Transferability of Graph Neural Networks using Graphon and Sampling Theories

Graph neural networks (GNNs) have become powerful tools for processing graph-based information in various domains. A desirable property of GNNs is transferability, where a trained network can swap in information from a different graph without retraining and retain its accuracy. A recent method of capturing transferability of GNNs is through the use of graphons, which are symmetric, measurable functions representing the limit of large dense graphs. In this work, we contribute to the application of graphons to GNNs by presenting an explicit two-layer graphon neural network (WNN) architecture. We prove its ability to approximate bandlimited signals within a specified error tolerance using a minimal number of network weights. We then leverage this result, to establish the transferability of an explicit two-layer GNN over all sufficiently large graphs in a sequence converging to a graphon. Our work addresses transferability between both deterministic weighted graphs and simple random graphs and overcomes issues related to the curse of dimensionality that arise in other GNN results. The proposed WNN and GNN architectures offer practical solutions for handling graph data of varying sizes while maintaining performance guarantees without extensive retraining

Load fluctuations drive actin network growth

The growth of actin filament networks is a fundamental biological process that drives a variety of cellular and intracellular motions. During motility, eukaryotic cells and intracellular pathogens are propelled by actin networks organized by nucleation-promoting factors, which trigger the formation of nascent filaments off the side of existing filaments in the network. A Brownian ratchet (BR) mechanism has been proposed to couple actin polymerization to cellular movements, whereby thermal motions are rectified by the addition of actin monomers at the end of growing filaments. Here, by following actin--propelled microspheres using three--dimensional laser tracking, we find that beads adhered to the growing network move via an object--fluctuating BR. Velocity varies with the amplitude of thermal fluctuation and inversely with viscosity as predicted for a BR. In addition, motion is saltatory with a broad distribution of step sizes that is correlated in time. These data point to a model in which thermal fluctuations of the microsphere or entire actin network, and not individual filaments, govern motility. This conclusion is supported by Monte Carlo simulations of an adhesion--based BR and suggests an important role for membrane tension in the control of actin--based cellular protrusions.Comment: To be published in PNA

Non-gaussianities and the Stimulated creation of quanta in the inflationary universe

Cosmological inflation generates a spectrum of density perturbations that can seed the cosmic structures we observe today. These perturbations are usually computed as the result of the gravitationally-induced spontaneous creation of perturbations from an initial vacuum state. In this paper, we compute the perturbations arising from gravitationally-induced stimulated creation when perturbations are already present in the initial state. The effect of these initial perturbations is not diluted by inflation and survives to its end, and beyond. We consider a generic statistical density operator $\rho$ describing an initial mixed state that includes probabilities for nonzero numbers of scalar perturbations to be present at early times during inflation. We analyze the primordial bispectrum for general configurations of the three different momentum vectors in its arguments. We find that the initial presence of quanta can significantly enhance non-gaussianities in the so-called squeezed limit. Our results show that an observation of non-gaussianities in the squeezed limit can occur for single-field inflation when the state in the very early inflationary universe is not the vacuum, but instead contains early-time perturbations. Valuable information about the initial state can then be obtained from observations of those non-gaussianities.Comment: 25 page

Identification of a membrane binding peptide in the envelope protein of MHV coronavirus

Coronaviruses (CoVs) are enveloped, positive sense, single strand RNA viruses that cause respiratory, intestinal and neurological diseases in mammals and birds. Following replication, CoVs assemble on intracellular membranes including the endoplasmic reticulum Golgi intermediate compartment (ERGIC) where the envelope protein (E) functions in virus assembly and release. In consequence, E potentially contains membrane-modifying peptides. To search for such peptides, the E coding sequence of Mouse Hepatitis Virus (MHV) was inspected for its amino acid conservation, proximity to the membrane and/or predicted amphipathic helices. Peptides identified in silico were synthesized and tested for membrane-modifying activity in the presence of giant unilamellar vesicles (GUVs) consisting of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), sphingomyelin and cholesterol. To confirm the presence of membrane binding peptides identified in the context of a full-length E protein, the wild type and a number of mutants in the putative membrane binding peptide were expressed in Lenti-X-293T mammalian and insect cells, and the distribution of E antigen within the expressing cell was assessed. Our data identify a role for the post-transmembrane region of MHV E in membrane binding

A fusion peptide in the spike protein of MERS coronavirus

Coronaviruses represent current and emerging threats for many species, including humans. Middle East respiratory syndrome-related coronavirus (MERS-CoV) is responsible for sporadic infections in mostly Middle Eastern countries, with occasional transfer elsewhere. A key step in the MERS-CoV replication cycle is the fusion of the virus and host cell membranes mediated by the virus spike protein, S. The location of the fusion peptide within the MERS S protein has not been precisely mapped. We used isolated peptides and giant unilamellar vesicles (GUV) to demonstrate membrane binding for a peptide located near the N-terminus of the S2 domain. Key residues required for activity were mapped by amino acid replacement and their relevance in vitro tested by their introduction into recombinant MERS S protein expressed in mammalian cells. Mutations preventing membrane binding in vitro also abolished S-mediated syncytium formation consistent with the identified peptide acting as the fusion peptide for the S protein of MERS-CoV

Bromine measurements in ozone depleted air over the Arctic Ocean

In situ measurements of ozone, photochemically active bromine compounds, and other trace gases over the Arctic Ocean in April 2008 are used to examine the chemistry and geographical extent of ozone depletion in the arctic marine boundary layer (MBL). Data were obtained from the NOAA WP-3D aircraft during the Aerosol, Radiation, and Cloud Processes affecting Arctic Climate (ARCPAC) study and the NASA DC-8 aircraft during the Arctic Research of the Composition of the Troposphere from Aircraft and Satellites (ARCTAS) study. Fast (1 s) and sensitive (detection limits at the low pptv level) measurements of BrCl and BrO were obtained from three different chemical ionization mass spectrometer (CIMS) instruments, and soluble bromide was measured with a mist chamber. The CIMS instruments also detected Br2. Subsequent laboratory studies showed that HOBr rapidly converts to Br2 on the Teflon instrument inlets. This detected Br2 is identified as active bromine and represents a lower limit of the sum HOBr + Br2. The measured active bromine is shown to likely be HOBr during daytime flights in the arctic. In the MBL over the Arctic Ocean, soluble bromide and active bromine were consistently elevated and ozone was depleted. Ozone depletion and active bromine enhancement were confined to the MBL that was capped by a temperature inversion at 200–500 m altitude. In ozone-depleted air, BrO rarely exceeded 10 pptv and was always substantially lower than soluble bromide that was as high as 40 pptv. BrCl was rarely enhanced above the 2 pptv detection limit, either in the MBL, over Alaska, or in the arctic free troposphere

Characteristics of tropospheric ozone depletion events in the Arctic spring: analysis of the ARCTAS, ARCPAC, and ARCIONS measurements and satellite BrO observations

Arctic ozone depletion events (ODEs) are caused by halogen catalyzed ozone loss. In situ chemistry, advection of ozone-poor air mass, and vertical mixing in the lower troposphere are important factors affecting ODEs. To better characterize the ODEs, we analyze the combined set of surface, ozonesonde, and aircraft in situ measurements of ozone and bromine compounds during the Arctic Research of the Composition of the Troposphere from Aircraft and Satellites (ARCTAS), the Aerosol, Radiation, and Cloud Processes affecting Arctic Climate (ARCPAC), and the Arctic Intensive Ozonesonde Network Study (ARCIONS) experiments (April 2008). Tropospheric BrO columns retrieved from satellite measurements and back trajectory calculations are also used to investigate the characteristics of observed ODEs. In situ observations from these field experiments are inadequate to validate tropospheric BrO columns derived from satellite measurements. In view of this difficulty, we construct an ensemble of tropospheric column BrO estimates from two satellite (OMI and GOME-2) measurements and with three independent methods of calculating stratospheric BrO columns. Furthermore, we select analysis methods that do not depend on the absolute magnitude of column BrO, such as time-lagged correlation analysis of ozone and tropospheric column BrO, to understand characteristics of ODEs. Time-lagged correlation analysis between in situ (surface and ozonesonde) measurements of ozone and satellite derived tropospheric BrO columns indicates that the ODEs are due to either local halogen-driven ozone loss or short-range (∼1 day) transport from nearby regions with ozone depletion. The effect of in situ ozone loss is also evident in the diurnal variation difference between low (10th and 25th percentiles) and higher percentiles of surface ozone concentrations at Alert, Canada. Aircraft observations indicate low-ozone air mass transported from adjacent high-BrO regions. Correlation analyses of ozone with potential temperature and time-lagged tropospheric BrO column show that the vertical extent of local ozone loss is surprisingly deep (1–2 km) at Resolute and Churchill, Canada. The unstable boundary layer during ODEs at Churchill could potentially provide a source of free-tropospheric BrO through convective transport and explain the significant negative correlation between free-tropospheric ozone and tropospheric BrO column at this site