Related papers: Subexponential growth of early Christianity
This paper determines the rate of growth to infinity of a scalar autonomous nonlinear functional differential equation with finite delay, where the right hand side is a positive continuous linear functional of $f(x)$. We assume $f$ grows…
We consider an asexual biological population of constant size $N$ evolving in discrete time under the influence of selection and mutation. Beneficial mutations appear at rate $U$ and their selective effects $s$ are drawn from a distribution…
We consider a preferential growth model where particles are added one by one to the system consisting of clusters of particles. A new particle can either form a new cluster (with probability q) or join an already existing cluster with a…
Optimization and expansion are two modes of staged evolution of complex systems where macroscopic observables change at a decreasing, respectively increasing, rate. A prime example of evolutionary expansion, Gross Domestic Product (GDP)…
We propose a simple dynamic model of cancer development that captures carcinogenesis and subsequent cancer progression. A central idea of the model is to include the immune system as an extinction threshold, similar to the strong Allee…
Growth-fragmentation processes describe the evolution of systems of cells which grow continuously and fragment suddenly; they are used in models of cell division and protein polymerisation. Typically, we may expect that in the long run, the…
The dynamic theory of inhomogeneous populations developed during the last decade predicts several essential new dynamic regimes applicable even to the well-known, simple population models. We show that, in an inhomogeneous population with a…
Under the commonly used assumption that clumped objects can be well described by a spherical top-hat matter density profile, we investigate the evolution of the cosmic growth index in clustering dark energy (CDE) scenarios on sub-horizon…
We investigate the evolution of the star formation rate in the early Galaxy using beryllium and oxygen abundances in metal poor stars. Specifically, we show that stars belonging to two previously identified kinematical classes (the…
Deterministic population growth models with power-law rates can exhibit a large variety of growth behaviors, ranging from algebraic, exponential to hyperexponential (finite time explosion). In this setup, selfsimilarity considerations play…
We present an explicit solution to a classic model of cell-population growth introduced by Luria and Delbrueck 70 years ago to study the emergence of mutations in bacterial populations. In this model a wild-type population is assumed to…
The Nancy Grace Roman Space Telescope (Roman) will unveil for the first time the full architecture of planetary systems across Galactic distances through the discovery of up to 200,000 cool and hot exoplanets using microlensing and transit…
We have proposed a new form of growth rate for population ecology. Generally, the growth rate is dependent on the size of the population at that particular epoch. We have introduced an alternative time-dependent form of growth rate. This…
The dynamics of the avalanche width in the evolution model is described using a random walk picture. In this approach the critical exponents for avalanche distribution, $\tau$, and avalanche average time, $\gamma$, are found to be the same…
We critically analyse a recent numerical method due to the first author, Rechnitzer and van Rensburg, which attempts to detect amenability or non-amenability in a finitely generated group by numerically estimating its asymptotic cogrowth…
Critical, or scale independent, systems are so ubiquitous, that gaining theoretical insights on their nature and properties has many direct repercussions in social and natural sciences. In this report, we start from the simplest possible…
Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights…
We consider a population distributed between two habitats, in each of which it experiences a growth rate that switches periodically between two values, $1- \varepsilon > 0$ or $ - (1 + \varepsilon) < 0$. We study the specific case where the…
Cancer poses danger because of its unregulated growth, development of resistant subclones, and metastatic spread to vital organs. Although the major transitions in cancer development are increasingly well understood, we lack quantitative…
The initial phase of an epidemic is often characterized by an exponential increase in the number of infected individuals. In this paper, we predict the exponential spreading rate of an epidemic on a complex network. We first find an…