Equivariant Polynomials for Graph Neural Networks

Graph Neural Networks (GNN) are inherently limited in their expressive power. Recent seminal works (Xu et al., 2019; Morris et al., 2019b) introduced the Weisfeiler-Lehman (WL) hierarchy as a measure of expressive power. Although this hierarchy has propelled significant advances in GNN analysis and architecture developments, it suffers from several significant limitations. These include a complex definition that lacks direct guidance for model improvement and a WL hierarchy that is too coarse to study current GNNs. This paper introduces an alternative expressive power hierarchy based on the ability of GNNs to calculate equivariant polynomials of a certain degree. As a first step, we provide a full characterization of all equivariant graph polynomials by introducing a concrete basis, significantly generalizing previous results. Each basis element corresponds to a specific multi-graph, and its computation over some graph data input corresponds to a tensor contraction problem. Second, we propose algorithmic tools for evaluating the expressiveness of GNNs using tensor contraction sequences, and calculate the expressive power of popular GNNs. Finally, we enhance the expressivity of common GNN architectures by adding polynomial features or additional operations / aggregations inspired by our theory. These enhanced GNNs demonstrate state-of-the-art results in experiments across multiple graph learning benchmarks

Fitness consequences of occasional outcrossing in a functionally asexual plant (Oenothera biennis)

Many clonal organisms occasionally outcross, but the long?term consequences of such infrequent events are often unknown. During five years, representing three to five plant generations, we followed 16 experimental field populations of the forb, Oenothera biennis, originally planted with the same 18 original genotypes. Oenothera biennis usually self fertilizes, which, due to its genetic system (permanent translocation heterozygosity), results in seeds that are clones of the maternal plant. However, rare outcrossing produces genetically novel offspring (but without recombination or increased heterozygosity). We sought to understand whether novel genotypes produced through natural outcrossing had greater fecundity or different multigenerational dynamics compared to our original genotypes. We further assessed whether any differences in fitness or abundances through time between original and novel genotypes were exaggerated in the presence vs. absence of insect herbivores. Over the course of the experiment, we genotyped >12,500 plants using microsatellite DNA markers to identify and track the frequency of specific genotypes and estimated fecundity on a subset (>3,000) of plants. The effective outcrossing rate was 7.3% in the first year and ultimately 50% of the plants were of outcrossed origin by the final year of the experiment. Lifetime fruit production per plant was on average 32% higher across all novel genotypes produced via outcrossing compared to the original genotypes, and this fecundity advantage was significantly enhanced in populations lacking herbivores. Among 43 novel genotypes that were abundant enough to phenotype with replication, plants produced nearly 30% more fruits than the average of their specific two parental genotypes, and marginally more fruits (8%) than their most fecund parent. Mean per capita fecundity of novel genotypes predicted their relative frequencies at the end of the experiment. Novel genotypes increased more dramatically in herbivore?present compared to suppressed populations (45% vs. 27% of all plants), countering the increased competition from dandelions (Taraxacum officinale) that resulted from herbivore suppression. Increased interspecific competition likely also lead to the lower realized fitness of novel vs. original genotypes in herbivore?suppressed populations. These results demonstrate that rare outcrossing and the generation of novel genotypes can create high?fecundity progeny, with the biotic environment influencing the dynamical outcome of such advantages.This study was supported by a grant to A. A. Agrawal from NSF DEB-0950231. M. T. J. Johnson received funding from NSERC. J. L. Maron was supported by NSF DEB-1553518

Response to Letter Regarding Article, "Hypertrophic Cardiomyopathy Is Predominantly a Disease of Left Ventricular Outflow Tract Obstruction"

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A Field Experiment Demonstrating Plant Life-History Evolution and its Eco-Evolutionary Feedback to Seed Predator Populations

The extent to which evolutionary change occurs in a predictable manner under field conditions and how evolutionary changes feed back to influence ecological dynamics are fundamental, yet unresolved, questions. To address these issues, we established eight replicate populations of native common evening primrose (Oenothera biennis). Each population was planted with 18 genotypes in identical frequency. By tracking genotype frequencies with microsatellite DNA markers over the subsequent three years (up to three generations, approximate to 5,000 genotyped plants), we show rapid and consistent evolution of two heritable plant life-history traits (shorter life span and later flowering time). This rapid evolution was only partially the result of differential seed production; genotypic variation in seed germination also contributed to the observed evolutionary response. Since evening primrose genotypes exhibited heritable variation for resistance to insect herbivores, which was related to flowering time, we predicted that evolutionary changes in genotype frequencies would feed back to influence populations of a seed predator moth that specializes on O. biennis. By the conclusion of the experiment, variation in the genotypic composition among our eight replicate field populations was highly predictive of moth abundance. These results demonstrate how rapid evolution in field populations of a native plant can influence ecological interactions

Cascade of Complexity in Evolving Predator-Prey Dynamics

We simulate an individual-based model that represents both the phenotype and genome of digital organisms with predator-prey interactions. We show how open-ended growth of complexity arises from the invariance of genetic evolution operators with respect to changes in the complexity, and that the dynamics which emerges is controlled by a non-equilibrium critical point. The mechanism is analogous to the development of the cascade in fluid turbulence.Comment: 5 pages, 3 figures; added comments on system size scaling and turbulence analogy, added error estimates of data collapse parameters. Slightly enhanced from the version which will appear in PR

An integrated approach to determine left atrial volume, mass and function in hypertrophic cardiomyopathy by two-dimensional echocardiography

Methods: The study included 25 hypertrophic cardiomyopathy (HCM) patients (15 non-obstructive and 10 obstructive) and 25 controls for assessment of left atrial (LA) volume, mass and function by two-dimensional echocardiography. Measurement included mean LA diameter (LAD), LA mass = {(mean LAD + anterior LA wall + posterior LA wall)3- mean LAD3} × 0.8 + 0.6, LA volume = [(8/3 φ L ̇ A1 ̇ A2), where L is LA length, A1 and A2 are LA area in 4-chambers and 2-chambers, respectively] including maximum (Vmax), minimum (Vmin), and pre-atrial contraction (Vpre-A), total atrial stroke volume (TA-SV), TA emptying fraction (TA-EF), active atrial SV (AA-SV), AA-EF, passive atrial SV (PA-SV), PA-EF, atrial expansion index (AEI), and LA kinetic energy (LA-KE) = 1/2 × AA-SV × P × V2. Results: LAD, LA mass, Vmax, Vmin, and Vpre-Awere significantly higher in HCM than controls. TA-SV and TA-EF were comparable in both HCM subgroups and controls. AA-SV and LA-KE were significantly higher in both HCM subgroups than controls. LA-KE was significantly higher in obstructive HCM than non-obstructive (P < 0.001). PA-EF and AEI were significantly lower in obstructive HCM than controls (P < 0.05). Conclusion: HCM is associated with increased LA size and augmented LA pump function especially obstructive type. LA conduit and reservoir functions are impaired in obstructive HCM

Gas-phase oxidative dehydrogenation of long chain alkenols for the production of key fragrance ingredients: from Rosalva isomers to Costenal analogues

The continuous-flow, gas-phase oxidative dehydrogenation (ODH) of an actual mixture of decen-1-ol isomers ("Isorosalva" alcohol) towards the corresponding mixture of aldehydes ("Costenal" analogues, valuable ingredients in perfumes formulation) is herein reported for the first time over noble metal-free catalysts. In particular, the optimisation of the reaction conditions over a copper ferrite (Cu/Fe/O), as well as dedicated characterizations and comparisons between the fresh, the post-reaction (reduced) and regenerated (re-oxidised) catalytic material, allowed us to underline the key role of well dispersed copper oxide over a Fe-enriched spinel in promoting the selective ODH of Isorosalva alcohol. The superior catalytic activity and selectivity of CuO/gamma-Fe2O3 synthesized ad hoc were attributed to the very high dispersion of Cu over the support as well as to a cooperative effect between Cu and Fe species in promoting the redox cycle

Establishment of a validation and benchmark database for the assessment of ship operation in adverse conditions

The Energy Efficiency Design Index (EEDI), introduced by the IMO [1] is applicable for various types of new-built ships since January 2013. Despite the release of an interim guideline [2], concerns regarding the sufficiency of propulsion power and steering devices to maintain manoeuvrability of ships in adverse conditions were raised. This was the motivation for the EU research project SHOPERA (Energy Efficient Safe SHip OPERAtion, 2013-2016 [3-6]). The aim of the project is the development of suitable methods, tools and guidelines to effectively address these concerns and to enable safe and green shipping. Within the framework of SHOPERA, a comprehensive test program consisting of more than 1,300 different model tests for three ship hulls of different geometry and hydrodynamic characteristics has been conducted by four of the leading European maritime experimental research institutes: MARINTEK, CEHIPAR, Flanders Hydraulics Research and Technische Universität Berlin. The hull types encompass two public domain designs, namely the KVLCC2 tanker (KRISO VLCC, developed by KRISO) and the DTC container ship (Duisburg Test Case, developed by Universität Duisburg-Essen) as well as a RoPax ferry design, which is a proprietary hull design of a member of the SHOPERA consortium. The tests have been distributed among the four research institutes to benefit from the unique possibilities of each facility and to gain added value by establishing data sets for the same hull model and test type at different under keel clearances (ukc). This publication presents the scope of the SHOPERA model test program for the two public domain hull models – the KVLCC2 and the DTC. The main particulars and loading conditions for the two vessels as well as the experimental setup is provided to support the interpretation of the examples of experimental data that are discussed. The focus lies on added resistance at moderate speed and drift force tests in high and steep regular head, following and oblique waves. These climates have been selected to check the applicability of numerical models in adverse wave conditions and to cover possible non-linear effects. The obtained test results with the KVLCC2 model in deep water at CEHIPAR are discussed and compared against the results obtained in shallow water at Flanders Hydraulics Research. The DTC model has been tested at MARINTEK in deep water and at Technische Universität Berlin and Flanders Hydraulics Research in intermediate/shallow water in different set-ups. Added resistance and drift force measurements from these facilities are discussed and compared. Examples of experimental data is also presented for manoeuvring in waves. At MARINTEK, turning circle and zig-zag tests have been performed with the DTC in regular waves. Parameters of variation are the initial heading, the wave period and height