Updating constraint preconditioners for KKT systems in quadratic programming via low-rank corrections

This work focuses on the iterative solution of sequences of KKT linear systems arising in interior point methods applied to large convex quadratic programming problems. This task is the computational core of the interior point procedure and an efficient preconditioning strategy is crucial for the efficiency of the overall method. Constraint preconditioners are very effective in this context; nevertheless, their computation may be very expensive for large-scale problems, and resorting to approximations of them may be convenient. Here we propose a procedure for building inexact constraint preconditioners by updating a "seed" constraint preconditioner computed for a KKT matrix at a previous interior point iteration. These updates are obtained through low-rank corrections of the Schur complement of the (1,1) block of the seed preconditioner. The updated preconditioners are analyzed both theoretically and computationally. The results obtained show that our updating procedure, coupled with an adaptive strategy for determining whether to reinitialize or update the preconditioner, can enhance the performance of interior point methods on large problems.Comment: 22 page

Exaggerated CpH methylation in the autism-affected brain.

BackgroundThe etiology of autism, a complex, heritable, neurodevelopmental disorder, remains largely unexplained. Given the unexplained risk and recent evidence supporting a role for epigenetic mechanisms in the development of autism, we explored the role of CpG and CpH (H = A, C, or T) methylation within the autism-affected cortical brain tissue.MethodsReduced representation bisulfite sequencing (RRBS) was completed, and analysis was carried out in 63 post-mortem cortical brain samples (Brodmann area 19) from 29 autism-affected and 34 control individuals. Analyses to identify single sites that were differentially methylated and to identify any global methylation alterations at either CpG or CpH sites throughout the genome were carried out.ResultsWe report that while no individual site or region of methylation was significantly associated with autism after multi-test correction, methylated CpH dinucleotides were markedly enriched in autism-affected brains (~2-fold enrichment at p < 0.05 cutoff, p = 0.002).ConclusionsThese results further implicate epigenetic alterations in pathobiological mechanisms that underlie autism

Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction

Extinction of an epidemic or a species is a rare event that occurs due to a large, rare stochastic fluctuation. Although the extinction process is dynamically unstable, it follows an optimal path that maximizes the probability of extinction. We show that the optimal path is also directly related to the finite-time Lyapunov exponents of the underlying dynamical system in that the optimal path displays maximum sensitivity to initial conditions. We consider several stochastic epidemic models, and examine the extinction process in a dynamical systems framework. Using the dynamics of the finite-time Lyapunov exponents as a constructive tool, we demonstrate that the dynamical systems viewpoint of extinction evolves naturally toward the optimal path.Comment: 21 pages, 5 figures, Final revision to appear in Bulletin of Mathematical Biolog

Leveraging Social Media to Promote EvidenceBased Continuing Medical Education

Importance New dissemination methods are needed to engage physicians in evidence-based continuing medical education (CME). Objective To examine the effectiveness of social media in engaging physicians in non-industry-sponsored CME. Design We tested the effect of different media platforms (e-mail, Facebook, paid Facebook and Twitter), CME topics, and different “hooks” (e.g., Q&A, clinical pearl and best evidence) on driving clicks to a landing site featuring non-industry sponsored CME. We modelled the effects of social media platform, CME topic, and hook using negative binomial regression on clicks to a single landing site. We used clicks to landing site adjusted for exposure and message number to calculate rate ratios. To understand how physicians interact with CME content on social media, we also conducted interviews with 10 physicians. Setting The National Physicians Alliance (NPA) membership. Participants NPA e-mail recipients, Facebook followers and friends, and Twitter followers. Main Outcomes and Measures Clicks to the NPA’s CME landing site. Results On average, 4,544 recipients received each message. Messages generated a total of 592 clicks to the landing site, for a rate of 5.4 clicks per 1000 recipients exposed. There were 5.4 clicks from e-mail, 11.9 clicks from Facebook, 5.5 clicks from paid Facebook, and 6.9 clicks from Twitter to the landing site for 1000 physicians exposed to each of 4 selected CME modules. A Facebook post generated 2.3x as many clicks to the landing site as did an e-mail after controlling for participant exposure, hook type and CME topic (p Conclusions Social media has a modest impact on driving traffic to evidence-based CME options. Facebook had a superior effect on driving physician web traffic to evidence-based CME compared to other social media platforms and email

Magnetism of two-dimensional defects in Pd: stacking faults, twin boundaries and surfaces

Careful first-principles density functional calculations reveal the importance of hexagonal versus cubic stacking of closed packed planes of Pd as far as local magnetic properties are concerned. We find that, contrary to the stable face centered cubic phase, which is paramagnetic, the hexagonal close-packed phase of Pd is ferromagnetic with a magnetic moment of 0.35 $\mu_{B}$/atom. Our results show that two-dimensional defects with local hcp stacking, like twin boundaries and stacking faults, in the otherwise fcc Pd structure, increase the magnetic susceptibility. The (111) surface also increases the magnetic susceptibility and it becomes ferromagnetic in combination with an individual stacking fault or twin boundary close to it. On the contrary, we find that the (100) surface decreases the tendency to ferromagnetism. The results are consistent with the magnetic moment recently observed in small Pd nanoparticles, with a large surface area and a high concentration of two-dimensional stacking defects.Comment: 8 pages, 10 figure

Dust Emissivity in the Far-Infrared

We have derived the dust emissivity in the Far-Infrared (FIR) using data available in the literature. We use two wavelength dependences derived from spectra of Galactic FIR emission (Reach et al. 1995). A value for the emissivity, normalised to the extinction efficiency in the V band, has been retrieved from maps of Galactic FIR emission, dust temperature and extinction (Schlegel et al. 1998). Our results are similar to other measurements in the Galaxy but only marginally consistent with the widely quoted values of Hildebrand (1983) derived on one reflection nebula. The discrepancy with measurements on other reflection nebulae (Casey 1991) is higher and suggests a different grain composition in these environments with respect to the diffuse interstellar medium. We measure dust masses for a sample of six spiral galaxies with FIR observations and obtain gas-to-dust ratios close to the Galactic value.Comment: 5 pages, 1 ps file, A&A letter accepte