Structural Rounding: Approximation Algorithms for Graphs Near an Algorithmically Tractable Class

We develop a framework for generalizing approximation algorithms from the structural graph algorithm literature so that they apply to graphs somewhat close to that class (a scenario we expect is common when working with real-world networks) while still guaranteeing approximation ratios. The idea is to edit a given graph via vertex- or edge-deletions to put the graph into an algorithmically tractable class, apply known approximation algorithms for that class, and then lift the solution to apply to the original graph. We give a general characterization of when an optimization problem is amenable to this approach, and show that it includes many well-studied graph problems, such as Independent Set, Vertex Cover, Feedback Vertex Set, Minimum Maximal Matching, Chromatic Number, (l-)Dominating Set, Edge (l-)Dominating Set, and Connected Dominating Set. To enable this framework, we develop new editing algorithms that find the approximately-fewest edits required to bring a given graph into one of a few important graph classes (in some cases these are bicriteria algorithms which simultaneously approximate both the number of editing operations and the target parameter of the family). For bounded degeneracy, we obtain an O(r log{n})-approximation and a bicriteria (4,4)-approximation which also extends to a smoother bicriteria trade-off. For bounded treewidth, we obtain a bicriteria (O(log^{1.5} n), O(sqrt{log w}))-approximation, and for bounded pathwidth, we obtain a bicriteria (O(log^{1.5} n), O(sqrt{log w} * log n))-approximation. For treedepth 2 (related to bounded expansion), we obtain a 4-approximation. We also prove complementary hardness-of-approximation results assuming P != NP: in particular, these problems are all log-factor inapproximable, except the last which is not approximable below some constant factor 2 (assuming UGC)

Benchmarking treewidth as a practical component of tensor-network--based quantum simulation

Tensor networks are powerful factorization techniques which reduce resource requirements for numerically simulating principal quantum many-body systems and algorithms. The computational complexity of a tensor network simulation depends on the tensor ranks and the order in which they are contracted. Unfortunately, computing optimal contraction sequences (orderings) in general is known to be a computationally difficult (NP-complete) task. In 2005, Markov and Shi showed that optimal contraction sequences correspond to optimal (minimum width) tree decompositions of a tensor network's line graph, relating the contraction sequence problem to a rich literature in structural graph theory. While treewidth-based methods have largely been ignored in favor of dataset-specific algorithms in the prior tensor networks literature, we demonstrate their practical relevance for problems arising from two distinct methods used in quantum simulation: multi-scale entanglement renormalization ansatz (MERA) datasets and quantum circuits generated by the quantum approximate optimization algorithm (QAOA). We exhibit multiple regimes where treewidth-based algorithms outperform domain-specific algorithms, while demonstrating that the optimal choice of algorithm has a complex dependence on the network density, expected contraction complexity, and user run time requirements. We further provide an open source software framework designed with an emphasis on accessibility and extendability, enabling replicable experimental evaluations and future exploration of competing methods by practitioners.Comment: Open source code availabl

Orbiter escape pole

A Shuttle type of aircraft (10) with an escape hatch (12) has an arcuately shaped pole housing (16) attachable to an interior wall and ceiling with its open end adjacent to the escape hatch. The pole housing 16 contains a telescopically arranged and arcuately shaped primary pole member (22) and extension pole member (23) which are guided by roller assemblies (30,35). The extension pole member (23) is slidable and extendable relative to the primary pole member (22). For actuation, a spring actuated system includes a spring (52) in the pole housing. A locking member (90) engages both pole members (22,23) through notch portions (85,86) in the pole members. The locking member selectively releases the extension pole member (23) and the primary pole member (22). An internal one-way clutch or anti-return mechanism prevents retraction of the extension pole member from an extended position. Shock absorbers (54)(150,152) are for absoring the energy of the springs. A manual backup deployment system is provided which includes a canted ring (104) biased by a spring member (108). A lever member (100) with a slot and pin connection (102) permits the mechanical manipulation of the canted ring to move the primary pole member. The ring (104) also prevents retraction of the main pole. The crew escape mechanism includes a magazine (60) and a number of lanyards (62), each lanyard being mounted by a roller loop (68) over the primary pole member (22). The strap on the roller loop has stitching for controlled release, a protection sheath (74) to prevent tangling and a hook member (69) for attachment to a crew harness

Integrating data types to estimate spatial patterns of avian migration across the Western Hemisphere

For many avian species, spatial migration patterns remain largely undescribed, especially across hemispheric extents. Recent advancements in tracking technologies and high-resolution species distribution models (i.e., eBird Status and Trends products) provide new insights into migratory bird movements and offer a promising opportunity for integrating independent data sources to describe avian migration. Here, we present a three-stage modeling framework for estimating spatial patterns of avian migration. First, we integrate tracking and band re-encounter data to quantify migratory connectivity, defined as the relative proportions of individuals migrating between breeding and nonbreeding regions. Next, we use estimated connectivity proportions along with eBird occurrence probabilities to produce probabilistic least-cost path (LCP) indices. In a final step, we use generalized additive mixed models (GAMMs) both to evaluate the ability of LCP indices to accurately predict (i.e., as a covariate) observed locations derived from tracking and band re-encounter data sets versus pseudo-absence locations during migratory periods and to create a fully integrated (i.e., eBird occurrence, LCP, and tracking/band re-encounter data) spatial prediction index for mapping species-specific seasonal migrations. To illustrate this approach, we apply this framework to describe seasonal migrations of 12 bird species across the Western Hemisphere during pre- and postbreeding migratory periods (i.e., spring and fall, respectively). We found that including LCP indices with eBird occurrence in GAMMs generally improved the ability to accurately predict observed migratory locations compared to models with eBird occurrence alone. Using three performance metrics, the eBird + LCP model demonstrated equivalent or superior fit relative to the eBird-only model for 22 of 24 species–season GAMMs. In particular, the integrated index filled in spatial gaps for species with over-water movements and those that migrated over land where there were few eBird sightings and, thus, low predictive ability of eBird occurrence probabilities (e.g., Amazonian rainforest in South America). This methodology of combining individual-based seasonal movement data with temporally dynamic species distribution models provides a comprehensive approach to integrating multiple data types to describe broad-scale spatial patterns of animal movement. Further development and customization of this approach will continue to advance knowledge about the full annual cycle and conservation of migratory birds

Molecular Characterization of a Novel Intracellular ADP-Ribosyl Cyclase

Background. ADP-ribosyl cyclases are remarkable enzymes capable of catalyzing multiple reactions including the synthesis of the novel and potent intracellular calcium mobilizing messengers, cyclic ADP-ribose and NAADP. Not all ADP-ribosyl cyclases however have been characterized at the molecular level. Moreover, those that have are located predominately at the outer cell surface and thus away from their cytosolic substrates. Methodology/Principal Findings. Here we report the molecular cloning of a novel expanded family of ADP-ribosyl cyclases from the sea urchin, an extensively used model organism for the study of inositol trisphosphate-independent calcium mobilization. We provide evidence that one of the isoforms (SpARC1) is a soluble protein that is targeted exclusively to the endoplasmic reticulum lumen when heterologously expressed. Catalytic activity of the recombinant protein was readily demonstrable in crude cell homogenates, even under conditions where luminal continuity was maintained. Conclusions/Significance. Our data reveal a new intracellular location for ADP-ribosyl cyclases and suggest that production of calcium mobilizing messengers may be compartmentalized

Linking Symptom Inventories using Semantic Textual Similarity

An extensive library of symptom inventories has been developed over time to measure clinical symptoms, but this variety has led to several long standing issues. Most notably, results drawn from different settings and studies are not comparable, which limits reproducibility. Here, we present an artificial intelligence (AI) approach using semantic textual similarity (STS) to link symptoms and scores across previously incongruous symptom inventories. We tested the ability of four pre-trained STS models to screen thousands of symptom description pairs for related content - a challenging task typically requiring expert panels. Models were tasked to predict symptom severity across four different inventories for 6,607 participants drawn from 16 international data sources. The STS approach achieved 74.8% accuracy across five tasks, outperforming other models tested. This work suggests that incorporating contextual, semantic information can assist expert decision-making processes, yielding gains for both general and disease-specific clinical assessment

American Gut: an Open Platform for Citizen Science Microbiome Research

McDonald D, Hyde E, Debelius JW, et al. American Gut: an Open Platform for Citizen Science Microbiome Research. mSystems. 2018;3(3):e00031-18