Related papers: Evolutionary Hamiltonian Graph Theory
Since Newton, all classical and quantum physics depends upon the "Newtonian Paradigm". Here the relevant variables of the system are identified. The boundary conditions creating the phase space of all possible values of the variables are…
One of the most well-known conjectures concerning Hamiltonicity in graphs asserts that any sufficiently large connected vertex transitive graph contains a Hamilton cycle. In this form, it was first written down by Thomassen in 1978,…
As one of the most fundamental and well-known NP-complete problems, the Hamilton cycle problem has been the subject of intensive research. Recent developments in the area have highlighted the crucial role played by the notions of expansion…
A Hamiltonian cycle of a graph is a closed path that visits each site once and only once. I study a field theoretic representation for the number of Hamiltonian cycles for arbitrary graphs. By integrating out quadratic fluctuations around…
A Temporal Knowledge Graph (TKG) is a sequence of KGs corresponding to different timestamps. TKG reasoning aims to predict potential facts in the future given the historical KG sequences. One key of this task is to mine and understand…
I analyse a model of an evolving network represented as a directed graph; each node corresponds to one molecular species and the links to catalytic interactions between species. Over short timescales the graph remains fixed while relative…
The delayed logistic equation (also known as Hutchinson's equation or Wright's equation) was originally introduced to explain oscillatory phenomena in ecological dynamics. While it motivated the development of a large number of mathematical…
This chapter is an overview of foundational results in the mathematical theory of replicator systems. Its primary aim is to provide a unified framework for the mathematical formalisation of evolutionary processes in the spirit of…
The Hamiltonian cycle (HC) problem in graph theory is a well-known NP-complete problem. We present an approach in terms of $\mathbb{Z}_2$ lattice gauge theory (LGT) defined on the lattice with the graph as its dual. When the coupling…
The idea that all life on earth traces back to a common beginning dates back at least to Charles Darwin's {\em Origin of Species}. Ever since, biologists have tried to piece together parts of this `tree of life' based on what we can observe…
Systems evolving according to the standard concept of biological or technological evolution are often described by catalytic evolution equations. We study the structure of these equations and find a deep relationship to classical…
Evolutionary computation (EC), as a powerful optimization algorithm, has been applied across various domains. However, as the complexity of problems increases, the limitations of EC have become more apparent. The advent of large language…
While modern physics and biology satisfactorily explain the passage from the Big Bang to the formation of Earth and the first cells to present-day life, respectively, the origins of biochemical life still remain an open question. Since…
We argue that C. Darwin and more recently W. Hennig worked at times under the simplifying assumption of an eternal biosphere. So motivated, we explicitly consider the consequences which follow mathematically from this assumption, and the…
In this paper we propose a new mathematical model capable of merging Darwinian Evolution, Human History and SETI into a single mathematical scheme: 1) Darwinian Evolution over the last 3.5 billion years is defined as one particular…
Newton set the stage for our view of how science should be done. We remain in what I will call the `Newtonian Paradigm' in all of physics, including Newton, Einstein, and Schrodinger. As I will show shortly, Newton invented and bequeathed…
The process of evolutionary diversification unfolds in a vast genotypic space of potential outcomes. During the past century there have been remarkable advances in the development of theory for this diversification, and the theory's success…
It has been hypothesized that in the era just before the last universal common ancestor emerged, life on earth was fundamentally collective. Ancient life forms shared their genetic material freely through massive horizontal gene transfer…
A central goal of evolutionary biology is to explain the origins and distribution of diversity across life. Beyond species or genetic diversity, we also observe diversity in the circuits (genetic or otherwise) underlying complex functional…
It is a longstanding conjecture that every simple drawing of a complete graph on $n \geq 3$ vertices contains a crossing-free Hamiltonian cycle. We strengthen this conjecture to "there exists a crossing-free Hamiltonian path between each…