Related Experiment Video
Updated: Jun 20, 2026
04:52
Following the Dynamics of Structural Variants in Experimentally Evolved Populations
Published on: February 3, 2023
Dynamics of discovery and the Heaps-Zipf relationship
Célestin Zimmerlin1, Thomas Louail1, Manuel Moussallam2
1UMR Géographie-cités, CNRS, and LabCom MIXTAPES, Campus Condorcet, FR-93322 Aubervilliers Cedex, France.
Physical Review. E
|June 19, 2026
Summary
Temporal correlations in sequences, like user activity, impact how new elements (types) emerge over time. This study reveals that sequence structure, not just element frequency, shapes this growth, challenging existing models.
Area of Science:
- Complex systems
- Data science
- Cognitive science
Background:
- Heaps' law describes how the number of distinct elements (types) grows with observations (tokens) in a sequence, often following a power law.
- This growth is frequently linked to Zipf's law and used to model human discovery, assuming temporal independence.
- However, real-world sequences often exhibit temporal correlations, violating this independence assumption.
Purpose of the Study:
- To investigate the impact of temporal correlations on the type-token curve, which measures vocabulary growth.
- To understand how sequence-specific ordering affects the relationship between type-token growth and rank-frequency distributions.
- To develop a model that captures diverse type-token trajectories influenced by temporal dynamics.
Main Methods:
- Analyzing type-token growth in human behavioral sequences (music listening, web browsing) with inherent temporal correlations.
- Comparing observed growth patterns against the predictions of the Heaps-Zipf framework.
- Developing and utilizing a minimal one-parameter model to simulate and reproduce type-token trajectories.
Main Results:
- Temporal correlations in human behavior sequences cause systematic deviations from the standard Heaps-Zipf law.
- The type-token plot is effectively decoupled from the rank-frequency distribution due to these correlations.
- The developed model successfully reproduces various type-token growth patterns, including boundary cases.
Conclusions:
- Type-token growth is influenced by both the frequency of elements and the temporal structure of the sequence.
- Existing models that assume temporal independence may mischaracterize human discovery processes.
- Accounting for domain-specific temporal dynamics is crucial for accurately applying scaling laws to human behavior data.
Related Concept Videos
01:37Social Loafing
Another way in which a group presence can affect performance is social loafing—the exertion of less effort by a person working together with a group. Social loafing occurs when our individual performance cannot be evaluated separately from the group. Thus, group performance declines on easy tasks (Karau & Williams, 1993). Essentially individual group members loaf and let other group members pick up the slack. Because each individual’s efforts cannot be evaluated, individuals become less...
01:41Social Traps
Social traps are negative situations where people get caught in a direction or relationship that later proves to be unpleasant, with no easy way to back out of or avoid. The concept was orignally introduced by John Platt who applied psychology to Garrett Hardin's "Tragedy of the Commons", where in New England herd owners could let their cattle graze in the common ground. This situation seems like a good idea, but an individual could have an advantage. If they owned more cows, the larger...
01:08The Availability Heuristic
A heuristic is a general problem-solving framework (Tversky & Kahneman, 1974). You can think of these as mental shortcuts that are used to solve problems. Different types of heuristics are used in different types of situations, and the impulse to use a heuristic occurs when one of five conditions is met (Pratkanis, 1989):
01:26Causes of Similarity-Dissimilarity Effect
The similarity-dissimilarity effect, a fundamental concept in social psychology, explains how interpersonal similarities and differences influence attraction and social interactions. This effect is supported by three key psychological perspectives: balance theory, social comparison theory, and consensual validation.Balance Theory and Cognitive ConsistencyBalance theory, developed by Fritz Heider, posits that individuals seek cognitive consistency in their relationships. When two people share...
02:12Relationship Formation
What do you think is the single most influential factor in determining with whom you become friends and whom you form romantic relationships? You might be surprised to learn that the answer is simple: the people with whom you have the most contact. This most important factor is proximity. You are more likely to be friends with people you have regular contact with. For example, there are decades of research that shows that you are more likely to become friends with people who live in your dorm,...
01:20Relation of DFT to z-Transform
The Discrete Fourier Transform (DFT) is a crucial tool for analyzing the frequency content of discrete-time signals. It converts a sequence of N samples from the time domain into its corresponding sequence in the frequency domain, where each sample represents a specific frequency component.
To understand how the DFT works, it's helpful to consider the z-transform, which is a method for representing discrete sequences in the complex frequency domain. The z-transform involves summing the terms of...
To understand how the DFT works, it's helpful to consider the z-transform, which is a method for representing discrete sequences in the complex frequency domain. The z-transform involves summing the terms of...