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Graphs are ubiquitous in various domains, such as social networks and biological systems. Despite the great successes of graph neural networks (GNNs) in modeling and analyzing complex graph data, the inductive bias of locality assumption, which involves exchanging information only within neighboring connected nodes, restricts GNNs in capturing long-range dependencies and global patterns in graphs. Inspired by the classic Brachistochrone problem, we seek how to devise a new inductive bias for cutting-edge graph application and present a general framework through the lens of variational analysis. The backbone of our framework is a two-way mapping between the discrete GNN model and continuous diffusion functional, which allows us to design application-specific objective function in the continuous domain and engineer discrete deep model with mathematical guarantees. First, we address over-smoothing in current GNNs. Specifically, our inference reveals that the existing layer-by-layer models of graph embedding learning are equivalent to a ℓ 2 -norm integral functional of graph gradients, which is the underlying cause of the over-smoothing problem. Similar to edge-preserving filters in image denoising, we introduce the total variation (TV) to promote alignment of the graph diffusion pattern with the global information present in community topologies. On top of this, we devise a new selective mechanism for inductive bias that can be easily integrated into existing GNNs and effectively address the trade-off between model depth and over-smoothing. Second, we devise a novel generative adversarial network (GAN) to predict the spreading flows in the graph through a neural transport equation. To avoid the potential issue of vanishing flows, we tailor the objective function to minimize the transportation within each community while maximizing the inter-community flows. Our new GNN models achieve state-of-the-art (SOTA) performance on graph learning benchmarks such as Cora, Citeseer, and Pubmed. 

IntroductionNosemais a diverse genus of unicellular microsporidian parasites of insects and other arthropods.Nosema muscidifuracisinfects parasitoid wasp species ofMuscidifurax zaraptorandM. raptor(Hymenoptera: Pteromalidae), causing ~50% reduction in longevity and ~90% reduction in fecundity. Methods and ResultsHere, we report the first assembly of theN. muscidifuracisgenome (14,397,169 bp in 28 contigs) of high continuity (contig N50 544.3 Kb) and completeness (BUSCO score 97.0%). A total of 2,782 protein-coding genes were annotated, with 66.2% of the genes having two copies and 24.0% of genes having three copies. These duplicated genes are highly similar, with a sequence identity of 99.3%. The complex pattern suggests extensive gene duplications and rearrangements across the genome. We annotated 57 rDNA loci, which are highly GC-rich (37%) in a GC-poor genome (25% genome average).Nosema-specific qPCR primer sets were designed based on 18S rDNA annotation as a diagnostic tool to determine its titer in host samples. We discovered highNosematiters inNosema-curedM. raptorandM. zaraptorusing heat treatment in 2017 and 2019, suggesting that the remedy did not completely eliminate theNosemainfection. Cytogenetic analyses revealed heavy infections ofN. muscidifuraciswithin the ovaries ofM. raptorandM. zaraptor, consistent with the titer determined by qPCR and suggesting a heritable component of infection and per ovum vertical transmission. DiscussionThe parasitoids-Nosemasystem is laboratory tractable and, therefore, can serve as a model to inform future genome manipulations ofNosema-host system for investigations of Nosemosis. 

ABSTRACT The orientation of the mitotic spindle determines the direction of cell division, and therefore contributes to tissue shape and cell fate. Interaction between the multifunctional scaffolding protein Discs large (Dlg) and the canonical spindle orienting factor GPSM2 (called Pins in Drosophila and LGN in vertebrates) has been established in bilaterian models, but its function remains unclear. We used a phylogenetic approach to test whether the interaction is obligate in animals, and in particular whether Pins/LGN/GPSM2 evolved in multicellular organisms as a Dlg-binding protein. We show that Dlg diverged in C. elegans and the syncytial sponge Opsacas minuta and propose that this divergence may correspond with differences in spindle orientation requirements between these organisms and the canonical pathways described in bilaterians. We also demonstrate that Pins/LGN/GPSM2 is present in basal animals, but the established Dlg-interaction site cannot be found in either Placozoa or Porifera. Our results suggest that the interaction between Pins/LGN/GPSM2 and Dlg appeared in Cnidaria, and we therefore speculate that it may have evolved to promote accurate division orientation in the nervous system. This work reveals the evolutionary history of the Pins/LGN/GPSM2-Dlg interaction and suggests new possibilities for its importance in spindle orientation during epithelial and neural tissue development. 

Abstract The orientation of the mitotic spindle at metaphase determines the placement of the daughter cells. Spindle orientation in animals typically relies on an evolutionarily conserved biological machine comprised of at least four proteins – called Pins, Gαi, Mud, and Dynein in flies – that exerts a pulling force on astral microtubules and reels the spindle into alignment. The canonical model for spindle orientation holds that the direction of pulling is determined by asymmetric placement of this machinery at the cell cortex. In most cell types, this placement is thought to be mediated by Pins, and a substantial body of literature is therefore devoted to identifying polarized cues that govern localized cortical enrichment of Pins. In this study we revisit the canonical model and find that it is incomplete. Spindle orientation in theDrosophilafollicular epithelium and embryonic ectoderm requires not only Pins localization but also direct interaction between Pins and the multifunctional protein Discs large. This requirement can be over‐ridden by interaction with another Pins interacting protein, Inscuteable.