Intonation in unaccompanied singing: Accuracy, drift, and a model of reference pitch memory

Copyright 2014 Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America. The following article appeared in J. Acoust. Soc. Am. 136, 401 (2014) and may be found at http://dx.doi.org/10.1121/1.4881915

Estimating water flow through a hillslope using the massively parallel processor

A new two-dimensional model of water flow in a hillslope has been implemented on the Massively Parallel Processor at the Goddard Space Flight Center. Flow in the soil both in the saturated and unsaturated zones, evaporation and overland flow are all modelled, and the rainfall rates are allowed to vary spatially. Previous models of this type had always been very limited computationally. This model takes less than a minute to model all the components of the hillslope water flow for a day. The model can now be used in sensitivity studies to specify which measurements should be taken and how accurate they should be to describe such flows for environmental studies

Programming a hillslope water movement model on the MPP

A physically based numerical model was developed of heat and moisture flow within a hillslope on a parallel architecture computer, as a precursor to a model of a complete catchment. Moisture flow within a catchment includes evaporation, overland flow, flow in unsaturated soil, and flow in saturated soil. Because of the empirical evidence that moisture flow in unsaturated soil is mainly in the vertical direction, flow in the unsaturated zone can be modeled as a series of one dimensional columns. This initial version of the hillslope model includes evaporation and a single column of one dimensional unsaturated zone flow. This case has already been solved on an IBM 3081 computer and is now being applied to the massively parallel processor architecture so as to make the extension to the one dimensional case easier and to check the problems and benefits of using a parallel architecture machine

The effect of precipitation and application rate on dicyandiamide persistence and efficiency in two Irish grassland soils

peer-reviewedThe nitrification inhibitor dicyandiamide (DCD) has had variable success in reducing nitrate (NO3-) leaching and nitrous oxide (N2O) emissions from soils receiving nitrogen (N) fertilisers. Factors such as soil type, temperature and moisture have been linked to the variable efficacy of DCD. Since DCD is water soluble it can be leached from the rooting zone where it is intended to inhibit nitrification. Intact soil columns (15 cm diameter by 35 cm long) were taken from luvic gleysol and haplic cambisol grassland sites and placed in growth chambers. DCD was applied at 15 or 30 kg DCD ha-1, with high or low precipitation. Leaching of DCD, mineral N and the residual soil DCD concentrations were determined over eight weeks High precipitation increased DCD in leachate and decreased recovery in soil. A soil x DCD rate interaction was detected for the DCD unaccounted (proxy for degraded DCD). In the cambisol degradation of DCD was high (circa 81%) and unaffected by DCD rate. In contrast DCD degradation in the gleysol was lower and differentially affected by rate, 67 and 46% for the 15 and 30 kg ha-1 treatments, respectively. Differences DCD degradation rates between soils may be related to differences in organic matter content and associated microbiological activity. Variable degradation rates of DCD in soil, unrelated to temperature or moisture, may contribute to varying DCD efficacy. Soil properties should be considered when tailoring DCD strategies for improving nitrogen use efficiency and crop yields, through the reduction of reactive nitrogen loss.This research was financially supported under the National Development Plan, through the Research Stimulus Fund, administered by the Department of Agriculture, Food and the Marine under grants 07519 and 07545

How to cluster in parallel with neural networks

Partitioning a set of N patterns in a d-dimensional metric space into K clusters - in a way that those in a given cluster are more similar to each other than the rest - is a problem of interest in astrophysics, image analysis and other fields. As there are approximately K(N)/K (factorial) possible ways of partitioning the patterns among K clusters, finding the best solution is beyond exhaustive search when N is large. Researchers show that this problem can be formulated as an optimization problem for which very good, but not necessarily optimal solutions can be found by using a neural network. To do this the network must start from many randomly selected initial states. The network is simulated on the MPP (a 128 x 128 SIMD array machine), where researchers use the massive parallelism not only in solving the differential equations that govern the evolution of the network, but also by starting the network from many initial states at once, thus obtaining many solutions in one run. Researchers obtain speedups of two to three orders of magnitude over serial implementations and the promise through Analog VLSI implementations of speedups comensurate with human perceptual abilities

A scalar nonlocal bifurcation of solitary waves for coupled nonlinear Schroedinger systems

An explanation is given for previous numerical results which suggest a certain bifurcation of `vector solitons' from scalar (single-component) solitary waves in coupled nonlinear Schroedinger (NLS) systems. The bifurcation in question is nonlocal in the sense that the vector soliton does not have a small-amplitude component, but instead approaches a solitary wave of one component with two infinitely far-separated waves in the other component. Yet, it is argued that this highly nonlocal event can be predicted from a purely local analysis of the central solitary wave alone. Specifically the linearisation around the central wave should contain asymptotics which grow at precisely the speed of the other-component solitary waves on the two wings. This approximate argument is supported by both a detailed analysis based on matched asymptotic expansions, and numerical experiments on two example systems. The first is the usual coupled NLS system involving an arbitrary ratio between the self-phase and cross-phase modulation terms, and the second is a coupled NLS system with saturable nonlinearity that has recently been demonstrated to support stable multi-peaked solitary waves. The asymptotic analysis further reveals that when the curves which define the proposed criterion for scalar nonlocal bifurcations intersect with boundaries of certain local bifurcations, the nonlocal bifurcation could turn from scalar to non-scalar at the intersection. This phenomenon is observed in the first example. Lastly, we have also selectively tested the linear stability of several solitary waves just born out of scalar nonlocal bifurcations. We found that they are linearly unstable. However, they can lead to stable solitary waves through parameter continuation.Comment: To appear in Nonlinearit

Discrete Dynamical Systems Embedded in Cantor Sets

While the notion of chaos is well established for dynamical systems on manifolds, it is not so for dynamical systems over discrete spaces with $N$ variables, as binary neural networks and cellular automata. The main difficulty is the choice of a suitable topology to study the limit $N\to\infty$. By embedding the discrete phase space into a Cantor set we provided a natural setting to define topological entropy and Lyapunov exponents through the concept of error-profile. We made explicit calculations both numerical and analytic for well known discrete dynamical models.Comment: 36 pages, 13 figures: minor text amendments in places, time running top to bottom in figures, to appear in J. Math. Phy

Stretching and folding versus cutting and shuffling: An illustrated perspective on mixing and deformations of continua

We compare and contrast two types of deformations inspired by mixing applications -- one from the mixing of fluids (stretching and folding), the other from the mixing of granular matter (cutting and shuffling). The connection between mechanics and dynamical systems is discussed in the context of the kinematics of deformation, emphasizing the equivalence between stretches and Lyapunov exponents. The stretching and folding motion exemplified by the baker's map is shown to give rise to a dynamical system with a positive Lyapunov exponent, the hallmark of chaotic mixing. On the other hand, cutting and shuffling does not stretch. When an interval exchange transformation is used as the basis for cutting and shuffling, we establish that all of the map's Lyapunov exponents are zero. Mixing, as quantified by the interfacial area per unit volume, is shown to be exponentially fast when there is stretching and folding, but linear when there is only cutting and shuffling. We also discuss how a simple computational approach can discern stretching in discrete data.Comment: REVTeX 4.1, 9 pages, 3 figures; v2 corrects some misprints. The following article appeared in the American Journal of Physics and may be found at http://ajp.aapt.org/resource/1/ajpias/v79/i4/p359_s1 . Copyright 2011 American Association of Physics Teachers. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the AAP

Discrete embedded solitons

We address the existence and properties of discrete embedded solitons (ESs), i.e., localized waves existing inside the phonon band in a nonlinear dynamical-lattice model. The model describes a one-dimensional array of optical waveguides with both the quadratic (second-harmonic generation) and cubic nonlinearities. A rich family of ESs was previously known in the continuum limit of the model. First, a simple motivating problem is considered, in which the cubic nonlinearity acts in a single waveguide. An explicit solution is constructed asymptotically in the large-wavenumber limit. The general problem is then shown to be equivalent to the existence of a homoclinic orbit in a four-dimensional reversible map. From properties of such maps, it is shown that (unlike ordinary gap solitons), discrete ESs have the same codimension as their continuum counterparts. A specific numerical method is developed to compute homoclinic solutions of the map, that are symmetric under a specific reversing transformation. Existence is then studied in the full parameter space of the problem. Numerical results agree with the asymptotic results in the appropriate limit and suggest that the discrete ESs may be semi-stable as in the continuous case.Comment: A revtex4 text file and 51 eps figure files. To appear in Nonlinearit

Liquidity and the drivers of search, due diligence and transaction times for UK commercial real estate investments

Trading commercial real estate involves a process of exchange that is costly and which occurs over an extended and uncertain period of time. This has consequences for the performance and risk of real estate investments. Most research on transaction times has occurred for residential rather than commercial real estate. We study the time taken to transact commercial real estate assets in the UK using a sample of 578 transactions over the period 2004 to 2013. We measure average time to transact from a buyer and seller perspective, distinguishing the search and due diligence phases of the process, and we conduct econometric analysis to explain variation in due diligence times between assets. The median time for purchase of real estate from introduction to completion was 104 days and the median time for sale from marketing to completion was 135 days. There is considerable variation around these times and results suggest that some of this variation is related to market state, type and quality of asset, and type of participants involved in the transaction. Our findings shed light on the drivers of liquidity at an individual asset level and can inform models that quantify the impact of uncertain time on market on real estate investment risk