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Related Concept Videos

Basic Continuous Time Signals01:22

Basic Continuous Time Signals

Basic continuous-time signals include the unit step function, unit impulse function, and unit ramp function, collectively referred to as singularity functions. Singularity functions are characterized by discontinuities or discontinuous derivatives.
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Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
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BIBO stability of continuous and discrete -time systems

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Wald-Wolfowitz Runs Test I01:17

Wald-Wolfowitz Runs Test I

The Wald-Wolfowitz test, also known as the runs test, is a nonparametric statistical test used to assess the randomness of a sequence of two different types of elements (e.g., positive/negative values, successes/failures). It examines whether the order of the elements in a sequence is random or if there is a pattern or trend present. This nonparametric test applies to any ordered data despite the population and sample data distribution, even if a higher sample size is available.
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Random Variables01:09

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Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...

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Continuous Measurement of Biological Noise in Escherichia Coli Using Time-lapse Microscopy
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Published on: April 27, 2021

Noisy continuous time random walks.

Jae-Hyung Jeon1, Eli Barkai, Ralf Metzler

  • 1Department of Physics, Tampere University of Technology, FI-33101 Tampere, Finland.

The Journal of Chemical Physics
|October 5, 2013
PubMed
Summary
This summary is machine-generated.

We introduce a new model for anomalous diffusion by adding noise to continuous time random walks. This noisy model better reflects real-world biomolecule movement in cells, showing diverse dynamic behaviors.

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Area of Science:

  • Biophysics
  • Statistical Mechanics
  • Cellular Dynamics

Background:

  • Analyzing single-molecule trajectories in cells is complex due to stochasticity.
  • Continuous Time Random Walks (CTRW) model anomalous diffusion with trapping.
  • Real cellular environments exhibit additional particle motion beyond simple CTRW.

Purpose of the Study:

  • To present and analyze an extended CTRW model incorporating additive Gaussian noise.
  • To investigate the impact of noise on anomalous diffusion dynamics in complex media.
  • To explore the emergence of different dynamic regimes, including ergodicity.

Main Methods:

  • Theoretical analysis of a CTRW model with superimposed additive Gaussian noise.
  • Mathematical modeling of tracer particle motion in complex cellular environments.
  • Investigation of ergodicity properties under varying noise strengths.

Main Results:

  • The extended CTRW model with noise displays a rich variety of apparent dynamic regimes.
  • Noisy CTRW processes can exhibit apparent ergodicity, unlike the bare CTRW.
  • The model captures the 'jiggling' motion observed in experimental tracer particle dynamics.

Conclusions:

  • Superimposing Gaussian noise onto CTRW provides a more realistic model for cellular diffusion.
  • This 'noisy CTRW' framework helps reconcile theoretical models with experimental observations.
  • Understanding these dynamics is crucial for accurate physical analysis of subdiffusion in cells.