Nikos I. Kavallaris

Urban road networks are highly sensitive to flooding, yet the systemic consequences of inundation on their structural and functional organization remain insufficiently understood. This study introduces a scale-independent analytical framework that integrates complex network measures such as degree, closeness, and betweenness centrality with community-structure analysis to quantify how flooding transforms network connectivity, accessibility, and mesoscale cohesion. This study assesses the impact of river flooding on the urban road network under two scenarios: a 100-year return period flood and the maximum probable scenario (BHF- Beräknat Högsta Flöde), which corresponds to an estimated extreme event with an approximate return period of 10,000 years. Our analysis shows that inundation under the two flood scenarios can generate non-linear and disproportionate impacts on connectivity, accessibility, and overall network cohesion. Specifically, our method: (a) localizes critically isolated nodes exposed to high risk; (b) identifies structural changes, showing that the flooded network is divided into three main large subnetworks with specific epicenters, along with 263 smaller subnetworks in the 100-year case and 553 in the BHF case; (c) estimates that network inefficiency, interpreted as analogous to mean travel time to a destination, increases by 120% and 170% for the 100-year and BHF scenarios, respectively; and (d) localizes critical roads that may serve as potential corridors during evacuation planning. These results offer actionable insights for disaster risk reduction, including planning for neighborhood-scale isolation, identifying vulnerable corridors, and designing redundant and decentralized emergency access routes. The framework is transferable to other urban areas where flood maps and road network data are available, supporting risk-informed spatial planning and strengthened civil protection.

We introduce a mechanistic, nonlocal tumour-growth model designed specifically to capture explosive dynamics that are not adequately explained by standard logistic reaction–diffusion descriptions. The motivation is empirical: the universal scaling law reported in [1] provides compelling cross-sectional evidence of superlinear tumour activity versus tumour burden, but as a phenomenological relationship it does not by itself supply a dynamical mechanism, nor does it rigorously describe how explosive growth emerges, how fast it develops, or how spatial interactions and tissue boundaries influence it. Our model addresses this gap by incorporating nonlocal proliferative feedback—cells respond to a spatially aggregated neighbourhood signal—and a singular, Kawarada-type acceleration that produces “quenching”: tumour density stays bounded while the proliferative drive becomes unbounded as the aggregated signal approaches a critical threshold. This offers a concrete mechanistic route to explosive escalation consistent with physical boundedness. We analyse the model under no-flux (Neumann) boundary conditions, appropriate for reflecting tissue interfaces. In the spatially homogeneous setting we prove finite-time onset of the explosive regime and obtain explicit rates for how rapidly it is approached. For spatially heterogeneous perturbations we derive a transparent spectral stability theory showing how the interaction kernel selects spatial scales and how the singular acceleration tightens stability margins as the explosive threshold is approached. These results provide interpretable links between nonlocal interaction structure, boundary effects, and the emergence of rapid growth. Finally, to connect mechanism to data in the spirit of [1], we embed the model in a Bayesian inference framework that treats the interaction kernel and the acceleration strength as unknown and learned from tumour-growth observations. This enables uncertainty-aware estimation of explosive onset times, escalation rates, and stability margins, while positioning the scaling law of [1] as an observable signature that our mechanistic model can explain and quantify rather than merely fit.

In this work, we present a computational framework for exploring and analyzing the macroscopic dynamics of complex agent-based network models by integrating Topological Data Analysis with the Equation-Free Method. To demonstrate the effectiveness of our method, we apply it to Erdős--Rényi-type random networks. Central to our approach is a Topological Data Analysis-based filtration process driven by the density of activated network nodes (agents), from which we extract a coarse-grained macroscopic topological observable. This observable is defined via persistent Betti numbers, thus requiring significantly reduced data dimensionality while retaining essential topological features. Subsequently, within the Equation-Free Method framework, we show firstly that a \textit{lifting procedure} can be achieved using topological properties and secondly, a data-driven evolution law that governs the dynamics of this macroscopic variable. Finally, we perform a numerical bifurcation and stability analysis to investigate the global behavior and qualitative transitions of the emergent macroscopic dynamics.

The purpose of the current paper is to unveil the key mechanism which is responsible for the occurrence of Turing-type instability for a nonlocal Fisher-KPP model. In particular, we prove that the solution of the considered nonlocal Fisher-KPP equation in the neighborhood of a constant stationary solution is destabilized via a diffusion-driven blow-up. It is also shown that the observed diffusion-driven blow-up is complete, while its blow-up rate is completely classified. Finally, the detected diffusion-driven instability results in the formation of unstable blow-up patterns, which are also identified through the determination of the blow-up profile of the solution.

In the current work, we study a stochastic parabolic problem. The presented problem is motivated by the study of an idealised electrically actuated MEMS (Micro-Electro-Mechanical System) device in the case of random fluctuations of the potential difference, a parameter that actually controls the operation of MEMS device. We first present the construction of the mathematical model, and then, we deduce some local existence results. Next for some particular versions of the model, relevant to various boundary conditions, we derive quenching results as well as estimations of the probability for such singularity to occur. Additional numerical study of the problem in one dimension follows, which also allows the further investigation the problem with respect to its quenching behaviour.