in billions of dollars in property damage. Being one of the major natural hazards, wildfires nowadays are also a global affair whose negative impact is particularly devastating in developing countries. As wildfires are expected to become more frequent and severe, more accurate models to predict wildfires are vital to mitigating risks and developing more informed decision-making. Artificial intelligence (AI) has a potential to enhance wildfire risk analytics on multiple fronts. For example, deep learning (DL) has been successfully used to classify active fires, burned scars, smoke plumes and to track the spread of active wildfires. Since wildfire spread tends to exhibit highly complex spatio-temporal dependencies which often cannot be accurately described with conventional Euclideanbased approaches, we postulate that the tools of topological and geometric deep learning, specifically designed for non-Euclidean objects such as manifolds and graphs, may offer a more competitive solution. We validate the proposed methodology to predict wildfire occurrences in Greece and several regions of Africa. Our results indicate that the Firecast Zigzag Convolutional Network (F-ZCN) outperforms the current baseline methods for wildfire prediction and opens a path for more accurate wildfire risk analytics, even in scenarios of limited and noisy data records. 

Learning time-evolving objects such as multivariate time series and dynamic networks requires the development of novel knowledge representation mechanisms and neural network architectures, which allow for capturing implicit time-dependent information contained in the data. Such information is typically not directly observed but plays a key role in the learning task performance. In turn, lack of time dimension in knowledge encoding mechanisms for time-dependent data leads to frequent model updates, poor learning performance, and, as a result, subpar decision-making. Here we propose a new approach to a time-aware knowledge representation mechanism that notably focuses on implicit time-dependent topological information along multiple geometric dimensions. In particular, we propose a new approach, named Temporal MultiPersistence (TMP), which produces multidimensional topological fingerprints of the data by using the existing single parameter topological summaries. The main idea behind TMP is to merge the two newest directions in topological representation learning, that is, multi-persistence which simultaneously describes data shape evolution along multiple key parameters, and zigzag persistence to enable us to extract the most salient data shape information over time. We derive theoretical guarantees of TMP vectorizations and show its utility, in application to forecasting on benchmark traffic flow, Ethereum blockchain, and electrocardiogram datasets, demonstrating the competitive performance, especially, in scenarios of limited data records. In addition, our TMP method improves the computational efficiency of the state-of-the-art multipersistence summaries up to 59.5 times. 

Satellite imagery is a readily available data source for monitoring a broad range of urban geographical contexts related to environmental, socio-demographic, and health disparities. To analyze satellite images, deep learning (DL) tools efficiently extract latent multi-dimensional characteristics, beyond identifying specific urban elements like roads and houses. However, current DL approaches tend to largely rely on Convolutional Neural Networks applied to high-resolution imagery, and as such may be limited to capturing only local contextual information. To address this fundamental limitation, we propose to fuse the modalities of satellite imagery and a large language model (LLM). In particular, we develop a novel LLM-based Simplicial Contrastive Learning model (LLM-SCL) based on mutual information maximization between the latent simplicial complex-level representations of two kinds of augmented (superpixel) graphs, which allows for cohesive integration of LLM prompts and learning of both local and global higher-order properties of satellite imagery (from all pixels in an image). Extensive experiments on satellite imagery at several resolutions in Tijuana, Mexico, Los Angeles and San Diego, USA, suggest that LLM-SCL significantly outperforms state-of-the-art baselines on unsupervised image classification tasks. As such, the proposed LLM-SCL opens a new path for more accurate evaluations of latent urban forms and their associations with environmental and health outcome disparities. 

Networks allow us to describe a wide range of interaction phenomena that occur in complex systems arising in such diverse fields of knowledge as neuroscience, engineering, ecology, finance, and social sciences. Until very recently, the primary focus of network models and tools has been on describing the pairwise relationships between system entities. However, increasingly more studies indicate that polyadic or higher-order group relationships among multiple network entities may be the key toward better understanding of the intrinsic mechanisms behind the functionality of complex systems. Such group interactions can be, in turn, described in a holistic manner by simplicial complexes of graphs. Inspired by these recently emerging results on the utility of the simplicial geometry of complex networks for contagion propagation and armed with a large-scale synthetic social contact network (also known as a digital twin) of the population in the U.S. state of Virginia, in this paper, we aim to glean insights into the role of higher-order social interactions and the associated varying social group determinants on COVID-19 propagation and mitigation measures. 

Graph neural networks (GNNs) have demonstrated a significant success in various graph learning tasks, from graph classification to anomaly detection. There recently has emerged a number of approaches adopting a graph pooling operation within GNNs, with a goal to preserve graph attributive and structural features during the graph representation learning. However, most existing graph pooling operations suffer from the limitations of relying on node-wise neighbor weighting and embedding, which leads to insufficient encoding of rich topological structures and node attributes exhibited by real-world networks. By invoking the machinery of persistent homology and the concept of landmarks, we propose a novel topological pooling layer and witness complex-based topological embedding mechanism that allow us to systematically integrate hidden topological information at both local and global levels. Specifically, we design new learnable local and global topological representations Wit-TopoPool which allow us to simultaneously extract rich discriminative topological information from graphs. Experiments on 11 diverse benchmark datasets against 18 baseline models in conjunction with graph classification tasks indicate that Wit-TopoPool significantly outperforms all competitors across all datasets.