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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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The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
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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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Gradually varying flow (GVF) in open channels describes situations where water depth changes slowly along the channel due to factors like non-uniform bed slope, channel shape variations, or obstructions. This flow type occurs when the depth adjusts gradually to balance gravitational forces, shear forces, and energy requirements, resulting in a low rate of depth change.Characteristics of Gradually Varying FlowGVF is commonly observed in natural streams, rivers, and canals, where flow depth...
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Estimating information in time-varying signals.

Sarah Anhala Cepeda-Humerez1, Jakob Ruess2,3, Gašper Tkačik1

  • 1Institute of Science and Technology Austria, A-3400 Klosterneuburg, Austria.

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|September 4, 2019
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Summary
This summary is machine-generated.

This study introduces decoding-based methods to accurately measure information in biological signaling networks from single-cell data. These new techniques better capture environmental information encoded in temporal dynamics compared to older methods.

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Area of Science:

  • Systems biology
  • Computational biology
  • Information theory

Background:

  • Biological systems encode environmental information in network dynamics.
  • Estimating this information from high-dimensional time-series data is challenging.
  • Current methods may not efficiently capture all relevant information.

Purpose of the Study:

  • To develop and evaluate decoding-based methods for estimating mutual information in single-cell, high-dimensional time-series data.
  • To provide a robust and unbiased measure for biological signaling network performance.
  • To compare decoding-based estimators against model-based approximations and existing methods.

Main Methods:

  • Developed decoding-based estimators to lower bound mutual information.
  • Derived model-based information approximations and analytical upper bounds for chemical reaction networks.
  • Benchmarked decoding estimators against model-based methods and k-nearest-neighbor estimators.
  • Applied methods to experimental data from Erk and Ca2+ signaling and yeast stress response.

Main Results:

  • Decoding-based estimators robustly extract a large fraction of information from high-dimensional trajectories with realistic sample sizes.
  • These estimators outperform the commonly-used k-nearest-neighbor estimator.
  • Substantial information about environmental states is encoded in non-trivial response statistics, even in stationary signals.
  • Applied to Erk, Ca2+, and yeast stress response data.

Conclusions:

  • Decoding-based information estimates offer a proper and unbiased measure of biological signaling network performance.
  • These methods are crucial for analyzing complex biological data and understanding cellular information processing.
  • The findings highlight the importance of temporal dynamics in biological information encoding.