61 research outputs found
Detecting the community structure and activity patterns of temporal networks: a non-negative tensor factorization approach
The increasing availability of temporal network data is calling for more
research on extracting and characterizing mesoscopic structures in temporal
networks and on relating such structure to specific functions or properties of
the system. An outstanding challenge is the extension of the results achieved
for static networks to time-varying networks, where the topological structure
of the system and the temporal activity patterns of its components are
intertwined. Here we investigate the use of a latent factor decomposition
technique, non-negative tensor factorization, to extract the community-activity
structure of temporal networks. The method is intrinsically temporal and allows
to simultaneously identify communities and to track their activity over time.
We represent the time-varying adjacency matrix of a temporal network as a
three-way tensor and approximate this tensor as a sum of terms that can be
interpreted as communities of nodes with an associated activity time series. We
summarize known computational techniques for tensor decomposition and discuss
some quality metrics that can be used to tune the complexity of the factorized
representation. We subsequently apply tensor factorization to a temporal
network for which a ground truth is available for both the community structure
and the temporal activity patterns. The data we use describe the social
interactions of students in a school, the associations between students and
school classes, and the spatio-temporal trajectories of students over time. We
show that non-negative tensor factorization is capable of recovering the class
structure with high accuracy. In particular, the extracted tensor components
can be validated either as known school classes, or in terms of correlated
activity patterns, i.e., of spatial and temporal coincidences that are
determined by the known school activity schedule
Phase diagram of a Schelling segregation model
The collective behavior in a variant of Schelling's segregation model is
characterized with methods borrowed from statistical physics, in a context
where their relevance was not conspicuous. A measure of segregation based on
cluster geometry is defined and several quantities analogous to those used to
describe physical lattice models at equilibrium are introduced. This physical
approach allows to distinguish quantitatively several regimes and to
characterize the transitions between them, leading to the building of a phase
diagram. Some of the transitions evoke empirical sudden ethnic turnovers. We
also establish links with 'spin-1' models in physics. Our approach provides
generic tools to analyze the dynamics of other socio-economic systems
Estimating the outcome of spreading processes on networks with incomplete information: a mesoscale approach
Recent advances in data collection have facilitated the access to
time-resolved human proximity data that can conveniently be represented as
temporal networks of contacts between individuals. While this type of data is
fundamental to investigate how information or diseases propagate in a
population, it often suffers from incompleteness, which possibly leads to
biased conclusions. A major challenge is thus to estimate the outcome of
spreading processes occurring on temporal networks built from partial
information. To cope with this problem, we devise an approach based on
Non-negative Tensor Factorization (NTF) -- a dimensionality reduction technique
from multi-linear algebra. The key idea is to learn a low-dimensional
representation of the temporal network built from partial information, to adapt
it to take into account temporal and structural heterogeneity properties known
to be crucial for spreading processes occurring on networks, and to construct
in this way a surrogate network similar to the complete original network. To
test our method, we consider several human-proximity networks, on which we
simulate a loss of data. Using our approach on the resulting partial networks,
we build a surrogate version of the complete network for each. We then compare
the outcome of a spreading process on the complete networks (non altered by a
loss of data) and on the surrogate networks. We observe that the epidemic sizes
obtained using the surrogate networks are in good agreement with those measured
on the complete networks. Finally, we propose an extension of our framework
when additional data sources are available to cope with the missing data
problem
Activity clocks: spreading dynamics on temporal networks of human contact
Dynamical processes on time-varying complex networks are key to understanding
and modeling a broad variety of processes in socio-technical systems. Here we
focus on empirical temporal networks of human proximity and we aim at
understanding the factors that, in simulation, shape the arrival time
distribution of simple spreading processes. Abandoning the notion of wall-clock
time in favour of node-specific clocks based on activity exposes robust
statistical patterns in the arrival times across different social contexts.
Using randomization strategies and generative models constrained by data, we
show that these patterns can be understood in terms of heterogeneous
inter-event time distributions coupled with heterogeneous numbers of events per
edge. We also show, both empirically and by using a synthetic dataset, that
significant deviations from the above behavior can be caused by the presence of
edge classes with strong activity correlations
Schelling segregation in an open city: a kinetically constrained Blume-Emery-Griffiths spin-1 system
In the 70's Schelling introduced a multi-agent model to describe the
segregation dynamics that may occur with individuals having only weak
preferences for 'similar' neighbors. Recently variants of this model have been
discussed, in particular, with emphasis on the links with statistical physics
models. Whereas these models consider a fixed number of agents moving on a
lattice, here we present a version allowing for exchanges with an external
reservoir of agents. The density of agents is controlled by a parameter which
can be viewed as measuring the attractiveness of the city-lattice. This model
is directly related to the zero-temperature dynamics of the
Blume-Emery-Griffiths (BEG) spin-1 model, with kinetic constraints. With a
varying vacancy density, the dynamics with agents making deterministic
decisions leads to a new variety of "phases" whose main features are the
characteristics of the interfaces between clusters of agents of different
types. The domains of existence of each type of interface are obtained
analytically as well as numerically. These interfaces may completely isolate
the agents leading to another type of segregation as compared to what is
observed in the original Schelling model, and we discuss its possible
socio-economic correlates.Comment: 10 pages, 7 figures, final version accepted for publication in PR
Change points, memory and epidemic spreading in temporal networks
Dynamic networks exhibit temporal patterns that vary across different time
scales, all of which can potentially affect processes that take place on the
network. However, most data-driven approaches used to model time-varying
networks attempt to capture only a single characteristic time scale in
isolation --- typically associated with the short-time memory of a Markov chain
or with long-time abrupt changes caused by external or systemic events. Here we
propose a unified approach to model both aspects simultaneously, detecting
short and long-time behaviors of temporal networks. We do so by developing an
arbitrary-order mixed Markov model with change points, and using a
nonparametric Bayesian formulation that allows the Markov order and the
position of change points to be determined from data without overfitting. In
addition, we evaluate the quality of the multiscale model in its capacity to
reproduce the spreading of epidemics on the temporal network, and we show that
describing multiple time scales simultaneously has a synergistic effect, where
statistically significant features are uncovered that otherwise would remain
hidden by treating each time scale independently.Comment: 9 pages, 6 figure
Wearable proximity sensors for monitoring a mass casualty incident exercise: a feasibility study
Over the past several decades, naturally occurring and man-made mass casualty
incidents (MCI) have increased in frequency and number, worldwide. To test the
impact of such event on medical resources, simulations can provide a safe,
controlled setting while replicating the chaotic environment typical of an
actual disaster. A standardised method to collect and analyse data from mass
casualty exercises is needed, in order to assess preparedness and performance
of the healthcare staff involved. We report on the use of wearable proximity
sensors to measure proximity events during a MCI simulation. We investigated
the interactions between medical staff and patients, to evaluate the time
dedicated by the medical staff with respect to the severity of the injury of
the victims depending on the roles. We estimated the presence of the patients
in the different spaces of the field hospital, in order to study the patients'
flow. Data were obtained and collected through the deployment of wearable
proximity sensors during a mass casualty incident functional exercise. The
scenario included two areas: the accident site and the Advanced Medical Post
(AMP), and the exercise lasted 3 hours. A total of 238 participants simulating
medical staff and victims were involved. Each participant wore a proximity
sensor and 30 fixed devices were placed in the field hospital. The contact
networks show a heterogeneous distribution of the cumulative time spent in
proximity by participants. We obtained contact matrices based on cumulative
time spent in proximity between victims and the rescuers. Our results showed
that the time spent in proximity by the healthcare teams with the victims is
related to the severity of the patient's injury. The analysis of patients' flow
showed that the presence of patients in the rooms of the hospital is consistent
with triage code and diagnosis, and no obvious bottlenecks were found
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