# Zipf’s, Heaps’ and Taylor’s Laws are Determined by the Expansion into the Adjacent Possible

@article{Tria2018ZipfsHA, title={Zipf’s, Heaps’ and Taylor’s Laws are Determined by the Expansion into the Adjacent Possible}, author={Francesca Tria and Vittorio Loreto and Vito Domenico Pietro Servedio}, journal={Entropy}, year={2018}, volume={20} }

Zipf’s, Heaps’ and Taylor’s laws are ubiquitous in many different systems where innovation processes are at play. Together, they represent a compelling set of stylized facts regarding the overall statistics, the innovation rate and the scaling of fluctuations for systems as diverse as written texts and cities, ecological systems and stock markets. Many modeling schemes have been proposed in literature to explain those laws, but only recently a modeling framework has been introduced that…

## 18 Citations

### Taylor’s Law in Innovation Processes

- Computer ScienceEntropy
- 2020

It is suggested that Taylor’'s law is a fundamental complement to Zipf’s and Heaps’ laws in unveiling the complex dynamical processes underlying the evolution of systems featuring innovation.

### Twitter as an innovation process with damping effect

- MathematicsScientific reports
- 2021

This work introduces an extremely general model, whose key element is the update function, that can be suitably chosen in order to reproduce the behaviour exhibited by the empirical data, and shows great performances with respect to Heaps’ law.

### Damping effect in innovation processes: case studies from Twitter

- Physics
- 2021

Understanding the innovation process, that is the underlying mechanisms through which novelties emerge, diffuse and trigger further novelties is undoubtedly of fundamental importance in many areas…

### Heaps’ Law and Heaps functions in tagged texts: evidences of their linguistic relevance

- LinguisticsRoyal Society Open Science
- 2020

The relationship between vocabulary size and text length in a corpus of 75 literary works in English is studied, distinguishing between the contributions of three grammatical classes (or ‘tags,’ namely, nouns, verbs and others), and the progressive appearance of new words of each tag along each individual text is analyzed.

### The Compressed Vocabulary of Microbial Life

- BiologyFrontiers in Microbiology
- 2021

The vocabularies of proteins (proteomes) and functions (functionomes) revealed a significant universal lexical core supporting a universal common ancestor, an ancestral evolutionary link between Bacteria and Eukarya, and distinct reductive evolutionary strategies of language compression in Archaea and Bacteria.

### The exploration of the Adjacent Possible explains the emergence and evolution of social networks

- Computer Science
- 2020

This work uses a recent mathematical formalization of the adjacent possible space to propose a first-principles theory of social exploration based on simple microscopic rules defining how people get in touch and interact and predicts both microscopic and macroscopic features of social networks.

### On the Dual Nature of Adoption Processes in Complex Networks

- Computer ScienceFrontiers in Physics
- 2021

This work proposes to look at adoption processes in socio-technological systems as two complementary aspects of the same adoption process: on the one hand, items spreading over a social network of individuals influencing each other, and on the other hand, individuals explore a network of similarities among items to adopt.

### Adjacent Possible

- ArtThe Palgrave Encyclopedia of the Possible
- 2020

Adjacent, i.e., nearby, possibilities constantly emerge in a multitude of settings for a multitude of entities. When these possibilities are explored, yet new possibilities emerge. The concept of the…

### The Language of Innovation

- Computer SciencePloS one
- 2020

The methods proposed in this paper provide a completely new way of understanding and forecasting innovation, by tackling it from a revealing perspective and opening interesting scenarios for a number of applications and further analytic approaches.

### Interacting discovery processes on complex networks

- EconomicsPhysical review letters
- 2020

A model in which many urns, representing different explorers, are coupled through the links of a social network and exploit opportunities coming from their contacts is proposed, showing that the pace of discovery of an explorer depends on its centrality in the social network.

## References

SHOWING 1-10 OF 52 REFERENCES

### Zipf's Law Leads to Heaps' Law: Analyzing Their Relation in Finite-Size Systems

- PhysicsPloS one
- 2010

The present analysis provides a clear picture about the relation between the Zipf's law and Heaps' law without the help of any specific stochastic model, namely the Heps' law is indeed a derivative phenomenon from the ZipF's law.

### There is More than a Power Law in Zipf

- EconomicsScientific reports
- 2012

The largest cities, the most frequently used words, the income of the richest countries, and the most wealthy billionaires, can be all described in terms of Zipf’s Law, a rank-size rule capturing the…

### Zipf's Law everywhere

- Economics, PhysicsGlottometrics
- 2002

At the 100th anniversary of the birth of George Kingsley Zipf, one striking fact about the statistical regularity that bears his name, Zipf's law, is that it seems to appear everywhere. We may ask…

### Untangling Herdan's law and Heaps' law: Mathematical and informetric arguments

- MathematicsJ. Assoc. Inf. Sci. Technol.
- 2007

Heaps’ law and Herdan’s law are equivalent, apart from the less important constant k, which is not well-known in linguistics: Heaps is a specialist in information retrieval.

### The dynamics of correlated novelties

- BiologyScientific reports
- 2014

A simple mathematical model is proposed that mimics the process of exploring a physical, biological, or conceptual space that enlarges whenever a novelty occurs and predicts statistical laws for the rate at which novelties happen and for the probability distribution on the space explored.

### Zipf’s word frequency law in natural language: A critical review and future directions

- Computer SciencePsychonomic bulletin & review
- 2014

It is shown that human language has a highly complex, reliable structure in the frequency distribution over and above Zipf’s law, although prior data visualization methods have obscured this fact.

### Power laws, Pareto distributions and Zipf's law

- Physics
- 2005

When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf's law or the…

### Modeling Statistical Properties of Written Text

- Computer SciencePloS one
- 2009

A generative model is introduced that explains the simultaneous emergence of bursty nature of rare words and the topical organization of texts and dynamic word ranking and memory across documents as key mechanisms explaining the non trivial organization of written text.

### Dynamics on Expanding Spaces: Modeling the Emergence of Novelties

- Art
- 2016

Novelties are part of our daily lives. We constantly adopt new technologies, conceive new ideas, meet new people, and experiment with new situations. Occasionally, we as individual, in a complicated…

### Waves of novelties in the expansion into the adjacent possible

- Computer SciencePloS one
- 2017

This paper quantifies the emergence of novelties and their rise and fall in popularity by empirically looking at different systems that display innovation at very different levels: the creation of hashtags in Twitter, the evolution of online code repositories, thecreation of texts and the listening of songs on online platforms.