Related papers: Evolutionary Hamiltonian Graph Theory
The evolution of complexity has been a central theme for Biology [2] and Artificial Life research [1]. It is generally agreed that complexity has increased in our universe, giving way to life, multi-cellularity, societies, and systems of…
Evolutionary dynamics have been traditionally studied in the context of homogeneous populations, mainly described my the Moran process. Recently, this approach has been generalized in \cite{LHN} by arranging individuals on the nodes of a…
An thorough introduction is given at an introductory level to the field of quantitative complex system science, with special emphasis on emergence in dynamical systems based on network topologies. Subjects treated include graph theory and…
Since the time of Darwin, scientists have struggled to reconcile the evolution of biological forms in a universe determined by fixed laws. These laws underpin the origin of life, evolution, human culture and technology, as set by the…
We focus on evolution equations on co-evolving, infinite, graphs and establish a rigorous link with a class of nonlinear continuity equations, whose vector fields depend on the graphs considered. More precisely, weak solutions of the…
Let $(G_t)_{t \geq 0}$ be the random graph process ($G_0$ is edgeless and $G_t$ is obtained by adding a uniformly distributed new edge to $G_{t-1}$), and let $\tau_k$ denote the minimum time $t$ such that the $k$-core of $G_t$ (its unique…
Evolution has fascinated quantitative and physical scientists for decades: how can the random process of mutation, recombination, and duplication of genetic information generate the diversity of life? What determines the rate of evolution?…
Large Language Models (LLMs) demonstrate an impressive capacity to recall a vast range of factual knowledge. However, understanding their underlying reasoning and internal mechanisms in exploiting this knowledge remains a key research area.…
Darwin's hypothesis that all extant life forms are descendants of a last common ancestor cell and diversification of life forms results from gradual mutation plus natural selection represents a mainstream view that has influenced biology…
We propose a generic model of eco-systems, with a {\it hierarchical} food web structure. In our computer simulations we let the eco-system evolve continuously for so long that that we can monitor extinctions as well as speciations over…
The standard Large Deviation Theory (LDT) is mathematically illustrated by the Boltzmann-Gibbs factor which describes the thermal equilibrium of short-range-interacting many-body Hamiltonian systems, the velocity distribution of which is…
We study non-linear evolution equations with periodic initial conditions. In particular, we use the graph method introduced by Galavotti to prove the existence of global solution of Hamiltonian perturbation of KdV without any restriction on…
The theory of interaction-based evolution argues that, at the most basic level of analysis, there is a third alternative for how adaptive evolution works besides a) accidental mutation and natural selection and b) Lamarckism, namely, c)…
The origin of life is often framed primarily as a chemical problem, yet life's defining feature is evolution. Advances in geochemistry, prebiotic chemistry, and molecular biology have produced diverse scenarios for the emergence of genomes,…
The origin of life must have been preceded by Darwin-like evolutionary dynamics that could propagate it. How did that adaptive dynamics arise? And from what prebiotic molecules? Using evolutionary invasion analysis, we develop a universal…
Evolution, the engine behind the survival and growth of life on Earth, operates through the population-based process of reproduction. Inspired by this principle, this paper formally defines a newly emerging problem -- the population-based…
Evolution is the theory that plants and animals today have come from kinds that have existed in the past. Scientists such as Charles Darwin and Alfred Wallace dedicate their life to observe how species interact with their environment, grow,…
We develop a new formalism to study nonlinear evolution in the growth of large-scale structure, by following the dynamics of gravitational clustering as it builds up in time. This approach is conveniently represented by Feynman diagrams…
Research idea generation is the innovation-driving step of automated scientific research. Recently, large language models (LLMs) have shown potential for automating idea generation at scale. However, existing methods mainly condition LLMs…
Following a problem posed by Lov\'asz in 1969, it is believed that every connected vertex-transitive graph has a Hamilton path. This is shown here to be true for cubic Cayley graphs arising from groups having a $(2,s,3)$-presentation, that…