Related papers: Extending the Monod Model of Microbial Growth with…
1. Spatial memory plays a role in the way animals perceive their environments, resulting in memory-informed movement patterns that are observable to ecologists. Developing mathematical techniques to understand how animals use memory in…
A classic problem in microbiology is that bacteria display two types of growth behavior when cultured on a mixture of two carbon sources: the two sources are sequentially consumed one after another (diauxie) or they are simultaneously…
We study the dynamics of proliferating cell collectives whose microscopic constituents' growth is inhibited by macroscopic growth-induced stress. Discrete particle simulations of a growing collective show the emergence of concentric-ring…
In this paper, we present a spatial version of phytoplankton-zooplankton model that includes some important factors such as external periodic forces, noise, and diffusion processes. The spatially extended phytoplankton-zooplankton system is…
The colonisation of a soft passive material by motile cells such as bacteria is common in biology. The resulting colonies of the invading cells are often observed to exhibit intricate patterns whose morphology and dynamics can depend on a…
Mammalian brains operate in a very special surrounding: to survive they have to react quickly and effectively to the pool of stimuli patterns previously recognized as danger. Many learning tasks often encountered by living organisms involve…
Memory models such as Recurrent Neural Networks (RNNs) and Transformers address Partially Observable Markov Decision Processes (POMDPs) by mapping trajectories to latent Markov states. Neither model scales particularly well to long…
Quantitative characterization of bacterial growth has gathered substantial attention since Monod's pioneering study. Theoretical and experimental work has uncovered several laws for describing the log growth phase, in which the number of…
In this paper, we consider a single phytoplankton species which relies on the light for maintaining the metabolism of life in a periodically evolving environment, where the light intensity and the death rate depend on the water column depth…
Textual analysis of typical microbial genomes reveals that they have the statistical characteristics of a DNA sequence of a much shorter length. This peculiar property supports an evolutionary model in which a genome evolves by random…
We present a modelling framework for the dynamics of cells structured by the concentration of a micromolecule they contain. We derive general equations for the evolution of the cell population and of the extra-cellular concentration of the…
A model for the aerobic and anaerobic growth of Escherichia coli (HB101 K12 pGLO) depending on the concentration of oxygen and DOC as substrate has been developed based on laboratory batch experiments. Using inverse modelling to obtain…
Density dependence is important in the ecology and evolution of microbial and cancer cells. Typically, we can only measure net growth rates, but the underlying density-dependent mechanisms that give rise to the observed dynamics can…
Despite their empirical success, how diffusion models generalize remains poorly understood from a mechanistic perspective. We demonstrate that diffusion models trained with flow-matching objectives exhibit grokking--delayed generalization…
One of the most challenging problems in microbiology is to understand how a small fraction of microbes that resists killing by antibiotics can emerge in a population of genetically identical cells, the phenomenon known as persistence or…
Existing accounts of grokking explain the phenomena in terms of mechanistic frameworks such as circuit efficiency or lazy-to-rich transitions. However, despite a known dependence between grokking and model size, how model capacity shapes…
In this paper we discuss a concept of dynamic memory and an application of fractional calculus to describe the dynamic memory. The concept of memory is considered from the standpoint of economic models in the framework of continuous time…
A theoretical model is presented for early evolutionary cell sorting within cellular aggregates. The model involves an energy-saving mechanism and principles of collective self-organization analogous to those observed in bicycle pelotons…
We consider a nonlinear coupled discrete-time model of population dynamics. This model describes the movement of populations within a heterogeneous landscape, where the growth of subpopulations are modelled by (possibly different) bounded…
In this work we develop a new framework to deal numerically with discontinuous solutions in nonconservative hyperbolic systems. First an extension of the MOOD methodology to nonconservative systems based on Taylor expansions is presented.…