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We give a summary of our recent studies of spatial and velocity biases of galaxy-size halos in cosmological models. Recent progress in numerical techniques made it possible to simulate halos in large volumes with a such accuracy that halos…
Temporal networks model how the interaction between elements in a complex system evolve over time. Just like complex systems display collective dynamics, here we interpret temporal networks as trajectories performing a collective motion in…
Superslow diffusion, i.e., the long-time diffusion of particles whose mean-square displacement (variance) grows slower than any power of time, is studied in the framework of the decoupled continuous-time random walk model. We show that this…
We study a simple model of a random walker in d dimensions moving in the presence of a local heterogeneous attracting factor expressed in terms of an assigned space-dependent "attractiveness function", a situation frequently encountered in…
We study synthetic temporal networks whose evolution is determined by stochastically evolving node variables - synthetic analogues of, e.g., temporal proximity networks of mobile agents. We quantify the long-timescale correlations of these…
Human mobility patterns deeply affect the dynamics of many social systems. In this paper, we empirically analyze the real-world human movements based GPS records, and observe rich scaling properties in the temporal-spatial patterns as well…
Long-range speckle correlations play an essential role in wave transport through disordered media, but have rarely been studied in other complex systems. Here we discover spatio-temporal intensity correlations for an optical pulse…
We study coupled transport in the nonequilibrium stationary state of a model consisting of independent random walkers, moving along a one-dimensional channel, which carry a conserved energy-like quantity, with density and temperature…
For more than a century lattice random walks have been employed ubiquitously, both as a theoretical laboratory to develop intuition about more complex stochastic processes and as a tool to interpret a vast array of empirical observations.…
For a continuous-time quantum walk on a line the variance of the position observable grows quadratically in time, whereas, for its classical counterpart on the same graph, it exhibits a linear, diffusive, behaviour. A quantum walk, thus,…
Continuous-time random walks are generalisations of random walks frequently used to account for the consistent observations that many molecules in living cells undergo anomalous diffusion, i.e. subdiffusion. Here, we describe the…
In this paper, I consider a thin suspended liquid film, surrounded by a different fluid. Examples of such a system are soap films and liquid crystal films, surrounded by air. They are considered good models for two dimensional fluid…
We calculate Euclidean correlation functions through next-to-leading order in the low energy effective theory of gravity. We focus on correlation functions of curvature and volume operators, calculating these functions through one-loop…
Eye movement data are outputs of an analyser tracking the gaze when a person is inspecting a scene. These kind of data are of increasing importance in scientific research as well as in applications, e.g. in marketing and man-machine…
We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…
We investigate the interplay between nonlinearity and inhomogeneities in discrete-time quantum walks on one-dimensional lattices. Nonlinear effects are introduced through a Kerr-like, intensity-dependent local phase, while spatial and…
Exploiting multi-dimensional quantum walks as feasible platforms for quantum computation and quantum simulation is attracting constantly growing attention from a broad experimental physics community. Here, we propose a two-dimensional…
This paper shows as the relativistic Doppler effect can be extended also to time and space associated to moving bodies. This extension derives from the analysis of the wave-fronts of the light emitted by a moving source in inertial motion…
Random walks process on networks plays a fundamental role in understanding the importance of nodes and the similarity of them, which has been widely applied in PageRank, information retrieval, and community detection, etc. Individual's…
We develop a continuous time random walk (CTRW) approach for the evolution of Lagrangian velocities in steady heterogeneous flows based on a stochastic relaxation process for the streamwise particle velocities. This approach describes…