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📰 "Identity-Based Language Shift Modeling"
arxiv.org/abs/2504.01552 #Physics.Soc-Ph #Dynamics #Math.Na #Cs.Na #Cell

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arXiv.orgIdentity-Based Language Shift ModelingThe preservation of endangered languages is a widely discussed issue nowadays. Languages represent essential cultural heritage and can provide valuable botanical, biological, and geographical information. Therefore, it is necessary to develop efficient measures to preserve and revitalize endangered languages. However, the language shift process is complex and requires an interdisciplinary approach, including mathematical modeling techniques. This paper develops a new mathematical model that extends previous works on this topic. We introduce the factor of ethnic identity, which is a proxy for a more complex nexus of variables involved in an individual's self-identity and/or a group's identity. This proxy is socially constructed rather than solely inherited, shaped by community-determined factors, with language both indexing and creating the identity. In our model, we divide speakers into groups depending on with which language they identify themselves with. Moreover, every group includes monolinguals and bilinguals. The proposed model naturally allows us to consider cases of language coexistence and describe a broader class of linguistic situations. For example, the simulation results show that our model can result in cyclic language dynamics, drawing a parallel to cell population models. In this way, the proposed mathematical model can serve as a useful tool for developing efficient measures for language preservation and revitalization.

📰 "The Granule-In-Cell Method for Simulating Sand--Water Mixtures"
arxiv.org/abs/2504.00745 #Physics.Flu-Dyn #Forces #Cs.Gr #Cell

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arXiv.orgThe Granule-In-Cell Method for Simulating Sand--Water MixturesThe simulation of sand--water mixtures requires capturing the stochastic behavior of individual sand particles within a uniform, continuous fluid medium, such as the characteristic of migration, deposition, and plugging across various scenarios. In this paper, we introduce a Granule-in-Cell (GIC) method for simulating such sand--water interaction. We leverage the Discrete Element Method (DEM) to capture the fine-scale details of individual granules and the Particle-in-Cell (PIC) method for its continuous spatial representation and particle-based structure for density projection. To combine these two frameworks, we treat granules as macroscopic transport flow rather than solid boundaries for the fluid. This bidirectional coupling allows our model to accommodate a range of interphase forces with different discretization schemes, resulting in a more realistic simulation with fully respect to the mass conservation equation. Experimental results demonstrate the effectiveness of our method in simulating complex sand--water interactions, while maintaining volume consistency. Notably, in the dam-breaking experiment, our simulation uniquely captures the distinct physical properties of sand under varying infiltration degree within a single scenario. Our work advances the state of the art in granule--fluid simulation, offering a unified framework that bridges mesoscopic and macroscopic dynamics.

📰 "A scalable gene network model of regulatory dynamics in single cells"
arxiv.org/abs/2503.20027 #Dynamics #Q-Bio.Mn #Cs.Lg #Cell

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arXiv.orgA scalable gene network model of regulatory dynamics in single cellsSingle-cell data provide high-dimensional measurements of the transcriptional states of cells, but extracting insights into the regulatory functions of genes, particularly identifying transcriptional mechanisms affected by biological perturbations, remains a challenge. Many perturbations induce compensatory cellular responses, making it difficult to distinguish direct from indirect effects on gene regulation. Modeling how gene regulatory functions shape the temporal dynamics of these responses is key to improving our understanding of biological perturbations. Dynamical models based on differential equations offer a principled way to capture transcriptional dynamics, but their application to single-cell data has been hindered by computational constraints, stochasticity, sparsity, and noise. Existing methods either rely on low-dimensional representations or make strong simplifying assumptions, limiting their ability to model transcriptional dynamics at scale. We introduce a Functional and Learnable model of Cell dynamicS, FLeCS, that incorporates gene network structure into coupled differential equations to model gene regulatory functions. Given (pseudo)time-series single-cell data, FLeCS accurately infers cell dynamics at scale, provides improved functional insights into transcriptional mechanisms perturbed by gene knockouts, both in myeloid differentiation and K562 Perturb-seq experiments, and simulates single-cell trajectories of A549 cells following small-molecule perturbations.

📰 "Empirical Hyper Element Integration Method (EHEIM) with Unified Integration Criteria for Efficient Hyper Reduced FE$^2$ Simulations"
arxiv.org/abs/2503.19483 #Physics.Comp-Ph #Mechanical #Math.Na #Cs.Na #Ecm

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arXiv.orgEmpirical Hyper Element Integration Method (EHEIM) with Unified Integration Criteria for Efficient Hyper Reduced FE$^2$ SimulationsNumerical homogenization for mechanical multiscale modeling by means of the finite element method (FEM) is an elegant way of obtaining structure-property relations, if the behavior of the constituents of the lower scale is well understood. However, the computational costs of this so-called FE$^2$ method are so high that reduction methods are essential. While the construction of a reduced basis for the microscopic nodal displacements using proper orthogonal decomposition (POD) has become a standard technique, the reduction of the computational effort for the projected nodal forces, the so-called hyper reduction, is an additional challenge, for which different strategies have been proposed in the literature. The empirical cubature method (ECM), which has been proven to be very robust, implemented the conservation of the total volume is used as a constraint in the resulting optimization problem, while energy-based criteria have been proposed in other contributions. The present contribution presents a unified integration criteria concept, involving the aforementioned criteria, among others. These criteria are used both with a Gauss point-based as well as with an element-based hyper reduction scheme, the latter retaining full compatibility with the common modular finite element framework. The methods are combined with a previously proposed clustered training strategy and a monolithic solver. Numerical examples empirically demonstrate that the additional criteria improve the accuracy for a given number of modes. Vice verse, less modes and thus lower computational costs are required to reach a given level of accuracy.

📰 "Reconstructing Cell Lineage Trees from Phenotypic Features with Metric Learning"
arxiv.org/abs/2503.13925 #Dynamics #Q-Bio.Gn #Cs.Lg #Cell

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arXiv.orgReconstructing Cell Lineage Trees from Phenotypic Features with Metric LearningHow a single fertilized cell gives rise to a complex array of specialized cell types in development is a central question in biology. The cells grow, divide, and acquire differentiated characteristics through poorly understood molecular processes. A key approach to studying developmental processes is to infer the tree graph of cell lineage division and differentiation histories, providing an analytical framework for dissecting individual cells' molecular decisions during replication and differentiation. Although genetically engineered lineage-tracing methods have advanced the field, they are either infeasible or ethically constrained in many organisms. In contrast, modern single-cell technologies can measure high-content molecular profiles (e.g., transcriptomes) in a wide range of biological systems. Here, we introduce CellTreeQM, a novel deep learning method based on transformer architectures that learns an embedding space with geometric properties optimized for tree-graph inference. By formulating lineage reconstruction as a tree-metric learning problem, we have systematically explored supervised, weakly supervised, and unsupervised training settings and present a Lineage Reconstruction Benchmark to facilitate comprehensive evaluation of our learning method. We benchmarked the method on (1) synthetic data modeled via Brownian motion with independent noise and spurious signals and (2) lineage-resolved single-cell RNA sequencing datasets. Experimental results show that CellTreeQM recovers lineage structures with minimal supervision and limited data, offering a scalable framework for uncovering cell lineage relationships in challenging animal models. To our knowledge, this is the first method to cast cell lineage inference explicitly as a metric learning task, paving the way for future computational models aimed at uncovering the molecular dynamics of cell lineage.

📰 "Communities in the Kuramoto Model: Dynamics and Detection via Path Signatures"
arxiv.org/abs/2503.17546 #Cond-Mat.Dis-Nn #Q-Bio.Nc #Q-Bio.Qm #Dynamics #Nlin.Ao #Stat.Ml #Matrix #Cs.Lg

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arXiv.orgCommunities in the Kuramoto Model: Dynamics and Detection via Path SignaturesThe behavior of multivariate dynamical processes is often governed by underlying structural connections that relate the components of the system. For example, brain activity which is often measured via time series is determined by an underlying structural graph, where nodes represent neurons or brain regions and edges represent cortical connectivity. Existing methods for inferring structural connections from observed dynamics, such as correlation-based or spectral techniques, may fail to fully capture complex relationships in high-dimensional time series in an interpretable way. Here, we propose the use of path signatures a mathematical framework that encodes geometric and temporal properties of continuous paths to address this problem. Path signatures provide a reparametrization-invariant characterization of dynamical data and, in particular, can be used to compute the lead matrix which reveals lead-lag phenomena. We showcase our approach on time series from coupled oscillators in the Kuramoto model defined on a stochastic block model graph, termed the Kuramoto stochastic block model (KSBM). Using mean-field theory and Gaussian approximations, we analytically derive reduced models of KSBM dynamics in different temporal regimes and theoretically characterize the lead matrix in these settings. Leveraging these insights, we propose a novel signature-based community detection algorithm, achieving exact recovery of structural communities from observed time series in multiple KSBM instances. Our results demonstrate that path signatures provide a novel perspective on analyzing complex neural data and other high-dimensional systems, explicitly exploiting temporal functional relationships to infer underlying structure.

📰 "Communities in the Kuramoto Model: Dynamics and Detection via Path Signatures"
arxiv.org/abs/2503.17546 #Cond-Mat.Dis-Nn #Q-Bio.Qm #Dynamics #Q-Bio.Nc #Stat.Ml #Nlin.Ao #Matrix #Cs.Lg

arXiv logo
arXiv.orgCommunities in the Kuramoto Model: Dynamics and Detection via Path SignaturesThe behavior of multivariate dynamical processes is often governed by underlying structural connections that relate the components of the system. For example, brain activity which is often measured via time series is determined by an underlying structural graph, where nodes represent neurons or brain regions and edges represent cortical connectivity. Existing methods for inferring structural connections from observed dynamics, such as correlation-based or spectral techniques, may fail to fully capture complex relationships in high-dimensional time series in an interpretable way. Here, we propose the use of path signatures a mathematical framework that encodes geometric and temporal properties of continuous paths to address this problem. Path signatures provide a reparametrization-invariant characterization of dynamical data and, in particular, can be used to compute the lead matrix which reveals lead-lag phenomena. We showcase our approach on time series from coupled oscillators in the Kuramoto model defined on a stochastic block model graph, termed the Kuramoto stochastic block model (KSBM). Using mean-field theory and Gaussian approximations, we analytically derive reduced models of KSBM dynamics in different temporal regimes and theoretically characterize the lead matrix in these settings. Leveraging these insights, we propose a novel signature-based community detection algorithm, achieving exact recovery of structural communities from observed time series in multiple KSBM instances. Our results demonstrate that path signatures provide a novel perspective on analyzing complex neural data and other high-dimensional systems, explicitly exploiting temporal functional relationships to infer underlying structure.

📰 "Accelerating Transient CFD through Machine Learning-Based Flow Initialization"
arxiv.org/abs/2503.15766 #Physics.Flu-Dyn #Dynamics #Cs.Lg #Cell

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arXiv.orgAccelerating Transient CFD through Machine Learning-Based Flow InitializationTransient computational fluid dynamics (CFD) simulations are essential for many industrial applications, but a significant portion of their computational cost stems from the time needed to reach statistical steadiness from initial conditions. We present a novel machine learning-based initialization method that reduces the cost of this subsequent transient solve substantially, achieving a 50% reduction in time-to-convergence compared to traditional uniform and potential flow-based initializations. Through a case study in automotive aerodynamics using a 16.7M-cell unsteady RANS simulation, we evaluate three ML-based initialization strategies. Two of these strategies are recommended for general use: (1) a physics-informed hybrid method combining ML predictions with potential flow solutions, and (2) a more versatile approach integrating ML predictions with uniform flow. Both strategies enable CFD solvers to achieve convergence times comparable to computationally expensive steady RANS initializations, while requiring only seconds of computation. We develop a robust statistical convergence metric based on windowed time-averaging for performance comparison between initialization strategies. Notably, these improvements are achieved using an ML model trained on a different dataset of automotive geometries, demonstrating strong generalization capabilities. The proposed methods integrate seamlessly with existing CFD workflows without requiring modifications to the underlying flow solver, providing a practical approach to accelerating industrial CFD simulations through improved ML-based initialization strategies.

📰 "AI-driven control of bioelectric signalling for real-time topological reorganization of cells"
arxiv.org/abs/2503.13489 #Physics.Bio-Ph #Morphogenesis #Q-Bio.Qm #Q-Bio.Cb #Eess.Sy #Cs.Sy #Cs.Ai #Cell

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arXiv.orgAI-driven control of bioelectric signalling for real-time topological reorganization of cellsUnderstanding and manipulating bioelectric signaling could present a new wave of progress in developmental biology, regenerative medicine, and synthetic biology. Bioelectric signals, defined as voltage gradients across cell membranes caused by ionic movements, play a role in regulating crucial processes including cellular differentiation, proliferation, apoptosis, and tissue morphogenesis. Recent studies demonstrate the ability to modulate these signals to achieve controlled tissue regeneration and morphological outcomes in organisms such as planaria and frogs. However, significant knowledge gaps remain, particularly in predicting and controlling the spatial and temporal dynamics of membrane potentials (V_mem), understanding their regulatory roles in tissue and organ development, and exploring their therapeutic potential in diseases. In this work we propose an experiment using Deep Reinforcement Learning (DRL) framework together with lab automation techniques for real-time manipulation of bioelectric signals to guide tissue regeneration and morphogenesis. The proposed framework should interact continuously with biological systems, adapting strategies based on direct biological feedback. Combining DRL with real-time measurement techniques -- such as optogenetics, voltage-sensitive dyes, fluorescent reporters, and advanced microscopy -- could provide a comprehensive platform for precise bioelectric control, leading to improved understanding of bioelectric mechanisms in morphogenesis, quantitative bioelectric models, identification of minimal experimental setups, and advancements in bioelectric modulation techniques relevant to regenerative medicine and cancer therapy. Ultimately, this research aims to utilize bioelectric signaling to develop new biomedical and bioengineering applications.

📰 "AI-driven control of bioelectric signalling for real-time topological reorganization of cells"
arxiv.org/abs/2503.13489 #Physics.Bio-Ph #Morphogenesis #Q-Bio.Qm #Q-Bio.Cb #Eess.Sy #Cs.Sy #Cs.Ai #Cell

arXiv logo
arXiv.orgAI-driven control of bioelectric signalling for real-time topological reorganization of cellsUnderstanding and manipulating bioelectric signaling could present a new wave of progress in developmental biology, regenerative medicine, and synthetic biology. Bioelectric signals, defined as voltage gradients across cell membranes caused by ionic movements, play a role in regulating crucial processes including cellular differentiation, proliferation, apoptosis, and tissue morphogenesis. Recent studies demonstrate the ability to modulate these signals to achieve controlled tissue regeneration and morphological outcomes in organisms such as planaria and frogs. However, significant knowledge gaps remain, particularly in predicting and controlling the spatial and temporal dynamics of membrane potentials (V_mem), understanding their regulatory roles in tissue and organ development, and exploring their therapeutic potential in diseases. In this work we propose an experiment using Deep Reinforcement Learning (DRL) framework together with lab automation techniques for real-time manipulation of bioelectric signals to guide tissue regeneration and morphogenesis. The proposed framework should interact continuously with biological systems, adapting strategies based on direct biological feedback. Combining DRL with real-time measurement techniques -- such as optogenetics, voltage-sensitive dyes, fluorescent reporters, and advanced microscopy -- could provide a comprehensive platform for precise bioelectric control, leading to improved understanding of bioelectric mechanisms in morphogenesis, quantitative bioelectric models, identification of minimal experimental setups, and advancements in bioelectric modulation techniques relevant to regenerative medicine and cancer therapy. Ultimately, this research aims to utilize bioelectric signaling to develop new biomedical and bioengineering applications.