Parallel Verification of Natural Deduction Proof Graphs

Graph-based interactive theorem provers offer a visual representation of proofs, explicitly representing the dependencies and inferences between each of the proof steps in a graph or hypergraph format. The number and complexity of these dependency links can determine how long it takes to verify the validity of the entire proof. Towards this end, we present a set of parallel algorithms for the formal verification of graph-based natural-deduction (ND) style proofs. We introduce a definition of layering that captures dependencies between the proof steps (nodes). Nodes in each layer can then be verified in parallel as long as prior layers have been verified. To evaluate the performance of our algorithms on proof graphs, we propose a framework for finding the performance bounds and patterns using directed acyclic network topologies (DANTs). This framework allows us to create concrete instances of DANTs for empirical evaluation of our algorithms. With this, we compare our set of parallel algorithms against a serial implementation with two experiments: one scaling both the problem size and the other scaling the number of threads. Our findings show that parallelization results in improved verification performance for certain DANT instances. We also show that our algorithms scale for certain DANT instances with respect to the number of threads.Comment: In Proceedings LFMTP 2023, arXiv:2311.0991

Bond Strength of Direct and Indirect Bonded Brackets After Thermocycling

Thermocycling simulates the temperature dynamics in the oral environment. With direct bonding, thermocycling reduces the bond strength of orthodontic adhesives to tooth structure. The purpose of this study was to evaluate the shear bond strengths (SBS) of one direct and two indirect bonding methods/adhesives after thermocycling. Sixty human premolars were divided into three groups. Teeth in group 1 were bonded directly with Transbond XT. Teeth in group 2 were indirect bonded with Transbond XT/Sondhi Rapid Set, which is chemically cured. Teeth in group 3 were indirect bonded with Enlight LV/Orthosolo and light cured. Each sample was thermocycled between 5°C and 55°C for 500 cycles. Mean SBS in groups 1, 2, and 3 were not statistically significantly different (13.6 ± 2.9, 12.3 ± 3.0, and 11.6 ± 3.2 MPa, respectively; P \u3e .05). However, when these values were compared with the results of a previous study using the same protocol, but without thermocycling, the SBS was reduced significantly (P = .001). Weibull analysis further showed that group 3 had the lowest bonding survival rate at the minimum clinically acceptable bond-strength range. The Adhesive Remnant Index was also determined, and group 2 had a significantly (P \u3c .05) higher percentage of bond failures at the resin/enamel interface

A Comparison of Bond Strength Between Direct- and Indirect-bonding Methods

The purpose of this study was to evaluate and compare the shear bond strength and the sites of bond failure for brackets bonded to teeth, using two indirect-bonding material protocols and a direct-bonding technique. Sixty extracted human premolars were collected and randomly divided into three groups. The direct-bonded group (group 1) used a light-cured adhesive and primer (Transbond XT). One indirect-bonded group (group 2) consisted of a chemical-cured primer (Sondhi Rapid Set) and light-cured adhesive (Transbond XT), whereas the other group (group 3) used a light-cured primer (Orthosolo) and adhesive (Enlight LV). Forty hours after bonding, the samples were debonded. Mean shear bond strengths were 16.27, 13.83, and 14.76 MPa for groups 1, 2, and 3, respectively. A one-way analysis of variance showed no significant difference in mean bond strength between groups (P = .21). Furthermore, a Weibull analysis showed all three groups tested provided over a 90% survival rate at normal masticatory and orthodontic force levels. For each tooth, an Adhesive Remnant Index (ARI) score was determined. Group 2 was found to have a significantly lower ARI score (P \u3c .05) compared with groups 1 and 3. In addition, Pearson correlation coefficients indicated no strong correlation between bond strength and ARI score within or across all groups

Implications of intraguild predation for sea turtle nest protection.

Loggerhead Nest predation Ocypode quadrata Predator removal Procyon lotor Raccoon A B S T R A C T In the United States, raccoons Procyon lotor are often removed from sea turtle nesting beaches to decrease egg mortality. However, raccoons also consume ghost crabs Ocypode quadrata, another common egg predator. Reducing predator populations can benefit secondary predators, inflating total predation pressure and leading to a decline in prey species. We used track and burrow counts to compare raccoon and ghost crab abundance at four beaches in Florida, USA, that differ in management activity and determined predation rates on loggerhead Caretta caretta nests by each predator. Mean raccoon abundance (range 0.12-0.46 tracks plot À1 night À1 ) and ghost crab density (0.09-0.19 burrows m À2 ) were inversely correlated. Ghost crabs were largest at the site with the fewest raccoons. The stable nitrogen isotope ratios of ghost crabs (mean 9.8&) were positively correlated with body mass, indicating larger ghost crabs feed at a higher trophic level and suggesting large ghost crabs may consume more loggerhead eggs. The highest rates of egg predation by both predators (31%) occurred where raccoon abundance was lowest and ghost crab abundance was highest, suggesting ghost crab burrows may facilitate predation by raccoons. Our data suggest that predation by raccoons limits ghost crabs and that removing raccoons can increase ghost crab abundance and sea turtle egg mortality. Although predator removal can be effective when nest predation rates are quite high, maintaining moderate raccoon densities may be important for controlling ghost crabs. These results highlight the importance of understanding food web connectivity in developing management strategies to achieve conservation goals, especially when the species of concern are threatened or facing extinction

A compositional account of motifs, mechanisms, and dynamics in biochemical regulatory networks

Regulatory networks depict promoting or inhibiting interactions between molecules in a biochemical system. We introduce a category-theoretic formalism for regulatory networks, using signed graphs to model the networks and signed functors to describe occurrences of one network in another, especially occurrences of network motifs. With this foundation, we establish functorial mappings between regulatory networks and other mathematical models in biochemistry. We construct a functor from reaction networks, modeled as Petri nets with signed links, to regulatory networks, enabling us to precisely define when a reaction network could be a physical mechanism underlying a regulatory network. Turning to quantitative models, we associate a regulatory network with a Lotka-Volterra system of differential equations, defining a functor from the category of signed graphs to a category of parameterized dynamical systems. We extend this result from closed to open systems, demonstrating that Lotka-Volterra dynamics respects not only inclusions and collapsings of regulatory networks, but also the process of building up complex regulatory networks by gluing together simpler pieces. Formally, we use the theory of structured cospans to produce a lax double functor from the double category of open signed graphs to that of open parameterized dynamical systems. Throughout the paper, we ground the categorical formalism in examples inspired by systems biology.Comment: 33 pages. Added several examples, plus minor revision

A CRISPR-based screen for Hedgehog signaling provides insights into ciliary function and ciliopathies.

Primary cilia organize Hedgehog signaling and shape embryonic development, and their dysregulation is the unifying cause of ciliopathies. We conducted a functional genomic screen for Hedgehog signaling by engineering antibiotic-based selection of Hedgehog-responsive cells and applying genome-wide CRISPR-mediated gene disruption. The screen can robustly identify factors required for ciliary signaling with few false positives or false negatives. Characterization of hit genes uncovered novel components of several ciliary structures, including a protein complex that contains δ-tubulin and ε-tubulin and is required for centriole maintenance. The screen also provides an unbiased tool for classifying ciliopathies and showed that many congenital heart disorders are caused by loss of ciliary signaling. Collectively, our study enables a systematic analysis of ciliary function and of ciliopathies, and also defines a versatile platform for dissecting signaling pathways through CRISPR-based screening

Tactical Themes for Rangeland Research

The problems threatening the conservation and management of rangeland, over one-half of the world’s terrestrial surfaces, are significant and growing. Current assessments of drivers and externalities shaping these problems have resulted in strategies intended to result in sustainable development of these lands and their resources. However, how can individual scientists and individual research programs support the needed strategies and goals? What can we realistically contribute and accomplish? We believe that technology can connect individual scientists and their science to the problems manifest in rangelands over the world, in a more rapid exchange than has occurred in the past. Recognition of local challenges, innovations, and scientific tests of the effectiveness of our technological solutions to these problems can keep pace with rapid change and help us adapt to that change. However, to do this, we have to invest in a process of connecting science to landscapes. Our tactics are to link, openly and collaboratively, the scientific method to discrete, specific, managed landscapes. We term these collective tactics, our fundamental research theme, “Landscape Portals”. All of the elements of this theme exist currently, to various degrees, but they lack cohesion and interactive, real-time connections. Future investment requires two basic, tactical scientific behaviors: a post-normal application of science in support of land management by hypothesis and a scientific method modified to accommodate a data intensive scientific inquiry directed towards adaptive management. These behaviors support our “Landscape Portals” theme: science conducted in a highly interactive, transparent, data enriched, locally relevant, globally connected, popularly translated, and ecologically robust manner