A dual number abstraction for static analysis of Clarke Jacobians

We present a novel abstraction for bounding the Clarke Jacobian of a Lipschitz continuous, but not necessarily differentiable function over a local input region. To do so, we leverage a novel abstract domain built upon dual numbers, adapted to soundly over-approximate all first derivatives needed to compute the Clarke Jacobian. We formally prove that our novel forward-mode dual interval evaluation produces a sound, interval domain-based over-approximation of the true Clarke Jacobian for a given input region. Due to the generality of our formalism, we can compute and analyze interval Clarke Jacobians for a broader class of functions than previous works supported – specifically, arbitrary compositions of neural networks with Lipschitz, but non-differentiable perturbations. We implement our technique in a tool called DeepJ and evaluate it on multiple deep neural networks and non-differentiable input perturbations to showcase both the generality and scalability of our analysis. Concretely, we can obtain interval Clarke Jacobians to analyze Lipschitz robustness and local optimization landscapes of both fully-connected and convolutional neural networks for rotational, contrast variation, and haze perturbations, as well as their compositions.

Effect of Luminance and Contrast Variation on Stereoacuity Measurements Using Smartphone Technology

Owing to the limitations of printed stereoacuity tests, the effects of luminance and contrast on stereopsis have not yet been sufficiently investigated, despite its important implications in designing stereoacuity measuring instruments, particularly for electronic devices. A stereopsis measurement system was established using two 4 K smartphones and a phoropter to evaluate the effects of luminance and contrast variations on the stereoacuity test. Seventeen young subjects with normal visual acuity and stereopsis were recruited. Two types of test symbols, contour-based and random-dot-based, were used in the experiment. Four series tests were established with different maximum brightness values, including 240 lux, 120 lux, 60 lux, and 30 lux. Each series test contained 19 pages with different contrasts between 95% and 5% and was calculated using the Michelson contrast formula. No significant difference was found for both contour-based and random-dot-based stereograms in any of the contrast groups with different maximum brightness. Similarly, no significant difference was found between contour-based and random-dot-based patterns under different contrasts of above 35%. As the contrast decreased below 30%, the stereopsis was significantly better in the contour-based pattern than in the random-dot-based pattern for some degrees of contrast. The luminance and contrast of the digital display are not critical factors for stereoacuity under normal circumstances. This implies that a standard monitor with a certain 3D technology can be used to measure the stereoacuity threshold without calibrating the luminance and contrast.

Endosymbiont Communities in Pachyseris speciosa Highlight Geographical and Methodological Variations

Reef-building corals live in symbiosis with the phototrophic dinoflagellate family Symbiodiniaceae, which comprises diverse genera such as Cladocopium and Durusdinium. Pachyseris speciosa, a widely distributed Indo-Pacific coral found in a variety of reef habitats, is known to be associated with these two Symbiodiniaceae genera, but little is known about the biogeographic variability of the endosymbiont communities across the region. In this study, the diversity and dominance patterns of Symbiodiniaceae at the western and eastern areas of the Central Indo-Pacific region were examined. We sampled Pachyseris speciosa colonies at seven and six sites in Singapore and Papua New Guinea, respectively, and genotyped their endosymbionts based on the internal transcribed spacer (ITS) markers using two distinct methods, quantitative polymerase chain reaction (qPCR) and high-throughput sequencing (HTS). Results showed 92% of all colonies in Singapore exhibiting Cladocopium dominance. There was a higher abundance of Durusdinium compared to Cladocopium in certain colonies from one site, Pulau Hantu (mean Durusdinium abundance of 90%, compared to 0–14% among all other sites). In contrast, variation in the endosymbiont communities was generally higher among sites in Papua New Guinea. Cladocopium expectedly dominated most colonies (75%), although colonies from Kimbe Bay (85%) and Kavieng (65%) showed Durusdinium dominance. Between localities, relative genus abundances based on qPCR were not significantly different, but HTS showed that the ratio of Durusdinium over Cladocopium was significantly higher in Papua New Guinea corals. Notably, 6% of colonies from Singapore and 15% from Papua New Guinea showed endosymbiont dominance patterns that were inconsistent between the two methods, underscoring the need for further validation of symbiotic algal quantification based on HTS. The richness of ITS2 type profiles was clearly lower among colonies from the impacted and turbid reefs of Singapore compared to the less urbanized reefs of Papua New Guinea. These coral intraspecific variations of Symbiodiniaceae communities within and among localities suggest that local conditions are important drivers of endosymbiosis and may ultimately influence corals’ resilience against global stressors such as ocean warming.