arXiv subjects

Mewen Crespo

Publications and source records attributed to Mewen Crespo.

4 recordsLinked to original sources

arXiv2025

A New Framework for Unidimensional Structures Based on Generalised Continua

The present work introduces a family of beam models derived from a three-dimensional higher-order elasticity framework. By incorporating three kinematic fields - the macroscopic displacement u, the micro-distortion tensor P, and the third-order tensor N - the study systematically explores three regimes: holonomic, semi-holonomic, and non-holonomic. These regimes correspond to varying levels of kinematic constraints, ranging from classical elasticity to a fully relaxed model. The holonomic case reduces to a higher-order Euler--Bernoulli beam model, while the semi-holonomic case generalises the Timoshenko beam model. The non-holonomic case provides a unified framework that naturally incorporates both dislocations and disclinations. Furthermore, the holonomic and semi-holonomic models are shown to emerge as singular limits of the non-holonomic model by increasing specific penalty coefficients. Simplified ordinary differential equation systems are derived for specific cases, such as pure traction and bending, illustrating the practical applicability of the models. The results highlight the hierarchical structure of the proposed framework and its ability to capture material defects in beam-like structures.

math.AP↗

arXiv2025

A novel attention mechanism for noise-adaptive and robust segmentation of microtubules in microscopy images

Segmenting cytoskeletal filaments in microscopy images is essential for studying their roles in cellular processes. However, this task is highly challenging due to the fine, densely packed, and intertwined nature of these structures. Imaging limitations further complicate analysis. While deep learning has advanced segmentation of large, well-defined biological structures, its performance often degrades under such adverse conditions. Additional challenges include obtaining precise annotations for curvilinear structures and managing severe class imbalance during training. We introduce a novel noise-adaptive attention mechanism that extends the Squeeze-and-Excitation (SE) module to dynamically adjust to varying noise levels. Integrated into a U-Net decoder with residual encoder blocks, this yields ASE_Res_UNet, a lightweight yet high-performance model. We also developed a synthetic dataset generation strategy that ensures accurate annotations of fine filaments in noisy images. We systematically evaluated loss functions and metrics to mitigate class imbalance, ensuring robust performance assessment. ASE_Res_UNet effectively segmented microtubules in noisy synthetic images, outperforming its ablated variants. It also demonstrated superior segmentation compared to models with alternative attention mechanisms or distinct architectures, while requiring fewer parameters, making it efficient for resource-constrained environments. Evaluation on a newly curated real microscopy dataset and a recently reannotated dataset highlighted ASE_Res_UNet's effectiveness in segmenting microtubules beyond synthetic images. For these datasets, ASE_Res_UNet was competitive with a recent synthetic data-driven approach that shares two cytoskeleton pretrained models. Importantly, ASE_Res_UNet showed strong transferability to other curvilinear structures (blood vessels and nerves) across diverse imaging conditions.

q-bio.QM↗

arXiv2025

Defects in unidimensional structures

In a previous work of the first authors, a non-holonomic model, generalising the micromorphic models and allowing for curvature (disclinations) to arise from the kinematic values, was presented. In the present paper, a generalisation of the classical models of Euler-Bernoulli and Timoshenko bending beams based on the mentioned work is proposed. The former is still composed of only one unidimensional scalar field, while the later introduces a third unidimensional scalar field, correcting the second order terms. The generalised Euler-Bernoulli beam is then shown to exhibit curvature (i.e. disclinations) linked to a third order derivative of the displacement, but no torsion (dislocations). Parallelly, the generalised Timoshenko beam is shown to exhibit both curvature and torsion, where the former is linked to the non-holonomy introduced in the generalisation. Lastly, using variational calculus, asymptotic values for the value taken by the curvature in static equilibrium are obtained when the second order contribution becomes negligible; along with an equation for the torsion in the generalised Timoshenko beam.

math-ph↗

arXiv2024

Two-Scale Geometric Modelling for Defective Media

A new geometrically exact micro-structured model is constructed using a generalisation of the notion of Riemann-Cartan manifolds and fibre bundle theory of rank 3. This model is based around the concept of two different length scales: a macroscopic scale -- of dimensions 1, 2, or 3 -- and a microscopic one -- of dimension 3. As they interact with each other, they produce emergent behaviours such as dislocations (torsion) and disclinations (curvature). A first-order placement map F : TB --> TE between a micro-structured body B and the micro-structured ambient space E is constructed, allowing to pull the ambient Riemann-Cartan geometry back onto the body. I norder to allow for curvature to arise, F is, in general, not required to be a gradient. Central to this model is the new notion of pseudo-metric, providing, in addition to a macroscopic metric (the usual Cauchy-Green tensor) and a microscopic metric, a notion of coupling between the microscopic and macroscopic realms. A notion of frame indifference is formalised and invariants are computed. In the case of a micro-linear structure, it is shown that the data of these invariants is equivalent to the data of the pseudo-metric.

math.DG↗