Stability of adversarial Markov chains, with an application to adaptive MCMC algorithms

We consider whether ergodic Markov chains with bounded step size remain bounded in probability when their transitions are modified by an adversary on a bounded subset. We provide counterexamples to show that the answer is no in general, and prove theorems to show that the answer is yes under various additional assumptions. We then use our results to prove convergence of various adaptive Markov chain Monte Carlo algorithms.Comment: Published at http://dx.doi.org/10.1214/14-AAP1083 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Open-Source Conceptual Sizing Models for the Hyperloop Passenger Pod

Hyperloop is a new mode of transportation proposed as an alternative to California's high speed rail project, with the intended benefits of higher performance at lower overall costs. It consists of a passenger pod traveling through a tube under a light vacuum and suspended on air bearings. The pod travels up to transonic speeds resulting in a 35 minute travel time between the intended route from Los Angeles and San Francisco. Of the two variants outlined, the smaller system includes a 1.1 meter tall passenger capsule traveling through a 2.2 meter tube at 700 miles per hour. The passenger pod features water-based heat exchangers as well as an on-board compression system that reduces the aerodynamic drag as it moves through the tube. Although the original proposal looks very promising, it assumes that tube and pod dimensions are independently sizable without fully acknowledging the constraints of the compressor system on the pod geometry. This work focuses on the aerodynamic and thermodynamic interactions between the two largest systems; the tube and the pod. Using open-source toolsets, a new sizing method is developed based on one-dimensional thermodynamic relationships that accounts for the strong interactions between these sub-systems. These additional considerations require a tube nearly twice the size originally considered and limit the maximum pod travel speed to about 620 miles per hour. Although the results indicate that Hyperloop will need to be larger and slightly slower than originally intended, the estimated travel time only increases by approximately five minutes, so the overall performance is not dramatically affected. In addition, the proposed on-board heat exchanger is not an ideal solution to achieve reasonable equilibrium air temperatures within the tube. Removal of this subsystem represents a potential reduction in weight, energy requirements and complexity of the pod. In light of these finding, the core concept still remains a compelling possibility, although additional engineering and economic analyses are markedly necessary before a more complete design can be developed

Calculating Nonlocal Optical Properties of Structures with Arbitrary Shape

In a recent Letter [Phys. Rev. Lett. 103, 097403 (2009)], we outlined a computational method to calculate the optical properties of structures with a spatially nonlocal dielectric function. In this Article, we detail the full method, and verify it against analytical results for cylindrical nanowires. Then, as examples of our method, we calculate the optical properties of Au nanostructures in one, two, and three dimensions. We first calculate the transmission, reflection, and absorption spectra of thin films. Because of their simplicity, these systems demonstrate clearly the longitudinal (or volume) plasmons characteristic of nonlocal effects, which result in anomalous absorption and plasmon blueshifting. We then study the optical properties of spherical nanoparticles, which also exhibit such nonlocal effects. Finally, we compare the maximum and average electric field enhancements around nanowires of various shapes to local theory predictions. We demonstrate that when nonlocal effects are included, significant decreases in such properties can occur.Comment: 30 pages, 12 figures, 1 tabl

Positional differences in reactive hyperemia provide insight into initial phase of exercise hyperemia.

Studies have reported a greater blood flow response to muscle contractions when the limb is below the heart compared with above the heart, and these results have been interpreted as evidence for a skeletal muscle pump contribution to exercise hyperemia. If limb position affects the blood flow response to other vascular challenges such as reactive hyperemia, this interpretation may not be correct. We hypothesized that the magnitude of reactive hyperemia would be greater with the limb below the heart. Brachial artery blood flow (Doppler ultrasound) and blood pressure (finger-cuff plethysmography) were measured in 10 healthy volunteers. Subjects lay supine with one arm supported in two different positions: above or below the heart. Reactive hyperemia was produced by occlusion of arterial inflow for varying durations: 0.5 min, 1 min, 2 min, or 5 min in randomized order. Peak increases in blood flow were 77 ± 11, 178 ± 24, 291 ± 25, and 398 ± 33 ml/min above the heart and 96 ± 19, 279 ± 62, 550 ± 60, and 711 ± 69 ml/min below the heart (P \u3c 0.05). Thus a standard stimulus (vascular occlusion) elicited different responses depending on limb position. To determine whether these differences were due to mechanisms intrinsic to the arterial wall, a second set of experiments was performed in which acute intraluminal pressure reduction for 0.5 min, 1 min, 2 min, or 5 min was performed in isolated rat soleus feed arteries (n = 12). The magnitude of dilation upon pressure restoration was greater when acute pressure reduction occurred from 85 mmHg (mimicking pressure in the arm below the heart; 28.3 ± 7.9, 37.5 ± 5.9, 55.1 ± 9.9, and 68.9 ± 8.6% dilation) than from 48 mmHg (mimicking pressure in the arm above the heart; 20.8 ± 4.8, 22.6 ± 4.4, 31.2 ± 5.8, and 49.2 ± 7.1% dilation). These data support the hypothesis that arm position differences in reactive hyperemia are at least partially mediated by mechanisms intrinsic to the arterial wall. Overall, these results suggest the need to reevaluate studies employing positional changes to examine muscle pump influences on exercise hyperemia

Fundamental Behavior of Electric Field Enhancements in the Gaps Between Closely Spaced Nanostructures

We demonstrate that the electric field enhancement that occurs in a gap between two closely spaced nanostructures, such as metallic nanoparticles, is the result of a transverse electromagnetic waveguide mode. We derive an explicit semianalytic equation for the enhancement as a function of gap size, which we show has a universal qualitative behavior in that it applies irrespective of the material or geometry of the nanostructures and even in the presence of surface plasmons. Examples of perfect electrically conducting and Ag thin-wire antennas and a dimer of Ag spheres are presented and discussed.Comment: 9 pages and 4 figure

Structural diversity in the type IV pili of multidrug-resistant Acinetobacter

Acinetobacter baumannii is a Gram-negative coccobacillus found primarily in hospital settings that has recently emerged as a source of hospital-acquired infections. A. baumannii expresses a variety of virulence factors, including type IV pili, bacterial extracellular appendages often essential for attachment to host cells. Here, we report the high resolution structures of the major pilin subunit, PilA, from three Acinetobacter strains, demonstrating thatA. baumannii subsets produce morphologically distinct type IV pilin glycoproteins. We examine the consequences of this heterogeneity for protein folding and assembly as well as host-cell adhesion by Acinetobacter. Comparisons of genomic and structural data with pilin proteins from other species of soil gammaproteobacteria suggest that these structural differences stem from evolutionary pressure that has resulted in three distinct classes of type IVa pilins, each found in multiple species

The dichotomous structure of the warm conveyor belt

The warm conveyor belt (WCB) of an extratropical cyclone generally splits into two branches. One branch (WCB1) turns anticyclonically into the downstream upper-level tropospheric ridge, while the second branch (WCB2) wraps cyclonically around the cyclone centre. Here, the WCB split in a typical North Atlantic cold-season cyclone is analysed using two numerical models: the Met Office Unified Model and the COSMO model. The WCB flow is defined using off-line trajectory analysis. The two models represent the WCB split consistently. The split occurs early in the evolution of the WCB with WCB1 experiencing maximum ascent at lower latitudes and with higher moisture content than WCB2. WCB1 ascends abruptly along the cold front where the resolved ascent rates are greatest and there is also line convection. In contrast, WCB2 remains at lower levels for longer before undergoing saturated large-scale ascent over the system's warm front. The greater moisture in WCB1 inflow results in greater net potential temperature change from latent heat release, which determines the final isentropic level of each branch. WCB1 also exhibits lower outflow potential vorticity values than WCB2. Complementary diagnostics in the two models are utilised to study the influence of individual diabatic processes on the WCB. Total diabatic heating rates along the WCB branches are comparable in the two models with microphysical processes in the large-scale cloud schemes being the major contributor to this heating. However, the different convective parameterisation schemes used by the models cause significantly different contributions to the total heating. These results have implications for studies on the influence of the WCB outflow in Rossby wave evolution and breaking. Key aspects are the net potential temperature change and the isentropic level of the outflow which together will influence the relative mass going into each WCB branch and the associated negative PV anomalies at the tropopause-level flow

Fluctuating hydrogen-bond networks govern anomalous electron transfer kinetics in a blue copper protein

We combine experimental and computational methods to address the anomalous kinetics of long-range electron transfer (ET) in mutants of Pseudomonas aeruginosa azurin. ET rates and driving forces for wild type (WT) and three N47X mutants (X = L, S, and D) of Ru(2,2′-bipyridine)2 (imidazole)(His83) azurin are reported. An enhanced ET rate for the N47L mutant suggests either an increase of the donor–acceptor (DA) electronic coupling or a decrease in the reorganization energy for the reaction. The underlying atomistic features are investigated using a recently developed nonadiabatic molecular dynamics method to simulate ET in each of the azurin mutants, revealing unexpected aspects of DA electronic coupling. In particular, WT azurin and all studied mutants exhibit more DA compression during ET (>2 Å) than previously recognized. Moreover, it is found that DA compression involves an extended network of hydrogen bonds, the fluctuations of which gate the ET reaction, such that DA compression is facilitated by transiently rupturing hydrogen bonds. It is found that the N47L mutant intrinsically disrupts this hydrogen-bond network, enabling particularly facile DA compression. This work, which reveals the surprisingly fluctional nature of ET in azurin, suggests that hydrogen-bond networks can modulate the efficiency of long-range biological ET