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Related Concept Videos

Transfer Function to State Space01:23

Transfer Function to State Space

State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
In an RLC...
State Space to Transfer Function01:21

State Space to Transfer Function

The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
Signal Flow Graphs01:18

Signal Flow Graphs

Signal-flow graphs offer a streamlined and intuitive approach to representing control systems, providing an alternative to traditional block diagrams. These graphs use branches to symbolize systems and nodes to represent signals, effectively illustrating the relationships and interactions within the system.
In a signal-flow graph, branches denote the system's transfer functions, while nodes represent the signals. The direction of signal flow is indicated by arrows, with the corresponding...
Pipe Flowrate Measurement01:28

Pipe Flowrate Measurement

In pipe flow measurement, orifice, nozzle, and Venturi meters are commonly used to determine fluid flowrates by constricting the flow area, which increases fluid velocity and reduces pressure. This pressure difference, governed by Bernoulli's principle and adjusted for real-world conditions, is essential for calculating flowrate. Each meter type is suited to specific applications based on accuracy, efficiency, and compatibility with various flow conditions.
The orifice meter is a simple,...
Uniform Depth Channel Flow01:27

Uniform Depth Channel Flow

Uniform depth channel flow keeps fluid depth consistent along channels such as irrigation canals. In natural channels, such as rivers, approximate uniform flow is often assumed. This condition occurs when the channel’s bottom slope matches the energy slope, balancing potential energy lost from gravity with head loss due to shear stress. This balance prevents depth changes along the channel length, resulting in a steady, uniform flow.Uniform flow in open channels with a constant cross-section...
Fundamental Theorem of Calculus I: Problem Solving01:22

Fundamental Theorem of Calculus I: Problem Solving

In many engineering and environmental applications, accumulated quantities are determined from rates that vary over time. A common example arises in water management, where a supply system pumps water into a storage tank at a rate that changes with time. Accurately determining how much water has entered the tank over a given period is essential for maintaining proper pressure, scheduling operations, and ensuring system safety.The flow rate of water into the tank is described by a time-dependent...

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A computational pipeline for spatial mechano-transcriptomics.

Adrien Hallou1,2,3, Ruiyang He4,5,6, Benjamin D Simons7,8,9

  • 1Kennedy Institute of Rheumatology, University of Oxford, Oxford, UK. adrien.hallou@kennedy.ox.ac.uk.

Nature Methods
|March 18, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a computational framework for analyzing spatial transcriptomics data alongside mechanical signals. It helps identify how cell mechanics and gene expression define tissue boundaries during development.

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Area of Science:

  • Developmental Biology
  • Computational Biology
  • Systems Biology

Background:

  • Spatial profiling technologies reveal molecular responses to local cues.
  • Cell fate and tissue patterning depend on biochemical and mechanical interactions.
  • Integrating mechanical and molecular data is crucial for understanding tissue development.

Purpose of the Study:

  • To develop a computational framework for joint analysis of transcriptional and mechanical signals.
  • To infer cellular forces and identify predictive signatures of tissue boundaries.
  • To uncover gene modules associated with cell mechanical behavior.

Main Methods:

  • Developed a computational framework for joint statistical analysis of spatial transcriptomics and mechanical signals.
  • Applied geoadditive structural equation modeling for unbiased identification of gene modules.
  • Utilized spatial transcriptomics data from developing mouse embryos.

Main Results:

  • Inferred forces acting on individual cells within developing mouse embryos.
  • Identified mechanical, morphometric, and gene expression signatures predictive of tissue compartment boundaries.
  • Discovered gene modules that predict cell mechanical behavior.

Conclusions:

  • The computational framework enables integrated analysis of biomolecular and mechanical cues in tissues.
  • This approach provides a generic scheme for exploring tissue development and organization.
  • The findings offer insights into the interplay of gene expression and cell mechanics in patterning.