Related papers: Homological percolation transitions in growing sim…
We investigate the decay of spatial correlations of $\mathcal{PT}$-symmetric non-Hermitian one-dimensional models that host higher-order exceptional points. Beyond a certain correlation length, they develop anomalous power-law behavior that…
Topological event detection allows for the distributed computation of homology by focusing on local changes occurring in a network over time. In this paper, a model for the monitoring of topological events in dynamically changing regions…
The dynamics of a 2D site percolation model on a square lattice is studied using the hierarchical approach introduced by Gabrielov et al., Phys. Rev. E, 60, 5293-5300, 1999. The key elements of the approach are the tree representation of…
To highlight certain similarities in combinatorial representations of several well known two-dimensional models of statistical mechanics, we introduce and study a new family of models which specializes to these cases after a proper tuning…
Graphs serve as powerful tools for modeling pairwise interactions in diverse fields such as biology, material science, and social networks. However, they inherently overlook interactions involving more than two entities. Simplicial…
We present a symmetry-adapted perturbation theory (SAPT) for the interaction of two high-spin open-shell molecules (described by their restricted open-shell Hartree-Fock determinants) resulting in low-spin states of the complex. The…
The rich set of interactions between individuals in the society results in complex community structure, capturing highly connected circles of friends, families, or professional cliques in a social network. Thanks to frequent changes in the…
Network topology is a flourishing interdisciplinary subject that is relevant for different disciplines including quantum gravity and brain research. The discrete topological objects that are investigated in network topology are simplicial…
Social fragmentation transition is a transition of social states between many disconnected communities with distinct opinions and a well-connected single network with homogeneous opinions. This is a timely research topic with high relevance…
Percolation in a scale-free hierarchical network is solved exactly by renormalization-group theory, in terms of the different probabilities of short-range and long-range bonds. A phase of critical percolation, with algebraic…
The quintessential property of neuronal systems is their intensive patterns of selective synaptic connections. The current work describes a physics-based approach to neuronal shape modeling and synthesis and its consideration for the…
In this paper we study the small-world network model of Watts and Strogatz, which mimics some aspects of the structure of networks of social interactions. We argue that there is one non-trivial length-scale in the model, analogous to the…
The past two decades have seen significant successes in our understanding of complex networked systems, from the mapping of real-world social, biological and technological networks to the establishment of generative models recovering their…
Using a set of $\Lambda$CDM simulations of cosmic structure formation, we study the evolving connectivity and changing topological structure of the cosmic web using state-of-the-art tools of multiscale topological data analysis (TDA). We…
In view of the important role helix-sheet transitions play in protein aggregation, we introduce a simple model to study secondary structural transitions of helix-coil-sheet systems using a Potts model starting with an effective Hamiltonian.…
Since the discovery a half century ago that 1/r^2-type long-range interactions in the one-dimensional Ising model change the phase transition type, long-range interactions in diverse systems have received considerable attention. Recently,…
Phase transitions are a central theme of statistical mechanics, and of probability more generally. Lattice spin models represent a general paradigm for phase transitions in finite dimensions, describing ferromagnets and even some fluids…
Simplicial complexes are a popular tool used to model higher-order interactions between elements of complex social and biological systems. In this paper, we study some combinatorial aspects of a class of simplicial complexes created by a…
Multilayer infrastructure is often interdependent, with nodes in one layer depending on nearby nodes in another layer to function. The links in each layer are often of limited length, due to the construction cost of longer links. Here, we…
To understand mesoscopic scaling in networks, we study the hierarchical configuration model (HCM), a random graph model with community structure. The connections between the communities are formed as in a configuration model. We study the…