arXiv subjects

Martina Conte

Publications and source records attributed to Martina Conte.

16 recordsLinked to original sources

arXiv2026

Speed and stability of segregated waves in a pressure-based model of heterogeneous cell populations

We consider a minimal pressure-based model of heterogeneous cell populations consisting of proliferative and non-proliferative cells with different mobilities. The model is formulated as a system of reaction--cross--diffusion equations describing the spatio-temporal dynamics of the cell densities. The model is known to admit one-dimensional travelling wave solutions with strictly segregated components: non-proliferative cells occupy a finite region at the leading edge, while proliferative cells remain at the rear. However, the speed, parameter dependence, and stability of these waves remain poorly understood. In this work, we derive an almost explicit variational bound on the wave speed by reformulating the problem as a free-boundary problem for a generalised porous--Fisher equation. The estimates we obtain apply to general pressure laws and growth kinetics, agree closely with the results of numerical simulations, and become sharp in the incompressible limit, where we formally recover a fully explicit characterisation of the wave speed. We then analyse the stability of the waves to show that segregated waves are stable only when non-proliferative cells are more mobile than proliferative cells. Finally, motivated by numerical observations of finger-like protrusions, we investigate the stability of incompressible segregated circular waves through asymptotic shape-perturbation analysis. This yields explicit expressions for the pressure, interface velocity, and growth rates of angular modes, thereby making evident the destabilisation mechanisms that may lead to the emergence of fingering instability. Interestingly, we find that, in contrast with the one-dimensional case, the stability of such circular waves is not determined solely by the relative value of the mobility coefficients, and thus instabilities may arise irrespective of which cell type has the larger mobility.

math.AP↗

arXiv2026

Hydrodynamic theories of chemotaxis-driven invasion in proliferating cell populations

Biased migration up chemical gradients and proliferation are fundamental drivers of collective invasion in several biological processes ranging from embryonic morphogenesis to cancer. Nonetheless, our understanding of how their interplay yields distinct invasion patterns remains incomplete. In this work, we propose a multiscale framework to systematically derive macroscopic hydrodynamic theories of cell invasion from a mesoscopic description of cells as biased self-propelled, interacting particles that proliferate. Our framework reveals how clump and stream invasion patterns emerge from the same kinetic equation under different asymptotic regimes of cell proliferation. Stream invasion is characteristic of cell populations in which proliferation balances cell motion. In contrast, clump invasion requires a separation of the hydrodynamic timescale of motion and the slower timescale of proliferation. By means of a multiple-scale approach, our analysis reveals that clump invasion is described as a slow evolution through a family of mass-dependent travelling-wave solutions. Overall, our work offers a novel approach to investigate multiscale regulation of cell invasion in systems where cell proliferation and collective invasion evolve on distinct timescales.

q-bio.CB↗

arXiv2026

Concise formulae in groups of non-positive curvature

We show that first-order formulae are concise in acylindrically hyperbolic groups and certain extensions thereof. We study further classes of groups, including Burnside groups, icc groups, groups with the `Big Powers' condition, torus knot groups and more, and prove conciseness for wide classes of formulae. We also explore properties of definable sets in these groups, such as their finiteness, depending on the type of formula considered.

math.GR↗

arXiv2026

Randomness-aware multiscale models of glioma invasion and treatment

In this work, we develop a stochastic multiscale model for glioma growth and invasion in the brain, incorporating the effects of therapeutic interventions. The model accounts for tumor cell migration influenced by brain tissue heterogeneity and anti-crowding mechanisms, while explicitly addressing treatment-related uncertainties through stochastic processes. Starting from a microscopic description of individual cell dynamics, we derive the corresponding system of macroscopic random reaction-diffusion-taxis equations governing cell density and tissue evolution. Finally, we conduct several numerical experiments to assess the efficacy of different treatment protocols, evaluated with respect to both established and newly proposed clinical criteria and measurable outcomes.

q-bio.CB↗

arXiv2025

A novel linear transport model with distinct scattering mechanisms for direction and speed

We introduce a novel linear transport equation that models the evolution of a one-particle distribution subject to free transport and two distinct scattering mechanisms: one affecting the particle's speed and the other its direction. These scattering processes occur at different time scales and with different intensities, leading to a kinetic equation where the total scattering operator is the sum of two separate operators. Each of them depends not only on the kernel characterizing the corresponding scattering mechanism, but also explicitly on the marginal distribution of either the speed or the direction. Therefore, unlike classical settings, the gain terms in our operators are not tied to a fixed equilibrium distribution but evolve in time through the marginals. As a result, typical analytical tools from kinetic theory, such as equilibrium characterization, entropy methods, spectral analysis in Hilbert spaces, and Fredholm theory, are not applicable in a standard fashion. In this work, we rigorously analyze the properties of this new class of scattering operators, including the structure of their non-standard pseudo-inverses and their asymptotic behavior. We also derive macroscopic (hydrodynamic) limits under different regimes of scattering frequencies, revealing new effective equations and highlighting the interplay between speed and directional relaxation.

math-ph↗

arXiv2025

Kinetic modeling of knowledge and wealth dynamics in national and global markets

We propose a kinetic model to describe the dynamical evolution of wealth and knowledge in national and global markets, starting from a microscopic description of individual interactions. The model is built upon interaction rules that account for a strong interdependence between the microscopic variables, influencing agents' trading and saving propensities, knowledge acquisition, and the stochastic market effects. We begin with a domestic market scenario and extend the framework to international trade, incorporating the possibility of individual transfers between different countries. The dynamics of the system are described through Boltzmann-type equations, which allow for a detailed study of the evolution of the agent distribution in each country. In this context, we study the evolution of macroscopic quantities of the system, focusing on the number density of individuals, and the mean wealth and knowledge of each population, and we discuss these results in relation to existing models in the literature. Finally, under a quasi-invariant trading limit, we derive simplified Fokker-Planck type equations that reveal some emergent behaviors of the system, including the formation of Pareto tails in the long-term wealth and knowledge distributions.

physics.soc-ph↗

arXiv2025

Conciseness of first-order formulae

A word $w$ is concise in a class of groups $\mathcal{C}$ if, for every group $G$ in $\mathcal{C}$, the verbal subgroup $w(G)$ is finite whenever $w$ takes only finitely many values in $G$. This notion can be naturally extended to first-order formulae in the language of groups. We consider this more general setting and establish conciseness for various classes of groups and formulae. We prove that all formulae are concise in the class of abelian groups and that every existential formula is concise in the class of torsion-free locally class-2 nilpotent groups. In addition, we construct new examples of weakly rational words, which allow us to produce a wide variety of formulae that are concise in the class of residually finite groups.

math.GR↗

arXiv2024

A kinetic derivation of spatial distributed models for tumor-immune system interactions

We propose a mathematical kinetic framework to investigate interactions between tumor cells and the immune system, focusing on the spatial dynamics of tumor progression and immune responses. We develop two kinetic models: one describes a conservative scenario where immune cells switch between active and passive states without proliferation, while the other incorporates immune cell proliferation and apoptosis. By considering specific assumptions about the microscopic processes, we derive macroscopic systems featuring linear diffusion, nonlinear cross-diffusion, and nonlinear self-diffusion. Our analysis provides insights into equilibrium configurations and stability, revealing clear correspondences among the macroscopic models derived from the same kinetic framework. Using dynamical systems theory, we examine the stability of equilibrium states and conduct numerical simulations to validate our findings. These results highlight the significance of spatial interactions in tumor-immune dynamics, paving the way for a structured exploration of therapeutic strategies and further investigations into immune responses in various pathological contexts.

q-bio.CB↗

arXiv2024

Action potential dynamics on heterogenous neural networks: from kinetic to macroscopic equations

In the context of multi-agent systems of binary interacting particles, a kinetic model for action potential dynamics on a neural network is proposed, accounting for heterogeneity in the neuron-to-neuron connections, as well as in the brain structure. Two levels of description are coupled: in a single area, pairwise neuron interactions for the exchange of membrane potential are statistically described; among different areas, a graph description of the brain network topology is included. Equilibria of the kinetic and macroscopic settings are determined and numerical simulations of the system dynamics are performed with the aim of studying the influence of the network heterogeneities on the membrane potential propagation and synchronization.

physics.bio-ph↗

arXiv2024

Multi-scale modeling of Snail-mediated response to hypoxia in tumor progression

Tumor cell migration within the microenvironment is a crucial aspect for cancer progression and, in this context, hypoxia has a significant role. An inadequate oxygen supply acts as an environmental stressor inducing migratory bias and phenotypic changes. In this paper, we propose a novel multi-scale mathematical model to analyze the pivotal role of Snail protein expression in the cellular responses to hypoxia. Starting from the description of single-cell dynamics driven by the Snail protein, we construct the corresponding kinetic transport equation that describes the evolution of the cell distribution. Subsequently, we employ proper scaling arguments to formally derive the equations for the statistical moments of the cell distribution, which govern the macroscopic tumor dynamics. Numerical simulations of the model are performed in various scenarios with biological relevance to provide insights into the role of the multiple tactic terms, the impact of Snail expression on cell proliferation, and the emergence of hypoxia-induced migration patterns. Moreover, quantitative comparison with experimental data shows the model's reliability in measuring the impact of Snail transcription on cell migratory potential. Through our findings, we shed light on the potential of our mathematical framework in advancing the understanding of the biological mechanisms driving tumor progression.

q-bio.CB↗

arXiv2023

Finite axiomatizability of the rank and the dimension of a pro-$\pi$ group

The Pr\"ufer rank $\mathrm{rk}(G)$ of a profinite group $G$ is the supremum, across all open subgroups $H$ of $G$, of the minimal number of generators $\mathrm{d}(H)$. It is known that, for any given prime $p$, a profinite group $G$ admits the structure of a $p$-adic analytic group if and only if $G$ is virtually a pro-$p$ group of finite rank. The dimension $\dim G$ of a $p$-adic analytic profinite group $G$ is the analytic dimension of $G$ as a $p$-adic manifold; it is known that $\dim G$ coincides with the rank $\mathrm{rk}(U)$ of any uniformly powerful open pro-$p$ subgroup $U$ of $G$. Let $\pi$ be a finite set of primes, let $r \in \mathbb{N}$ and let $\mathbf{r} = (r_p)_{p \in \pi}, \mathbf{d} = (d_p)_{p \in \pi}$ be tuples in $\{0, 1, \ldots,r\}$. We show that there is a single sentence $\sigma_{\pi,r,\mathbf{r},\mathbf{d}}$ in the first-order language of groups such that for every pro-$\pi$ group $G$ the following are equivalent: (i) $\sigma_{\pi,r,\mathbf{r},\mathbf{d}}$ holds true in the group $G$, that is, $G \models \sigma_{\pi,r,\mathbf{r},\mathbf{d}}$; (ii) $G$ has rank $r$ and, for each $p \in \pi$, the Sylow pro-$p$ subgroups of $G$ have rank $r_p$ and dimension $d_p$. Loosely speaking, this shows that, for a pro-$\pi$ group $G$ of bounded rank, the precise rank of $G$ as well as the ranks and dimensions of the Sylow subgroups of $G$ can be recognized by a single sentence in the first-order language of groups.

math.GR↗

arXiv2023

Kinetic and macroscopic equations for action potential in neural networks

Starting from the concept of binary interactions between pairs of particles, a kinetic framework for the description of the action potential dynamics on a neural network is proposed. It consists of two coupled levels: the description of a single brain region dynamics and the interactions among different regions. On one side, the pairwise interaction between neurons exchanging membrane potential is statistically described to account for the unmanageable number of neuron synapses within a single brain region. On the other, the network connections accounting for the brain region topology are represented and studied using concepts of the graph theory. Equilibrium and stability of the obtained macroscopic systems are analyzed as well as numerical simulations of the system dynamics are performed in different scenarios. In particular, the latter allows us to observe the influence of the discrete network topology on the membrane potential propagation and synchronization through the different regions, in terms of its spiking characteristics.

physics.bio-ph↗

arXiv2022

A non-local kinetic model for cell migration: a study of the interplay between contact guidance and steric hindrance

We propose a non-local model for contact guidance and steric hindrance depending on a single external cue, namely the extracellular matrix, that affects in a twofold way the polarization and speed of motion of the cells. We start from a microscopic description of the stochastic processes underlying the cell re-orientation mechanism related to the change of cell speed and direction. Then, we formally derive the corresponding kinetic model that implements exactly the prescribed microscopic dynamics and, from it, it is possible to deduce the macroscopic limit in the appropriate regime. Moreover, we test our model in several scenarios. In particular, we numerically investigate the minimal microscopic mechanisms that are necessary to reproduce cell dynamics by comparing the outcomes of our model with some experimental results related to breast cancer cell migration. This allows us to validate the proposed modeling approach and, also, to highlight its capability of predicting the qualitative cell behaviors in diverse heterogeneous microenvironments.

q-bio.CB↗

arXiv2022

A stochastic hierarchical model for low grade glioma evolution

A stochastic hierarchical model for the evolution of low grade gliomas is proposed. Starting with the description of cell motion using piecewise diffusion Markov processes (PDifMPs) at the cellular level, we derive an equation for the density of the transition probability of this Markov process using the generalised Fokker-Planck equation. Then a macroscopic model is derived via parabolic limit and Hilbert expansions in the moment equations. After setting up the model, we perform several numerical tests to study the role of the local characteristics and the extended generator of the PDifMP in the process of tumour progression. The main aim focuses on understanding how the variations of the jump rate function of this process at the microscopic scale and the diffusion coefficient at the macroscopic scale are related to the diffusive behaviour of the glioma cells and to the onset of malignancy, i.e., the transition from low-grade to high-grade gliomas.

q-bio.TO↗

arXiv2022

Mathematical modeling of glioma invasion and therapy approaches via kinetic theory of active particles

We propose here a multiscale model for study the effect of combined therapies on glioma spread in the brain under the influence of vascularization. The model accounts for the interplay between the different components of the neoplasm and the healthy tissue and it investigates and compares various therapy approaches. Precisely, these involve radio- and chemotherapy in a concurrent or adjuvant manner together with anti-angiogenic therapy affecting the vascular component of the system. We assess tumor growth and spread on the basis of DTI data, which allows us to reconstruct a realistic brain geometry and tissue structure, and we apply our model to real glioma patient data. In this latter case, a space-dependent radiotherapy description is considered using data about the corresponding isodose curves.

q-bio.CB↗

arXiv2020

Mathematical modeling of glioma invasion: acid- and vasculature mediated go-or-grow dichotomy and the influence of tissue anisotropy

Starting from kinetic transport equations and subcellular dynamics we deduce a multiscale model for glioma invasion relying on the go-or-grow dichotomy and the influence of vasculature, acidity, and brain tissue anisotropy. Numerical simulations are performed for this model with multiple taxis, in order to assess the solution behavior under several scenarios of taxis and growth for tumor and endothelial cells. An extension of the model to incorporate the macroscopic evolution of normal tissue and necrotic matter allows us to perform tumor grading.

q-bio.TO↗