Understanding and extending subgraph GNNs by rethinking their symmetries

Subgraph GNNs are a recent class of expressive Graph Neural Networks (GNNs) which model graphs as collections of subgraphs. So far, the design space of possible Subgraph GNN architectures as well as their basic theoretical properties are still largely unexplored. In this paper, we study the most prominent form of subgraph methods, which employs node-based subgraph selection policies such as ego-networks or node marking and deletion. We address two central questions: (1) What is the upper-bound of the expressive power of these methods? and (2) What is the family of equivariant message passing layers on these sets of subgraphs?. Our first step in answering these questions is a novel symmetry analysis which shows that modelling the symmetries of node-based subgraph collections requires a significantly smaller symmetry group than the one adopted in previous works. This analysis is then used to establish a link between Subgraph GNNs and Invariant Graph Networks (IGNs). We answer the questions above by first bounding the expressive power of subgraph methods by 3-WL, and then proposing a general family of message-passing layers for subgraph methods that generalises all previous node-based Subgraph GNNs. Finally, we design a novel Subgraph GNN dubbed SUN, which theoretically unifies previous architectures while providing better empirical performance on multiple benchmarks

Electric fields in plasmas under pulsed currents

Electric fields in a plasma that conducts a high-current pulse are measured as a function of time and space. The experiment is performed using a coaxial configuration, in which a current rising to 160 kA in 100 ns is conducted through a plasma that prefills the region between two coaxial electrodes. The electric field is determined using laser spectroscopy and line-shape analysis. Plasma doping allows for 3D spatially resolved measurements. The measured peak magnitude and propagation velocity of the electric field is found to match those of the Hall electric field, inferred from the magnetic-field front propagation measured previously.Comment: 13 pages, 13 figures, submitted to PR

Role of the Meso Substituent in Defining the Reduction of Uranyl Dipyrrin Complexes

The uranyl complex UVIO2Cl(LMes) of the redox-active, acyclic dipyrrin–diimine anion LMes– [HLMes = 1,9-di-tert-butyl-imine-5-(mesityl)dipyrrin] is reported, and its redox property is explored and compared with that of the previously reported UVIO2Cl(LF) [HLF = 1,9-di-tert-butyl-imine-5-(pentafluorophenyl)dipyrrin] to understand the influence of the meso substituent. Cyclic voltammetry, electron paramagnetic resonance spectroscopy, and density functional theory studies show that the alteration from an electron-withdrawing meso substituent to an electron-donating meso substituent on the dipyrrin ligand significantly modifies the stability of the products formed after reduction. For UVIO2Cl(LMes), the formation of a diamond-shaped, oxo-bridged uranyl(V) dimer, [UVO2(LMes)]2 is seen, whereas in contrast, for UVIO2Cl(LF), only ligand reduction occurs. Computational modeling of these reactions shows that while ligand reduction followed by chloride dissociation occurs in both cases, ligand-to-metal electron transfer is favorable for UVIO2Cl(LMes) only, which subsequently facilitates uranyl(V) dimerization

The onset of a small-scale turbulent dynamo at low magnetic Prandtl numbers

We study numerically the dependence of the critical magnetic Reynolds number Rmc for the turbulent small-scale dynamo on the hydrodynamic Reynolds number Re. The turbulence is statistically homogeneous, isotropic, and mirror--symmetric. We are interested in the regime of low magnetic Prandtl number Pm=Rm/Re<1, which is relevant for stellar convective zones, protostellar disks, and laboratory liquid-metal experiments. The two asymptotic possibilities are Rmc->const as Re->infinity (a small-scale dynamo exists at low Pm) or Rmc/Re=Pmc->const as Re->infinity (no small-scale dynamo exists at low Pm). Results obtained in two independent sets of simulations of MHD turbulence using grid and spectral codes are brought together and found to be in quantitative agreement. We find that at currently accessible resolutions, Rmc grows with Re with no sign of approaching a constant limit. We reach the maximum values of Rmc~500 for Re~3000. By comparing simulations with Laplacian viscosity, fourth-, sixth-, and eighth-order hyperviscosity and Smagorinsky large-eddy viscosity, we find that Rmc is not sensitive to the particular form of the viscous cutoff. This work represents a significant extension of the studies previously published by Schekochihin et al. 2004, PRL 92, 054502 and Haugen et al. 2004, PRE, 70, 016308 and the first detailed scan of the numerically accessible part of the stability curve Rmc(Re).Comment: 4 pages, emulateapj aastex, 2 figures; final version as published in ApJL (but with colour figures

Exploring the Redox Properties of Bench-Stable Uranyl(VI) Diamido–Dipyrrin Complexes

[Image: see text] The uranyl complexes UO(2)(OAc)(L) and UO(2)Cl(L) of the redox-active, acyclic diamido–dipyrrin anion L(–) are reported and their redox properties explored. Because of the inert nature of the complexes toward hydrolysis and oxidation, synthesis of both the ligands and complexes was conducted under ambient conditions. Voltammetric, electron paramagnetic resonance spectroscopy, and density functional theory studies show that one-electron chemical reduction by the reagent CoCp(2) leads to the formation of a dipyrrin radical for both complexes [Cp(2)Co][UO(2)(OAc)(L(•))] and [Cp(2)Co][UO(2)Cl(L(•))]

Self-similar turbulent dynamo

The amplification of magnetic fields in a highly conducting fluid is studied numerically. During growth, the magnetic field is spatially intermittent: it does not uniformly fill the volume, but is concentrated in long thin folded structures. Contrary to a commonly held view, intermittency of the folded field does not increase indefinitely throughout the growth stage if diffusion is present. Instead, as we show, the probability-density function (PDF) of the field strength becomes self-similar. The normalized moments increase with magnetic Prandtl number in a powerlike fashion. We argue that the self-similarity is to be expected with a finite flow scale and system size. In the nonlinear saturated state, intermittency is reduced and the PDF is exponential. Parallels are noted with self-similar behavior recently observed for passive-scalar mixing and for map dynamos.Comment: revtex, 4 pages, 5 figures; minor changes to match published versio