arXiv subjects

Vasilii Tiselko

Publications and source records attributed to Vasilii Tiselko.

3 recordsLinked to original sources

arXiv2026

Griffiths phase in clique percolation in random geometric graphs

In this study, we discuss the clique percolation in the ensembles of random geometric graphs with different kernels that quantify the geometrical constraints. For the sharp cut-off we find the wide Griffiths phase of extended criticality with the power-law behavior. One boundary of the Griffiths phase is the generalization of a percolation critical point for the ER ensemble when the percolation within the large but finite cluster emerges. The second boundary corresponds to the point in the parameter space when the percolation in the entire clustered system becomes available. For the power-law kernel, richer behavior with a clique-size-dependent boundary between the effective ER and geometric regimes has been identified. The Griffiths phase in this case exists as well. Finally, the pattern with the exponential kernel has been analyzed. We briefly discuss the possible applications of our findings.

cond-mat.dis-nn↗

arXiv2025

Neural Receptive Fields, Stimulus Space Embedding and Effective Geometry of Scale-Free Networks

Understanding how receptive fields emerge and organize within brain networks and how neural dynamics couple with stimuli space is fundamental to neuroscience. Models often rely on fine-tuning connectivity to match empirical data, which may limit biological plausibility. Here we propose a physiologically grounded alternative where receptive fields and population-level attractor dynamics arise naturally from the effective hyperbolic geometry of scale-free networks. By associating stimulus space with the boundary of a hyperbolic embedding, we simulate neural dynamics using rate-based and spiking models, revealing localized activity patterns that reflect stimulus space structure without synaptic fine-tuning. The resulting receptive fields follow experimentally observed statistics and properties, and their sizes depends on neuron's connectivity degree. The model generalizes across stimuli dimensionalities and various modalities, such as orientation and place selectivity. Experimental analyses of hippocampal place fields recorded on a linear track support these findings. This framework offers a novel organizing principle linking network structure, stimulus space encoding, and neural dynamics, providing insights into receptive field formation across diverse brain areas.

q-bio.NC↗

arXiv2023

Localization transition in non-Hermitian systems depending on reciprocity and hopping asymmetry

We studied the single-particle Anderson localization problem for non-Hermitian systems on directed graphs. Random regular graph and various undirected standard random graph models were modified by controlling reciprocity and hopping asymmetry parameters. We found the emergence of left, biorthogonal and right localized states depending on both parameters and graph structure properties such as node degree $d$. For directed random graphs, the occurrence of biorthogonal localization near exceptional points is described analytically and numerically. The clustering of localized states near the center of the spectrum and the corresponding mobility edge for left and right states are shown numerically. Structural features responsible for localization, such as topologically invariant nodes or drains and sources, were also described. Considering the diagonal disorder, we observed the disappearance of localization dependence on reciprocity around $W \sim 20$ for a random regular graph $d=4$. With a small diagonal disorder, the average biorthogonal fractal dimension drastically reduces. Around $W \sim 5$ localization scars occur within the spectrum, alternating as vertical bands of clustering of left and right localized states.

cond-mat.dis-nn↗