Elena Agliari

Random walks on deterministic scale-free networks: Exact results

We study the random walk problem on a class of deterministic scale-free networks displaying a degree sequence for hubs scaling as a power law with an exponent gamma=log 3/log 2. We find exact results concerning different first-passage phenomena and, in particular, we calculate the probability of first return to the main hub. These results allow to derive the exact analytic expression for the mean time to first reach the main hub, whose leading behavior is given by tau approximately V1-1/gamma, where V denotes the size of the structure, and the mean is over a set of starting points distributed uniformly over all the other sites of the graph. Interestingly, the process turns out to be particularly efficient. We also discuss the thermodynamic limit of the structure and some local topological properties.

Exact mean first-passage time on the T-graph

We consider a simple random walk on the T-fractal and we calculate the exact mean time taug to first reach the central node i0. The mean is performed over the set of possible walks from a given origin and over the set of starting points uniformly distributed throughout the sites of the graph, except i0. By means of analytic techniques based on decimation procedures, we find the explicit expression for taug as a function of the generation g and of the volume V of the underlying fractal. Our results agree with the asymptotic ones already known for diffusion on the T-fractal and, more generally, they are consistent with the standard laws describing diffusion on low-dimensional structures.

Exact calculations of first-passage quantities on recursive networks.

We present general methods to exactly calculate mean first-passage quantities on self-similar networks defined recursively. In particular, we calculate the mean first-passage time and the splitting probabilities associated to a source and one or several targets; averaged quantities over a given set of sources (e.g., same-connectivity nodes) are also derived. The exact estimate of such quantities highlights the dependency of first-passage processes with respect to the source-target distance, which has recently revealed to be a key parameter in characterizing transport in complex media. We explicitly perform calculations for different classes of recursive networks [finitely ramified fractals, scale-free (trans)fractals, nonfractals, mixtures between fractals and nonfractals, nondecimable hierarchical graphs] of arbitrary size. Our approach unifies and significantly extends the available results in the field.

Efficiency of information spreading in a population of diffusing agents.

We introduce a model for information spreading among a population of N agents diffusing on a square L x L lattice, starting from an informed agent (Source). Information passing from informed to unaware agents occurs whenever the relative distance is < or = 1. Numerical simulations show that the time required for the information to reach all agents scales as N(-alpha)L(beta), where alpha and beta are noninteger. A decay factor z takes into account the degeneration of information as it passes from one agent to another; the final average degree of information of the population tau(av)(z) is thus history dependent. We find that the behavior of tau(av)(z) is nonmonotonic with respect to N and L and displays a set of minima. Part of the results are recovered with analytical approximations.

Dynamics of continuous-time quantum walks in restricted geometries

We study quantum transport on finite discrete structures and we model the process by means of continuous-time quantum walks. A direct and effective comparison between quantum and classical walks can be attained based on the average displacement of the walker as a function of time. Indeed, a fast growth of the average displacement can be advantageously exploited to build up efficient search algorithms. By means of analytical and numerical investigations, we show that the finiteness and the inhomogeneity of the substrate jointly weaken the quantum-walk performance. We further highlight the interplay between the quantum-walk dynamics and the underlying topology by studying the temporal evolution of the transfer probability distribution and the lower bound of long-time averages.

Effective target arrangement in a deterministic scale-free graph.

We study the random-walk problem on a deterministic scale-free network, in the presence of a set of static, identical targets; due to the strong inhomogeneity of the underlying structure the mean first-passage time (MFPT), meant as a measure of transport efficiency, is expected to depend sensitively on the position of targets. We consider several spatial arrangements for targets and we calculate, mainly rigorously, the related MFPT, where the average is taken over all possible starting points and over all possible paths. For all the cases studied, the MFPT asymptotically scales like ∼Nθ, being N the volume of the substrate and θ ranging from 1-log 2/log 3, for central target(s), to 1, for a single peripheral target.

Retrieval capabilities of hierarchical networks: From dyson to hopfield

Elena Agliari, Adriano Barra, Andrea Galluzzi, Francesco Guerra, Daniele Tantari, and Flavia Tavani Dipartimento di Fisica, Sapienza Università di Roma, P.le A. Moro 2, 00185, Roma, Italy. Dipartimento di Matematica, Sapienza Università di Roma, P.le Aldo Moro 2, 00185, Roma, Italy. Dipartimento SBAI (Ingegneria), Sapienza Università di Roma, Via A. Scarpa 14, 00185, Roma, Italy. (Dated: July 21, 2014)

Cancer-driven dynamics of immune cells in a microfluidic environment

Scope of the present work is to infer the migratory ability of leukocytes by stochastic processes in order to distinguish the spontaneous organization of immune cells against an insult (namely cancer). For this purpose, spleen cells from immunodeficient mice, selectively lacking the transcription factor IRF-8 (IRF-8 knockout; IRF-8 KO), or from immunocompetent animals (wild-type; WT), were allowed to interact, alternatively, with murine B16.F10 melanoma cells in an ad hoc microfluidic environment developed on a LabOnChip technology. In this setting, only WT spleen cells were able to establish physical interactions with melanoma cells. Conversely, IRF-8 KO immune cells exhibited poor dynamical reactivity towards the neoplastic cells. In the present study, we collected data on the motility of these two types of spleen cells and built a complete set of observables that recapitulate the biological complexity of the system in these experiments. With remarkable accuracy, we concluded that the IRF-8 KO cells performed pure uncorrelated random walks, while WT splenocytes were able to make singular drifted random walks that collapsed on a straight ballistic motion for the system as a whole, hence giving rise to a highly coordinate response. These results may provide a useful system to quantitatively analyse the real time cell-cell interactions and to foresee the behavior of immune cells with tumor cells at the tissue level.

Immune networks: multitasking capabilities near saturation

Pattern-diluted associative networks were introduced recently as models for the immune system, with nodes representing T-lymphocytes and stored patterns representing signalling protocols between T- and B-lymphocytes. It was shown earlier that in the regime of extreme pattern dilution, a system with

A Hebbian approach to complex-network generation

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