Martino S. Centonze | Searcharxiv

arXiv2026

Contagion Effects of Heterogeneous Cyber Risk on Network Security and Systemic Stability

Understanding how heterogeneous cyber risk shapes security investments and contagion is a key challenge for the resilience of interconnected digital systems. Existing studies on cybersecurity investments and network contagion typically rely on homogeneous assets, uniform attack incentives, or non-strategic threat propagation. We develop a Stackelberg security game that combines contagion dynamics with heterogeneous cyber risk, allowing attackers and defenders to assign different values to network nodes, reflecting differences in asset criticality, information, and objectives. We characterize the equilibrium allocation of cybersecurity investments and derive an analytical approximation for the optimal defense strategy based on endogenous network protection metrics. We show that cyber-risk heterogeneity significantly affects attack incentives and resource allocation, while neglecting it leads to systematic defense misallocation. Our results suggest that cybersecurity policies should leverage both actual and perceived differences in node criticality, as cyber-deception mechanisms can create strategic misperceptions that redirect attacks and enhance systemic resilience.

cs.CR↗

arXiv2025

On the supra-linear storage in dense networks of grid and place cells

Place-cell networks, typically forced to pairwise synaptic interactions, are widely studied as models of cognitive maps: such models, however, share a severely limited storage capacity, scaling linearly with network size and with a very small critical storage. This limitation is a challenge for navigation in 3-dimensional space because, oversimplifying, if encoding motion along a one-dimensional trajectory embedded in 2-dimensions requires $O(K)$ patterns (interpreted as bins), extending this to a 2-dimensional manifold embedded in a 3-dimensional space -- yet preserving the same resolution -- requires roughly $O(K^2)$ patterns, namely a supra-linear amount of patterns. In these regards, dense Hebbian architectures, where higher-order neural assemblies mediate memory retrieval, display much larger capacities and are increasingly recognized as biologically plausible, but have never linked to place cells so far. Here we propose a minimal two-layer model, with place cells building a layer and leaving the other layer populated by neural units that account for the internal representations (so to qualitatively resemble grid cells in the MEC of mammals): crucially, by assuming that each place cell interacts with pairs of grid cells, we show how such a model is formally equivalent to a dense Battaglia-Treves-like Hebbian network of grid cells only endowed with four-body interactions. By studying its emergent computational properties by means of statistical mechanics of disordered systems, we prove -- analytically -- that such effective higher-order assemblies (constructed under the guise of biological plausibility) can support supra-linear storage of continuous attractors; furthermore, we prove -- numerically -- that the present neural network is capable of recognition and navigation on general surfaces embedded in a 3-dimensional space.

cond-mat.dis-nn↗