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A model is discussed where all operators are constructed from a quantum scalar field whose energy spectrum takes on all real values. The Schr\"odinger picture wave function depends upon space and time coordinates for each particle, as well…
One of the main results of Scale Relativity as regards the foundation of quantum mechanics is its explanation of the origin of the complex nature of the wave function. The Scale Relativity theory introduces an explicit dependence of…
Recently, a novel model to describe ordering in systems comprising agents which, although matching in their binarity (i.e., maintaining the iconic Ising features of ``+'' or ``-'', ``up'' or ``down'', ``yes'' or ``no''), still differing in…
We study diffusion (random walks) on recursive scale-free graphs, and contrast the results to similar studies in other analytically soluble media. This allows us to identify ways in which diffusion in scale-free graphs is special. Most…
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…
Scaling behavior of scale-free evolving networks arising in communications, citations, collaborations, etc. areas is studied. We derive universal scaling relations describing properties of such networks and indicate limits of their…
The increased availability of data on real networks has favoured an explosion of activity in the elaboration of models able to reproduce both qualitatively and quantitatively the measured properties. What has been less explored is the…
Scale-free networks are prevalently observed in a great variety of complex systems, which triggers various researches relevant to networked models of such type. In this work, we propose a family of growth tree networks $\mathcal{T}_{t}$,…
In general, the laws of physics are not invariant under a change of scale. To find out whether the 'scale-invariance hypothesis' corresponds to nature or not, a careful examination to its implications is required. As a consequence, the…
We study the imaginary-time relaxation critical dynamics of a quantum system with a vanishing initial correlation length and an arbitrary initial order parameter $M_0$. We find that in quantum critical dynamics, the behavior of $M_0$ under…
We study the spatial patterns formed by a system of interacting particles where the mobility of any individual is determined by the population crowding at two different spatial scales. In this way we model the behavior of some biological…
Co-evolution exhibited by a network system, involving the intricate interplay between the dynamics of the network itself and the subsystems connected by it, is a key concept for understanding the self-organized, flexible nature of…
Understanding the dynamic processes of a real game system requires an appropriate dynamics model, and rigorously testing a dynamics model is non-trivial. In our methodological research, we develop an approach to testing the validity of game…
The spatial distribution of people exhibits clustering across a wide range of scales, from household ($\sim 10^{-2}$ km) to continental ($\sim 10^4$ km) scales. Empirical data indicates simple power-law scalings for the size distribution of…
We study a modified version of a model previously proposed by Jackson and Wolinsky to account for communicating information and allocating goods in socioeconomic networks. In the model, the utility function of each node is given by a…
We investigate time-dependent properties of a single particle model in which a random walker moves on a triangle and is subjected to non-local boundary conditions. This model exhibits spontaneous breaking of a Z_2 symmetry. The reduced size…
Urban mobility models are essential tools for understanding and forecasting how people and goods move within cities, which is vital for transportation planning. The spatial scale at which urban mobility is analysed is a crucial determinant…
Recently it has been shown that a large variety of different networks have power-law (scale-free) distributions of connectivities. We investigate the robustness of such a distribution in discrete threshold networks under neutral evolution.…
We investigate the properties of mobility edge in an Aubry-Andr\'e-Harper model with non-reciprocal long-range hopping. The results reveal that there can be a new type of mobility edge featuring both strength-dependent and scale-free…
In recent years, mobility models have been reconsidered based on findings by analyzing some big datasets collected by GPS sensors, cellphone call records, and Geotagging. To understand the fundamental statistical properties of the frequency…