Models of soil organic carbon (SOC) frequently overlook the effects of spatial dimensions and microbiological activities. In this paper, we focus on two reaction-diffusion chemotaxis models for SOC dynamics, both supporting chemotaxis-driven instability and exhibiting a variety of spatial patterns as stripes, spots and hexagons when the microbial chemotactic sensitivity is above a critical threshold. We use symplectic techniques to numerically approximate chemotaxis-driven spatial patterns and explore the effectiveness of the piecewise Dynamic Mode Decomposition (pDMD) to reconstruct them. Moreover, we analyse the predictive performance of the pDMD for moderate time horizons. Our findings show that pDMD is effective at precisely recreating and predicting chemotaxis-driven spatial patterns, therefore broadening the range of application of the method to classes of solutions different than Turing patterns. By validating its efficacy across a wider range of models, this research lays the groundwork for applying pDMD to experimental spatiotemporal data, advancing predictions crucial for soil microbial ecology and agricultural sustainability.

We study pattern formation in a chemotaxis model of bacteria and soil carbon dynamics as an example system where transient dynamics can give rise to pattern formation outside of Turing unstable regimes. We use a detailed analysis of the reactivity of the non-spatial and spatial dynamics, stability analyses, and numerical continuation to uncover detailed aspects of this system’s pattern-forming potential. In addition to patterning in Turing unstable parameter regimes, reactivity of the spatial system can itself lead to a range of parameters where a spatially uniform state is asymptotically stable, but exhibits transient growth that can induce pattern formation. We show that this occurs in the bistable region of a subcritical Turing bifurcation. Intriguingly, such bistable regions appear in two spatial dimensions, but not in a one-dimensional domain, suggesting important interplays between geometry, transient growth, and the emergence of multistable patterns. We discuss the implications of our analysis for the bacterial soil organic carbon system, as well as for reaction-transport modeling more generally.

Dynamic Mode Decomposition (DMD) is an equation-free method that aims at reconstructing the best linear fit from temporal datasets. In this paper, we show that DMD does not provide accurate approximation for datasets describing oscillatory dynamics, like spiral waves, relaxation oscillations and spatio-temporal Turing instability. Inspired by the classical “divide and conquer” approach, we propose a piecewise version of DMD (pDMD) to overcome this problem. The main idea is to split the original dataset in N submatrices and then apply the exact (randomized) DMD method in each subset of the obtained partition. We describe the pDMD algorithm in detail and we introduce some error indicators to evaluate its performance when N is increased. Numerical experiments show that very accurate reconstructions are obtained by pDMD for datasets arising from time snapshots of certain reaction-diffusion PDE systems, like the FitzHugh-Nagumo model, a λ-ω system and the DIB morpho-chemical system for battery modeling. Finally, a discussion about the overall computational load and the future prediction features of the new algorithm is also provided.

Bursting behaviors, driven by environmental variability, can substantially influence ecosystem services and functions and have the potential to cause abrupt population breakouts in host-parasitoid systems. We explore the impact of environment on the host-parasitoid interaction by investigating separately the effect of grazing-dependent habitat variation on the host density and the effect of environmental fluctuations on the average host population growth rate. We hence focus on the discrete host-parasitoid Beddington-Free-Lawton model and show that a more comprehensive mathematical study of the dynamics behind the onset of on-off intermittency in host-parasitoid systems may be achieved by considering a deterministic, chaotic system that represents the dynamics of the environment. To this aim, some of the key model parameters are allowed to vary in time according to an evolution law that can exhibit chaotic behavior. Fixed points and stability properties of the resulting 3D nonlinear discrete dynamical system are investigated and on-off intermittency is found to emerge strictly above the blowout bifurcation threshold. We show, however, that, in some cases, this phenomenon can also emerge in the sub-threshold. We hence introduce the novel concept of long-term reactivity and show that it can be considered as a necessary condition for the onset of on-off intermittency. Investigations in the time-dependent regimes and kurtosis maps are provided to support the above results. Our study also suggests how important it is to carefully monitor environmental variability caused by random fluctuations in natural factors or by anthropogenic disturbances in order to minimize its effects on throphic interactions and protect the potential function of parasitoids as biological control agents.

Ecological systems are subject to environmental variability and fluctuations: understanding the role of such stochastic perturbations in inducing on–off intermittency is the central motivation for this study. This research extends the exploration of parameters leading to the emergence of on–off intermittency within a discrete Beddington-Free-Lawton host-parasitoid model. We introduce random perturbation factors that impact both the grazing intensity and the growth rate of the host population. An intriguing aspect of this study is the numerical evidence of the reactivity of the free-parasitoid fixed point as a route to on–off intermittency. This finding is significant because it sheds light on how stable ecological equilibria can transition into intermittency before progressing toward chaotic behaviour. Moreover, our study explores the host-parasitoid coupling within the Beddington-Free-Lawton model when it is applied to a complex network, a significant framework for modelling ecological interactions. The paper reveals that such network-based interactions induce parasitoid bursts that are not observed in a single population scenario.

The volume collects the long abstracts of the 79 contributions presented during the fourth edition of the “Young Applied Mathematicians Conference” (YAMC, www.yamc.it). Organized in Rome under the sponsorship of the Institute for Applied Mathematics (IAC) of the CNR and the Department of Mathematics at Sapienza, University of Rome, the conference took place from September 16 to 20, 2024, and brought together primarily young researchers (students, PhD candidates, post-docs, etc.) from 37 universities and research centers across 8 countries. This volume is intended to promote the communication of the research presented in the field of applied mathematics, with a primary focus on numerical analysis, artificial intelligence, statistics, and mathematical modeling.

Vitamin D has been proven to be a strong stimulator of mechanisms associated with the elimination of pathogens. Because of its recognized effectiveness against viral infections, during SARS-CoV-2 infection, the effects of Vitamin D supplementation have been the object of debate. This study aims to contribute to this debate by the means of a qualitative phenomenological mathematical model in which the role of Vitamin D and its interactions with the innate immune system are explicitly considered. We show that Vitamin D influx and degradation can be considered as possible control parameters for the disease evaluation and recovery. By varying Vitamin D influx, three dynamical scenarios have been found with different modalities of recovery from the disease. Inside each scenario, Vitamin D degradation has been related to different degrees of severity in disease development. Interestingly, the emergence of hysteretic phenomenologies when Vitamin D influx is too low can be related to the onset of Long-COVID syndrome, confirming clinical evidence from recent studies on the topic.

We investigate a suitable application of Model Order Reduction (MOR) techniques for the numerical approximation of Turing patterns, that are stationary solutions of reaction-diffusion PDE (RD-PDE) systems. We show that solutions of surrogate models built by classical Proper Orthogonal Decomposition (POD) exhibit an unstable error behaviour over the dimension of the reduced space. To overcome this drawback, first of all, we propose a POD-DEIM technique with a correction term that includes missing information in the reduced models. To improve the computational efficiency, we propose an adaptive version of this algorithm in time that accounts for the peculiar dynamics of the RD-PDE in presence of Turing instability. We show the effectiveness of the proposed methods in terms of accuracy and computational cost for a selection of RD systems, i.e., FitzHugh-Nagumo, Schnakenberg and the morphochemical DIB models, with increasing degree of nonlinearity and more structured patterns.

Next-generation battery research will heavily rely on physico-chemical models, combined with deep learning methods and high-throughput and quantitative analysis of experimental datasets, encoding spectral information in space and time. These tasks will require highly efficient computational approaches, to yield rapidly accurate approximations of the models. This paper explores the capabilities of a representative range of model reduction techniques to face this problem in the case of a well-assessed electrochemical phase-formation model. We consider the Proper Orthogonal Decomposition (POD) with a Galerkin projection and the Dynamic Mode Decomposition (DMD) techniques to deal first of all with a semi-linear heat equation 2D in space as a test problem. As an application, we show that it is possible to save computational time by applying POD-Galerkin for different choices of the parameters without recalculating the snapshot matrix. Finally, we consider two reaction–diffusion (RD) PDE systems with Turing-type dynamics: the well-known Schnackenberg model and the DIB model for electrochemical phase formation. We show that their reduced models obtained by POD and DMD with suitable low-dimensional projections are able to approximate carefully both the Turing patterns at the steady state and the reactivity dynamics in the transient regime. Finally, for the DIB model we show that POD-Galerkin applied for different choices of parameters, by calculating once the snapshot matrices, is able to find reduced Turing patterns of different morphology.

Background: Radiotherapy (RT) plays a fundamental role in the treatment of pediatric central nervous system (CNS) malignancies, but its late sequelae are still a challenging question. Despite developments in modern high-conformal photon techniques and proton beam therapy (PBT) are improving the normal tissues dose-sparing while maintaining satisfactory target coverage, clinical advantages supporting the optimal treatment strategy have to be better evaluated in long-term clinical studies and assessed in further radiobiological analyses. Our analysis aimed to systematically review current knowledge on the dosimetric advantages of PBT in the considered setting, which should be the basis for future specific studies. Materials and methods: A PubMed and Google Scholar search was conducted in June 2019 to select dosimetric studies comparing photon versus proton RT for pediatric patients affected by CNS tumors. Then, a systematic review and meta-analysis according to the PRISMA statement was performed. Average and standard deviation values of Conformity Index, Homogeneity Index, and mean and maximum doses to intracranial and extracranial organs at risk (OARs) were specifically evaluated for secondary dosimetric comparisons. The standardized mean differences (SMDs) for target parameters and the mean differences (MDs) for OARs were summarized in forest plots (P < 0.05 was considered statistically significant). Publication bias was also assessed by the funnel plot and Egger's regression test. Results: Among the 88 identified papers, a total of twelve studies were included in the meta-analysis. PBT showed dosimetric advantages in target homogeneity (significant especially in the subgroup comparing PBT and 3D conformal RT), as well as in the dose sparing of almost all analyzed OARs (significantly superior results for brainstem, normal brain, and hippocampal dose constraints and for extracranial OARs parameters, excluding the kidneys). Publication bias was observed for Conformity Index. Conclusion: Our analysis supports the evidence of dosimetric advantages of PBT over photon RT, especially in the dose sparing of normal growing tissues. Confirmations from wider well-designed studies are required.