High order recombination and an application to cubature on Wiener space

Particle methods are widely used because they can provide accurate descriptions of evolving measures. Recently it has become clear that by stepping outside the Monte Carlo paradigm these methods can be of higher order with effective and transparent error bounds. A weakness of particle methods (particularly in the higher order case) is the tendency for the number of particles to explode if the process is iterated and accuracy preserved. In this paper we identify a new approach that allows dynamic recombination in such methods and retains the high order accuracy by simplifying the support of the intermediate measures used in the iteration. We describe an algorithm that can be used to simplify the support of a discrete measure and give an application to the cubature on Wiener space method developed by Lyons and Victoir [Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 460 (2004) 169-198].Comment: Published in at http://dx.doi.org/10.1214/11-AAP786 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Validation of an expert system intended for research in distributed artificial intelligence

The expert system discussed in this paper is designed to function as a testbed for research on cooperating expert systems. Cooperating expert systems are members of an organization which dictates the manner in which the expert systems will interact when solving a problem. The Blackbox Expert described in this paper has been constructed using the C Language Integrated Production System (CLIPS), C++, and X windowing environment. CLIPS is embedded in a C++ program which provides objects that are used to maintain the state of the Blackbox puzzle. These objects are accessed by CLIPS rules through user-defined functions calls. The performance of the Blackbox Expert is validated by experimentation. A group of people are asked to solve a set of test cases for the Blackbox puzzle. A metric has been devised which evaluates the 'correctness' of a solution proposed for a test case of Blackbox. Using this metric and the solutions proposed by the humans, each person receives a rating for their ability to solve the Blackbox puzzle. The Blackbox Expert solves the same set of test cases and is assigned a rating for its ability. Then the rating obtained by the Blackbox Expert is compared with the ratings of the people, thus establishing the skill level of our expert system

Symmetric mixed states of nn qubits: local unitary stabilizers and entanglement classes

We classify, up to local unitary equivalence, local unitary stabilizer Lie algebras for symmetric mixed states into six classes. These include the stabilizer types of the Werner states, the GHZ state and its generalizations, and Dicke states. For all but the zero algebra, we classify entanglement types (local unitary equivalence classes) of symmetric mixed states that have those stabilizers. We make use of the identification of symmetric density matrices with polynomials in three variables with real coefficients and apply the representation theory of SO(3) on this space of polynomials.Comment: 10 pages, 1 table, title change and minor clarifications for published versio

Algebraic structure of stochastic expansions and efficient simulation

We investigate the algebraic structure underlying the stochastic Taylor solution expansion for stochastic differential systems.Our motivation is to construct efficient integrators. These are approximations that generate strong numerical integration schemes that are more accurate than the corresponding stochastic Taylor approximation, independent of the governing vector fields and to all orders. The sinhlog integrator introduced by Malham & Wiese (2009) is one example. Herein we: show that the natural context to study stochastic integrators and their properties is the convolution shuffle algebra of endomorphisms; establish a new whole class of efficient integrators; and then prove that, within this class, the sinhlog integrator generates the optimal efficient stochastic integrator at all orders.Comment: 19 page

Kusuoka-Stroock gradient bounds for the solution of the filtering equation

© 2014 Elsevier Inc.We obtain sharp gradient bounds for perturbed diffusion semigroups. In contrast with existing results, the perturbation is here random and the bounds obtained are pathwise. Our approach builds on the classical work of Kusuoka and Stroock [13,14,16,17], and extends their program developed for the heat semi-group to solutions of stochastic partial differential equations. The work is motivated by and applied to nonlinear filtering. The analysis allows us to derive pathwise gradient bounds for the un-normalised conditional distribution of a partially observed signal. It uses a pathwise representation of the perturbed semigroup following Ocone [22]. The estimates we derive have sharp small time asymptotics

Cortical correlates of psychedelic-induced shaking behavior revealed by voltage imaging

(1) From mouse to man, shaking behavior (head twitches and/or wet dog shakes) is a reliable readout of psychedelic drug action. Shaking behavior like psychedelia is thought to be mediated by serotonin 2A receptors on cortical pyramidal cells. The involvement of pyramidal cells in psychedelic-induced shaking behavior remains hypothetical, though, as experimental in vivo evidence is limited. (2) Here, we use cell type-specific voltage imaging in awake mice to address this issue. We intersectionally express the genetically encoded voltage indicator VSFP Butterfly 1.2 in layer 2/3 pyramidal neurons. We simultaneously capture cortical hemodynamics and cell type-specific voltage activity while mice display psychedelic shaking behavior. (3) Shaking behavior is preceded by high-frequency oscillations and overlaps with low-frequency oscillations in the motor cortex. Oscillations spectrally mirror the rhythmics of shaking behavior and reflect layer 2/3 pyramidal cell activity complemented by hemodynamics. (4) Our results reveal a clear cortical fingerprint of serotonin-2A-receptor-mediated shaking behavior and open a promising methodological avenue relating a cross-mammalian psychedelic effect to cell-type specific brain dynamics

Accelerated return to sport after osteochondral autograft plug transfer

Background:Previous studies have reported varying return-to-sport protocols after knee cartilage restoration procedures.Purpose:To (1) evaluate the time for return to sport in athletes with an isolated chondral injury who underwent an accelerated return-to-sport protocol after osteochondral autograft plug transfer (OAT) and (2) evaluate clinical outcomes to assess for any consequences from the accelerated return to sport.Study Design:Case series; Level of evidence, 4.Methods:An institutional cohort of 152 OAT procedures was reviewed, of which 20 competitive athletes met inclusion and exclusion criteria. All patients underwent a physician-directed accelerated rehabilitation program after their procedure. Return to sport was determined for all athletes. Clinical outcomes were assessed using International Knee Documentation Committee (IKDC) and Tegner scores as well as assessment of level of participation on return to sport.Results:Return-to-sport data were available for all 20 athletes; 13 of 20 athletes (65%) were available for clinical evaluation at a mean 4.4-year follow-up. The mean time for return to sport for all 20 athletes was 82.9 ± 25 days (range, 38-134 days). All athletes were able to return to sport at their previous level and reported that they were satisfied or very satisfied with their surgical outcome and ability to return to sport. The mean postoperative IKDC score was 84.5 ± 9.5. The mean Tegner score prior to injury was 8.9 ± 1.7; it was 7.7 ± 1.9 at final follow-up.Conclusion:Competitive athletes with traumatic chondral defects treated with OAT managed using this protocol had reduced time to preinjury activity levels compared with what is currently reported, with excellent clinical outcomes and no serious long-term sequelae.</jats:sec

A Visual Environment for Real-Time Image Processing in Hardware (VERTIPH)

Real-time video processing is an image-processing application that is ideally suited to implementation on FPGAs. We discuss the strengths and weaknesses of a number of existing languages and hardware compilers that have been developed for specifying image processing algorithms on FPGAs. We propose VERTIPH, a new multiple-view visual language that avoids the weaknesses we identify. A VERTIPH design incorporates three different views, each tailored to a different aspect of the image processing system under development; an overall architectural view, a computational view, and a resource and scheduling view

Comparing Single-Objective Optimization Protocols for Calibrating the Birds Nest Aquifer Model—A Problem Having Multiple Local Optima

To best represent reality, simulation models of environmental and health-related systems might be very nonlinear. Model calibration ideally identifies globally optimal sets of parameters to use for subsequent prediction. For a nonlinear system having multiple local optima, calibration can be tedious. For such a system, we contrast calibration results from PEST, a commonly used automated parameter estimation program versus several meta-heuristic global optimizers available as external packages for the Python computer language—the Gray Wolf Optimization (GWO) algorithm; the DYCORS optimizer framework with a Radial Basis Function surrogate simulator (DRB); and particle swarm optimization (PSO). We ran each optimizer 15 times, with nearly 10,000 MODFLOW simulations per run for the global optimizers, to calibrate a steady-state, groundwater flow simulation model of the complex Birds Nest aquifer, a three-layer system having 8 horizontal hydraulic conductivity zones and 25 head observation locations. In calibrating the eight hydraulic conductivity values, GWO averaged the best root mean squared error (RMSE) between observed and simulated heads—20 percent better (lower) than the next lowest optimizer, DRB. The best PEST run matched the best GWO RMSE, but both the average PEST RMSE and the range of PEST RMSE results were an order of magnitude larger than any of the global optimizers