Related papers: Emergent Topological Complexity in the Barabasi-Al…
A transition from asymmetric to symmetric patterns in time-dependent extended systems is described. It is found that one dimensional cellular automata, started from fully random initial conditions, can be forced to evolve into complex…
Biomolecular structure comparison not only reveals evolutionary relationships, but also sheds light on biological functional properties. However, traditional definitions of structure or sequence similarity always involve superposition or…
Real growing networks like the WWW or personal connection based networks are characterized by a high degree of clustering, in addition to the small-world property and the absence of a characteristic scale. Appropriate modifications of the…
The non-trivial topological features in the energy band of non-Hermitian systems provide promising pathways to achieve robust physical behaviors in classical or quantum open systems. A key topological feature, unique to non-Hermitian…
We present a coherent and consistent framework for explicit time-dependence in non-Hermitian quantum mechanics. The area of non-Hermitian quantum mechanics has been growing rapidly over the past twenty years. This has been driven by the…
The organization of interactions in complex systems can be described by networks connecting different units. These graphs are useful representations of the local and global complexity of the underlying systems. The origin of their…
Recently, some studies started to unveil the wealthy of interactions that occur between groups of nodes when looking at the small scale of interactions taking place in complex networks. Such findings claim for a new systematic methodology…
We consider the ferromagnetic large-$q$ state Potts model in complex evolving networks, which is equivalent to an optimal cooperation problem, in which the agents try to optimize the total sum of pair cooperation benefits and the supports…
Amorphous topological states, which are independent of the specific spatial distribution of microscopic constructions, have gained much attention. Recently, higher-order topological insulators, which are a new class of topological phases of…
The approximate homogeneity of spatial sections of the Universe is well supported observationally, but the inhomogeneity of the spatial sections is even better supported. Here, we consider the implications of inhomogeneity in dust models…
Complex molecules and mesoscopic structures are naturally described by general networks of elementary building blocks and tight-binding is one of the simplest quantum model suitable for studying the physical properties arising from the…
We develop a unified view of topological phase transitions (TPTs) in solids by revising the classical band theory with the inclusion of topology. Re-evaluating the band evolution from an "atomic crystal" [a normal insulator (NI)] to a solid…
Critical phenomena can show unusual phase diagrams when defined in complex network topologies. The case of classical phase transitions such as the classical Ising model and the percolation transition has been studied extensively in the last…
We quantify the topological expansion properties of bounded degree simplicial complexes in terms of a family of sublinear functions, in analogy with the separation profile of Benjamini-Schramm-Tim\'ar for classical expansion of bounded…
Dense Associative Memory (DAM) models generalize the classical Hopfield model by incorporating n-body or exponential interactions that greatly enhance storage capacity. While the criticality of DAM models has been largely investigated,…
Non-Hermitian systems have been at the center of intense research for over a decade, partly due to their nontrivial energy topology formed by intersecting Riemann manifolds with branch points known as exceptional points (EPs). This spectral…
In the past decades, topological concepts have emerged to classify matter states beyond the Ginzburg-Landau symmetry breaking paradigm. The underlying global invariants are usually characterized by integers, such as Chern or winding…
We develop a theoretical description of non-Hermitian time evolution that accounts for the break- down of the adiabatic theorem. We obtain closed-form expressions for the time-dependent state amplitudes, involving the complex eigen-energies…
The degree distributions of many real world networks follow power-laws whose exponents tend to fall between two and three. Within the framework of the Barabasi-Albert model (BA model), we explain this empirical observation by a simple fact.…
Real-world networks process structured connections since they have non-trivial vertex degree correlation and clustering. Here we propose a toy model of structure formation in real-world weighted network. In our model, a network evolves by…