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Related Concept Videos

Linear time-invariant Systems01:23

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.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be calculated...
Static Equilibrium - I01:05

Static Equilibrium - I

A rigid body is said to be in dynamic equilibrium when both its linear and angular acceleration are zero, relative to an inertial frame of reference. This means that a body in equilibrium can be moving, but only when its linear and angular velocities are constant. A rigid body is said to be in static equilibrium when it is at rest in the selected frame of reference. The distinction between static equilibrium (e.g., a state of rest) and dynamic equilibrium (e.g, a state of uniform motion) is...
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Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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Constraints and Statical Determinacy01:26

Constraints and Statical Determinacy

In structural engineering, the equilibrium of a system is not only determined by its equations of equilibrium but also with the help of constraints. Constraints refer to restrictions on the motion of a system. The proper combinations of constraints can minimize the total number of constraints needed to maintain a system in mechanical equilibrium. When this happens, the system is said to be statically determinate. For such systems, the unknown reaction supports can be estimated using equilibrium...
Non-inertial Frames of Reference01:27

Non-inertial Frames of Reference

A reference frame accelerating or decelerating relative to an inertial frame is a non-inertial frame. To help understand this, consider what taking off in an airplane, turning a corner in a car, riding a merry-go-round, and the circular motion of a tropical cyclone all have in common. All these systems are accelerating, decelerating, or rotating relative to the Earth; hence, they all are non-inertial frames. All these systems exhibit inertial forces, which merely seem to arise from motion,...
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In certain chromatographic separations, solutes transfer between the mobile phase and the stationary phase via sorption, which typically refers to the process of adsorption. For many chromatographic systems, the sorption process often depends on the polarity of the compounds—an expression of the overall dipole moment within the molecule. During the separation process, there is competition between the solute and solvent for adsorption to the stationary phase. Highly polar compounds and solvents...

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Information in the nonstationary case.

Vincent Q Vu1, Bin Yu, Robert E Kass

  • 1Department of Statistics, University of California, Berkeley, CA 94720, USA. vqv@stat.berkeley.edu

Neural Computation
|October 22, 2008
PubMed
Summary
This summary is machine-generated.

The direct method for estimating information provides a useful measure of response variability over time. Under specific conditions, it accurately estimates mutual information between stimulus and response.

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Area of Science:

  • Computational Neuroscience
  • Information Theory
  • Statistical Inference

Background:

  • Estimating mutual information is crucial for understanding neural coding.
  • Direct methods offer an alternative to complex joint distribution estimation.
  • These methods focus on marginal and conditional response entropies.

Purpose of the Study:

  • To analyze the convergence properties of direct information estimation methods.
  • To clarify the conditions under which direct estimates reflect mutual information.
  • To investigate the interpretation of direct estimates with nonstationary or deterministic stimuli.

Main Methods:

  • Theoretical analysis of information estimators.
  • Asymptotic analysis as the number of trials increases.
  • Examination of stationarity and ergodicity assumptions.

Main Results:

  • Direct estimates of marginal and conditional entropies converge to specific time-averaged distributions.
  • Under stationarity and ergodicity, the difference converges to mutual information.
  • For deterministic or nonstationary stimuli, the estimate measures response variability.

Conclusions:

  • Direct information estimation is a robust measure of response variability.
  • Its interpretation as mutual information is contingent on stimulus properties.
  • The method provides valuable insights into neural system dynamics.