Characterizing Graph Datasets for Node Classification: Homophily-Heterophily Dichotomy and Beyond

Homophily is a graph property describing the tendency of edges to connect similar nodes; the opposite is called heterophily. It is often believed that heterophilous graphs are challenging for standard message-passing graph neural networks (GNNs), and much effort has been put into developing efficient methods for this setting. However, there is no universally agreed-upon measure of homophily in the literature. In this work, we show that commonly used homophily measures have critical drawbacks preventing the comparison of homophily levels across different datasets. For this, we formalize desirable properties for a proper homophily measure and verify which measures satisfy which properties. In particular, we show that a measure that we call adjusted homophily satisfies more desirable properties than other popular homophily measures while being rarely used in graph machine learning literature. Then, we go beyond the homophily-heterophily dichotomy and propose a new characteristic that allows one to further distinguish different sorts of heterophily. The proposed label informativeness (LI) characterizes how much information a neighbor's label provides about a node's label. We prove that this measure satisfies important desirable properties. We also observe empirically that LI better agrees with GNN performance compared to homophily measures, which confirms that it is a useful characteristic of the graph structure

(Mechano)synthesis of azomethine- and terpyridine-linked diketopyrrolopyrrole-based polymers

Three efficient synthetic approaches towards new azomethine- and terpyridine-containing 2,5-dihydropyrrolo[3,4-c]pyrrole-1,4-dione (diketopyrrolopyrrole, DPP) based polymers, such as P1 and P2, are reported. The first approach involves the Pd-catalyzed synthesis via two- or three-component Suzuki or Stille cross-coupling reaction in solution. The second approach involves Pd-catalyzed Suzuki cross-coupling reaction under ball-milling conditions. And, finally, the third approach involves Pd-free condensation reaction under ball-milling conditions. The newly obtained polymers exhibited absorbance around 700 nm and emission around 900 nm, and, thus, these polymers are considered to be NIR-fluorophores

The role of lateral inhibition in binocular motion rivalry

It is generally believed that percept alternations in binocular rivalry result from the interplay between mutual inhibition and slow adaptation of the competing percepts. This view is supported by growing evidence that dynamic changes in adaptation indeed support percept alternations in binocular rivalry. Empirical evidence for the involvement of mutual inhibition, however, is still scarce. To fill this gap, we presented human subjects with dichoptic random-dot motion stimuli and manipulated the angle between the monocular directions of motion from pure opponent horizontal motion to pure vertical motion in the same direction. We hypothesized that this decrease in motiondirection disparity increases the cross-inhibition gain due to lateral inhibition between neurons in the brain that are coarsely tuned to adjacent directions of visual motion, which predicts the largest changes in dominance at the smallest instead of the largest motion-direction disparities. We found that decreasing the angle between the two monocular directions of motion indeed systematically increased the predominance and mean dominance durations of the motion pattern presented to the ocular dominant eye (as identified by the hole-incard test). Moreover, this effect was stronger if the contrast of the stimuli was lowered. Simulations showed that these features are indeed hallmark of weighted lateral inhibition between populations of directionally tuned motion-sensitive neurons. Our findings thus suggest dominance and suppression in binocular rivalry arises naturally from this fundamental principle in sensory processing. Interestingly, if the two monocular directions of motion differed ,608, the percept alternations also included transitions to in-between (vertical) motion percepts. We speculate that this behavior might result from positive feedback arising from adapting disinhibitory circuits in the network

Adaptation mutual-inhibition models account for our results.

<p>(A) Model used in the simulations (modified after Noest et al., 2006). Each unit received visual input (X_i) from one eye via a nonlinear input stage (F(x)). The dynamics of each unit were given by a set of differential equations which specified the ‘local field’ dynamics and the ‘shunting-type’ adaptation component of each unit. The local field activity of each unit (H_i) was converted into a spike-rate output (Y_i) via a sigmoid function (S(z) = z²/[z²+1] if z>0, otherwise S(z) = 0), and depended on the visual inputs (X₁, X₂), the adaptation dynamics (A₁,A₂), and the amount of cross inhibition (for details, see Noest et al., 2007). Parameters of the competition stage were: unit time constant, τ_h = 0.02s; adaptation time constant, τ_a = 4s, adaptation strength, α = 5; cross-inhibition gain, γ = 3.33 (adopted from Noest et al., 2006). Unit 1 and 2 were considered dominant if Y₁>Y₂ and Y₂>Y₁, respectively. (B) Different nonlinear input functions (F(x)) were used to simulate the effects of contrast and coherence manipulations. For contrast, we assumed a nonlinear compression function: F(x) = a⋅x^b/[x^b+1], with a = 2.17 and b = 0.5. For coherence, we assumed a linear relation with coherence plus a constant bias: F(x) = a⋅x+b, with a = 0.1 and b = 1. (C) Dominance durations of the two units when the two inputs were varied simultaneously (i.e, symmetric condition: X₁ = X₂). Input values are in arbitrary units. Same format as Figs. 1 and 4. Note peaked response curve for coherence and monotonic decrease for contrast. (D-E) Dominance durations of the two units as a function of X₁ when X₂ was kept constant (i.e., asymmetric condition, X₂ = 5). Gray and black curves are the results for unit 1 and 2, respectively. Same format as Figs. 2 and 3. Note that mean dominance durations changed in both units but for ‘contrast’ manipulations (D), the biggest effect occurred in the contralateral unit (gray curve) while for ‘coherence’ manipulations (E) the effects were strongest in the unit which received the stronger input.</p

Coherence manipulation in both eyes.

<p>Predominance (A) and mean dominance durations (B) of exclusive (black solid curve), mixed (gray dotted curve) and null (gray dashed curve) percept as a function of motion coherence in the two eyes. Data averaged across n = 4 observers. Error bars indicate ±1 SEM. Gray line segments are linear regression lines fitted to sections of the data.</p

Motion coherence manipulation in one eye.

<p>A,B: Predominance (A) and mean dominance duration (B) of the ipsilateral (black solid curves) and contralateral (gray solid curves) eye both changed as a function of ipsilateral coherence. Mixed percepts (gray dotted curves) rarely occurred. Noise-like null percepts (gray dashed curves) comprised only ∼10% of the total viewing time, and their mean durations were comparatively short. Data averaged across n = 6 observers. C,D: Mean dominance durations from two individual subjects (S1 and S2) illustrating that observed response patterns ranged from asymmetric (C) to more or less mirror-symmetric (D). Coherence in the contralateral eye was fixed at 20%, which corresponded with 5× the subjects’ 75%-correct motion discrimination threshold for coherence (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0071931#s2" target="_blank">Methods</a>). Error bars indicate ±1 SEM.</p

The role of putative human anterior intraparietal sulcus area in observed manipulative action discrimination

INTRODUCTION: Although it has become widely accepted that the action observation network (AON) includes three levels (occipito-temporal, parietal and premotor), little is known concerning the specific role of these levels within perceptual tasks probing action observation. Recent single cell studies suggest that the parietal level carries the information required to discriminate between two-alternative observed actions, but do not exclude possible contributions from the other two levels. METHODS: Two functional magnetic resonance imaging experiments used a task-based attentional modulation paradigm in which subjects viewed videos of an actor performing a manipulative action on a coloured object, and discriminated between either two observed manipulative actions, two actors or two colours. RESULTS: Both experiments demonstrated that relative to actor and colour discrimination, discrimination between observed manipulative actions involved the putative human anterior intraparietal sulcus (phAIP) area in parietal cortex. In one experiment, where the observed actions also differed with regard to effectors, premotor cortex was also specifically recruited. CONCLUSIONS: Our results highlight the primary role of parietal cortex in discriminating between two-alternative observed manipulative actions, consistent with the view that this level plays a major role in representing the identity of an observed action.status: publishe

Comparison of contrast and coherence manipulations.

<p>Mean dominance durations of coherent motion percepts (i.e., exclusive dominance states) plotted as a function of stimulus strength, where stimulus strength was normalized by dividing the contrast and coherence values by their respective 75%-correct motion discrimination thresholds. (A) Mean dominance durations of the controlateral (gray) and ipsilateral (black) eye obtained with asymmetric contrast (solid curves) and coherence (dashed curves) manipulations. Data are from the contrast and first coherence experiments. (B) Mean dominance durations obtained with symmetric contrast and coherence manipulations. Circles and triangles represent averaged subject-data from the contrast and second coherence experiments, respectively. Error bars indicate ±1 SEM.</p

Contrast manipulation in both eyes.

<p>Predominance (A) and mean durations (B) of exclusive (black solid curves), mixed (gray dotted curves) and null (gray dashed curves) percepts as a function of stimulus contrast (in % Michelson) in the two eyes. Data are pooled across both eyes (exclusive percepts), and averaged across n = 5 subjects. Error bars indicate ±1 SEM as computed from the ANOVA sum of squares <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0071931#pone.0071931-Loftus1" target="_blank">[47]</a>.</p