A Primal-Dual Method for Optimal Control and Trajectory Generation in High-Dimensional Systems

Presented is a method for efficient computation of the Hamilton-Jacobi (HJ) equation for time-optimal control problems using the generalized Hopf formula. Typically, numerical methods to solve the HJ equation rely on a discrete grid of the solution space and exhibit exponential scaling with dimension. The generalized Hopf formula avoids the use of grids and numerical gradients by formulating an unconstrained convex optimization problem. The solution at each point is completely independent, and allows a massively parallel implementation if solutions at multiple points are desired. This work presents a primal-dual method for efficient numeric solution and presents how the resulting optimal trajectory can be generated directly from the solution of the Hopf formula, without further optimization. Examples presented have execution times on the order of milliseconds and experiments show computation scales approximately polynomial in dimension with very small high-order coefficients.Comment: Updated references and funding sources. To appear in the proceedings of the 2018 IEEE Conference on Control Technology and Application

The Impact of Message Passing in Agent-Based Submodular Maximization

Submodular maximization problems are a relevant model set for many real-world applications. Since these problems are generally NP-Hard, many methods have been developed to approximate the optimal solution in polynomial time. One such approach uses an agent-based greedy algorithm, where the goal is for each agent to choose an action from its action set such that the union of all actions chosen is as high-valued as possible. Recent work has shown how the performance of the greedy algorithm degrades as the amount of information shared among the agents decreases, whereas this work addresses the scenario where agents are capable of sharing more information than allowed in the greedy algorithm. Specifically, we show how performance guarantees increase as agents are capable of passing messages, which can augment the allowable decision set for each agent. Under these circumstances, we show a near-optimal method for message passing, and how much such an algorithm could increase performance for any given problem instance

The association between implementation strategy use and the uptake of hepatitis C treatment in a national sample

Abstract Background Hepatitis C virus (HCV) is a common and highly morbid illness. New medications that have much higher cure rates have become the new evidence-based practice in the field. Understanding the implementation of these new medications nationally provides an opportunity to advance the understanding of the role of implementation strategies in clinical outcomes on a large scale. The Expert Recommendations for Implementing Change (ERIC) study defined discrete implementation strategies and clustered these strategies into groups. The present evaluation assessed the use of these strategies and clusters in the context of HCV treatment across the US Department of Veterans Affairs (VA), Veterans Health Administration, the largest provider of HCV care nationally. Methods A 73-item survey was developed and sent to all VA sites treating HCV via electronic survey, to assess whether or not a site used each ERIC-defined implementation strategy related to employing the new HCV medication in 2014. VA national data regarding the number of Veterans starting on the new HCV medications at each site were collected. The associations between treatment starts and number and type of implementation strategies were assessed. Results A total of 80 (62%) sites responded. Respondents endorsed an average of 25 ± 14 strategies. The number of treatment starts was positively correlated with the total number of strategies endorsed (r = 0.43, p < 0.001). Quartile of treatment starts was significantly associated with the number of strategies endorsed (p < 0.01), with the top quartile endorsing a median of 33 strategies, compared to 15 strategies in the lowest quartile. There were significant differences in the types of strategies endorsed by sites in the highest and lowest quartiles of treatment starts. Four of the 10 top strategies for sites in the top quartile had significant correlations with treatment starts compared to only 1 of the 10 top strategies in the bottom quartile sites. Overall, only 3 of the top 15 most frequently used strategies were associated with treatment. Conclusions These results suggest that sites that used a greater number of implementation strategies were able to deliver more evidence-based treatment in HCV. The current assessment also demonstrates the feasibility of electronic self-reporting to evaluate ERIC strategies on a large scale. These results provide initial evidence for the clinical relevance of the ERIC strategies in a real-world implementation setting on a large scale. This is an initial step in identifying which strategies are associated with the uptake of evidence-based practices in nationwide healthcare systems

Frequency-stabilization to 6x10^-16 via spectral-hole burning

We demonstrate two-stage laser stabilization based on a combination of Fabry- Perot and spectral-hole burning techniques. The laser is first pre-stabilized by the Fabry-Perot cavity to a fractional-frequency stability of sigma_y(tau) < 10^-13. A pattern of spectral holes written in the absorption spectrum of Eu3+:Y2SiO5 serves to further stabilize the laser to sigma_y(tau) = 6x10^-16 for 2 s < tau < 8 s. Measurements characterizing the frequency sensitivity of Eu3+:Y2SiO5 spectral holes to environmental perturbations suggest that they can be more frequency stable than Fabry-Perot cavities

Pseudomonas aeruginosa PilY1 Binds Integrin in an RGD- and Calcium-Dependent Manner

PilY1 is a type IV pilus (tfp)-associated protein from the opportunistic pathogen Pseudomonas aeruginosa that shares functional similarity with related proteins in infectious Neisseria and Kingella species. Previous data have shown that PilY1 acts as a calcium-dependent pilus biogenesis factor necessary for twitching motility with a specific calcium binding site located at amino acids 850–859 in the 1,163 residue protein. In addition to motility, PilY1 is also thought to play an important role in the adhesion of P. aeruginosa tfp to host epithelial cells. Here, we show that PilY1 contains an integrin binding arginine-glycine-aspartic acid (RGD) motif located at residues 619–621 in the PilY1 from the PAK strain of P. aeruginosa; this motif is conserved in the PilY1s from the other P. aeruginosa strains of known sequence. We demonstrate that purified PilY1 binds integrin in vitro in an RGD-dependent manner. Furthermore, we identify a second calcium binding site (amino acids 600–608) located ten residues upstream of the RGD. Eliminating calcium binding from this site using a D608A mutation abolished integrin binding; in contrast, a calcium binding mimic (D608K) preserved integrin binding. Finally, we show that the previously established PilY1 calcium binding site at 851–859 also impacts the protein's association with integrin. Taken together, these data indicate that PilY1 binds to integrin in an RGD- and calcium-dependent manner in vitro. As such, P. aeruginosa may employ these interactions to mediate host epithelial cell binding in vivo