Related papers: On a population model with memory
The field of artificial intelligence faces significant challenges in achieving both biological plausibility and computational efficiency, particularly in visual learning tasks. Current artificial neural networks, such as convolutional…
Progressive diseases worsen over time and are characterised by monotonic change in features that track disease progression. Here we connect ideas from two formerly separate methodologies -- event-based and hidden Markov modelling -- to…
Large sets of genotypes give rise to the same phenotype because phenotypic expression is highly redundant. Accordingly, a population can accept mutations without altering its phenotype, as long as thegenotype mutates into another one on the…
We investigate two stochastic models of a growing population subject to selection and mutation. In our models each individual carries a fitness which determines its mean offspring number. Many of these offspring inherit their parent's…
The prevalence of sexual reproduction ("sex") in eukaryotes is an enigma of evolutionary biology. Sex increases genetic variation only tells its long-term superiority in essence. The accumulation of harmful mutations causes an immediate and…
Infinite population models are important tools for studying population dynamics of evolutionary algorithms. They describe how the distributions of populations change between consecutive generations. In general, infinite population models…
Using a lattice model based on Monte Carlo simulations, we study the role of the reproduction pattern on the fate of an evolving population. Each individual is under the selection pressure from the environment and random mutations. The…
A generalization of the economic model of natural growth, which takes into account the power-law memory effect, is suggested. The memory effect means the dependence of the process not only on the current state of the process, but also on…
Replay in neural networks involves training on sequential data with memorized samples, which counteracts forgetting of previous behavior caused by non-stationarity. We present a method where these auxiliary samples are generated on the fly,…
Populations evolving in fluctuating environments face the fundamental challenge of balancing adaptation to current conditions against preparation for uncertain futures. Here, we study microbial evolution in partially predictable…
The task of a neural associative memory is to retrieve a set of previously memorized patterns from their noisy versions using a network of neurons. An ideal network should have the ability to 1) learn a set of patterns as they arrive, 2)…
The paper discusses a connection between asymmetric reproduction -- that is reproduction in a parent-child relationship where the parent does not mutate during reproduction --, the fact that all non-viral lifeforms bear genes of their…
In many applications of evolutionary algorithms the computational cost of applying operators and storing populations is comparable to the cost of fitness evaluation. Furthermore, by knowing what exactly has changed in an individual by an…
We present a general approach to study a class of random growth models in $n$-dimensional Euclidean space. These models are designed to capture basic growth features which are expected to manifest at the mesoscopic level for several…
A large class of linear memory differential equations in one dimension, where the evolution depends on the whole history, can be equivalently described as a projection of a Markov process living in a higher dimensional space. Starting with…
For a class of processes modeling the evolution of a spatially structured population with migration and a logistic local regulation of the reproduction dynamics, we show convergence to an upper invariant measure from a suitable class of…
We consider a model of asexually reproducing individuals with random mutations and selection. The rate of mutations is proportional to the population size, $N$. The mutations may be either beneficial or deleterious. In a paper by Yu,…
We consider a fitness-structured population model with competition and migration between nearest neighbors. Under a combination of large population and rare migration limits we are particularly interested in the asymptotic behavior of the…
We consider a one-dimensional dyadic branching Brownian motion on $\mathbb{R}$ with positive drift $\beta \in (0,1)$, branching rate $1/2$, reflected at $0$ and killed at a boundary $L > 0$. The killing boundary $L$ is chosen so that the…
Population genetics struggles to model extinction; standard models track the relative rather than absolute fitness of genotypes, while the exceptions describe only the short-term transition from imminent doom to evolutionary rescue. But…