arXiv subjects

Raffaella Burioni

Publications and source records attributed to Raffaella Burioni.

71 records · Page 4Linked to original sources

arXiv2011

Rohlin Distance and the Evolution of Influenza A virus: Weak Attractors and Precursors

The evolution of the hemagglutinin amino acids sequences of Influenza A virus is studied by a method based on an informational metrics, originally introduced by Rohlin for partitions in abstract probability spaces. This metrics does not require any previous functional or syntactic knowledge about the sequences and it is sensitive to the correlated variations in the characters disposition. Its efficiency is improved by algorithmic tools, designed to enhance the detection of the novelty and to reduce the noise of useless mutations. We focus on the USA data from 1993/94 to 2010/2011 for A/H3N2 and on USA data from 2006/07 to 2010/2011 for A/H1N1 . We show that the clusterization of the distance matrix gives strong evidence to a structure of domains in the sequence space, acting as weak attractors for the evolution, in very good agreement with the epidemiological history of the virus. The structure proves very robust with respect to the variations of the clusterization parameters, and extremely coherent when restricting the observation window. The results suggest an efficient strategy in the vaccine forecast, based on the presence of "precursors" (or "buds") populating the most recent attractor.

q-bio.PE↗

arXiv2011

Transport and Scaling in Quenched 2D and 3D Lévy Quasicrystals

We consider correlated Lévy walks on a class of two- and three-dimensional deterministic self-similar structures, with correlation between steps induced by the geometrical distribution of regions, featuring different diffusion properties. We introduce a geometric parameter $α$, playing a role analogous to the exponent characterizing the step-length distribution in random systems. By a {\it single-long jump} approximation, we analytically determine the long-time asymptotic behavior of the moments of the probability distribution, as a function of $α$ and of the dynamic exponent $z$ associated to the scaling length of the process. We show that our scaling analysis also applies to experimentally relevant quantities such as escape-time and transmission probabilities. Extensive numerical simulations corroborate our results which, in general, are different from those pertaining to uncorrelated Lévy-walks models.

cond-mat.stat-mech↗

arXiv2011

Mean-field cooperativity in chemical kinetics

We consider cooperative reactions and we study the effects of the interaction strength among the system components on the reaction rate, hence realizing a connection between microscopic and macroscopic observables. Our approach is based on statistical mechanics models and it is developed analytically via mean-field techniques. First of all, we show that, when the coupling strength is set positive, the model is able to consistently recover all the various cooperative measures previously introduced, hence obtaining a single unifying framework. Furthermore, we introduce a criterion to discriminate between weak and strong cooperativity, based on a measure of "susceptibility". We also properly extend the model in order to account for multiple attachments phenomena: this is realized by incorporating within the model $p$-body interactions, whose non-trivial cooperative capability is investigated too.

q-bio.QM↗

arXiv2010

A Two-populations Ising model on diluted Random Graphs

We consider the Ising model for two interacting groups of spins embedded in an Erdös-Rényi random graph. The critical properties of the system are investigated by means of extensive Monte Carlo simulations. Our results evidence the existence of a phase transition at a value of the inter-groups interaction coupling $J_{12}^C$ which depends algebraically on the dilution of the graph and on the relative width of the two populations, as explained by means of scaling arguments. We also measure the critical exponents, which are consistent with those of the Curie-Weiss model, hence suggesting a wide robustness of the universality class.

cond-mat.stat-mech↗

arXiv2010

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 N^{theta}, being N the volume of the substrate and theta ranging from (1 - log 2/log3), for central target(s), to 1, for a single peripheral target.

cond-mat.stat-mech↗

arXiv2010

A Diffusive Strategic Dynamics for Social Systems

We propose a model for the dynamics of a social system, which includes diffusive effects and a biased rule for spin-flips, reproducing the effect of strategic choices. This model is able to mimic some phenomena taking place during marketing or political campaigns. Using a cost function based on the Ising model defined on the typical quenched interaction environments for social systems (Erdos-Renyi graph, small-world and scale-free networks), we find, by numerical simulations, that a stable stationary state is reached, and we compare the final state to the one obtained with standard dynamics, by means of total magnetization and magnetic susceptibility. Our results show that the diffusive strategic dynamics features a critical interaction parameter strictly lower than the standard one. We discuss the relevance of our findings in social systems.

physics.soc-ph↗

arXiv2009

Acquaintance role for decision making and exchanges in social networks

We model a social network by a random graph whose nodes represent agents and links between two of them stand for a reciprocal interaction; each agent is also associated to a binary variable which represents a dichotomic opinion or attribute. We consider both the case of pair-wise (p=2) and multiple (p>2) interactions among agents and we study the behavior of the resulting system by means of the energy-entropy scheme, typical of statistical mechanics methods. We show, analytically and numerically, that the connectivity of the social network plays a non-trivial role: while for pair-wise interactions (p=2) the connectivity weights linearly, when interactions involve contemporary a number of agents larger than two (p>2), its weight gets more and more important. As a result, when p is large, a full consensus within the system, can be reached at relatively small critical couplings with respect to the p=2 case usually analyzed, or, otherwise stated, relatively small coupling strengths among agents are sufficient to orient most of the system.

physics.soc-ph↗

arXiv2009

New perspectives in the equilibrium statistical mechanics approach to social and economic sciences

In this work we review some recent development in the mathematical modelling of quantitative sociology by means of statistical mechanics. After a short pedagogical introduction to static and dynamic properties of many body systems, we develop a theory for agents interactions on random graph. Our approach is based on describing a social network as a graph whose nodes represent agents and links between two of them stand for a reciprocal interaction. Each agent has to choose among a dichotomic option (i.e. agree or disagree) with respect to a given matter and he is driven by external influences (as media) and peer to peer interactions. These mimic the imitative behavior of the collectivity and may possibly be zero if the two nodes are disconnected. For this scenario we work out both the dynamics and the corresponding equilibria (statics). Once the 2-body theory is completely explored, we analyze, on the same random graph, a "diffusive strategic dynamics" with pairwise interactions, where detailed balance constraint is relaxed. The dynamic encodes some relevant processes which are expected to play a crucial role in the approach to equilibrium in social systems, i.e. diffusion of information and strategic choices. We observe numerically that such a dynamics reaches a well defined steady state that fulfills a "shift property": the critical interaction strength for the phase transition is lower with respect to the one expected from canonical equilibrium. Finally, we show how the stationary states obtained with this dynamics can be described by statistical mechanics equilibria of a diluted p-spin model, for a suitable non-integer real p>2. Several implications from a sociological perspective are discussed together with some general outlooks.

physics.soc-ph↗

arXiv2009

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 $γ=\log 3/\log2$. 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 $τ\sim V^{1-1/γ}$, 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.

cond-mat.stat-mech↗

arXiv2009

Effective Interactions in Group Competition with Strategic Diffusive Dynamics

We analyze, on a random graph, a diffusive strategic dynamics with pairwise interactions, where nor Glauber prescription, neither detailed balance hold. We observe numerically that such a dynamics reaches a well defined steady state that fulfills a shift property: the critical temperature of the canonical ferromagnetic phase transition is higher with respect to the expected equilibrium one, known both numerically via Glauber relaxation or Monte Carlo simulations as well as analytically via cavity techniques or replica approaches. We show how the relaxed states of this kind of dynamics can be described by statistical mechanics equilibria of a diluted p-spin model, for a suitable non-integer real p. Several implications from both theoretical physics and quantitative sociology points of view are discussed.

cond-mat.dis-nn↗

arXiv2009

Word-of-mouth and dynamical inhomogeneous markets: Efficiency measure and optimal sampling policies for the pre-launch stage

An important assumption lying behind innovation diffusion models and word-of-mouth processes is that of homogeneous mixing: at any time, the individuals making up the market are uniformly distributed in space. When the geographical parameters of the market, such as its area extension, become important, the movement of individuals must be explicitly taken into account. The authors introduce a model for a "micro-level" process for the diffusion of an innovative product, based on a word-of-mouth mechanism, and they explicitly consider the inhomogeneity of markets and the spatial extent of the geographical region where the process takes place. This results in an unexpected behaviour of macro (aggregate) level measurable quantities. The authors study the particular case of the pre-launch stage, where a product is first presented to the market through free sample distribution. The first triers of the samples then inform the other potential customers via word-of-mouth; additional advertising is absent. The authors find an unexpected general failure of the word-of-mouth mechanism for high market densities and they obtain quantitative results for the optimal sampling policy. By introducing a threshold to discriminate between individuals who will purchase and those who will not purchase according to their individual goodwill, they calculate the length of the pre-launch campaign and the final goodwill as a function of the firm's expenditure. These results are applied to a set of major US urban areas.

physics.soc-ph↗

arXiv2005

Topology, Hidden Spectra and Bose Einstein Condensation on low dimensional complex networks

Topological inhomogeneity gives rise to spectral anomalies that can induce Bose-Einstein Condensation (BEC) in low dimensional systems. These anomalies consist in energy regions composed of an infinite number of states with vanishing weight in the thermodynamic limit (hidden states). Here we present a rigorous result giving the most general conditions for BEC on complex networks. We prove that the presence of hidden states in the lowest region of the spectrum is the necessary and sufficient condition for condensation in low dimension (spectral dimension $\bar{d}\leq 2$), while it is shown that BEC always occurs for $\bar{d}>2$.

cond-mat.stat-mech↗

arXiv1998

The $n\to\infty$ limit of O(n) model on graphs

Thirty years ago, Stanley showed that an O(n) spin model on a lattice tends to a spherical model as $n\to\infty$. This means that at any temperature the corresponding free energies coincide. This fundamental result, providing the basis for more detailed studies of continuous symmetry spin models, is no longer valid on more general discrete structures lacking of translation invariance, i.e. on graphs. However only the singular parts of the free energies determine the critical behavior of the two statistical models. Here we show that such singular parts still coincide even on general graphs in the thermodynamic limit. This implies that the critical exponents of O(n) models on graphs for $n\to\infty$ tend to the spherical ones and therefore they only depend on the graph spectral dimension.

cond-mat↗

arXiv1998

Magnetization bound for classical spin models on graphs

In this paper we prove the existence of phase transitions at finite temperature for O(n) classical ferromagnetic spin models on infrared finite graphs. Infrared finite graphs are infinite graphs with $\lim {m\to 0^+} {\bar Tr (L+m)^{-1} < \infty$, where $L$ is the Laplacian operator of the graph. The ferromagnetic couplings are only requested to be bounded by two positive constants. The proof, inspired by the classical result of Fröhlich, Simon and Spencer on lattices, is given through a rigorous bound on the average magnetization. The result holds for $n\ge 1$ and it includes as a particular case the Ising model.

cond-mat.stat-mech↗

arXiv1997

Cutting-Decimation Renormalization for diffusive and vibrational dynamics on fractals

Recently, we pointed out that on a class on non exactly decimable fractals two different parameters are required to describe diffusive and vibrational dynamics. This phenomenon we call dynamical dimension splitting is related to the lack of exact decimation invariance for these structures, which turn out to be invariant under a more complex cutting-decimation transform. In this paper we study in details the dynamical dimension splitting on these fractals analyzing the mathematical properties of the cutting-decimation transform. Our results clarify how the splitting arises from the cutting transform and show that the dynamical dimension degeneration is a very peculiar consequence of exact decimability.

cond-mat.stat-mech↗

arXiv1997

Diffusion on non exactly decimable tree-like fractals

We calculate the spectral dimension of a wide class of tree-like fractals by solving the random walk problem through a new analytical technique, based on invariance under generalized cutting-decimation transformations. These fractals are generalizations of the NTD lattices and they are characterized by non integer spectral dimension equal or greater then 2, non anomalous diffusion laws, dynamical dimension splitting and absence of phase transitions for spin models.

cond-mat.stat-mech↗

arXiv1997

Geometrical universality in vibrational dynamics

A good generalization of the Euclidean dimension to disordered systems and non crystalline structures is commonly required to be related to large scale geometry and it is expected to be independent of local geometrical modifications. The spectral dimension, defined according to the low frequency density of vibrational states, appears to be the best candidate as far as dynamical and thermodynamical properties are concerned. In this letter we give the rigorous analytical proof of its independence of finite scale geometry. We show that the spectral dimension is invariant under local rescaling of couplings and under addition of finite range couplings, or infinite range couplings decaying faster then a characteristic power law. We also prove that it is left unchanged by coarse graining transformations, which are the generalization to graphs and networks of the usual decimation on regular structures. A quite important consequence of all these properties is the possibility of dealing with simplified geometrical models with nearest-neighbors interactions to study the critical behavior of systems with geometrical disorder.

cond-mat.stat-mech↗