Related papers: Conjugate Distribution Laws in Cultural Evolution …
Stochastic models play an essential role in accounting for the variability and unpredictability seen in real-world. This paper focuses on the application of the gamma distribution to analysis of the stationary distributions of populations…
The biological theory of adaptive dynamics proposes a description of the long-term evolution of a structured asexual population. It is based on the assumptions of large population, rare mutations and small mutation steps, that lead to a…
We study how a behavior (an idea, buying a product, having a disease, adopting a cultural fad or a technology) spreads among agents in an a social network that exhibits segregation or homophily (the tendency of agents to associate with…
Adoption processes in socio-technological systems have been widely studied both empirically and theoretically. The way in which social norms, behaviors, and even items such as books, music, or other commercial or technological product…
Understanding the interplay between human behavioral phenomena and infectious disease dynamics has been one of the central challenges of mathematical epidemiology. However, socio-cognitive processes critical for the initiation of desired…
Cooperation is a major factor in the evolution of human societies. The structure of human social networks, which affects the dynamics of cooperation and other interpersonal phenomena, have common structural signatures. One of these…
The distributed genome hypothesis states that the set of genes in a population of bacteria is distributed over all individuals that belong to the specific taxon. It implies that certain genes can be gained and lost from generation to…
We develop an analytical framework for understanding how the generated distribution evolves during diffusion model training. Leveraging a Gaussian-equivalence principle, we solve the full-batch gradient-flow dynamics of linear and…
For taxonomic levels higher than species, the abundance distributions of number of subtaxa per taxon tend to approximate power laws, but often show strong deviationns from such a law. Previously, these deviations were attributed to…
We present a two-species population model in a well-mixed environment where the dynamics involves, in addition to birth and death, changes due to environmental factors and inter-species interactions. The novel dynamical components are…
Social trends or fashions are spontaneous collective decisions made by large portions of a community, often without an apparent good reason. The spontaneous formation of trends provides a well documented mechanism for the spread of…
Zipf's power-law distribution is a generic empirical statistical regularity found in many complex systems. However, rather than universality with a single power-law exponent (equal to 1 for Zipf's law), there are many reported deviations…
There is little doubt in scientific circles that--counting from the origin of life towards today--evolution has led to an increase in the amount of information stored within the genomes of the biosphere. This trend of increasing information…
Recent theories suggest that Neural Scaling Laws arise whenever the task is linearly decomposed into power-law distributed units. Alternatively, scaling laws also emerge when data exhibit a hierarchically compositional structure, as is…
Current social networks are of extremely large-scale generating tremendous information flows at every moment. How information diffuse over social networks has attracted much attention from both industry and academics. Most of the existing…
This paper aims to shed light on the evolutionary dynamics of diverse and social populations by introducing the rich expressiveness of generative models into the trait expression of social agent-based evolutionary models. Specifically, we…
Natural populations often show enhanced genetic drift consistent with a strong skew in their offspring number distribution. The skew arises because the variability of family sizes is either inherently strong or amplified by population…
Natural selection and random drift are competing phenomena for explaining the evolution of populations. Combining a highly fit mutant with a population structure that improves the odds that the mutant spreads through the whole population…
Many analyses of resource-allocation problems employ simplistic models of the population. Using the example of a resource-allocation problem of Marecek et al. [arXiv:1406.7639], we introduce rather a general behavioural model, where the…
We examine the evolution of expression patterns and the organization of genetic information in populations of self-replicating digital organisms. Seeding the experiments with a linearly expressed ancestor, we witness the development of…