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Related Concept Videos

BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
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Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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Linear time-invariant Systems

A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
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Introduction to Limits01:30

Introduction to Limits

A limit describes the value a function approaches as its input moves closer to a particular point. Even when a function is undefined at a specific value, limits allow us to analyze its behavior near that point. This concept is fundamental in calculus and essential for understanding continuity, derivatives, and integrals.Mathematically, a function f(x) has a limit L at x = a if its values L approach x as x gets arbitrarily close to a. This is written as:This notation expresses that the function...
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Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Published on: December 4, 2017

Past-future information bottleneck in dynamical systems.

Felix Creutzig1, Amir Globerson, Naftali Tishby

  • 1Berkeley Institute of the Environment, University of California, Berkeley, California 94720, USA. creutzig@nature.berkeley.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2009
PubMed
Summary
This summary is machine-generated.

Biological systems balance information accuracy and coding costs. This study develops a framework to predict future outputs from past inputs, revealing system dynamics and reducing model complexity.

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Area of Science:

  • Theoretical biology
  • Information theory
  • Systems biology

Background:

  • Biological systems require real-time information processing.
  • There is an inherent trade-off between information accuracy and coding costs.
  • Understanding these dynamics is crucial for modeling biological functions.

Purpose of the Study:

  • To operationalize the trade-off between information accuracy and coding costs.
  • To develop an information-theoretic framework for selective information extraction.
  • To link information-theoretic optimization with system identification and model reduction.

Main Methods:

  • Developed an information-theoretic framework.
  • Formulated a generalized eigenvalue problem.
  • Analyzed input-output relationships and state-space dimensions.

Main Results:

  • Identified selective information extraction from past inputs predictive of future outputs.
  • Unraveled input history through structural phase transitions.
  • Demonstrated connections to canonical correlation analysis with a numerical example.

Conclusions:

  • The framework provides a method for understanding information processing in biological systems.
  • Relates information-theoretic optimization to system identification and model reduction.
  • Offers insights into the structure of biological system dynamics.