arXiv subjects

Loïc Le Marrec

Publications and source records attributed to Loïc Le Marrec.

9 recordsLinked to original sources

arXiv2026

Integrating Structure and Attributes for Transportation Network Partitioning via Optimal Transport

Transportation network partitioning is essential for applications such as traffic analysis, simulation, and mobility pattern identification. However, transportation networks combine structural information with heterogeneous operational attributes, ranging from scalar indicators to temporal profiles. Existing approaches generally rely on predefined formulations to integrate these sources of information, limiting the ability to control their relative influence. This paper proposes a flexible framework for partitioning heterogeneous transportation networks represented as attributed graphs. The proposed methodology relies on a distance-based graph representation and an optimal transport formulation based on the semi-relaxed Fused Gromov-Wasserstein discrepancy, enabling joint consideration of network structure and attributes with explicit control over their trade-off. The proposed methodology is evaluated on two transportation systems with distinct characteristics: an urban road network for traffic-oriented partitioning and a bicycle-sharing system for identifying usage-based communities. Results demonstrate the ability of the framework to adapt the resulting partitions according to different structural and attribute preferences.

stat.AP↗

arXiv2026

Optimal Transport-Based Clustering of Attributed Graphs with an Application to Road Traffic Data

In many real-world contexts, such as social or transport networks, data exhibit both structural connectivity and node-level attributes. For example, roads in a transport network can be characterized not only by their connectivity but also by traffic flow or speed profiles. Understanding such systems therefore requires jointly analyzing the network structure and node attributes, a challenge addressed by attributed graph partitioning, which clusters nodes according on both connectivity and attributes. In this work, we adapt transport-based approaches based on Gromov--Wasserstein (GW) discrepancy. We investigate how GW methods, traditionally used for general-purpose tasks such as graph matching, can be specifically adapted for node partitioning, an area that has been relatively underexplored. In the context of node-attributed graphs, we introduce an adaptation of the Fused GW method, offering theoretical guarantees and the ability to handle heterogeneous attribute types. Additionally, we propose to incorporate distance-based embeddings to enhance performance. The proposed approaches are systematically evaluated using a dedicated simulation framework and illustrated on a real-world transportation dataset. Experiments investigate the influence of target choice, assess robustness to noise, and provide practical guidance for attributed graph clustering. In the context of road networks, our results demonstrate that these methods can effectively leverage both structural and attribute information to reveal meaningful clusters, offering insights for improved network understanding.

stat.ME↗

arXiv2026

Modeling phononic band gap in microstructured solids using the Riemann-Cartan geometric framework

This paper discusses the modeling of acoustic wave fields in microstructured elastic solids within the framework of Riemann-Cartan geometry. We consider a scenario in which microstructural deformations occur significantly faster than those of the bulk material. This time-scale separation creates apparent geometric incompatibilities at the macroscopic level, even in the absence of permanent inelastic deformation or damage. We formalize this phenomenon by using a non-holonomic frame field to represent macroscopic elastic deformations and an associated torsion field to characterize the resulting geometric incompatibilities. The spatial components of the torsion tensor quantify the instantaneous geometric incompatibility of the macroscopic deformations, while its temporal components capture the inertial effects arising from the reversible energy exchange between the micro- and macro-scales. A key finding is that the model's dispersion relation predicts a complete frequency band gap. Furthermore, the governing equations exhibit a mathematical analogy to Maxwell's equations, potentially bridging the modeling of phononic and photonic metamaterials.

math-ph↗

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

Kinesin-12 KLP-18 contributes to the kinetochore-microtubule poleward flux during the metaphase of C. elegans one-cell embryo

The mitotic spindle partitions chromosomes during cell division by connecting the poles to kinetochores through microtubules (MTs). Their plus-ends, facing the chromosomes, exhibit dynamic instability, which is critical for proper attachment. The poleward flux implicates the displacement of Mts towards the spindle poles, while plus-ends polymerise. It may result from minus-end depolymerisation (treadmilling), sliding by kinesins (e.g., Kinesin-5), or pushing by chromokinesins. Intriguingly, such flux had not been reported in the C. elegans zygote, despite homologs of flux-associated proteins being present. To investigate this, we fluorescently labelled Mts and used photobleaching. We observed no global flux; instead, the bleached zone's edges moved inward. The centrosome-facing front reflected MT dynamic instability, but the chromosome-facing front showed faster recovery, suggesting an additional mechanism. This extra velocity was spatially restricted to the vicinity of chromosomes, suggesting that only the kinetochore Mts may undergo flux. Supporting this, flux required key kinetochore regulators: NDC-80, $\text{CLS-2}^\text{CLASP}$, and $\text{ZYG-9}^\text{XMAP215}$. Flux declined as metaphase progressed, correlating with the attachment maturation from lateral to end-on, and was suppressed by SKA-1 recruitment. Classic treadmilling was unlikely, as most kinetochore MTs in C. $elegans$ do not reach spindle poles. Instead, depleting $\text{KLP-18}^\text{KIF15}$, a kinesin that cross-links and organises Mts during meiosis, reduced front movement. We propose that only kinetochore Mts undergo flux, sliding along the spindle Mts, likely powered by KLP-18. This localised sliding contrasts with global flux seen in other systems, and aligns with observations in human cells showing flux reduction as chromosome-to-pole distance increases.

q-bio.SC↗

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↗

arXiv2025

Timoshenko beam under finite and dynamic transformations: Lagrangian coordinates and Hamiltonian structures

In the framework of Timoshenko beam, the material parameters are inherently prescribed on the material moving frame. In this regard, we derive the strong and weak formulations of the dynamics under finite transformation in Lagrangian coordinates. Accordingly, analytical mechanics tools are used to deduce a new Hamiltonian formulation of the model which proves to be remarkably simple and synthetic.

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↗

arXiv2012

Time-domain numerical simulations of multiple scattering to extract elastic effective wavenumbers

Elastic wave propagation is studied in a heterogeneous 2-D medium consisting of an elastic matrix containing randomly distributed circular elastic inclusions. The aim of this study is to determine the effective wavenumbers when the incident wavelength is similar to the radius of the inclusions. A purely numerical methodology is presented, with which the limitations usually associated with low scatterer concentrations can be avoided. The elastodynamic equations are integrated by a fourth-order time-domain numerical scheme. An immersed interface method is used to accurately discretize the interfaces on a Cartesian grid. The effective field is extracted from the simulated data, and signal-processing tools are used to obtain the complex effective wavenumbers. The numerical reference solution thus-obtained can be used to check the validity of multiple scattering analytical models. The method is applied to the case of concrete. A parametric study is performed on longitudinal and transverse incident plane waves at various scatterers concentrations. The phase velocities and attenuations determined numerically are compared with predictions obtained with multiple scattering models, such as the Independent Scattering Approximation model, the Waterman-Truell model, and the more recent Conoir-Norris model.

physics.class-ph↗