Related papers: Quantum statistics in Network Geometry with Fracti…
Complex networks can be used to represent complex systems which originate in the real world. Here we study a transformation of these complex networks into simplicial complexes, where cliques represent the simplices of the complex. We extend…
Both, spin and statistics of a quantum system can be seen to arise from underlying (quantum) group symmetries. We show that the spin-statistics theorem is equivalent to a unification of these symmetries. Besides covering the Bose-Fermi case…
Geometry of networks endowed with a causal structure is discussed using the conventional framework of equilibrium statistical mechanics. The popular growing network models appear as particular causal models. We focus on a class of tree…
In the context of canonical quantum gravity in 3+1 dimensions, we introduce a new notion of bubble network that represents discrete 3d space geometries. These are natural extensions of twisted geometries, which represent the geometrical…
Many real-world networks are theorized to have core-periphery structure consisting of a densely-connected core and a loosely-connected periphery. While this phenomenon has been extensively studied in a range of scientific disciplines, it…
We study the problem of detecting latent geometric structure in random graphs. To this end, we consider the soft high-dimensional random geometric graph $\mathcal{G}(n,p,d,q)$, where each of the $n$ vertices corresponds to an independent…
Understanding the intricate architecture of brain networks and its connection to brain function is essential for deciphering the underlying principles of cognition and disease. While traditional graph-theoretical measures have been widely…
Identical quantum particles exhibit only two types of statistics: bosonic and fermionic. Theoretically, this restriction is commonly established through the symmetrization postulate or (anti)commutation constraints imposed on the algebra of…
As one of the main subjects of investigation in data science, network science has been demonstrated a wide range of applications to real-world networks analysis and modeling. For example, the pervasive presence of structural or topological…
Quantum information geometry studies families of quantum states by means of differential geometry. A new approach is followed with the intention to facilitate the introduction of a more general theory in subsequent work. To this purpose,…
We investigate the thermodynamic geometry of classical and quantum ideal gases in the relativistic regime, with particular emphasis on the effects of particle mass and spatial dimensionality. Relativistic kinematics is incorporated through…
We consider the fractal characteristic of the quantum mechanical paths and we obtain for any universal class of fractons labeled by the Hausdorff dimension defined within the interval 1$ $$ < $$ $$h$$ $$ <$$ $$ 2$, a fractal distribution…
In the past decade, geometric network models have received vast attention in the literature. These models formalize the natural idea that similar vertices are likely to connect. Because of that, these models are able to adequately capture…
We propose a semiparametric model for dyadic link formations in directed networks. The model contains a set of degree parameters that measure different effects of popularity or outgoingness across nodes, a regression parameter vector that…
This paper describes how realistic neuromorphic networks can have their connectivity properties fully characterized in analytical fashion. By assuming that all neurons have the same shape and are regularly distributed along the…
Quantum network is a set of nodes connected with channels, through which the nodes communicate photons and classical information. Classical structural complexity of a quantum network may be defined through its physical structure, i.e.…
Network models with latent geometry have been used successfully in many applications in network science and other disciplines, yet it is usually impossible to tell if a given real network is geometric, meaning if it is a typical element in…
Equation of state with quantum statistics corrections is derived for systems of the Fermi and Bose particles by using their van der Waals (vdW) and effective density-dependent Skyrme mean-field interactions. First few orders of these…
Exchangeability is a desired statistical property of network ensembles requiring their invariance upon relabelling of the nodes. However combining sparsity of network ensembles with exchangeability is challenging. Here we propose a…
We investigate simplicial complexes deterministically growing from a single vertex. In the first step, a vertex and an edge connecting it to the primordial vertex are added. The resulting simplicial complex has a 1-dimensional simplex and…