Efficient Interpolation for the Theory of Arrays

Existing techniques for Craig interpolation for the quantifier-free fragment of the theory of arrays are inefficient for computing sequence and tree interpolants: the solver needs to run for every partitioning $(A, B)$ of the interpolation problem to avoid creating $AB$-mixed terms. We present a new approach using Proof Tree Preserving Interpolation and an array solver based on Weak Equivalence on Arrays. We give an interpolation algorithm for the lemmas produced by the array solver. The computed interpolants have worst-case exponential size for extensionality lemmas and worst-case quadratic size otherwise. We show that these bounds are strict in the sense that there are lemmas with no smaller interpolants. We implemented the algorithm and show that the produced interpolants are useful to prove memory safety for C programs.Comment: long version of the paper at IJCAR 201

Accommodative Exercises to Lower Intraocular Pressure

Purpose. This study investigated how a conscious change in ocular accommodation affects intraocular pressure (IOP) and ocular biometrics in healthy adult volunteers of different ages. Methods. Thirty-five healthy volunteers without ocular disease or past ocular surgery, and with refractive error between −3.50 and +2.50 diopters, were stratified into 20, 40, and 60 year old (y.o.) age groups. Baseline measurements of central cornea thickness, anterior chamber depth, anterior chamber angle, cornea diameter, pupil size, and ciliary muscle thickness were made by autorefraction and optical coherence tomography (OCT), while IOP was measured by pneumotonometry. Each subject’s right eye focused on a target 40 cm away. Three different tests were performed in random order: (1) 10 minutes of nonaccommodation (gazing at the target through lenses that allowed clear vision without accommodating), (2) 10 minutes of accommodation (addition of a minus 3 diopter lens), and (3) 10 minutes of alternating between accommodation and nonaccommodation (1-minute intervals). IOP was measured immediately after each test. A 20-minute rest period was provided between tests. Data from 31 subjects were included in the study. ANOVA and paired t-tests were used for statistical analyses. Results. Following alternating accommodation, IOP decreased by 0.7 mmHg in the right eye when all age groups were combined (p = 0.029). Accommodation or nonaccommodation alone did not decrease IOP. Compared to the 20 y.o. group, the 60 y.o. group had a thicker ciliary muscle within 75 μm of the scleral spur, a thinner ciliary muscle at 125–300 μm from the scleral spur, narrower anterior chamber angles, shallower anterior chambers, and smaller pupils during accommodation and nonaccommodation (p’s < 0.01). Conclusion. Alternating accommodation, but not constant accommodation, significantly decreased IOP. This effect was not lost with aging despite physical changes to the aging eye. A greater accommodative workload and/or longer test period may improve the effect

Endogenous cellulases in animals: Isolation of β-1,4-endoglucanase genes from two species of plant-parasitic cyst nematodes

β-1,4-Endoglucanases (EGases, EC 3.2.1.4) degrade polysaccharides possessing β-1,4-glucan backbones such as cellulose and xyloglucan and have been found among extremely variegated taxonomic groups. Although many animal species depend on cellulose as their main energy source, most omnivores and herbivores are unable to produce EGases endogenously. So far, all previously identified EGase genes involved in the digestive system of animals originate from symbiotic microorganisms. Here we report on the synthesis of EGases in the esophageal glands of the cyst nematodes Globodera rostochiensis and Heterodera glycines. From each of the nematode species, two cDNAs were characterized and hydrophobic cluster analysis revealed that the four catalytic domains belong to family 5 of the glycosyl hydrolases (EC 3.2.1, 3.2.2, and 3.2.3). These domains show 37–44% overall amino acid identity with EGases from the bacteria Erwinia chrysanthemi, Clostridium acetobutylicum, and Bacillus subtilis. One EGase with a bacterial type of cellulose-binding domain was identified for each nematode species. The leucine-rich hydrophobic core of the signal peptide and the presence of a polyadenylated 3′ end precluded the EGases from being of bacterial origin. Cyst nematodes are obligatory plant parasites and the identified EGases presumably facilitate the intracellular migration through plant roots by partial cell wall degradation