87 research outputs found
Glass transition and random walks on complex energy landscapes
We present a simple mathematical model of glassy dynamics seen as a random
walk in a directed, weighted network of minima taken as a representation of the
energy landscape. Our approach gives a broader perspective to previous studies
focusing on particular examples of energy landscapes obtained by sampling
energy minima and saddles of small systems. We point out how the relation
between the energies of the minima and their number of neighbors should be
studied in connection with the network's global topology, and show how the
tools developed in complex network theory can be put to use in this context
On the definition of temperature in dense granular media
In this Letter we report the measurement of a pseudo-temperature for
compacting granular media on the basis of the Fluctuation-Dissipation relations
in the aging dynamics of a model system. From the violation of the
Fluctuation-Dissipation Theorem an effective temperature emerges (a dynamical
temperature T_{dyn}) whose ratio with the equilibrium temperature T_d^{eq}
depends on the particle density. We compare the results for the
Fluctuation-Dissipation Ratio (FDR) T_{dyn}/T_d^{eq} at several densities with
the outcomes of Edwards' approach at the corresponding densities. It turns out
that the FDR and the so-called Edwards' ratio coincide at several densities
(very different ages of the system), opening in this way the door to
experimental checks as well as theoretical constructions.Comment: RevTex4 4 pages, 4 eps figure
Dynamical and bursty interactions in social networks
We present a modeling framework for dynamical and bursty contact networks
made of agents in social interaction. We consider agents' behavior at short
time scales, in which the contact network is formed by disconnected cliques of
different sizes. At each time a random agent can make a transition from being
isolated to being part of a group, or vice-versa. Different distributions of
contact times and inter-contact times between individuals are obtained by
considering transition probabilities with memory effects, i.e. the transition
probabilities for each agent depend both on its state (isolated or interacting)
and on the time elapsed since the last change of state. The model lends itself
to analytical and numerical investigations. The modeling framework can be
easily extended, and paves the way for systematic investigations of dynamical
processes occurring on rapidly evolving dynamical networks, such as the
propagation of an information, or spreading of diseases
Modeling the evolution of weighted networks
We present a general model for the growth of weighted networks in which the
structural growth is coupled with the edges' weight dynamical evolution. The
model is based on a simple weight-driven dynamics and a weights' reinforcement
mechanism coupled to the local network growth. That coupling can be generalized
in order to include the effect of additional randomness and non-linearities
which can be present in real-world networks. The model generates weighted
graphs exhibiting the statistical properties observed in several real-world
systems. In particular, the model yields a non-trivial time evolution of
vertices properties and scale-free behavior with exponents depending on the
microscopic parameters characterizing the coupling rules. Very interestingly,
the generated graphs spontaneously achieve a complex hierarchical architecture
characterized by clustering and connectivity correlations varying as a function
of the vertices' degree
Arrival Time Statistics in Global Disease Spread
Metapopulation models describing cities with different populations coupled by
the travel of individuals are of great importance in the understanding of
disease spread on a large scale. An important example is the Rvachev-Longini
model [{\it Math. Biosci.} {\bf 75}, 3-22 (1985)] which is widely used in
computational epidemiology. Few analytical results are however available and in
particular little is known about paths followed by epidemics and disease
arrival times. We study the arrival time of a disease in a city as a function
of the starting seed of the epidemics. We propose an analytical Ansatz, test it
in the case of a spreading on the world wide air transportation network, and
show that it predicts accurately the arrival order of a disease in world-wide
cities
Vulnerability of weighted networks
In real networks complex topological features are often associated with a
diversity of interactions as measured by the weights of the links. Moreover,
spatial constraints may as well play an important role, resulting in a complex
interplay between topology, weight, and geography. In order to study the
vulnerability of such networks to intentional attacks, these attributes must be
therefore considered along with the topological quantities. In order to tackle
this issue, we consider the case of the world-wide airport network, which is a
weighted heterogeneous network whose evolution and structure are influenced by
traffic and geographical constraints. We first characterize relevant
topological and weighted centrality measures and then use these quantities as
selection criteria for the removal of vertices. We consider different attack
strategies and different measures of the damage achieved in the network. The
analysis of weighted properties shows that centrality driven attacks are
capable to shatter the network's communication or transport properties even at
very low level of damage in the connectivity pattern. The inclusion of weight
and traffic therefore provides evidence for the extreme vulnerability of
complex networks to any targeted strategy and need to be considered as key
features in the finding and development of defensive strategies
Weighted evolving networks: coupling topology and weights dynamics
We propose a model for the growth of weighted networks that couples the
establishment of new edges and vertices and the weights' dynamical evolution.
The model is based on a simple weight-driven dynamics and generates networks
exhibiting the statistical properties observed in several real-world systems.
In particular, the model yields a non-trivial time evolution of vertices'
properties and scale-free behavior for the weight, strength and degree
distributions.Comment: 4 pages, 4 figure
Dynamics of Annihilation II: Fluctuations of Global Quantities
We develop a theory for fluctuations and correlations in a gas evolving under
ballistic annihilation dynamics. Starting from the hierarchy of equations
governing the evolution of microscopic densities in phase space, we
subsequently restrict to a regime of spatial homogeneity, and obtain explicit
predictions for the fluctuations and time correlation of the total number of
particles, total linear momentum and total kinetic energy. Cross-correlations
between these quantities are worked out as well. These predictions are
successfully tested against Molecular Dynamics and Monte-Carlo simulations.
This provides strong support for the theoretical approach developed, including
the hydrodynamic treatment of the spectrum of the linearized Boltzmann
operator. This article is a companion paper to arXiv:0801.2299 and makes use of
the spectral analysis reported there.Comment: 19 page
Estimating Potential Infection Transmission Routes in Hospital Wards Using Wearable Proximity Sensors
Contacts between patients, patients and health care workers (HCWs) and among
HCWs represent one of the important routes of transmission of hospital-acquired
infections (HAI). A detailed description and quantification of contacts in
hospitals provides key information for HAIs epidemiology and for the design and
validation of control measures. We used wearable sensors to detect close-range
interactions ("contacts") between individuals in the geriatric unit of a
university hospital. Contact events were measured with a spatial resolution of
about 1.5 meters and a temporal resolution of 20 seconds. The study included 46
HCWs and 29 patients and lasted for 4 days and 4 nights. 14037 contacts were
recorded. The number and duration of contacts varied between mornings,
afternoons and nights, and contact matrices describing the mixing patterns
between HCW and patients were built for each time period. Contact patterns were
qualitatively similar from one day to the next. 38% of the contacts occurred
between pairs of HCWs and 6 HCWs accounted for 42% of all the contacts
including at least one patient, suggesting a population of individuals who
could potentially act as super-spreaders. Wearable sensors represent a novel
tool for the measurement of contact patterns in hospitals. The collected data
provides information on important aspects that impact the spreading patterns of
infectious diseases, such as the strong heterogeneity of contact numbers and
durations across individuals, the variability in the number of contacts during
a day, and the fraction of repeated contacts across days. This variability is
associated with a marked statistical stability of contact and mixing patterns
across days. Our results highlight the need for such measurement efforts in
order to correctly inform mathematical models of HAIs and use them to inform
the design and evaluation of prevention strategies
Social network dynamics of face-to-face interactions
The recent availability of data describing social networks is changing our
understanding of the "microscopic structure" of a social tie. A social tie
indeed is an aggregated outcome of many social interactions such as
face-to-face conversations or phone-calls. Analysis of data on face-to-face
interactions shows that such events, as many other human activities, are
bursty, with very heterogeneous durations. In this paper we present a model for
social interactions at short time scales, aimed at describing contexts such as
conference venues in which individuals interact in small groups. We present a
detailed anayltical and numerical study of the model's dynamical properties,
and show that it reproduces important features of empirical data. The model
allows for many generalizations toward an increasingly realistic description of
social interactions. In particular in this paper we investigate the case where
the agents have intrinsic heterogeneities in their social behavior, or where
dynamic variations of the local number of individuals are included. Finally we
propose this model as a very flexible framework to investigate how dynamical
processes unfold in social networks.Comment: 20 pages, 25 figure
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