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

Scaling01:26

Scaling

671
In designing and analyzing filters, resonant circuits, or circuit analysis at large, working with standard element values like 1 ohm, 1 henry, or 1 farad can be convenient before scaling these values to more realistic figures. This approach is widely utilized by not employing realistic element values in numerous examples and problems; it simplifies mastering circuit analysis through convenient component values. The complexity of calculations is thereby reduced, with the understanding that...
671
Modeling with Differential Equations01:25

Modeling with Differential Equations

279
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...
279
Scale-Up Processes01:14

Scale-Up Processes

89
The scale-up of microbial fermentation processes is essential in industrial biotechnology, allowing the transition from laboratory-scale experiments to commercial-scale production while aiming to maintain product yield and quality. This process requires meticulous adjustment of equipment design, process parameters, and contamination control strategies to accommodate increasing culture volumes.At the laboratory scale, cultures are typically maintained in 1 to 10-liter glass or autoclavable...
89
Sampling Plans01:23

Sampling Plans

1.3K
Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
Random sampling is a method where each member of the population has an equal chance of being selected for the sample. It involves selecting individuals randomly, often using random number generators or lottery-type methods. For example, when analyzing the properties of a...
1.3K
Conservation of Declining Populations02:07

Conservation of Declining Populations

13.6K
Conservation of declining population focuses on ways of detecting, diagnosing, and halting a population decline. The approach uses methods to prevent populations from going extinct.
13.6K
Downsampling01:20

Downsampling

817
When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
817

You might also read

Related Articles

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

Sort by
Same author

Reply to Górski et al.: Polarization requires opinions, not just negative ties.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same author

Adhesion-driven rigidity transition decoupled from density-driven jamming triggers epithelial organization in embryonic tissues.

Nature physics·2026
Same author

Adaptive self-organization of global swidden forests.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same author

Tissue rigidity phase transition shapes morphogen gradients.

Nature cell biology·2026
Same author

Supply chain network rewiring dynamics at the firm level.

PNAS nexus·2026
Same author

Inferring firm-level supply chain networks with realistic systemic risk from industry sector-level data.

Scientific reports·2026
Same journal

The TaMYB55-TaSnRK1α1-TabZIP9 module confers heat stress tolerance in wheat.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Superstatistics approach to turbulent circulation fluctuations.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

A molecular timescale for evolution of cobamide biosynthesis.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Pierre Chambon, a pioneer of molecular biology and gene regulation in eukaryotes.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Granulosa cell glycogen fuels the avascular corpus luteum.

Proceedings of the National Academy of Sciences of the United States of America·2026
Same journal

Synthetic essentiality of TRAIL/TNFSF10 in VHL-deficient renal cell carcinoma.

Proceedings of the National Academy of Sciences of the United States of America·2026
See all related articles

Related Experiment Video

Updated: Apr 15, 2026

Reservoir Condition Pore-scale Imaging of Multiple Fluid Phases Using X-ray Microtomography
08:02

Reservoir Condition Pore-scale Imaging of Multiple Fluid Phases Using X-ray Microtomography

Published on: February 25, 2015

13.2K

Understanding scaling through history-dependent processes with collapsing sample space.

Bernat Corominas-Murtra1, Rudolf Hanel1, Stefan Thurner2

  • 1Section for Science of Complex Systems, Medical University of Vienna, A-1090 Vienna, Austria;

Proceedings of the National Academy of Sciences of the United States of America
|April 15, 2015
PubMed
Summary
This summary is machine-generated.

Sample-space-reducing (SSR) processes, common in complex systems, naturally lead to Zipf's law. Adding noise to these processes explains a wide range of scaling exponents, offering a new perspective on complex system dynamics.

Keywords:
Zipf’s lawnetwork diffusionpath dependencerandom walksscaling laws

More Related Videos

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

699
Kinematic History of a Salient-recess Junction Explored through a Combined Approach of Field Data and Analog Sandbox Modeling
06:55

Kinematic History of a Salient-recess Junction Explored through a Combined Approach of Field Data and Analog Sandbox Modeling

Published on: August 5, 2016

8.6K

Related Experiment Videos

Last Updated: Apr 15, 2026

Reservoir Condition Pore-scale Imaging of Multiple Fluid Phases Using X-ray Microtomography
08:02

Reservoir Condition Pore-scale Imaging of Multiple Fluid Phases Using X-ray Microtomography

Published on: February 25, 2015

13.2K
Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

699
Kinematic History of a Salient-recess Junction Explored through a Combined Approach of Field Data and Analog Sandbox Modeling
06:55

Kinematic History of a Salient-recess Junction Explored through a Combined Approach of Field Data and Analog Sandbox Modeling

Published on: August 5, 2016

8.6K

Area of Science:

  • Complex Systems Science
  • Statistical Physics
  • Network Science

Background:

  • History-dependent processes are prevalent in natural and social systems.
  • Many complex stochastic processes exhibit sample-space reduction (SSR) as they evolve.
  • This reduction in possible outcomes is a key characteristic of aging systems.

Purpose of the Study:

  • To demonstrate that sample-space-reducing processes inherently generate Zipf's law.
  • To investigate the impact of noise on these processes and their resulting distributions.
  • To provide a new framework for understanding scaling phenomena in complex systems.

Main Methods:

  • Mathematical modeling of sample-space-reducing (SSR) processes.
  • Analysis of rank distributions resulting from SSR processes with and without added noise.
  • Theoretical derivation of the relationship between scaling exponents and process parameters.

Main Results:

  • SSR processes necessarily lead to Zipf's law in outcome rank distributions.
  • Adding noise to SSR processes results in power-law distributions (p(x) ~ x(-λ)).
  • The scaling exponent (λ) is directly related to the mixing ratio of the SSR process and noise, explaining exponents from 2 to infinity.

Conclusions:

  • SSR processes offer a novel explanation for Zipf's law and scaling phenomena.
  • The framework provides a precise interpretation of scaling exponents based on sample space reduction.
  • Applications include word frequencies, network diffusion, and fragmentation processes, offering an alternative to existing models.