Accelerating MCMC with active subspaces

The Markov chain Monte Carlo (MCMC) method is the computational workhorse for Bayesian inverse problems. However, MCMC struggles in high-dimensional parameter spaces, since its iterates must sequentially explore the high-dimensional space. This struggle is compounded in physical applications when the nonlinear forward model is computationally expensive. One approach to accelerate MCMC is to reduce the dimension of the state space. Active subspaces are part of an emerging set of tools for subspace-based dimension reduction. An active subspace in a given inverse problem indicates a separation between a low-dimensional subspace that is informed by the data and its orthogonal complement that is constrained by the prior. With this information, one can run the sequential MCMC on the active variables while sampling independently according to the prior on the inactive variables. However, this approach to increase efficiency may introduce bias. We provide a bound on the Hellinger distance between the true posterior and its active subspace- exploiting approximation. And we demonstrate the active subspace-accelerated MCMC on two computational examples: (i) a two-dimensional parameter space with a quadratic forward model and one-dimensional active subspace and (ii) a 100-dimensional parameter space with a PDE-based forward model and a two-dimensional active subspace

Modulation of human corticospinal excitability by paired associative stimulation

Paired Associative Stimulation (PAS) has come to prominence as a potential therapeutic intervention for the treatment of brain injury/disease, and as an experimental method with which to investigate Hebbian principles of neural plasticity in humans. Prototypically, a single electrical stimulus is directed to a peripheral nerve in advance of transcranial magnetic stimulation (TMS) delivered to the contralateral primary motor cortex (M1). Repeated pairing of the stimuli (i.e., association) over an extended period may increase or decrease the excitability of corticospinal projections from M1, in manner that depends on the interstimulus interval (ISI). It has been suggested that these effects represent a form of associative long-term potentiation (LTP) and depression (LTD) that bears resemblance to spike-timing dependent plasticity (STDP) as it has been elaborated in animal models. With a large body of empirical evidence having emerged since the cardinal features of PAS were first described, and in light of the variations from the original protocols that have been implemented, it is opportune to consider whether the phenomenology of PAS remains consistent with the characteristic features that were initially disclosed. This assessment necessarily has bearing upon interpretation of the effects of PAS in relation to the specific cellular pathways that are putatively engaged, including those that adhere to the rules of STDP. The balance of evidence suggests that the mechanisms that contribute to the LTP- and LTD-type responses to PAS differ depending on the precise nature of the induction protocol that is used. In addition to emphasizing the requirement for additional explanatory models, in the present analysis we highlight the key features of the PAS phenomenology that require interpretation

Upper Surface Nacelle Influence on SCAR Aerodynamic Characteristics at Transonic Speeds

The arrow-wing transport configuration with detached engines located over the wing to produce upper surface exhaust flow effects was tested at angles of attack from -4 deg to 8 deg and jet total-pressure ratios from 1 (Jet off) to approximately 10. Wing tip leading edge flap deflections of -10 deg to 10 deg were tested with the wing-body configuration only (no nacelles). Tests were made with various nacelle chordwise, spanwise, and vertical height locations over the Mach number, angle of attack, and jet total-pressure ratio ranges. Deflecting the wing tip leading edge flap from 0 deg to -10 deg increased maximum lift to drag ratio by 1.0 at subsonic speeds. Installation of upper surface nacelles (no wing/nacelle pylons) increased the wing-body pitching moment at all Mach numbers and decreased the drag of the wing-body configuration at subsonic Mach numbers. Jet exhaust interference effects were negligible

Experimental and analytical investigation of axisymmetric supersonic cruise nozzle geometry at Mach numbers from 0.60 to 1.30

Quantitative pressure and force data for five axisymmetric boattail nozzle configurations were examined. These configurations simulate the variable-geometry feature of a single nozzle design operating over a range of engine operating conditions. Five nozzles were tested in the Langley 16-Foot Transonic Tunnel at Mach numbers from 0.60 to 1.30. The experimental data were also compared with theoretical predictions

Particle sizing in the process industry using Hertz-Zener impact theory and acoustic emission spectra

The cost of implementing real-time monitoring and control of industrial processes is a significant barrier for many companies. Acoustic techniques provide complementary information to optical spectroscopic sensors and have a number of advantages: they are relatively inexpensive, can be applied non-invasively, are non-destructive, multi-point measurements are possible, opaque samples can be analysed in containers that are made from opaque materials (e.g. steel or concrete) and the analysis can be conducted in real-time. In this paper a new theoretical model is proposed which describes the transport of particles in a stirred reactor, their collision with the reactor walls, the subsequent vibrations which are then transmitted through the vessel walls, and their detection by an ultrasonic transducer. The particle-wall impact is modelled using Hertz-Zener impact theory. Experimental data is then used in conjunction with this (forward) model to form an inverse problem for the particle size distribution using a least squares cost function. Application of an integral smoothing operator to the power spectra greatly enhances the accuracy and robustness of the approach. One advantage of this new approach is that since it operates in the frequency domain, it can cope with the industrially relevant case of many particle-wall collisions. The technique will be illustrated using data from a set of controlled experiments. In the first instance a set of simplified experiments involving single particles being dropped in air onto a substrate are utilised. The second set of experiments involves particles in a carrier fluid being stirred in a reactor vessel. In each case the approach is able to successfully recover the associated particle size

Characterization of recombination and control electrodes for spacecraft nickel- cadmium cells

Characterization of recombination and control electrodes for spacecraft nickel cadmium cell

On the Calculation of Effective Actions by String Methods

Strassler's formulation of the string-derived Bern-Kosower formalism is reconsidered with particular emphasis on effective actions and form factors. Two- and three point form factors in the nonabelian effective action are calculated and compared with those obtained in the heat kernel approach of Barvinsky, Vilkovisky et al. We discuss the Fock-Schwinger gauge and propose a manifestly covariant calculational scheme for one-loop effective actions in gauge theory.Comment: 12 pages, Plain TEX, HD-THEP-93-2