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Related Concept Videos

Classification of Systems-I01:26

Classification of Systems-I

Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
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Linear time-invariant Systems01:23

Linear time-invariant Systems

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Linear Approximation in Frequency Domain01:26

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Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

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Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
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Linear Differential Equations

The integrating factor method provides a systematic way to solve first-order linear differential equations, especially those that cannot be handled by separation of variables. This method is particularly useful in modeling time-dependent physical systems influenced by both constant inputs and resistive forces. A common example is the motion of a car subjected to a constant engine force while experiencing air resistance proportional to its velocity.In such scenarios, Newton’s second law yields a...

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Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

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Published on: August 30, 2013

Bilinear dynamical systems.

W Penny1, Z Ghahramani, K Friston

  • 1Wellcome Department of Imaging Neuroscience, University College, London WC1N 3BG, UK. wpenny@fil.ion.ucl.ac.uk

Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences
|August 10, 2005
PubMed
Summary
This summary is machine-generated.

This study introduces bilinear dynamical systems (BDS) for model-based fMRI time-series deconvolution. This approach reveals underlying neuronal activity from haemodynamic signals, advancing brain connectivity research.

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Area of Science:

  • Neuroscience
  • Computational Biology
  • Signal Processing

Background:

  • Functional magnetic resonance imaging (fMRI) measures haemodynamic responses, which are indirect indicators of neuronal activity.
  • Deconvolving fMRI time-series is crucial for accurately estimating underlying neuronal signals.
  • Existing methods may lack the sophistication to fully capture the complex dynamics between neuronal activity and haemodynamic responses.

Purpose of the Study:

  • To propose and evaluate bilinear dynamical systems (BDS) for model-based deconvolution of fMRI time-series.
  • To enable informed deconvolution of haemodynamic time-series to disclose underlying neuronal activity.
  • To provide a method for estimating neuronal responses essential for brain functional integration and connectivity models.

Main Methods:

  • Development of a stochastic bilinear neurodynamical model in discrete time.
  • Incorporation of linear convolution kernels to model haemodynamics.
  • Derivation of an expectation-maximization (EM) algorithm for parameter estimation.
  • Application of the EM algorithm with deconvolution in the E-step and parameter updates in the M-step.

Main Results:

  • Preliminary results demonstrate the utility of BDS for fMRI time-series deconvolution.
  • The study investigates the implications of the stochastic nature of the neurodynamic model.
  • Performance comparison of the proposed BDS method against Wiener deconvolution is presented.

Conclusions:

  • Bilinear dynamical systems offer a promising framework for model-based fMRI deconvolution.
  • This approach enhances the ability to infer neuronal activity from haemodynamic signals.
  • The findings contribute to more accurate modeling of brain functional integration and connectivity.