Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Application of Nonlinear Inequalities01:29

Application of Nonlinear Inequalities

281
A nonlinear inequality describes a comparison involving an expression that curves or behaves more complexly than a straight line. These inequalities often appear in forms that include squares, products, or variables in the denominator.To solve such an inequality, one starts by rewriting it so that zero appears on one side. For example, the inequality:  can be factored as: This form makes it easier to identify the values that cause the expression to equal zero. In this case, the...
281
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

408
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.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
408
Introduction to Nonlinear Inequalities01:25

Introduction to Nonlinear Inequalities

255
Linear and nonlinear inequalities are fundamental for analyzing variable relationships and identifying ranges satisfying specific conditions. A linear inequality involves variables raised only to the first power, resulting in a straight-line graph. This line partitions the coordinate plane into two distinct regions: one that satisfies the inequality and one that does not. Each region represents a set of solutions where the linear relationship holds true under the specified constraint.Nonlinear...
255
Fast Fourier Transform01:10

Fast Fourier Transform

1.0K
The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log⁡2N multiplications, offering a much faster performance.
The computational efficiency of the FFT becomes...
1.0K
Linearization and Approximation01:26

Linearization and Approximation

115
Linearization is a mathematical technique used to approximate complex, nonlinear functions with simpler linear models in the vicinity of a chosen reference point. The method is based on the idea that, although a function may be difficult to evaluate exactly, its behavior near a specific input value can often be closely approximated by the tangent line at that point. This approach is particularly useful when small deviations from a known value are involved.Consider the square root function, for...
115
Properties of the z-Transform I01:17

Properties of the z-Transform I

669
The z-transform is a fundamental tool in digital signal processing, enabling the analysis of discrete-time systems through its various properties. It is an invaluable tool for analyzing discrete-time systems, offering a range of properties that simplify complex signal manipulations. One fundamental property is linearity. For any two discrete-time signals, the z-transform of their linear combination equals the same linear combination of their individual z-transforms. This property is essential...
669

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Compression detects changes in spiking neural data from cortical lesions.

Journal of neural engineering·2026
Same author

Compression Detects Changes in Spiking Neural Data from Cortical Lesions.

bioRxiv : the preprint server for biology·2026
Same author

A Framework for Compressive On-Chip Action Potential Recording.

IEEE transactions on bio-medical engineering·2025
Same author

Pan-conserved segment tags identify ultra-conserved sequences across assemblies in the human pangenome.

Cell reports methods·2023
Same author

Magnetic DNA random access memory with nanopore readouts and exponentially-scaled combinatorial addressing.

Scientific reports·2023
Same author

Reference-free lossless compression of nanopore sequencing reads using an approximate assembly approach.

Scientific reports·2023
Same journal

Correction to: 'Stokes settling and particle-laden plumes: implications for deep-sea mining and volcanic eruption plumes' (2020), by Mingotti et al.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

A stable hothouse triggered by a tipping mechanism.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Beyond distance: quantifying point cloud dynamics with persistent homology and dynamic optimal transport.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Global stability of the Atlantic overturning circulation: edge state, long transients and boundary crisis under CO2 forcing.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Morse index classification and landscape of Kuramoto system for Hebbian-based binary pattern recognition.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Interpretable and equation-free response theory for complex systems.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
See all related articles

Related Experiment Video

Updated: Mar 2, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

43.7K

Information-computation trade-offs in nonlinear transforms.

Connor Ding1, Abhiram Gorle1, Jiwon Jeong1

  • 1Stanford University , Stanford, CA, USA.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|February 28, 2026
PubMed
Summary
This summary is machine-generated.

This study explores nonlinear transforms for efficient data compression, analyzing implicit neural representations, Gaussian splatting, and textual transforms. These methods balance coding efficiency and computational cost for AI tasks.

Keywords:
Lempel–Ziv universalitycompression-computation trade-offgenerative AIimplicit neural representationsmodel pruningnonlinear transformsrate-distortion theorytextual transforms

More Related Videos

An Experimental Protocol for Assessing the Performance of New Ultrasound Probes Based on CMUT Technology in Application to Brain Imaging
16:01

An Experimental Protocol for Assessing the Performance of New Ultrasound Probes Based on CMUT Technology in Application to Brain Imaging

Published on: September 24, 2017

11.0K

Related Experiment Videos

Last Updated: Mar 2, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

43.7K
An Experimental Protocol for Assessing the Performance of New Ultrasound Probes Based on CMUT Technology in Application to Brain Imaging
16:01

An Experimental Protocol for Assessing the Performance of New Ultrasound Probes Based on CMUT Technology in Application to Brain Imaging

Published on: September 24, 2017

11.0K

Area of Science:

  • Information Theory
  • Computer Science
  • Artificial Intelligence

Background:

  • Modern information processing demands efficient compression techniques.
  • Nonlinear transformations offer novel approaches to data compression and representation.

Purpose of the Study:

  • To investigate the interplay between information and computation in nonlinear transform-based compression.
  • To analyze emerging nonlinear data transformation frameworks for image compression and other AI tasks.

Main Methods:

  • Analysis of implicit neural representations (INRs) and 2D Gaussian splatting (GS) for image compression.
  • Introduction of a textual transform for ultra-low bit rate compression and denoising.
  • Description of a Lempel-Ziv (LZ78) transform for universal compression.

Main Results:

  • Key trade-offs identified between INR's flexibility and GS's parallelizability.
  • Textual transform enhances perceptual satisfaction and aids denoising.
  • LZ78 transform ensures asymptotic universality for new compressor families.

Conclusions:

  • Nonlinear transforms offer fundamental trade-offs between coding efficiency and computational cost.
  • Insights extend to classification, denoising, and generative AI, guiding resource-constrained AI development.
  • This work contributes to sustainable AI through efficient information processing.