arXiv subjects

Meskerem Abebaw Mebratie

Publications and source records attributed to Meskerem Abebaw Mebratie.

3 recordsLinked to original sources

arXiv2026

Mathematical Modeling of Early Embryonic Cell Cycles of Drosophila melanogaster

In the early stages of development, Drosophila melanogaster embryos possess very fast and well-coordinated cell cycles. In the cell cycle, CDK activity is essentially regulated by binding CDK and CycB to form an active complex and by phosphorylating CDK via CDC25 and dephosphorylating it via Wee1. We develop a mathematical model for the embryonic cell cycle which is biochemically sound and which can be rigorously analysed after a model reduction. We show that there exists a region in the parameter space where the model describes oscillations. We then focus on the role of two parameters: the CycB synthesis and the activation coefficient of APC. Our main biological hypothesis is that the first one is responsible for the period lengthening over the first 14 cycles which can be experimentally observed and this hypothesis is supported by numerical simulations of our model: if the CycB synthesis is made time-dependent with a prescribed dynamics, then our simulations show qualitatively a very similar behavior to experimental data reported in the literature.

q-bio.QM↗

arXiv2026

Structural Identifiability and Discrete Symmetries

We discuss the use of symmetries for analysing the structural identifiability and observability of control systems. Special emphasis is put on the role of discrete symmetries, in contrast to the more commonly studied continuous or Lie symmetries. We argue that discrete symmetries are the origin of parameters which are structurally locally identifiable, but not globally. We exploit this fact to present a methodology for structural identifiability analysis that detects such parameters and characterizes the symmetries in which they are involved. We demonstrate the use of our methodology by applying it to four case studies.

math.DS↗

arXiv2024

Machine Learning Conservation Laws of Dynamical systems

Conservation laws are of great theoretical and practical interest. We describe a novel approach to machine learning conservation laws of finite-dimensional dynamical systems using trajectory data. It is the first such approach based on kernel methods instead of neural networks which leads to lower computational costs and requires a lower amount of training data. We propose the use of an "indeterminate" form of kernel ridge regression where the labels still have to be found by additional conditions. We use here a simple approach minimising the length of the coefficient vector to discover a single conservation law.

physics.comp-ph↗