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Related Concept Videos

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.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
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.
In the...
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...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
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.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

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.
In the absence of...

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Related Experiment Videos

A trade-off between sample complexity and computational complexity in learning Boolean networks from time-series

Theodore J Perkins1, Michael T Hallett

  • 1McGill University, 3480 University St., Montreal, Quebec, Canada. tperkins@ohri.ca

IEEE/ACM Transactions on Computational Biology and Bioinformatics
|February 13, 2010
PubMed
Summary
This summary is machine-generated.

Inferring gene regulatory networks from expression data is challenging. This study provides bounds on data needed and an algorithm, showing sample and computational complexity depend inversely on time-series correlations.

Related Experiment Videos

Area of Science:

  • Computational Biology
  • Systems Biology
  • Genomics

Background:

  • Inferring gene regulatory relationships from gene expression data is a fundamental challenge in molecular biology.
  • Boolean networks are simplified models for gene regulatory interactions, often using time-series data.

Purpose of the Study:

  • To develop theoretical bounds on the data required for inferring gene regulatory relationships in a Boolean network model.
  • To investigate the impact of time-series correlations on both data and computational complexity.

Main Methods:

  • Modeling gene expression as Boolean variables with deterministic dependencies on input variables.
  • Analyzing time-series expression data with varying degrees of correlation between successive samples.
  • Deriving bounds on sample complexity and developing a fixed-parameter tractable algorithm.

Main Results:

  • Established bounds on the expected data needed for inferring Boolean network structures.
  • Demonstrated that sample complexity and computational complexity are inversely related to time-series correlation.
  • Identified that uncorrelated samples minimize data but maximize computation, while correlated samples have the opposite effect.

Conclusions:

  • The findings provide theoretical insights into the data requirements for gene regulatory network inference.
  • The inverse relationship between sample and computational complexity has practical implications for experimental design in gene expression studies.
  • The developed algorithm offers a partial solution for computationally intractable inference problems.