Cancer cells are often seen to prefer glycolytic metabolism over oxidative phosphorylation even in the presence of oxygen-a phenomenon termed the Warburg effect. Despite significant strides in the decades since its discovery, a clear basis is yet to be established for the Warburg effect and why cancer cells show such a preference for aerobic glycolysis. In this review, we draw on what is known about similar metabolic shifts both in normal mammalian physiology and overflow metabolism in microbes to shed new light on whether aerobic glycolysis in cancer represents some form of optimisation of cellular metabolism. From microbes to cancer, we find that metabolic shifts favouring glycolysis are sometimes driven by the need for faster growth, but the growth rate is by no means a universal goal of optimal metabolism. Instead, optimisation goals at the cellular level are often multi-faceted and any given metabolic state must be considered in the context of both its energetic costs and benefits over a range of environmental contexts. For this purpose, we identify the conceptual framework of resource allocation as a potential testbed for the investigation of the cost-benefit balance of cellu
In the study of drug function and precision medicine, identifying new drug-microbe associations is crucial. However, current methods isolate association and similarity analysis of drug and microbe, lacking effective inter-view optimization and coordinated multi-view feature fusion. In our study, a multi-view Divergence-Convergence Feature Augmentation framework for Drug-related Microbes Prediction (DCFA_DMP) is proposed, to better learn and integrate association information and similarity information. In the divergence phase, DCFA_DMP strengthens the complementarity and diversity between heterogeneous information and similarity information by performing Adversarial Learning method between the association network view and different similarity views, optimizing the feature space. In the convergence phase, a novel Bidirectional Synergistic Attention Mechanism is proposed to deeply synergize the complementary features between different views, achieving a deep fusion of the feature space. Moreover, Transformer graph learning is alternately applied on the drug-microbe heterogeneous graph, enabling each drug or microbe node to focus on the most relevant nodes. Numerous experiments demonst
Microbes thrive in diverse porous environments -- from soil and riverbeds to human lungs and cancer tissues -- spanning multiple scales and conditions. Short- to long-term fluctuations in local factors induce spatio-temporal heterogeneities, often leading to physiologically stressful settings. How microbes respond and adapt to such biophysical constraints is an active field of research where considerable insight has been gained over the last decade and a half. With a focus on bacteria, here we review recent advances in microbial self-organization and dispersal in inorganic and organic porous settings, highlighting the role of active interactions and feedback which mediate their survival and fitness. We conclude by discussing open questions and opportunities for leveraging integrative cross-disciplinary approaches to advance our understanding of the biophysical strategies that microbes employ -- at both species and community scales -- to make porous settings habitable. Active and responsive behaviour is key to microbial survival in porous environments, with far-reaching ramifications for developing strategies to mitigate anthropogenic impacts, innovate subsurface storage solutions,
This paper is concerned with non-uniform fully-mixed FEMs for dynamic coupled Stokes-Darcy model with the well-known Beavers-Joseph-Saffman (BJS) interface condition. In particular, a decoupled algorithm with the lowest-order mixed non-uniform FE approximations (MINI for the Stokes equation and RT0-DG0 for the Darcy equation) and the classical Nitsche-type penalty is studied. The method with the combined approximation of different orders is commonly used in practical simulations. However, the optimal error analysis of methods with non-uniform approximations for the coupled Stokes-Darcy flow model has remained challenging, although the analysis for uniform approximations has been well done. The key question is how the lower-order approximation to the Darcy flow influences the accuracy of the Stokes solution through the interface condition. In this paper, we prove that the decoupled algorithm provides a truly optimal convergence rate in L^2-norm in spatial direction: O(h^2) for Stokes velocity and O(h) for Darcy flow in the coupled Stokes-Darcy model. This implies that the lower-order approximation to the Darcy flow does not pollute the accuracy of numerical velocity for Stokes flow.
This paper presents a case study of microbe transportation in the Mars-satellites system. We examined the spatial distribution of potential impact-transported microbes on the Martian moons using impact physics by following a companion study (Fujita et al.). We used sterilization data from the precede studies. We considered that the microbes came mainly from the Zunil crater on Mars. We found that 70-80% of the microbes are likely to be dispersed all over the moon surface and are rapidly sterilized due to radiation except for those microbes within a thick ejecta deposit produced by meteoroids. The other 20-30% might be shielded from radiation by thick regolith layers that formed at collapsed layers in craters produced by Mars rock impacts. The total number of potentially surviving microbes at the thick ejecta deposits is estimated to be 3-4 orders of magnitude lower than at the Mars rock craters. The microbe concentration is irregular in the horizontal direction and is largely depth-dependent due to the radiation sterilization. The surviving fraction of transported microbes would be only 1 ppm on Phobos and 100 ppm on Deimos, suggesting that the transport processes and radiation sev
In a recent work (Dick et al, arXiv:2310.06187), we considered a linear stochastic elasticity equation with random Lamé parameters which are parameterized by a countably infinite number of terms in separate expansions. We estimated the expected values over the infinite dimensional parametric space of linear functionals ${\mathcal L}$ acting on the continuous solution $\vu$ of the elasticity equation. This was achieved by truncating the expansions of the random parameters, then using a high-order quasi-Monte Carlo (QMC) method to approximate the high dimensional integral combined with the conforming Galerkin finite element method (FEM) to approximate the displacement over the physical domain $Ω.$ In this work, as a further development of aforementioned article, we focus on the case of a nearly incompressible linear stochastic elasticity equation. To serve this purpose, in the presence of stochastic inhomogeneous (variable Lamé parameters) nearly compressible material, we develop a new locking-free symmetric nonconforming Galerkin FEM that handles the inhomogeneity. In the case of nearly incompressible material, one known important advantage of nonconforming approximations is that th
Correlation networks are commonly used to infer associations between microbes and metabolites. The resulting p-values are then corrected for multiple comparisons using existing methods such as the Benjamini and Hochberg procedure to control the false discovery rate (FDR). However, most existing methods for FDR control assume the p-values are weakly dependent. Consequently, they can have low power in recovering microbe-metabolite association networks that exhibit important topological features, such as the presence of densely associated modules. We propose a novel inference procedure that is both powerful for detecting significant associations in the microbe-metabolite network and capable of controlling the FDR. Power enhancement is achieved by modeling latent structures in the form of a bipartite stochastic block model. We develop a variational expectation-maximization algorithm to estimate the model parameters and incorporate the learned graph in the testing procedure. In addition to FDR control, this procedure provides a clustering of microbes and metabolites into modules, which is useful for interpretation. We demonstrate the merit of the proposed method in simulations and an ap
The present contribution aims at developing a non-overlapping Domain Decomposition (DD) approach to the solution of acoustic wave propagation boundary value problems based on the Helmholtz equation, on both bounded and unbounded domains. This DD solver, called Generalized Optimized Schwarz Method (GOSM), is a substructuring method, that is, the unknowns of an iteration are associated with the subdomains interfaces. We extend the analysis presented in a previous paper of one of the author to a fully discrete setting. We do not consider only a specific set of boundary conditions, but a whole class including, e.g., Dirichlet, Neumann, and Robin conditions. Our analysis will also cover interface conditions corresponding to a Finite Element Method - Boundary Element Method (FEM-BEM) coupling. In particular, we shall focus on three classical FEM-BEM couplings, namely the Costabel, Johnson-Nédélec and Bielak-MacCamy couplings. As a remarkable outcome, the present contribution yields well-posed substructured formulations of these classical FEM-BEM couplings for wavenumbers different from classical spurious resonances. We also establish an explicit relation between the dimensions of the ker
In this work, we analyze a penalized variant of the φ-FEM scheme for the Poisson equation with Dirichlet boundary conditions. The φ-FEM is a recently introduced unfitted finite element method based on a level-set description of the geometry, which avoids the need for boundary-fitted meshes. Unlike the original φ-FEM formulation, the method proposed here enforces boundary conditions through a penalization term. This approach has the advantage that the level-set function is required only on the cells adjacent to the boundary in the variational formulation. The scheme is stabilized using a ghost penalty technique. We derive a priori error estimates, showing optimal convergence in the H1 semi-norm and quasi-optimal convergence in the L2 norm under suitable regularity assumptions. Numerical experiments are presented to validate the theoretical results and to compare the proposed method with both the original φ-FEM and the standard fitted finite element method.
We establish a simple, rigorous, and easy to implement connection between the classical continuous finite element method (FEM) and the discontinuous Galerkin (DG) method for Poisson's problem. The key idea is to insert a vanishing-thickness layer of "dummy" elements along cell interfaces. By modifying the diffusion coefficient on these elements to be proportional to their thickness, we prove the FEM formulation converges to Babuška-Zlámal DG with trapezoidal edge quadrature. The scheme is trivial to implement by (i) a mesh edit that introduces degenerate interface elements and (ii) a single Jacobian threshold in an otherwise unmodified FEM code to handle the degenerate elements via the tempered finite element (TFEM) framework. We provide a rigorous derivation of the resulting TFEM-DG scheme, prove optimal $H^1$ and $L^2$ error estimates, and present numerical experiments in 2D and 3D. The method allows for simple implementation of DG in a FEM code and even adaptive element-by-element switching between FEM and DG with minimal coding effort. The framework is readily extensible, as we will demonstrate in a companion paper dedicated to evolutionary nonlinear first-order hyperbolic syst
The recent focus on microbes in human medicine highlights their potential role in the genetic framework of diseases. To decode the complex interactions among genes, microbes, and diseases, computational predictions of gene-microbe-disease (GMD) associations are crucial. Existing methods primarily address gene-disease and microbe-disease associations, but the more intricate triple-wise GMD associations remain less explored. In this paper, we propose a Heterogeneous Causal Metapath Graph Neural Network (HCMGNN) to predict GMD associations. HCMGNN constructs a heterogeneous graph linking genes, microbes, and diseases through their pairwise associations, and utilizes six predefined causal metapaths to extract directed causal subgraphs, which facilitate the multi-view analysis of causal relations among three entity types. Within each subgraph, we employ a causal semantic sharing message passing network for node representation learning, coupled with an attentive fusion method to integrate these representations for predicting GMD associations. Our extensive experiments show that HCMGNN effectively predicts GMD associations and addresses association sparsity issue by enhancing the graph's
Analysis of Galerkin-mixed FEMs for incompressible miscible flow in porous media has been investigated extensively in the last several decades. Of particular interest in practical applications is the lowest-order Galerkin-mixed method, { in which a linear Lagrange FE approximation is used for the concentration and the lowest-order Raviart-Thomas FE approximation is used for the velocity/pressure. The previous works only showed the first-order accuracy of the method in $L^2$-norm in spatial direction,} which however is not optimal and valid only under certain extra restrictions on both time step and spatial mesh. In this paper, we provide new and optimal $L^2$-norm error estimates of Galerkin-mixed FEMs for all three components in a general case. In particular, for the lowest-order Galerkin-mixed FEM, we show unconditionally the second-order { accuracy in $L^2$-norm} for the concentration. Numerical results for both two and three-dimensional models are presented to confirm our theoretical analysis. More important is that our approach can be extended to the analysis of mixed FEMs for many strongly coupled systems to obtain optimal error estimates for all components.
This paper concerns the inclusion of Newton's method into an adaptive finite element method (FEM) for the solution of nonlinear partial differential equations (PDEs). It features an adaptive choice of the damping parameter in the Newton iteration for the discretized nonlinear problems on each level ensuring both global linear and local quadratic convergence. In contrast to energy-based arguments in the literature, a novel approach in the analysis considers the discrete dual norm of the residual as a computable measure for the linearization error. As a consequence, this paper provides the first convergence analysis with optimal rates of an adaptive iteratively linearized FEM beyond energy-minimization problems. The presented theory applies to strongly monotone operators with locally Lipschitz continuous Fréchet derivative. We present a class of semilinear PDEs fitting into this framework and provide numerical experiments to underline the theoretical results.
The Finite Element Method (FEM) is a powerful computational tool for solving partial differential equations (PDEs). Although commercial and open-source FEM software packages are widely available, an independent implementation of FEM provides significant educational value, provides a deeper understanding of the method, and enables the development of custom solutions tailored to specialized applications or integration with other solvers. This work introduces a 3D $\mathbb{P}_m$-element FEM implementation in MATLAB/Octave that is designed to balance educational clarity with computational efficiency. A key feature is its integration with GMSH, an open-source 3D mesh generator with CAD capabilities that streamlines mesh generation for complex geometries. By leveraging GMSH data structures, we provide a seamless connection between geometric modeling and numerical simulation. The implementation focuses on solving the general convection-diffusion-advection equation and serves as a flexible foundation for addressing advanced problems, including elasticity, mixed formulations, and integration with other numerical methods.
We verify quasi-optimality of the Crouzeix-Raviart FEM for nonlinear problems of $p$-Laplace type. More precisely, we show that the error of the Crouzeix-Raviart FEM with respect to a quasi-norm is bounded from above by a uniformly bounded constant times the best-approximation error plus a data oscillation term. As a byproduct, we verify a novel more localized a priori error estimate for the conforming lowest-order Lagrange FEM.
We propose a novel technique to probe shape of a single microbe embedded in a nematic liquid crystal (NLC) sample by observing geometry of dark brushes with optical microscope using a cross-polarizer set up. Assuming certain anchoring conditions for the NLC director at the surface of the microbe, we determine the resulting shapes of brushes using numerical simulations. Our results suggest that for asymmetrical microbes (such as cylindrical shaped bacteria/viruses), resulting brushes may carry the imprints of this asymmetry (e.g. the aspect ratio of cylindrical shape) at relatively large distances to be able to be seen using simple optical microscopy even for microbe sizes in few tens to few hundred nanometer range.
Organic material in anoxic sediment represents a globally significant carbon reservoir that acts to stabilize Earth's atmospheric composition. The dynamics by which microbes organize to consume this material remain poorly understood. Here we observe the collective dynamics of a microbial community, collected from a salt marsh, as it comes to steady state in a two-dimensional ecosystem, covered by flowing water and under constant illumination. Microbes form a very thin front at the oxic-anoxic interface that moves towards the surface with constant velocity and comes to rest at a fixed depth. Fronts are stable to all perturbations while in the sediment, but develop bioconvective plumes in water. We observe the transient formation of parallel fronts. We model these dynamics to understand how they arise from the coupling between metabolism, aerotaxis, and diffusion. These results identify the typical timescale for the oxygen flux and penetration depth to reach steady state.
We are interested in time-harmonic acoustic scattering by an impenetrable obstacle in a medium where the wavenumber is constant in an exterior unbounded subdomain and is possibly heterogeneous in a bounded subdomain. The associated Helmholtz boundary value problem can be solved by coupling the Finite Element Method (FEM) in the heterogeneous subdomain with the Boundary Element Method (BEM) in the homogeneous subdomain. Recently, we designed and analyzed a new substructured FEM-BEM formulation, called Generalized Optimized Schwarz Method (GOSM). Unfortunately, it is well known that, even when the initial boundary value problem is well-posed, the variational formulation of classical FEM-BEM couplings can be ill-posed for certain wavenumbers, called spurious resonances. In this paper, we focus on the Johnson-Nédélec and Costabel couplings and show that the GOSM derived from both is not immune to that issue. In particular, we give an explicit expression of the kernel of the local operator associated with the interface between the FEM and BEM subdomains. That kernel and the one of classical FEM-BEM couplings are simultaneously non-trivial.
Researchers have discovered that beneficial soil bacteria give plants an unexpected survival advantage in salty soils。 Instead of helping plants keep salt out, the microbes stimulate the production of lignin, a natural compound that strengthens roots and makes plants more resilient。 Greenhouse and field tests showed healthier plants and higher yiel
Physics-Informed Neural Networks (PINNs) solve partial differential equations (PDEs) by embedding governing equations and boundary/initial conditions into the loss function. However, enforcing Dirichlet boundary conditions accurately remains challenging, often leading to soft enforcement that compromises convergence and reliability in complex domains. We propose a hybrid approach, PINN-FEM, which combines PINNs with finite element methods (FEM) to impose strong Dirichlet boundary conditions via domain decomposition. This method incorporates FEM-based representations near the boundary, ensuring exact enforcement without compromising convergence. Through six experiments of increasing complexity, PINN-FEM outperforms standard PINN models, showcasing superior accuracy and robustness. While distance functions and similar techniques have been proposed for boundary condition enforcement, they lack generality for real-world applications. PINN-FEM bridges this gap by leveraging FEM near boundaries, making it well-suited for industrial and scientific problems.