136 research outputs found
Spatiotemporal multi-resolution approximation of the Amari type neural field model
Neural fields are spatially continuous state variables described by integro-differential equations, which are well suited to describe the spatiotemporal evolution of cortical activations on multiple scales. Here we develop a multi-resolution approximation (MRA) framework for the integro-difference equation (IDE) neural field model based on semi-orthogonal cardinal B-spline wavelets. In this way, a flexible framework is created, whereby both macroscopic and microscopic behavior of the system can be represented simultaneously. State and parameter estimation is performed using the expectation maximization (EM) algorithm. A synthetic example is provided to demonstrate the framework
Spherical harmonic decomposition applied to spatial-temporal analysis of human high-density EEG
We demonstrate an application of spherical harmonic decomposition to analysis
of the human electroencephalogram (EEG). We implement two methods and discuss
issues specific to analysis of hemispherical, irregularly sampled data.
Performance of the methods and spatial sampling requirements are quantified
using simulated data. The analysis is applied to experimental EEG data,
confirming earlier reports of an approximate frequency-wavenumber relationship
in some bands.Comment: 12 pages, 8 figures, submitted to Phys. Rev. E, uses APS RevTeX
style
Detection of fixed points in spatiotemporal signals by clustering method
We present a method to determine fixed points in spatiotemporal signals. A
144-dimensioanl simulated signal, similar to a Kueppers-Lortz instability, is
analyzed and its fixed points are reconstructed.Comment: 3 pages, 3 figure
Central peak position in magnetization loops of high- superconductors
Exact analytical results are obtained for the magnetization of a
superconducting thin strip with a general behavior J_c(B) of the critical
current density. We show that within the critical-state model the magnetization
as function of applied field, B_a, has an extremum located exactly at B_a=0.
This result is in excellent agreement with presented experimental data for a
YBCO thin film. After introducing granularity by patterning the film, the
central peak becomes shifted to positive fields on the descending field branch
of the loop. Our results show that a positive peak position is a definite
signature of granularity in superconductors.Comment: $ pages, 6 figure
Recognizing recurrent neural networks (rRNN): Bayesian inference for recurrent neural networks
Recurrent neural networks (RNNs) are widely used in computational
neuroscience and machine learning applications. In an RNN, each neuron computes
its output as a nonlinear function of its integrated input. While the
importance of RNNs, especially as models of brain processing, is undisputed, it
is also widely acknowledged that the computations in standard RNN models may be
an over-simplification of what real neuronal networks compute. Here, we suggest
that the RNN approach may be made both neurobiologically more plausible and
computationally more powerful by its fusion with Bayesian inference techniques
for nonlinear dynamical systems. In this scheme, we use an RNN as a generative
model of dynamic input caused by the environment, e.g. of speech or kinematics.
Given this generative RNN model, we derive Bayesian update equations that can
decode its output. Critically, these updates define a 'recognizing RNN' (rRNN),
in which neurons compute and exchange prediction and prediction error messages.
The rRNN has several desirable features that a conventional RNN does not have,
for example, fast decoding of dynamic stimuli and robustness to initial
conditions and noise. Furthermore, it implements a predictive coding scheme for
dynamic inputs. We suggest that the Bayesian inversion of recurrent neural
networks may be useful both as a model of brain function and as a machine
learning tool. We illustrate the use of the rRNN by an application to the
online decoding (i.e. recognition) of human kinematics
Peak effect, vortex-lattice melting-line and order - disorder transition in conventional and high-T superconductors
We investigate the order - disorder transition line from a Bragg glass to an
amorphous vortex glass in the H-T phase diagram of three-dimensional type-II
superconductors with account of both pinning-caused and thermal fluctuations of
the vortex lattice. Our approach is based on the Lindemann criterion and on
results of the collective pinning theory and generalizes previous work of other
authors. It is shown that the shapes of the order - disorder transition line
and the vortex lattice melting curve are determined only by the Ginzburg
number, which characterizes thermal fluctuations, and by a parameter which
describes the strength of the quenched disorder in the flux-line lattice. In
the framework of this unified approach we obtain the H-T phase diagrams for
both conventional and high-Tc superconductors. Several well-known experimental
results concerning the fishtail effect and the phase diagram of high-Tc
superconductors are naturally explained by assuming that a peak effect in the
critical current density versus H signalizes the order - disorder transition
line in superconductors with point defects.Comment: 15 pages including 11 figure
Multi-basin depositional framework for moisture-balance reconstruction during the last 1300 years at Lake Bogoria, central Kenya Rift Valley
Multi-proxy analysis of sediment cores from five key locations in hypersaline, alkaline Lake Bogoria (central Kenya Rift Valley) has allowed reconstruction of its history of depositional and hydrological change during the past 1300years. Analyses including organic matter and carbonate content, granulometry, mineralogical composition, charcoal counting and high-resolution scanning of magnetic susceptibility and elemental geochemistry resulted in a detailed sedimentological and compositional characterization of lacustrine deposits in the three lake basins and on the two sills separating them. Thesepalaeolimnological data were supplemented with information on present-day sedimentation conditions based on seasonal sampling of settling particles and on measurement of physicochemical profiles through the water column. A new age model based on Pb-210, Cs-137 and C-14 dating captures the sediment chronology of this hydrochemically complex and geothermally fed lake. An extensive set of chronological tie points between the equivalent high-resolution proxy time series of the five sediment sequences allowed transfer of radiometric dates between the basins, enabling interbasin comparison of sedimentation dynamics through time. The resulting reconstruction demonstrates considerable moisture-balance variability through time, reflecting regional hydroclimate dynamics over the past 1300years. Between ca 690 and 950AD, the central and southern basins of Lake Bogoria were reduced to shallow and separated brine pools. In the former, occasional near-complete desiccation triggered massive trona precipitation. Between ca 950 and 1100AD, slightly higher water levels allowed the build-up of high pCO(2) leading to precipitation of nahcolite still under strongly evaporative conditions. Lake Bogoria experienced a pronounced highstand between ca 1100 and 1350AD, only to recede again afterwards. For a substantial part of the time between ca 1350 and 1800AD, the northern basin was probably disconnected from the united central and southern basins. Throughout the last two centuries, lake level has been relatively high compared to the rest of the past millennium. Evidence for increased terrestrial sediment supply in recent decades, due to anthropogenic soil erosion in the wider Bogoria catchment, is a reason for concern about possible adverse impacts on the unique ecosystem of Lake Bogoria
Time Scale Hierarchies in the Functional Organization of Complex Behaviors
Traditional approaches to cognitive modelling generally portray cognitive events in terms of ‘discrete’ states (point attractor dynamics) rather than in terms of processes, thereby neglecting the time structure of cognition. In contrast, more recent approaches explicitly address this temporal dimension, but typically provide no entry points into cognitive categorization of events and experiences. With the aim to incorporate both these aspects, we propose a framework for functional architectures. Our approach is grounded in the notion that arbitrary complex (human) behaviour is decomposable into functional modes (elementary units), which we conceptualize as low-dimensional dynamical objects (structured flows on manifolds). The ensemble of modes at an agent’s disposal constitutes his/her functional repertoire. The modes may be subjected to additional dynamics (termed operational signals), in particular, instantaneous inputs, and a mechanism that sequentially selects a mode so that it temporarily dominates the functional dynamics. The inputs and selection mechanisms act on faster and slower time scales then that inherent to the modes, respectively. The dynamics across the three time scales are coupled via feedback, rendering the entire architecture autonomous. We illustrate the functional architecture in the context of serial behaviour, namely cursive handwriting. Subsequently, we investigate the possibility of recovering the contributions of functional modes and operational signals from the output, which appears to be possible only when examining the output phase flow (i.e., not from trajectories in phase space or time)
Beyond in-phase and anti-phase coordination in a model of joint action
In 1985, Haken, Kelso and Bunz proposed a system of coupled nonlinear oscillators as a model of rhythmic movement patterns in human bimanual coordination. Since then, the Haken–Kelso–Bunz (HKB) model has become a modelling paradigm applied extensively in all areas of movement science, including interpersonal motor coordination. However, all previous studies have followed a line of analysis based on slowly varying amplitudes and rotating wave approximations. These approximations lead to a reduced system, consisting of a single differential equation representing the evolution of the relative phase of the two coupled oscillators: the HKB model of the relative phase. Here we take a different approach and systematically investigate the behaviour of the HKB model in the full four-dimensional state space and for general coupling strengths. We perform detailed numerical bifurcation analyses and reveal that the HKB model supports previously unreported dynamical regimes as well as bistability between a variety of coordination patterns. Furthermore, we identify the stability boundaries of distinct coordination regimes in the model and discuss the applicability of our findings to interpersonal coordination and other joint action tasks
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