Cortical Dynamics of Feature Binding and Reset: Control of Visual Persistence

An analysis of the reset of visual cortical circuits responsible for the binding or segmentation of visual features into coherent visual forms yields a model that explains properties of visual persistence. The reset mechanisms prevent massive smearing or visual percepts in response to rapidly moving images. The model simulates relationships among psychophysical data showing inverse relations of persistence to flash luminance and duration, greaterr persistence of illusory contours than real contours, a U-shaped temporal function for persistence of illusory contours, a reduction of persistence: due to adaptation with a stimulus of like orientation, an increase or persistence due to adaptation with a stimulus of perpendicular orientation, and an increase of persistence with spatial separation of a masking stimulus. The model suggests that a combination of habituative, opponent, and endstopping mechanisms prevent smearing and limit persistence. Earlier work with the model has analyzed data about boundary formation, texture segregation, shape-from-shading, and figure-ground separation. Thus, several types of data support each model mechanism and new predictions are made.

Linear and nonlinear dynamics of a dust bicrystal consisting of positive and negative dust particles

A dusty plasma crystalline configuration consisting of charged dust grains of alternating charge sign (.../+/-/+/-/+/...) and mass is considered. Both charge and mass of each dust species are taken to be constant. Considering the equations of longitudinal motion, a dispersion relation for linear longitudinal vibrations is derived from first principles and then analyzed. Two harmonic modes are obtained, namely, an acoustic mode and an inverse-dispersive optic-like one. The nonlinear aspects of acoustic longitudinal dust grain motion are addressed via a generalized Boussinesq (and, alternatively, a generalized Korteweg-de Vries) description. (C) 2005 American Institute of Physics.

Estimation of Clarinet Reed Parameters by Inverse Modelling

Analysis of the acoustical functioning of musical instruments invariably involves the estimation of model parameters. The broad aim of this paper is to develop methods for estimation of clarinet reed parameters that are representative of actual playing conditions. This presents various challenges because of the di?culties of measuring the directly relevant variables without interfering with the control of the instrument. An inverse modelling approach is therefore proposed, in which the equations governing the sound generation mechanism of the clarinet
are employed in an optimisation procedure to determine the reed parameters from the mouthpiece pressure and volume ?ow signals. The underlying physical model captures most of the reed dynamics and is simple enough to be used in an inversion process. The optimisation procedure is ?rst tested by applying it to numerically synthesised signals, and then applied to mouthpiece signals acquired during notes blown by a human player. The proposed inverse modelling approach raises the possibility of revealing information about the way in which the embouchure-related reed parameters are controlled by the player, and also facilitates physics-based re-synthesis of clarinet sounds.

A robotic apparatus that dictates torque fields around joints without affecting inherent joint dynamics

This manuscript describes how motor behaviour researchers who are not at the same time expert roboticists may implement an experimental apparatus, which has the ability to dictate torque fields around a single joint on one limb or single joints on multiple limbs without otherwise interfering with the inherent dynamics of those joints. Such an apparatus expands the exploratory potential of the researcher wherever experimental distinction of factors may necessitate independent control of torque fields around multiple limbs, or the shaping of torque fields of a given joint independently of its plane of motion, or its directional phase within that plane. The apparatus utilizes torque motors. The challenge with torque motors is that they impose added inertia on limbs and thus attenuate joint dynamics. We eliminated this attenuation by establishing an accurate mathematical model of the robotic device using the Box-Jenkins method, and cancelling out its dynamics by employing the inverse of the model as a compensating controller. A direct measure of the remnant inertial torque as experienced by the hand during a 50 s period of wrist oscillations that increased gradually in frequency from 1.0 to 3.8 Hz confirmed that the removal of the inertial effect of the motor was effectively complete.

Dynamics of a dust crystal with positive and negative dust

A dust crystal consisting of charged dust grains of alternating charge sign (.../+/-/+/-/+/...) and mass is considered. Considering the equations of longitudinal motion, a linear dispersion relation is derived from first principles, and then analyzed. Two modes are obtained, including an acoustic mode and an inverse-dispersive optic-like one. The nonlinear aspects of longitudinal dust grain motion are also briefly addressed, via a Boussineq and Korteweg- de Vries description.

A musculoskeletal shoulder model based on pseudo-inverse and null-space optimization.

The goal of the present work was assess the feasibility of using a pseudo-inverse and null-space optimization approach in the modeling of the shoulder biomechanics. The method was applied to a simplified musculoskeletal shoulder model. The mechanical system consisted in the arm, and the external forces were the arm weight, 6 scapulo-humeral muscles and the reaction at the glenohumeral joint, which was considered as a spherical joint. The muscle wrapping was considered around the humeral head assumed spherical. The dynamical equations were solved in a Lagrangian approach. The mathematical redundancy of the mechanical system was solved in two steps: a pseudo-inverse optimization to minimize the square of the muscle stress and a null-space optimization to restrict the muscle force to physiological limits. Several movements were simulated. The mathematical and numerical aspects of the constrained redundancy problem were efficiently solved by the proposed method. The prediction of muscle moment arms was consistent with cadaveric measurements and the joint reaction force was consistent with in vivo measurements. This preliminary work demonstrated that the developed algorithm has a great potential for more complex musculoskeletal modeling of the shoulder joint. In particular it could be further applied to a non-spherical joint model, allowing for the natural translation of the humeral head in the glenoid fossa.

Setting boundaries: brain dynamics of modal and amodal illusory shape completion in humans.

Normal visual perception requires differentiating foreground from background objects. Differences in physical attributes sometimes determine this relationship. Often such differences must instead be inferred, as when two objects or their parts have the same luminance. Modal completion refers to such perceptual "filling-in" of object borders that are accompanied by concurrent brightness enhancement, in turn termed illusory contours (ICs). Amodal completion is filling-in without concurrent brightness enhancement. Presently there are controversies regarding whether both completion processes use a common neural mechanism and whether perceptual filling-in is a bottom-up, feedforward process initiating at the lowest levels of the cortical visual pathway or commences at higher-tier regions. We previously examined modal completion (Murray et al., 2002) and provided evidence that the earliest modal IC sensitivity occurs within higher-tier object recognition areas of the lateral occipital complex (LOC). We further proposed that previous observations of IC sensitivity in lower-tier regions likely reflect feedback modulation from the LOC. The present study tested these proposals, examining the commonality between modal and amodal completion mechanisms with high-density electrical mapping, spatiotemporal topographic analyses, and the local autoregressive average distributed linear inverse source estimation. A common initial mechanism for both types of completion processes (140 msec) that manifested as a modulation in response strength within higher-tier visual areas, including the LOC and parietal structures, is demonstrated, whereas differential mechanisms were evident only at a subsequent time period (240 msec), with amodal completion relying on continued strong responses in these structures.

Mathematical Modelling of the Dynamics of Granular Materials in a Rotating Cylinder

The current study is aimed at the development of a theoretical simulation tool based on Discrete Element Method (DEM) to 'interpret granular dynamics of solid bed in the cross section of the horizontal rotating cylinder at the microscopic level and subsequently apply this model to establish the transition behaviour, mixing and segregation.The simulation of the granular motion developed in this work is based on solving Newton's equation of motion for each particle in the granular bed subjected to the collisional forces, external forces and boundary forces. At every instant of time, the forces are tracked and the positions velocities and accelarations of each partcle is The software code for this simulation is written in VISUAL FORTRAN 90 After checking the validity of the code with special tests, it is used to investigate the transition behaviour of granular solids motion in the cross section of a rotating cylinder for various rotational speeds and fill fraction.This work is hence directed towards a theoretical investigation based on Discrete Element Method (DEM) of the motion of granular solids in the radial direction of the horizontal cylinder to elucidate the relationship between the operating parameters of the rotating cylinder geometry and physical properties ofthe granular solid.The operating parameters of the rotating cylinder include the various rotational velocities of the cylinder and volumetric fill. The physical properties of the granular solids include particle sizes, densities, stiffness coefficients, and coefficient of friction Further the work highlights the fundamental basis for the important phenomena of the system namely; (i) the different modes of solids motion observed in a transverse crosssection of the rotating cylinder for various rotational speeds, (ii) the radial mixing of the granular solid in terms of active layer depth (iii) rate coefficient of mixing as well as the transition behaviour in terms of the bed turnover time and rotational speed and (iv) the segregation mechanisms resulting from differences in the size and density of particles.The transition behaviour involving its six different modes of motion of the granular solid bed is quantified in terms of Froude number and the results obtained are validated with experimental and theoretical results reported in the literature The transition from slumping to rolling mode is quantified using the bed turnover time and a linear relationship is established between the bed turn over time and the inverse of the rotational speed of the cylinder as predicted by Davidson et al. [2000]. The effect of the rotational speed, fill fraction and coefficient of friction on the dynamic angle of repose are presented and discussed. The variation of active layer depth with respect to fill fraction and rotational speed have been investigated. The results obtained through simulation are compared with the experimental results reported by Van Puyvelde et. at. [2000] and Ding et at. [2002].The theoretical model has been further extended, to study the rmxmg and segregation in the transverse direction for different particle sizes and their size ratios. The effect of fill fraction and rotational speed on the transverse mixing behaviour is presented in the form of a mixing index and mixing kinetics curve. The segregation pattern obtained by the simulation of the granular solid bed with respect to the rotational speed of the cylinder is presented both in graphical and numerical forms. The segregation behaviour of the granular solid bed with respect to particle size, density and volume fraction of particle size has been investigated. Several important macro parameters characterising segregation such as mixing index, percolation index and segregation index have been derived from the simulation tool based on first principles developed in this work.

Parameter identification of structural dynamic models by inverse statistical analysis

Auf dem Gebiet der Strukturdynamik sind computergestützte Modellvalidierungstechniken inzwischen weit verbreitet. Dabei werden experimentelle Modaldaten, um ein numerisches Modell für weitere Analysen zu korrigieren. Gleichwohl repräsentiert das validierte Modell nur das dynamische Verhalten der getesteten Struktur. In der Realität gibt es wiederum viele Faktoren, die zwangsläufig zu variierenden Ergebnissen von Modaltests führen werden: Sich verändernde Umgebungsbedingungen während eines Tests, leicht unterschiedliche Testaufbauten, ein Test an einer nominell gleichen aber anderen Struktur (z.B. aus der Serienfertigung), etc. Damit eine stochastische Simulation durchgeführt werden kann, muss eine Reihe von Annahmen für die verwendeten Zufallsvariablengetroffen werden. Folglich bedarf es einer inversen Methode, die es ermöglicht ein stochastisches Modell aus experimentellen Modaldaten zu identifizieren. Die Arbeit beschreibt die Entwicklung eines parameter-basierten Ansatzes, um stochastische Simulationsmodelle auf dem Gebiet der Strukturdynamik zu identifizieren. Die entwickelte Methode beruht auf Sensitivitäten erster Ordnung, mit denen Parametermittelwerte und Kovarianzen des numerischen Modells aus stochastischen experimentellen Modaldaten bestimmt werden können.

Evolving graphs: dynamical models, inverse problems and propagation

Applications such as neuroscience, telecommunication, online social networking, transport and retail trading give rise to connectivity patterns that change over time. In this work, we address the resulting need for network models and computational algorithms that deal with dynamic links. We introduce a new class of evolving range-dependent random graphs that gives a tractable framework for modelling and simulation. We develop a spectral algorithm for calibrating a set of edge ranges from a sequence of network snapshots and give a proof of principle illustration on some neuroscience data. We also show how the model can be used computationally and analytically to investigate the scenario where an evolutionary process, such as an epidemic, takes place on an evolving network. This allows us to study the cumulative effect of two distinct types of dynamics.

Efficient non-linear data assimilation in geophysical fluid dynamics

New ways of combining observations with numerical models are discussed in which the size of the state space can be very large, and the model can be highly nonlinear. Also the observations of the system can be related to the model variables in highly nonlinear ways, making this data-assimilation (or inverse) problem highly nonlinear. First we discuss the connection between data assimilation and inverse problems, including regularization. We explore the choice of proposal density in a Particle Filter and show how the ’curse of dimensionality’ might be beaten. In the standard Particle Filter ensembles of model runs are propagated forward in time until observations are encountered, rendering it a pure Monte-Carlo method. In large-dimensional systems this is very inefficient and very large numbers of model runs are needed to solve the data-assimilation problem realistically. In our approach we steer all model runs towards the observations resulting in a much more efficient method. By further ’ensuring almost equal weight’ we avoid performing model runs that are useless in the end. Results are shown for the 40 and 1000 dimensional Lorenz 1995 model.

Segmental dynamics in entangled linear polymer melts

We present molecular dynamics (MD) and slip-springs model simulations of the chain segmental dynamics in entangled linear polymer melts. The time-dependent behavior of the segmental orientation autocorrelation functions and mean-square segmental displacements are analyzed for both flexible and semiflexible chains, with particular attention paid to the scaling relations among these dynamic quantities. Effective combination of the two simulation methods at different coarse-graining levels allows us to explore the chain dynamics for chain lengths ranging from Z ≈ 2 to 90 entanglements. For a given chain length of Z ≈ 15, the time scales accessed span for more than 10 decades, covering all of the interesting relaxation regimes. The obtained time dependence of the monomer mean square displacements, g1(t), is in good agreement with the tube theory predictions. Results on the first- and second-order segmental orientation autocorrelation functions, C1(t) and C2(t), demonstrate a clear power law relationship of C2(t) C1(t)m with m = 3, 2, and 1 in the initial, free Rouse, and entangled (constrained Rouse) regimes, respectively. The return-to-origin hypothesis, which leads to inverse proportionality between the segmental orientation autocorrelation functions and g1(t) in the entangled regime, is convincingly verified by the simulation result of C1(t) g1(t)−1 t–1/4 in the constrained Rouse regime, where for well-entangled chains both C1(t) and g1(t) are rather insensitive to the constraint release effects. However, the second-order correlation function, C2(t), shows much stronger sensitivity to the constraint release effects and experiences a protracted crossover from the free Rouse to entangled regime. This crossover region extends for at least one decade in time longer than that of C1(t). The predicted time scaling behavior of C2(t) t–1/4 is observed in slip-springs simulations only at chain length of 90 entanglements, whereas shorter chains show higher scaling exponents. The reported simulation work can be applied to understand the observations of the NMR experiments.

Inverse problems in neural field theory

We study inverse problems in neural field theory, i.e., the construction of synaptic weight kernels yielding a prescribed neural field dynamics. We address the issues of existence, uniqueness, and stability of solutions to the inverse problem for the Amari neural field equation as a special case, and prove that these problems are generally ill-posed. In order to construct solutions to the inverse problem, we first recast the Amari equation into a linear perceptron equation in an infinite-dimensional Banach or Hilbert space. In a second step, we construct sets of biorthogonal function systems allowing the approximation of synaptic weight kernels by a generalized Hebbian learning rule. Numerically, this construction is implemented by the Moore–Penrose pseudoinverse method. We demonstrate the instability of these solutions and use the Tikhonov regularization method for stabilization and to prevent numerical overfitting. We illustrate the stable construction of kernels by means of three instructive examples.

Nonlinear error dynamics for cycled data assimilation methods

We investigate the error dynamics for cycled data assimilation systems, such that the inverse problem of state determination is solved at tk, k = 1, 2, 3, ..., with a first guess given by the state propagated via a dynamical system model from time tk − 1 to time tk. In particular, for nonlinear dynamical systems that are Lipschitz continuous with respect to their initial states, we provide deterministic estimates for the development of the error ||ek|| := ||x(a)k − x(t)k|| between the estimated state x(a) and the true state x(t) over time. Clearly, observation error of size δ > 0 leads to an estimation error in every assimilation step. These errors can accumulate, if they are not (a) controlled in the reconstruction and (b) damped by the dynamical system under consideration. A data assimilation method is called stable, if the error in the estimate is bounded in time by some constant C. The key task of this work is to provide estimates for the error ||ek||, depending on the size δ of the observation error, the reconstruction operator Rα, the observation operator H and the Lipschitz constants K(1) and K(2) on the lower and higher modes of controlling the damping behaviour of the dynamics. We show that systems can be stabilized by choosing α sufficiently small, but the bound C will then depend on the data error δ in the form c||Rα||δ with some constant c. Since ||Rα|| → ∞ for α → 0, the constant might be large. Numerical examples for this behaviour in the nonlinear case are provided using a (low-dimensional) Lorenz '63 system.