The shifted ODE method for underdamped Langevin MCMC

In this paper, we consider the underdamped Langevin diffusion (ULD) and propose a numerical approximation using its associated ordinary differential equation (ODE). When used as a Markov Chain Monte Carlo (MCMC) algorithm, we show that the ODE approximation achieves a $2$-Wasserstein error of $\varepsilon$ in $\mathcal{O}\big(d^{\frac{1}{3}}/\varepsilon^{\frac{2}{3}}\big)$ steps under the standard smoothness and strong convexity assumptions on the target distribution. This matches the complexity of the randomized midpoint method proposed by Shen and Lee [NeurIPS 2019] which was shown to be order optimal by Cao, Lu and Wang. However, the main feature of the proposed numerical method is that it can utilize additional smoothness of the target log-density $f$. More concretely, we show that the ODE approximation achieves a $2$-Wasserstein error of $\varepsilon$ in $\mathcal{O}\big(d^{\frac{2}{5}}/\varepsilon^{\frac{2}{5}}\big)$ and $\mathcal{O}\big(\sqrt{d}/\varepsilon^{\frac{1}{3}}\big)$ steps when Lipschitz continuity is assumed for the Hessian and third derivative of $f$. By discretizing this ODE using a third order Runge-Kutta method, we can obtain a practical MCMC method that uses just two additional gradient evaluations per step. In our experiment, where the target comes from a logistic regression, this method shows faster convergence compared to other unadjusted Langevin MCMC algorithms

Lear

This opera, Lear, draws its libretto directly from William Shakespeare's King Lear. Some supporting characters and subplots have been removed, and some characters have been fused to reduce the time and forces needed to produce this piece. Parent/child relationships, eyesight, and deception/disguises are important themes in this adapted libretto. The last point, deception and disguises, receives special attention in the opera. Each time a character dons a disguise a "transformation" motive is heard. Simultaneously, at least one of the woodwind players will switch to a traditional doubling instrument to add a timbral change to the visual change on the stage. Two characters in the opera never sing, but only speak: Lear and Gloucester. This separates them from the rest of the cast to highlight their paternal nature. The music for spoken sections includes liberal use of fermatas, vamps, and other forms of repetition to underscore the speech. Most characters have musical motives and/or signature styles to aid in their characterization. Goneril and Edmund are intelligent, eloquent, and manipulative. heir music can be triadic and diatonic when they need it to be, and their lines are often winding and chromatic. Regan and Oswald, on the other hand, are more characters of action than thought. Their music is more blunt and to the point. The harmony of the opera moves among diatonic, quartal, whole-tone, octatonic, hexatonic, and more complicated harmonies, depending on the character singing or speaking and what his motives are at that moment. At several points in the opera, a rhythmic pattern will continue over a bar that obscures the meter. Sometimes multiple patterns will be present at once. The harmony is at its most complicated when these patterns overlap, or when two characters' personal motives are presented simultaneously. The opera's duration is approximately two hours. The cast calls for two sopranos, two mezzo-sopranos, two baritones, a bass-baritone, and two male actors. The opera is scored for Flute (doubling Piccolo and Alto Flute), Oboe (doubling English Horn), Bb Clarinet (doubling Bass Clarinet), Bassoon, Horn in F, Percussion (one player), Piano, String Quartet, and Double Bass

Multiplicity of morphologies in poly (L-lactide) bioresorbable vascular scaffolds

Poly(L-lactide) (PLLA) is the structural material of the first clinically approved bioresorbable vascular scaffold (BVS), a promising alternative to permanent metal stents for treatment of coronary heart disease. BVSs are transient implants that support the occluded artery for 6 mo and are completely resorbed in 2 y. Clinical trials of BVSs report restoration of arterial vasomotion and elimination of serious complications such as late stent thrombosis. It is remarkable that a scaffold made from PLLA, known as a brittle polymer, does not fracture when crimped onto a balloon catheter or during deployment in the artery. We used X-ray microdiffraction to discover how PLLA acquired ductile character and found that the crimping process creates localized regions of extreme anisotropy; PLLA chains in the scaffold change orientation from the hoop direction to the radial direction on micrometer-scale distances. This multiplicity of morphologies in the crimped scaffold works in tandem to enable a low-stress response during deployment, which avoids fracture of the PLLA hoops and leaves them with the strength needed to support the artery. Thus, the transformations of the semicrystalline PLLA microstructure during crimping explain the unexpected strength and ductility of the current BVS and point the way to thinner resorbable scaffolds in the future

Quasi-extinction risk and population targets for the Eastern, migratory population of monarch butterflies (Danaus plexippus)

The Eastern, migratory population of monarch butterflies (Danaus plexippus), an iconic North American insect, has declined by ~80% over the last decade. The monarch’s multi-generational migration between overwintering grounds in central Mexico and the summer breeding grounds in the northern U.S. and southern Canada is celebrated in all three countries and creates shared management responsibilities across North America. Here we present a novel Bayesian multivariate auto-regressive state-space model to assess quasi-extinction risk and aid in the establishment of a target population size for monarch conservation planning. We find that, given a range of plausible quasi-extinction thresholds, the population has a substantial probability of quasi-extinction, from 11–57% over 20 years, although uncertainty in these estimates is large. Exceptionally high population stochasticity, declining numbers, and a small current population size act in concert to drive this risk. An approximately 5-fold increase of the monarch population size (relative to the winter of 2014–15) is necessary to halve the current risk of quasi-extinction across all thresholds considered. Conserving the monarch migration thus requires active management to reverse population declines, and the establishment of an ambitious target population size goal to buffer against future environmentally driven variability

Crimping-induced structural gradients explain the lasting strength of poly L-lactide bioresorbable vascular scaffolds during hydrolysis

Biodegradable polymers open the way to treatment of heart disease using transient implants (bioresorbable vascular scaffolds, BVSs) that overcome the most serious complication associated with permanent metal stents—late stent thrombosis. Here, we address the long-standing paradox that the clinically approved BVS maintains its radial strength even after 9 mo of hydrolysis, which induces a ∼40% decrease in the poly L-lactide molecular weight (Mn). X-ray microdiffraction evidence of nonuniform hydrolysis in the scaffold reveals that regions subjected to tensile stress during crimping develop a microstructure that provides strength and resists hydrolysis. These beneficial morphological changes occur where they are needed most—where stress is localized when a radial load is placed on the scaffold. We hypothesize that the observed decrease in Mn reflects the majority of the material, which is undeformed during crimping. Thus, the global measures of degradation may be decoupled from the localized, degradation-resistant regions that confer the ability to support the artery for the first several months after implantation

Crimping-induced structural gradients explain the lasting strength of poly L-lactide bioresorbable vascular scaffolds during hydrolysis

Biodegradable polymers open the way to treatment of heart disease using transient implants (bioresorbable vascular scaffolds, BVSs) that overcome the most serious complication associated with permanent metal stents—late stent thrombosis. Here, we address the long-standing paradox that the clinically approved BVS maintains its radial strength even after 9 mo of hydrolysis, which induces a ∼40% decrease in the poly L-lactide molecular weight (Mn). X-ray microdiffraction evidence of nonuniform hydrolysis in the scaffold reveals that regions subjected to tensile stress during crimping develop a microstructure that provides strength and resists hydrolysis. These beneficial morphological changes occur where they are needed most—where stress is localized when a radial load is placed on the scaffold. We hypothesize that the observed decrease in Mn reflects the majority of the material, which is undeformed during crimping. Thus, the global measures of degradation may be decoupled from the localized, degradation-resistant regions that confer the ability to support the artery for the first several months after implantation

The Integrated Monarch Monitoring Program: From Design to Implementation

Steep declines in North American monarch butterfly (Danaus plexippus) populations have prompted continent-wide conservation efforts. While monarch monitoring efforts have existed for years, we lack a comprehensive approach to monitoring population vital rates integrated with habitat quality to inform adaptive management and effective conservation strategies. Building a geographically and ecologically representative dataset of monarchs and their habitat will improve these efforts. These data will help track long-term changes in the distribution and abundance of monarchs and their habitats, refine population and habitat models, and illuminate how conservation activities affect monarchs and their habitats. The Monarch Conservation Science Partnership developed the Integrated Monarch Monitoring Program (IMMP) to profile breeding habitats and their use by monarchs in North America. A spatially balanced random sampling framework guides site selection, while also allowing opportunistic inclusion of sites chosen by participants, such as conservation areas. The IMMP weaves new protocols together with those from existing monitoring programs to improve data compatibility for assessing milkweed (Asclepias spp.) density, nectar resources, monarch reproduction and survival, and adult monarch habitat use. Participants may select a protocol subset according to interests or local monitoring objectives, thereby maximizing contributions. Conservation partners, including public and private land managers, academic researchers, and citizen scientists contribute data to a national dataset available for analyses at multiple scales. We describe the program and its development, implementation elements that make the program robust and feasible, participation to date, and how IMMP data can advance research and conservation for monarchs, pollinators, and their habitats

Consumption of Bt Maize Pollen Expressing Cry1Ab or Cry3Bb1 Does Not Harm Adult Green Lacewings, Chrysoperla carnea (Neuroptera: Chrysopidae)

Adults of the common green lacewing, Chrysoperla carnea (Stephens) (Neuroptera: Chrysopidae), are prevalent pollen-consumers in maize fields. They are therefore exposed to insecticidal proteins expressed in the pollen of insect-resistant, genetically engineered maize varieties expressing Cry proteins derived from Bacillus thuringiensis (Bt). Laboratory experiments were conducted to evaluate the impact of Cry3Bb1 or Cry1Ab-expressing transgenic maize (MON 88017, Event Bt176) pollen on fitness parameters of adult C. carnea. Adults were fed pollen from Bt maize varieties or their corresponding near isolines together with sucrose solution for 28 days. Survival, pre-oviposition period, fecundity, fertility and dry weight were not different between Bt or non-Bt maize pollen treatments. In order to ensure that adults of C. carnea are not sensitive to the tested toxins independent from the plant background and to add certainty to the hazard assessment, adult C. carnea were fed with artificial diet containing purified Cry3Bb1 or Cry1Ab at about a 10 times higher concentration than in maize pollen. Artificial diet containing Galanthus nivalis agglutinin (GNA) was included as a positive control. No differences were found in any life-table parameter between Cry protein containing diet treatments and control diet. However, the pre-oviposition period, daily and total fecundity and dry weight of C. carnea were significantly negatively affected by GNA-feeding. In both feeding assays, the stability and bioactivity of Cry proteins in the food sources as well as the uptake by C. carnea was confirmed. These results show that adults of C. carnea are not affected by Bt maize pollen and are not sensitive to Cry1Ab and Cry3Bb1 at concentrations exceeding the levels in pollen. Consequently, Bt maize pollen consumption will pose a negligible risk to adult C. carnea

Common Features at the Start of the Neurodegeneration Cascade

A single-molecule study reveals that neurotoxic proteins share common structural features that may trigger neurodegeneration, thus identifying new targets for therapy and diagnosis