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Graph neural networks are typically trained on individual datasets, often requiring highly specialized models and extensive hyperparameter tuning. This dataset-specific approach arises because each graph dataset often has unique node features and diverse connectivity structures, making it difficult to build a generalist model. To address these challenges, we introduce a scalable multi-graph multi-task pretraining approach specifically tailored for node classification tasks across diverse graph datasets from different domains. Our method, Graph Foundation Model (GraphFM), leverages a Perceiver-based encoder that employs learned latent tokens to compress domain-specific features into a common latent space. This approach enhances the model's ability to generalize across different graphs and allows for scaling across diverse data. We demonstrate the efficacy of our approach by training a model on 152 different graph datasets comprising over 7.4 million nodes and 189 million edges, establishing the first set of scaling laws for multi-graph pretraining on datasets spanning many domains (e.g., molecules, citation and product graphs). Our results show that pretraining on a diverse array of real and synthetic graphs improves the model's adaptability and stability, while performing competitively with state-of-the-art specialist models. This work illustrates that multi-graph pretraining can significantly reduce the burden imposed by the current graph training paradigm, unlocking new capabilities for the field of graph neural networks by creating a single generalist model that performs competitively across a wide range of datasets and tasks.

Vaccine hesitancy, or the reluctance to be vaccinated, is a phenomenon that has recently become particularly significant, in conjunction with the vaccination campaign against COVID-19. During the lockdown period, necessary to control the spread of the virus, social networks have played an important role in the Italian debate on vaccination, generally representing the easiest and safest way to exchange opinions and maintain some form of sociability. Among social network platforms, Twitter has assumed a strategic role in driving the public opinion, creating compact groups of users sharing similar views towards the utility, uselessness or even dangerousness of vaccines. In this paper, we present a new, publicly available, dataset of Italian tweets, TwitterVax, collected in the period January 2019--May 2022. Considering monthly data, gathered into forty one retweet networks -- where nodes identify users and edges are present between users who have retweeted each other -- we performed community detection within the networks, analyzing their evolution and polarization with respect to NoVax and ProVax users through time. This allowed us to clearly discover debate trends as well as identify potential key moments and actors in opinion flows, characterizing the main features and tweeting behavior of the two communities.

In Graph Neural Networks (GNNs), hierarchical pooling operators generate local summaries of the data by coarsening the graph structure and the vertex features. While considerable attention has been devoted to analyzing the expressive power of message-passing (MP) layers in GNNs, a study on how graph pooling affects the expressiveness of a GNN is still lacking. Additionally, despite the recent advances in the design of pooling operators, there is not a principled criterion to compare them. In this work, we derive sufficient conditions for a pooling operator to fully preserve the expressive power of the MP layers before it. These conditions serve as a universal and theoretically grounded criterion for choosing among existing pooling operators or designing new ones. Based on our theoretical findings, we analyze several existing pooling operators and identify those that fail to satisfy the expressiveness conditions. Finally, we introduce an experimental setup to verify empirically the expressive power of a GNN equipped with pooling layers, in terms of its capability to perform a graph isomorphism test.

Graph Neural Networks (GNNs) have become the leading paradigm for learning on (static) graph-structured data. However, many real-world systems are dynamic in nature, since the graph and node/edge attributes change over time. In recent years, GNN-based models for temporal graphs have emerged as a promising area of research to extend the capabilities of GNNs. In this work, we provide the first comprehensive overview of the current state-of-the-art of temporal GNN, introducing a rigorous formalization of learning settings and tasks and a novel taxonomy categorizing existing approaches in terms of how the temporal aspect is represented and processed. We conclude the survey with a discussion of the most relevant open challenges for the field, from both research and application perspectives.

Graph Neural Networks (GNNs) are a large class of relational models for graph processing. Recent theoretical studies on the expressive power of GNNs have focused on two issues. On the one hand, it has been proven that GNNs are as powerful as the Weisfeiler-Lehman test (1-WL) in their ability to distinguish graphs. Moreover, it has been shown that the equivalence enforced by 1-WL equals unfolding equivalence. On the other hand, GNNs turned out to be universal approximators on graphs modulo the constraints enforced by 1-WL/unfolding equivalence. However, these results only apply to Static Attributed Undirected Homogeneous Graphs (SAUHG) with node attributes. In contrast, real-life applications often involve a much larger variety of graph types. In this paper, we conduct a theoretical analysis of the expressive power of GNNs for two other graph domains that are particularly interesting in practical applications, namely dynamic graphs and SAUGHs with edge attributes. Dynamic graphs are widely used in modern applications; hence, the study of the expressive capability of GNNs in this domain is essential for practical reasons and, in addition, it requires a new analyzing approach due to the difference in the architecture of dynamic GNNs compared to static ones. On the other hand, the examination of SAUHGs is of particular relevance since they act as a standard form for all graph types: it has been shown that all graph types can be transformed without loss of information to SAUHGs with both attributes on nodes and edges. This paper considers generic GNN models and appropriate 1-WL tests for those domains. Then, the known results on the expressive power of GNNs are extended to the mentioned domains: it is proven that GNNs have the same capability as the 1-WL test, the 1-WL equivalence equals unfolding equivalence and that GNNs are universal approximators modulo 1-WL/unfolding equivalence.

This article presents a complete second order theory for a large class of geometric functionals on homogeneous Poisson input. In particular, the results don't require the existence of a radius of stabilisation. Hence they can be applied to geometric functionals of spatial shot-noise fields excursions such as volume, perimeter, or Euler characteristic (the method still applies to stabilising functionals). More generally, it must be checked that a local contribution to the functional is not strongly affected under a perturbation of the input far away. In this case the exact asymptotic variance is given, as well as the likely optimal speed of convergence in the central limit theorem. This goes through a general mixing-type condition that adapts nicely to both proving asymptotic normality and that variance is of volume order.

We present final Spitzer trigonometric parallaxes for 361 L, T, and Y dwarfs. We combine these with prior studies to build a list of 525 known L, T, and Y dwarfs within 20 pc of the Sun, 38 of which are presented here for the first time. Using published photometry and spectroscopy as well as our own follow-up, we present an array of color–magnitude and color–color diagrams to further characterize census members, and we provide polynomial fits to the bulk trends. Using these characterizations, we assign each object a T(eff) value and judge sample completeness over bins of T(eff) and spectral type. Except for types ≥T8 and T(eff) < 600 K, our census is statistically complete to the 20 pc limit. We compare our measured space densities to simulated density distributions and find that the best fit is a power law (dN/dM ∝ M^(-α) with α = 0.6 ± 0.1. We find that the evolutionary models of Saumon & Marley correctly predict the observed magnitude of the space density spike seen at 1200 K < T(eff) < 1350 K, believed to be caused by an increase in the cooling timescale across the L/T transition. Defining the low-mass terminus using this sample requires a more statistically robust and complete sample of dwarfs ≥Y0.5 and with T(eff) < 400 K. We conclude that such frigid objects must exist in substantial numbers, despite the fact that few have so far been identified, and we discuss possible reasons why they have largely eluded detection.

As a result of the importance of black soldier fly larvae (BSFL) in the insect sector, demand and production of this species are increasing quickly. Consequently, a larger scale production of BSFL involves an increased importance of transport and storage of the insects as part of the logistic chain. The management of this logistic chain within or between companies producing and/or processing BSFL is essential in order to prevent economical losses and optimize the insect sector. Research regarding methods for stable transport and storage of insects is scarce and therefore necessary. Water can be an promising transport or storage medium for living insects. It not only provides the possibility of combining washing and storage/transport, but can also contribute to fast and easy cooling of the insects and can allow the insects to be "pumped" through or between facilities. A high survival is of course crucial when applying a storage technique. Hence, in this study, the survival of BSFL in water of different temperatures is currently being investigated as a first step in assessing the potential of water in insect storage or transport. Samples of living, freshly harvested BSFL are submerged in preconditioned water (3:1 ratio insects:water (m/m)) at three different temperatures (ambient, 15 °C and 4 °C) and stored for five days at their respective temperatures. With intervals of 12 to 24 h, samples are being evaluated for the survival of the larvae. Additionally, the pH of the water during the storage period is monitored in order to investigate the impact of the residing larvae on the pH of the water over time. In a next study, also the impact of the microbiological quality of the water and the insects as well as excretion of frass during storage on the survival rate can be included. Based on the results from this and following studies, guidelines for storage or transport in water can be developed for the insect industry. [ABSTRACT FROM AUTHOR]