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Many cellular functions are based on the rhythmic organization of biological processes into self-repeating cascades of events. Some of these periodic processes, such as the cell cycles of several species, exhibit conspicuous irregularities…
Animals use past experiences to adapt future behavior. To enable this rapid learning, vertebrates and invertebrates have evolved analogous neural structures like the vertebrate cerebellum or insect mushroom body. A defining feature of these…
Exploiting the information provided by the molecular noise of a biological process has proven to be valuable in extracting knowledge about the underlying kinetic parameters and sources of variability from single cell measurements. However,…
The slime mould Physarum polycephalum displays adaptive transport dynamics and network formation that have inspired its use as a model of biological computation. We develop a Lagrangian formulation of Physarum's adaptive dynamics on…
Understanding whether and to what extent large language models (LLMs) have memorised training data has important implications for the reliability of their output and the privacy of their training data. In order to cleanly measure and…
When do diffusion models reproduce their training data, and when are they able to generate samples beyond it? A practically relevant theoretical understanding of this interplay between memorization and generalization may significantly…
This paper explores seasonal and long-memory time series properties by using the seasonal fractional ARIMA model when the seasonal data has one and two seasonal periods and short-memory counterparts. The stationarity and invertibility…
We propose a simple model of recognition, short-term memory, long-term memory and learning.
We present a novel parameter identification algorithm for the estimation of parameters in models of cell motility using imaging data of migrating cells. Two alternative formulations of the objective functional that measures the difference…
We present a novel and simple method to numerically calculate Fisher Information Matrices for stochastic chemical kinetics models. The linear noise approximation is used to derive model equations and a likelihood function which leads to an…
Modeling of biomolecular systems plays an essential role in understanding biological processes, such as ionic flow across channels, protein modification or interaction, and cell signaling. The continuum model described by the…
Single-particle traces of the diffusive motion of molecules, cells, or animals are by-now routinely measured, similar to stochastic records of stock prices or weather data. Deciphering the stochastic mechanism behind the recorded dynamics…
Much work has been devoted to analysing thermodynamic models for solid dispersions with a view to identifying regions in the phase diagram where amorphous phase separation or drug recrystallization can occur. However, detailed partial…
Behaviour change lies at the heart of many observable collective phenomena such as the transmission and control of infectious diseases, adoption of public health policies, and migration of animals to new habitats. Representing the process…
In the fields of computation and neuroscience, much is still unknown about the underlying computations that enable key cognitive functions including learning, memory, abstraction and behavior. This paper proposes a mathematical and…
Over the last two decades, scientific literature has been blooming with various means of simulating epithelial cell colonies. Each of these simulations can be separated by their respective efficiency (expressed in terms of consumed…
Simulations show that sliding bilayers of colloidal particles can exhibit a new phase, the ``melt-freeze'' phase, where the layers stochastically alternate between solidlike and liquidlike states. We introduce a mean field phenomenological…
Recent progress in diverse intelligence has shown simple learning capacities below the organism level - single cells and even molecular networks. However, there are still many knowledge gaps around learning capacity above the organism…
The gamma process is a natural model for monotonic degradation processes. In practice, it is desirable to extend the single gamma process to incorporate measurement error and to construct models for the degradation of several nominally…
We introduce a data-driven fractional modeling framework aimed at complex materials, and particularly bio-tissues. From multi-step relaxation experiments of distinct anatomical locations of porcine urinary bladder, we identify an anomalous…