Initiating a Network Effect in a Social Network - A Facebook ExperimentNasri Messarra
- Can we initiate network effects on the Facebook social network in a non-automated experiment under controlled environment?
- How to put into evidence network effects in a social network?
Big Data, Social Networks & Human Behavior (Jukka-Pekka Onnela)UN Global Pulse
Presentation by Jukka-Pekka Onnela, Assistant Professor of Biostatistics at Harvard University's School of Public Health. Presented at roundtable on "BIg Data for Development" hosted by Global Pulse, an innovation initiative of the United Nations (www.unglobalpulse.org).
Brain network modelling: connectivity metrics and group analysisGael Varoquaux
Slides of the course that I gave at the HBM 2012 connectome course on brain network modelling methods, with a focus on extracting connectivity graphs from correlation matrices and comparing them.
Neural Networks Models for Large Social SystemsSSA KPI
AACIMP 2010 Summer School lecture by Alexander Makarenko. "Applied Mathematics" stream. "General Tasks and Problems of Modelling of Social Systems. Problems and Models in Sustainable Development" course. Part 3.
More info at http://summerschool.ssa.org.ua
Initiating a Network Effect in a Social Network - A Facebook ExperimentNasri Messarra
- Can we initiate network effects on the Facebook social network in a non-automated experiment under controlled environment?
- How to put into evidence network effects in a social network?
Big Data, Social Networks & Human Behavior (Jukka-Pekka Onnela)UN Global Pulse
Presentation by Jukka-Pekka Onnela, Assistant Professor of Biostatistics at Harvard University's School of Public Health. Presented at roundtable on "BIg Data for Development" hosted by Global Pulse, an innovation initiative of the United Nations (www.unglobalpulse.org).
Brain network modelling: connectivity metrics and group analysisGael Varoquaux
Slides of the course that I gave at the HBM 2012 connectome course on brain network modelling methods, with a focus on extracting connectivity graphs from correlation matrices and comparing them.
Neural Networks Models for Large Social SystemsSSA KPI
AACIMP 2010 Summer School lecture by Alexander Makarenko. "Applied Mathematics" stream. "General Tasks and Problems of Modelling of Social Systems. Problems and Models in Sustainable Development" course. Part 3.
More info at http://summerschool.ssa.org.ua
The role of students developing Nation, steps ,measures, inspirations, role models. how do students involve in transforming their nation and key thoughts
This project will investigate the SIR model and use numeric methods t.pdfjkcs20004
This project will investigate the SIR model and use numeric methods to find solutions to the
system of coupled, non-linear differential equations. We will work through the derivation of the
model and some assumptions. You will need to use technology, in the form of a spreadsheet
(Excel/Google Sheets) or computer code (C, C++, Python, Java, etc) to obtain approximate
numeric solutions. Some Background The SIR model is a very useful compartmental model to
help understand the spread of disease through a population during some given time. The
mathematical model has three compartments: Susceptible members of the population (S),
Infected members of the population (I), and Recovered-or Removed-members of the population
(R). As with any mathematical model we will make some assumptions that we should be mindful
of when using this in a "real-world" context. Lets begin with some initial information. 1. We will
assume, for simplicity, that the number of susceptible individuals in a population at some time t
can be given by the function S(t), and further that each of the infected and removed individuals
will be given by functions I(t) and R(t) respectively. 2. We can also assume that for a population
N,S(t)+I(t)+R(t)=N. Explain why this is a reasonable assumption. 3. We will also assume that the
population we are studying is closed, that is we never add to the susceptible members and that
once removed, you will not be susceptible. Explain why this simplification may not reflect a
real-world scenario. Deriving some differential equations: First, lets look at how the susceptible
population might be changing. We will fix a model parameter, called , that will be the number of
daily contacts each infected person has with a susceptible person resulting in disease infection.
We can write it like this: dtdS=NS(t)I(t) Explain why this is reasonable. Why is there an I(t) ?
Why do we have NS(t) ? Why is it negative?
For reasons of convenience, instead of considering the change in numbers of each compartment
we will look at the change in proportion of each compartment, so we can say that:
s(t)=NS(t)i(t)=NI(t)r(t)=NR(t) We will get the following changes: s(t)+i(t)+r(t)=1 and the
differential equation for change in proportion of susceptible will be: dtds=s(t)i(t) Now consider
the change in removed proportion. For this we will need to introduce another parameter, , which
you can think of as a fixed proportion of the infected members who will be recovered/removed
each day or as the recovery rate: 1/ (days to recover). So we get: dtdr=i(t) We know that
s(t)+i(t)+r(t)=1, so it follows that if we take the derivative with respect to t we get:
dtd(s(t)+i(t)+r(t))=dtd(1) Write the resulting equation below: Use the equation you found to
solve for dtdi and substitute to find dtdi in terms of the model parameters and , and the functions
s(t),i(t),r(t). Write it below:
Together these three equations give a system of coupled, non-linear differential equations. Fill in
the missing e.
Bayesian inference for mixed-effects models driven by SDEs and other stochast...Umberto Picchini
An important, and well studied, class of stochastic models is given by stochastic differential equations (SDEs). In this talk, we consider Bayesian inference based on measurements from several individuals, to provide inference at the "population level" using mixed-effects modelling. We consider the case where dynamics are expressed via SDEs or other stochastic (Markovian) models. Stochastic differential equation mixed-effects models (SDEMEMs) are flexible hierarchical models that account for (i) the intrinsic random variability in the latent states dynamics, as well as (ii) the variability between individuals, and also (iii) account for measurement error. This flexibility gives rise to methodological and computational difficulties.
Fully Bayesian inference for nonlinear SDEMEMs is complicated by the typical intractability of the observed data likelihood which motivates the use of sampling-based approaches such as Markov chain Monte Carlo. A Gibbs sampler is proposed to target the marginal posterior of all parameters of interest. The algorithm is made computationally efficient through careful use of blocking strategies, particle filters (sequential Monte Carlo) and correlated pseudo-marginal approaches. The resulting methodology is is flexible, general and is able to deal with a large class of nonlinear SDEMEMs [1]. In a more recent work [2], we also explored ways to make inference even more scalable to an increasing number of individuals, while also dealing with state-space models driven by other stochastic dynamic models than SDEs, eg Markov jump processes and nonlinear solvers typically used in systems biology.
[1] S. Wiqvist, A. Golightly, AT McLean, U. Picchini (2020). Efficient inference for stochastic differential mixed-effects models using correlated particle pseudo-marginal algorithms, CSDA, https://doi.org/10.1016/j.csda.2020.107151
[2] S. Persson, N. Welkenhuysen, S. Shashkova, S. Wiqvist, P. Reith, G. W. Schmidt, U. Picchini, M. Cvijovic (2021). PEPSDI: Scalable and flexible inference framework for stochastic dynamic single-cell models, bioRxiv doi:10.1101/2021.07.01.450748.
A new incomplete data model, the trunsored model, in lifetime analysis is introduced. This model can be regarded as a unified model of the censored and truncated models. Using the model, we can not only estimate the ratio of the fragile population to the mixed fragile and durable populations, but also test a hypothesis that the ratio is equal to a prescribed value. A central point of the paper is that such a test can easily be realized through the newly introduced trunsored model, because it has been difficult to do such a hypothesis test under only the framework of censored and truncated models. Therefore, the relationship of the trunsored model to the censored and truncated models is clarified because the trunsored model unifies the censored and truncated models. The paper also shows how to obtain the estimates of the parameters in lifetime estimation, and corresponding confidence intervals for the fragile population. Typical examples applied to electronic board failures, and to breast cancer data, for lifetime estimation are demonstrated, and successfully worked using the trunsored model.
The role of students developing Nation, steps ,measures, inspirations, role models. how do students involve in transforming their nation and key thoughts
This project will investigate the SIR model and use numeric methods t.pdfjkcs20004
This project will investigate the SIR model and use numeric methods to find solutions to the
system of coupled, non-linear differential equations. We will work through the derivation of the
model and some assumptions. You will need to use technology, in the form of a spreadsheet
(Excel/Google Sheets) or computer code (C, C++, Python, Java, etc) to obtain approximate
numeric solutions. Some Background The SIR model is a very useful compartmental model to
help understand the spread of disease through a population during some given time. The
mathematical model has three compartments: Susceptible members of the population (S),
Infected members of the population (I), and Recovered-or Removed-members of the population
(R). As with any mathematical model we will make some assumptions that we should be mindful
of when using this in a "real-world" context. Lets begin with some initial information. 1. We will
assume, for simplicity, that the number of susceptible individuals in a population at some time t
can be given by the function S(t), and further that each of the infected and removed individuals
will be given by functions I(t) and R(t) respectively. 2. We can also assume that for a population
N,S(t)+I(t)+R(t)=N. Explain why this is a reasonable assumption. 3. We will also assume that the
population we are studying is closed, that is we never add to the susceptible members and that
once removed, you will not be susceptible. Explain why this simplification may not reflect a
real-world scenario. Deriving some differential equations: First, lets look at how the susceptible
population might be changing. We will fix a model parameter, called , that will be the number of
daily contacts each infected person has with a susceptible person resulting in disease infection.
We can write it like this: dtdS=NS(t)I(t) Explain why this is reasonable. Why is there an I(t) ?
Why do we have NS(t) ? Why is it negative?
For reasons of convenience, instead of considering the change in numbers of each compartment
we will look at the change in proportion of each compartment, so we can say that:
s(t)=NS(t)i(t)=NI(t)r(t)=NR(t) We will get the following changes: s(t)+i(t)+r(t)=1 and the
differential equation for change in proportion of susceptible will be: dtds=s(t)i(t) Now consider
the change in removed proportion. For this we will need to introduce another parameter, , which
you can think of as a fixed proportion of the infected members who will be recovered/removed
each day or as the recovery rate: 1/ (days to recover). So we get: dtdr=i(t) We know that
s(t)+i(t)+r(t)=1, so it follows that if we take the derivative with respect to t we get:
dtd(s(t)+i(t)+r(t))=dtd(1) Write the resulting equation below: Use the equation you found to
solve for dtdi and substitute to find dtdi in terms of the model parameters and , and the functions
s(t),i(t),r(t). Write it below:
Together these three equations give a system of coupled, non-linear differential equations. Fill in
the missing e.
Bayesian inference for mixed-effects models driven by SDEs and other stochast...Umberto Picchini
An important, and well studied, class of stochastic models is given by stochastic differential equations (SDEs). In this talk, we consider Bayesian inference based on measurements from several individuals, to provide inference at the "population level" using mixed-effects modelling. We consider the case where dynamics are expressed via SDEs or other stochastic (Markovian) models. Stochastic differential equation mixed-effects models (SDEMEMs) are flexible hierarchical models that account for (i) the intrinsic random variability in the latent states dynamics, as well as (ii) the variability between individuals, and also (iii) account for measurement error. This flexibility gives rise to methodological and computational difficulties.
Fully Bayesian inference for nonlinear SDEMEMs is complicated by the typical intractability of the observed data likelihood which motivates the use of sampling-based approaches such as Markov chain Monte Carlo. A Gibbs sampler is proposed to target the marginal posterior of all parameters of interest. The algorithm is made computationally efficient through careful use of blocking strategies, particle filters (sequential Monte Carlo) and correlated pseudo-marginal approaches. The resulting methodology is is flexible, general and is able to deal with a large class of nonlinear SDEMEMs [1]. In a more recent work [2], we also explored ways to make inference even more scalable to an increasing number of individuals, while also dealing with state-space models driven by other stochastic dynamic models than SDEs, eg Markov jump processes and nonlinear solvers typically used in systems biology.
[1] S. Wiqvist, A. Golightly, AT McLean, U. Picchini (2020). Efficient inference for stochastic differential mixed-effects models using correlated particle pseudo-marginal algorithms, CSDA, https://doi.org/10.1016/j.csda.2020.107151
[2] S. Persson, N. Welkenhuysen, S. Shashkova, S. Wiqvist, P. Reith, G. W. Schmidt, U. Picchini, M. Cvijovic (2021). PEPSDI: Scalable and flexible inference framework for stochastic dynamic single-cell models, bioRxiv doi:10.1101/2021.07.01.450748.
A new incomplete data model, the trunsored model, in lifetime analysis is introduced. This model can be regarded as a unified model of the censored and truncated models. Using the model, we can not only estimate the ratio of the fragile population to the mixed fragile and durable populations, but also test a hypothesis that the ratio is equal to a prescribed value. A central point of the paper is that such a test can easily be realized through the newly introduced trunsored model, because it has been difficult to do such a hypothesis test under only the framework of censored and truncated models. Therefore, the relationship of the trunsored model to the censored and truncated models is clarified because the trunsored model unifies the censored and truncated models. The paper also shows how to obtain the estimates of the parameters in lifetime estimation, and corresponding confidence intervals for the fragile population. Typical examples applied to electronic board failures, and to breast cancer data, for lifetime estimation are demonstrated, and successfully worked using the trunsored model.
Estimation for the number of fragile samples in the trunsored and truncated m...Hideo Hirose
A method to obtain the estimate and its confidence interval for the number of fragile samples in mixed populations of the fragile and durable samples, i.e., in the trunsored model, is introduced. The confidence interval in the trunsored model is compared with that in the truncated model. Although the maximum likelihood estimates for the parameters in the underlying probability distribution in both models are the same, the confidence interval for the estimated number of samples in the trunsored model is differ from that in the truncated model. When the censoring time goes to infinity, the confidence interval in the truncated model converges to zero, whereas the confidence interval in the trunsored model converges to a positive constant value.
The error for the number of fragile samples in the trunsored model is affected by the two kinds of fluctuation effect due to the censoring time: one is the fluctuation of the parameter estimates, and the other is the ratio of the number of fragile samples to the total number of samples. However, in the truncated model, the fluctuation depends only on the parameter estimates, and the error by this effect will vanish when the censoring time goes to infinity.
A typical example of the method is applied to the case fatality ratio for the infectious diseases such as SARS.
The simple Poisson process is characterized by a constant rate at whi.pdfankitgarg9513
The simple Poisson process is characterized by a constant rate at which events occur per unit
time. A generalization of this is to suppose that the probability of exactly one event occurring in
the interval [ t , t + t ] is ( t ) t + o ( t ) . It can then be shown that the number of events occurring
during an interval [ t 1 , t 2 ] has a Poisson distribution with parameter = t 2 t 1 ( t ) d t The
occurrence of events over time in this situation is called a nonhomogeneous Poisson process. The
article "Inference Based on Retrospective Ascertainment," J. Amer. Stat. Assoc., 1989: 360-372,
considers the intensity function ( t ) = exp ( + t ) as appropriate for events involving transmission
of HIV (the AIDS virus) via blood transfusion. Suppose that a = 2 and b = .6 (close to values
suggested in the paper), with time in years. 2.a What is the expected number of events in the
interval [ 0 , 4 ] ? In [ 2 , 6 ] ? 2.b What is the probability that at most 15 events occur in the
interval [ 0 , .9907 ] ?.
Temporal network epidemiology: Subtleties and algorithmsPetter Holme
The SIR and SIS models are the canonical model of epidemics of infections that make people immune upon recovery. Many open questions in computational epidemiology concern the underlying contact structure’s impact on models like the SIR or SIS. Temporal networks constitute a theoretical framework capable of encoding structures both in the networks of who could infect whom and when these contacts happen. In this talk, we discuss the detailed assumptions behind such simulations—how to make them comparable with analytically tractable formulations of the SIR model, and at the same time, as realistic as possible. We also discuss fast algorithms for such simulations and the challenges in improving them.
The dynamics of human social behavior in communication networksEsteban Moro
Slides of my invited talk at the TNETS workshop during the ECCS'13 conference in Barcelona.
More info about this research here: http://markov.uc3m.es/2013/05/are-you-a-social-keeper-or-a-social-explorer/
Phenomics assisted breeding in crop improvementIshaGoswami9
As the population is increasing and will reach about 9 billion upto 2050. Also due to climate change, it is difficult to meet the food requirement of such a large population. Facing the challenges presented by resource shortages, climate
change, and increasing global population, crop yield and quality need to be improved in a sustainable way over the coming decades. Genetic improvement by breeding is the best way to increase crop productivity. With the rapid progression of functional
genomics, an increasing number of crop genomes have been sequenced and dozens of genes influencing key agronomic traits have been identified. However, current genome sequence information has not been adequately exploited for understanding
the complex characteristics of multiple gene, owing to a lack of crop phenotypic data. Efficient, automatic, and accurate technologies and platforms that can capture phenotypic data that can
be linked to genomics information for crop improvement at all growth stages have become as important as genotyping. Thus,
high-throughput phenotyping has become the major bottleneck restricting crop breeding. Plant phenomics has been defined as the high-throughput, accurate acquisition and analysis of multi-dimensional phenotypes
during crop growing stages at the organism level, including the cell, tissue, organ, individual plant, plot, and field levels. With the rapid development of novel sensors, imaging technology,
and analysis methods, numerous infrastructure platforms have been developed for phenotyping.
Professional air quality monitoring systems provide immediate, on-site data for analysis, compliance, and decision-making.
Monitor common gases, weather parameters, particulates.
Salas, V. (2024) "John of St. Thomas (Poinsot) on the Science of Sacred Theol...Studia Poinsotiana
I Introduction
II Subalternation and Theology
III Theology and Dogmatic Declarations
IV The Mixed Principles of Theology
V Virtual Revelation: The Unity of Theology
VI Theology as a Natural Science
VII Theology’s Certitude
VIII Conclusion
Notes
Bibliography
All the contents are fully attributable to the author, Doctor Victor Salas. Should you wish to get this text republished, get in touch with the author or the editorial committee of the Studia Poinsotiana. Insofar as possible, we will be happy to broker your contact.
The ability to recreate computational results with minimal effort and actionable metrics provides a solid foundation for scientific research and software development. When people can replicate an analysis at the touch of a button using open-source software, open data, and methods to assess and compare proposals, it significantly eases verification of results, engagement with a diverse range of contributors, and progress. However, we have yet to fully achieve this; there are still many sociotechnical frictions.
Inspired by David Donoho's vision, this talk aims to revisit the three crucial pillars of frictionless reproducibility (data sharing, code sharing, and competitive challenges) with the perspective of deep software variability.
Our observation is that multiple layers — hardware, operating systems, third-party libraries, software versions, input data, compile-time options, and parameters — are subject to variability that exacerbates frictions but is also essential for achieving robust, generalizable results and fostering innovation. I will first review the literature, providing evidence of how the complex variability interactions across these layers affect qualitative and quantitative software properties, thereby complicating the reproduction and replication of scientific studies in various fields.
I will then present some software engineering and AI techniques that can support the strategic exploration of variability spaces. These include the use of abstractions and models (e.g., feature models), sampling strategies (e.g., uniform, random), cost-effective measurements (e.g., incremental build of software configurations), and dimensionality reduction methods (e.g., transfer learning, feature selection, software debloating).
I will finally argue that deep variability is both the problem and solution of frictionless reproducibility, calling the software science community to develop new methods and tools to manage variability and foster reproducibility in software systems.
Exposé invité Journées Nationales du GDR GPL 2024
Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...Ana Luísa Pinho
Functional Magnetic Resonance Imaging (fMRI) provides means to characterize brain activations in response to behavior. However, cognitive neuroscience has been limited to group-level effects referring to the performance of specific tasks. To obtain the functional profile of elementary cognitive mechanisms, the combination of brain responses to many tasks is required. Yet, to date, both structural atlases and parcellation-based activations do not fully account for cognitive function and still present several limitations. Further, they do not adapt overall to individual characteristics. In this talk, I will give an account of deep-behavioral phenotyping strategies, namely data-driven methods in large task-fMRI datasets, to optimize functional brain-data collection and improve inference of effects-of-interest related to mental processes. Key to this approach is the employment of fast multi-functional paradigms rich on features that can be well parametrized and, consequently, facilitate the creation of psycho-physiological constructs to be modelled with imaging data. Particular emphasis will be given to music stimuli when studying high-order cognitive mechanisms, due to their ecological nature and quality to enable complex behavior compounded by discrete entities. I will also discuss how deep-behavioral phenotyping and individualized models applied to neuroimaging data can better account for the subject-specific organization of domain-general cognitive systems in the human brain. Finally, the accumulation of functional brain signatures brings the possibility to clarify relationships among tasks and create a univocal link between brain systems and mental functions through: (1) the development of ontologies proposing an organization of cognitive processes; and (2) brain-network taxonomies describing functional specialization. To this end, tools to improve commensurability in cognitive science are necessary, such as public repositories, ontology-based platforms and automated meta-analysis tools. I will thus discuss some brain-atlasing resources currently under development, and their applicability in cognitive as well as clinical neuroscience.
This presentation explores a brief idea about the structural and functional attributes of nucleotides, the structure and function of genetic materials along with the impact of UV rays and pH upon them.
Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...University of Maribor
Slides from talk:
Aleš Zamuda: Remote Sensing and Computational, Evolutionary, Supercomputing, and Intelligent Systems.
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Inter-Society Networking Panel GRSS/MTT-S/CIS Panel Session: Promoting Connection and Cooperation
https://www.etran.rs/2024/en/home-english/
6. @estebanmoro
form/decay
t1 t2 t3
Tie activity
is bursty t
Groups of
conversation
t1 t1+dt
Hidalgo et al., Physica A (2008), Burt, Soc.Net.(2000)
Barabasi, Nature (2005)
Kovanen et al. J.Stat.Mech (2011), Zhao et al. NetMob (2011)
Ties appear/disappear
t1 t2 t3
Barabasi et al., Physica A (2002), Holme et al. Soc.Net.(2004)
Nodes
Timescale
7. @estebanmoro
form/decay
t1 t2 t3
Tie activity
is bursty t
Groups of
conversation
t1 t1+dt
Hidalgo et al., Physica A (2008), Burt, Soc.Net.(2000)
Barabasi, Nature (2005)
Kovanen et al. J.Stat.Mech (2011), Zhao et al. NetMob (2011)
Ties appear/disappear
t1 t2 t3
Barabasi et al., Physica A (2002), Holme et al. Soc.Net.(2004)
Nodes
Communities
form/change/decay
t1 t2
Palla et al. Proc.of SPIE (2007)
Communities
Timescale
8. @estebanmoro
form/decay
t1 t2 t3
Tie activity
is bursty t
Groups of
conversation
t1 t1+dt
Hidalgo et al., Physica A (2008), Burt, Soc.Net.(2000)
Barabasi, Nature (2005)
Kovanen et al. J.Stat.Mech (2011), Zhao et al. NetMob (2011)
Ties appear/disappear
t1 t2 t3
Barabasi et al., Physica A (2002), Holme et al. Soc.Net.(2004)
Nodes
Communities
form/change/decay
t1 t2
Palla et al. Proc.of SPIE (2007)
Communities
Networks
form/change/decay
t1 t2
Kossinets and Watts, Science (2006)
Network
Timescale
9. @estebanmoro
Christakis & Fowler ’10
= -
• Reach
• How many people are infected from a initial
spreader?
• Time
• How long does it take to infect them?
• Early detection of an outbreak, possible?
• Optimization
• How do we choose a given a number N of initial spreaders, so that reach is
maximize in a given time? What is the optimal N for a given cost?
• How do we choose a given number of immune people so that reach of the
disease is minimized? (resiliance of networks)
• How do we choose sensors to detect propagation?
10. @estebanmoro
- -
• SI / SIR / SIS models (Kermack & McKendrick ’27)
• S: suceptible (non infected)
• I: Infected
• R: resiliant
• S + I + R = N
• R0: basic reproductive number
IS R
dS
dt
= IS
dI
dt
= IS I
dR
dt
= I
dI
dt
= (R0S/N 1)I
R0 = N
R0 > N/S(0) ) dI/dt > 0
R0 < N/S(0) ) dI/dt < 0
11. @estebanmoro
- -
• SI / SIR / SIS models (Kermack & McKendrick ’27)
• S: suceptible (non infected)
• I: Infected
• R: resiliant
• S + I + R = N
• R0: basic reproductive number
IS R
dS
dt
= IS
dI
dt
= IS I
dR
dt
= I
dI
dt
= (R0S/N 1)I
R0 = N
R0 > N/S(0) ) dI/dt > 0
R0 < N/S(0) ) dI/dt < 0
12. @estebanmoro
- -
• SI / SIR / SIS models (Kermack & McKendrick ’27)
• S: suceptible (non infected)
• I: Infected
• R: resiliant
• S + I + R = N
• R0: basic reproductive number
IS R
dS
dt
= IS
dI
dt
= IS I
dR
dt
= I
dI
dt
= (R0S/N 1)I
R0 = N
R0 > N/S(0) ) dI/dt > 0
R0 < N/S(0) ) dI/dt < 0
25. i
j
˜Tij
P. Grassberger, On the critical behavior of the general
epidemic process and dynamical percolation, Math.
Biosci., 63 (1983), pp. 157–172.
Newman, M., 2002. Spread of epidemic
disease on networks. Physical Review E,
66(1), p.16128.
26. @estebanmoro
= -
• Real data
• Time Shuffled data
⌦
⌦
P(dt) heavy tailed
Correlated bursts
Correlated tie activity
Temporal motifs
Tie dynamics
P(dt) exponential
Uncorrelated bursts
Uncorrelated tie activity
No temporal motifs
No tie dynamics
27. @estebanmoro
- =
vi, vj, t
1,5,412
2,3,523
5,4,631
3,7,782
1,2,921
2,7,999
vi, vj, t
1,5,412
2,3,523
5,4,631
3,7,782
1,2,921
4,7,999
Select seed
+
infect in each
contact with
probability
=
• SIR model on real contact data
1
5
7
4
28. @estebanmoro
- =
vi, vj, t
1,2,412
2,3,523
1,5,631
2,7,782
3,7,921
5,4,999
vi, vj, t
1,2,412
2,3,523
1,5,631
2,7,782
3,7,921
5,4,999
Select seed
+
infect in each
contact with
probability
=
• SIR model on shuffled contact data
1
2
7
3
vi, vj, t
1,5,412
2,3,523
5,4,631
3,7,782
1,2,921
2,7,999
Real data Shuffled data
29. 2Effect of tie activity
form/decay
t1 t2 t3
Tie activity
is bursty t
Groups of
conversation
t1 t1+dt
Ties
Communities
form/change/decay
t1 t2
Communities
Networks
form/change/decay
t1 t2
Network
30. @estebanmoro
- =-
• Spreading (SIR) on contact networks
• Hypothesis:
• In every contact there is a
probability to infect
• Nodes only remain infected for a
time “ “
• Transmissibility: probability that i
infects j after being infected at
icular, the possible heavy-tail proper-
directly inherited by P(⇤ij). Fig. 2
d) results for P( tij) and P(⇤ij). For
so show the results obtained when i)
f the ⇥ ⇤ i events are randomly se-
mplete CDR, thus destroying any possi-
lation with i ⇤ j and e ectively mim-
ii) when the whole CDR time-stamps
destroying both tie temporal patterns
ween ties. Both shu⌅ings preserve the
18], i.e. the number of calls and their
the circadian rhythms of human com-
The result for P( tij) shows that small
nt times are more probable for the real
shu⌅ed ones, where the pdf is almost
Poissonian process, apart from a small
he circadian rhythms. This bursty pat-
as been found in numerous examples
i j
⇥ i
t t
t
ij tij
FIG. 1. (color online) Schematic view of communicati
events around individual i: each horizontal segment indica
an event between i ! j (top) and ⇤ ! i (bottom). At e
t↵ in the ⇤ ! i time series, ⇥ij is the time elapsed to the n
i ! j event, which is di erent from the inter-event time
in the i ! j time series. The red shaded area represents
recover time window Ti after t↵.
10
0
3
)
T
T ' 1/
t↵
i
j
wij
⇤
t↵
Miritello, G., Moro, E. & Lara, R., 2011. Dynamical
strength of social ties in information spreading.
Physical Review E, 83(4), p.045102.
31. @estebanmoro
- =-
• Transmissibility:
• where
rticular, the possible heavy-tail proper-
re directly inherited by P(⇤ij). Fig. 2
led) results for P( tij) and P(⇤ij). For
also show the results obtained when i)
of the ⇥ ⇤ i events are randomly se-
omplete CDR, thus destroying any possi-
relation with i ⇤ j and e ectively mim-
nd ii) when the whole CDR time-stamps
s destroying both tie temporal patterns
etween ties. Both shu⌅ings preserve the
[18], i.e. the number of calls and their
o the circadian rhythms of human com-
The result for P( tij) shows that small
vent times are more probable for the real
he shu⌅ed ones, where the pdf is almost
a Poissonian process, apart from a small
the circadian rhythms. This bursty pat-
has been found in numerous examples
ior [6] and seems to be universal in the
vidual schedules tasks. Here we see that
i j
⇥ i
t t
t
ij tij
FIG. 1. (color online) Schematic view of communica
events around individual i: each horizontal segment ind
an event between i ! j (top) and ⇤ ! i (bottom). At
t↵ in the ⇤ ! i time series, ⇥ij is the time elapsed to the
i ! j event, which is di erent from the inter-event tim
in the i ! j time series. The red shaded area represent
recover time window Ti after t↵.
10
0
10
3
tij)
)
T
t↵
i
j
wij
⇤
here each tie is described by
hat represents the probability
nsmitted from i to j and is a
er i becomes infected at time
munication events i ⇤ j in the
t ), then the transmissibility
g.1) Tij = 1 (1 )nij (t↵)
.
d at any ⇥ ⇤ i communication
ents independent and equally
which shows the one-to-one
tensity wij and the transmis
case: the more intense the c
the probability of infection.
Fig. 2, the real i ⇤ j and ⇥ ⇤
independent and Poissonian
the e ect of real patterns of c
missibility we approximate E
nij(t ) = number of events in
the time interval
i ! j
[t↵, t↵ + T]
32. @estebanmoro
- =-
• Assuming contacts are independent and equally probable in the
observation period
⇤ ! i
real (black circles) and shu ed ⇥ i (red squares) data with
respect to the overall-shu ed data. Right panel (c) shows the
ratio of the average size of the outbreaks (black circles) and
of R1 calculated using Eq. 6 (dashed blue line).
probable, we can average Tij over all the t events to get
Tij[ , T] = ⌃1 (1 )nij (t↵)
⌥ . (2)
If the number of ⇥ ⇤ i events is large enough we could
use a probabilistic description of Eq.(2) in terms of the
probability P(nij = n; T) that the number of communi-
cation events between i and j in a given time interval T
s n. Thus
Tij[ , T] =
1
n=0
P(nij = n; T)[1 (1 )n
], (3)
ata
me
la-
he
ior
nd
uf-
ge
ate
ics
ci-
ge
an
id-
et-
in
ase
probable, we can average Tij over all the t events to get
Tij[ , T] = ⌃1 (1 )nij (t↵)
⌥ . (2)
If the number of ⇥ ⇤ i events is large enough we could
use a probabilistic description of Eq.(2) in terms of the
probability P(nij = n; T) that the number of communi-
cation events between i and j in a given time interval T
is n. Thus
Tij[ , T] =
1
n=0
P(nij = n; T)[1 (1 )n
], (3)
which in principle can be non symmetric (Tij ⌅= Tji).
This quantity represents the real probability of infection
from i to j and defines the dynamical strength of the tie.
Note that Tij depends on the series of communication
events between i and j, but also on the time series of
calls received by i. In [17] Newman studied the case in
Probability of having n interactions between
i and j in a time interval of length T
33. @estebanmoro
- =-
• Example: suppose that the
interactions are equally distributed in the
observation period.
• Then we have a Poisson process:
• The interevent time distribution is the
exponential pdf
• The number of events in a window of
length T is given by the Poisson
distribution.
wij
⌦
⌦
2
events and in particular, the possible heavy-tail proper-
ties of P( tij) are directly inherited by P(⇤ij). Fig. 2
shows our (rescaled) results for P( tij) and P(⇤ij). For
comparison, we also show the results obtained when i)
the time-stamps of the ⇥ ⇤ i events are randomly se-
lected from the complete CDR, thus destroying any possi-
ble temporal correlation with i ⇤ j and e ectively mim-
icking Eq. (1) and ii) when the whole CDR time-stamps
are shu⌅ed thus destroying both tie temporal patterns
and correlation between ties. Both shu⌅ings preserve the
tie intensity wij [18], i.e. the number of calls and their
duration and also the circadian rhythms of human com-
munication [15]. The result for P( tij) shows that small
and large inter-event times are more probable for the real
series than for the shu⌅ed ones, where the pdf is almost
exponential as in a Poissonian process, apart from a small
deviation due to the circadian rhythms. This bursty pat-
tern of activity has been found in numerous examples
of human behavior [6] and seems to be universal in the
way a single individual schedules tasks. Here we see that
it also happens at the level of two individuals interac-
tion confirming recent results in mobile [15] and online
communities [7] dynamics. The pdf for ⇤ij is also heavy-
tailed but displays a larger number of short ⇤ij compared
i j
⇥ i
t t
t
ij tij
FIG. 1. (color online) Schematic view of communications
events around individual i: each horizontal segment indicates
an event between i ! j (top) and ⇤ ! i (bottom). At each
t↵ in the ⇤ ! i time series, ⇥ij is the time elapsed to the next
i ! j event, which is di erent from the inter-event time tij
in the i ! j time series. The red shaded area represents the
recover time window Ti after t↵.
10
-2
10
0
10
-6
10
-3
10
0
10
3
P(⇥ij/tij)
P(tij/tij)
P( tij) = ⇢e ⇢ tij
⇢ = wij/T0
P(nij = n; T) =
e ⇢T
(⇢T)n
n!
34. @estebanmoro
- =-
• Thus in the homogeneous (Poissonian) case:
• For small
• For general processes? Real data?
hich both time series are given by independent Poisson
ocesses in the whole observation interval [0, T0]. Thus,
(nij = n; T) is the Poisson distribution with rate ⇥ij =
ijT/T0, where wij is total number of calls from i to j
[0, T0], thus
˜Tij[ , T] = 1 e ⇥⇤
= 1 e ⇥wij T/T0
, (4)
hich shows the one-to-one relationship between the in-
nsity wij and the transmissibility Tij in the Poissonian
se: the more intense the communication is, the larger
e probability of infection. However, as we have seen in
g. 2, the real i ⇤ j and ⇥ ⇤ i series are far from being
dependent and Poissonian and in order to investigate
e e ect of real patterns of communication on the trans-
issibility we approximate Eq. (2). For small values of
˜Tij[ , T] ' wij
T
T0
35. @estebanmoro
- =-
• General process. Approximations
• If
• If
where
ior
nd
n
uf-
rge
ate
ics
ci-
rge
an
id-
et-
in
ase
ow
ata
on
ach
use a probabilistic description of Eq.(2) in terms of the
probability P(nij = n; T) that the number of communi-
cation events between i and j in a given time interval T
is n. Thus
Tij[ , T] =
1
n=0
P(nij = n; T)[1 (1 )n
], (3)
which in principle can be non symmetric (Tij ⌅= Tji).
This quantity represents the real probability of infection
from i to j and defines the dynamical strength of the tie.
Note that Tij depends on the series of communication
events between i and j, but also on the time series of
calls received by i. In [17] Newman studied the case in
which both time series are given by independent Poisson
processes in the whole observation interval [0, T0]. Thus,
P(nij = n; T) is the Poisson distribution with rate ⇥ij =
wijT/T0, where wij is total number of calls from i to j
in [0, T0], thus
⌧ 1 ) 1 (1 )n
' n
Tij ⇥nij⇤t↵
' 1 ) 1 (1 )n
' 1 for n > 0
Tij ⇥ 1 P0
ij
P0
ij = P(nij = 0; T) =
Z 1
T
P( ij)d ij
36. @estebanmoro
- =-
• General process. Approximations
• If
• If
where
ior
nd
n
uf-
rge
ate
ics
ci-
rge
an
id-
et-
in
ase
ow
ata
on
ach
use a probabilistic description of Eq.(2) in terms of the
probability P(nij = n; T) that the number of communi-
cation events between i and j in a given time interval T
is n. Thus
Tij[ , T] =
1
n=0
P(nij = n; T)[1 (1 )n
], (3)
which in principle can be non symmetric (Tij ⌅= Tji).
This quantity represents the real probability of infection
from i to j and defines the dynamical strength of the tie.
Note that Tij depends on the series of communication
events between i and j, but also on the time series of
calls received by i. In [17] Newman studied the case in
which both time series are given by independent Poisson
processes in the whole observation interval [0, T0]. Thus,
P(nij = n; T) is the Poisson distribution with rate ⇥ij =
wijT/T0, where wij is total number of calls from i to j
in [0, T0], thus
⌧ 1 ) 1 (1 )n
' n
Tij ⇥nij⇤t↵
' 1 ) 1 (1 )n
' 1 for n > 0
Tij ⇥ 1 P0
ij
P0
ij = P(nij = 0; T) =
Z 1
T
P( ij)d ij
37. @estebanmoro
- =-
•
• Probability of no event
P0
ij = P(nij = 0; T) =
Z 1
T
P( ij)d ij
3
1
1.2
1.4
1.6
1.8
1 10
1
1.05
1.1
1.15
0.05 0.10 0.15 0.20
0.6
0.8
1.0
1.2
1.4
nij⇥/˜nij⇥P0/˜P0
s⇥/˜s⇥
a
b
c
,R1/˜R1
T (in days)
icking Eq. (1) and ii) when the whole CDR time-stamps
are shu⌅ed thus destroying both tie temporal patterns
and correlation between ties. Both shu⌅ings preserve the
tie intensity wij [18], i.e. the number of calls and their
duration and also the circadian rhythms of human com-
munication [15]. The result for P( tij) shows that small
and large inter-event times are more probable for the real
series than for the shu⌅ed ones, where the pdf is almost
exponential as in a Poissonian process, apart from a small
deviation due to the circadian rhythms. This bursty pat-
tern of activity has been found in numerous examples
of human behavior [6] and seems to be universal in the
way a single individual schedules tasks. Here we see that
it also happens at the level of two individuals interac-
tion confirming recent results in mobile [15] and online
communities [7] dynamics. The pdf for ⇤ij is also heavy-
tailed but displays a larger number of short ⇤ij compared
to the shu⌅ed one. The abundance of short ⇤ij suggests
that receiving an information (⇥ ⇤ i) triggers commu-
nication with other people (i ⇤ j), a manifestation of
group conversations [11–13]. While the fat-tail of P(⇤ij)
is accurately described by Eq. (1), i.e. large transmission
intervals ⇤ij are mostly due to large inter-event commu-
nication times in the i ⇤ j tie, the behavior of P(⇤ij) is
not only due to the bursty patterns of tij, but also to the
temporal correlation between the i ⇤ j and the ⇥ ⇤ i
events. In fact, if the correlation between the i ⇤ j and
the ⇥ ⇤ i series is destroyed, the probability of short-
time intervals decreases and approaches the Poissonian
case (Fig. 2). In summary, relay times depend on two
main properties of human communication that compete
to one another. While the bursty nature of human ac-
tivity yields to large transmission times hindering any
possible infection, group conversations translate into an
FIG. 1. (color online) Schematic view of communications
events around individual i: each horizontal segment indicates
an event between i ! j (top) and ⇤ ! i (bottom). At each
t↵ in the ⇤ ! i time series, ⇥ij is the time elapsed to the next
i ! j event, which is di erent from the inter-event time tij
in the i ! j time series. The red shaded area represents the
recover time window Ti after t↵.
10
-6
10
-4
10
-2
10
0
10
210
-4
10
-2
10
0
10
-4
10
-2
10
0
10
2
10
-6
10
-3
10
0
10
3
⇥ij / tij
P(⇥ij/tij)
P(tij/tij)
FIG. 2. (color online) Distribution of the relay time inter-
vals ⇥ij (main) and of the inter-event times tij (inset) in the
i ! j tie rescaled by tij. The black circles correspond to
the real data, while the red squares is the overall-shu⇥ed re-
sult. Blue diamonds correspond to the case in which only the
⇤ ! i sequence is randomized. Only ties with wij 10 are
considered. In both graphs the dashed line correspond to the
e x
function.
tional reasons we consider the latter case. Nodes remain
infected during a time Ti until they decay into the re-
covered state. For the sake of simplicity we simulate the
Tij ⇥ 1 P0
ij
Long waiting times (bursts)
make transmissibility smaller
Tij ⇥ 1 P0
ij
Tij
˜Tij
' 1 ) 1 (1 )n
' 1 for n > 0
38. @estebanmoro
- =-
•
• Probability of no event
P0
ij = P(nij = 0; T) =
Z 1
T
P( ij)d ij
3
1
1.2
1.4
1.6
1.8
1 10
1
1.05
1.1
1.15
0.05 0.10 0.15 0.20
0.6
0.8
1.0
1.2
1.4
nij⇥/˜nij⇥P0/˜P0
s⇥/˜s⇥
a
b
c
,R1/˜R1
T (in days)
icking Eq. (1) and ii) when the whole CDR time-stamps
are shu⌅ed thus destroying both tie temporal patterns
and correlation between ties. Both shu⌅ings preserve the
tie intensity wij [18], i.e. the number of calls and their
duration and also the circadian rhythms of human com-
munication [15]. The result for P( tij) shows that small
and large inter-event times are more probable for the real
series than for the shu⌅ed ones, where the pdf is almost
exponential as in a Poissonian process, apart from a small
deviation due to the circadian rhythms. This bursty pat-
tern of activity has been found in numerous examples
of human behavior [6] and seems to be universal in the
way a single individual schedules tasks. Here we see that
it also happens at the level of two individuals interac-
tion confirming recent results in mobile [15] and online
communities [7] dynamics. The pdf for ⇤ij is also heavy-
tailed but displays a larger number of short ⇤ij compared
to the shu⌅ed one. The abundance of short ⇤ij suggests
that receiving an information (⇥ ⇤ i) triggers commu-
nication with other people (i ⇤ j), a manifestation of
group conversations [11–13]. While the fat-tail of P(⇤ij)
is accurately described by Eq. (1), i.e. large transmission
intervals ⇤ij are mostly due to large inter-event commu-
nication times in the i ⇤ j tie, the behavior of P(⇤ij) is
not only due to the bursty patterns of tij, but also to the
temporal correlation between the i ⇤ j and the ⇥ ⇤ i
events. In fact, if the correlation between the i ⇤ j and
the ⇥ ⇤ i series is destroyed, the probability of short-
time intervals decreases and approaches the Poissonian
case (Fig. 2). In summary, relay times depend on two
main properties of human communication that compete
to one another. While the bursty nature of human ac-
tivity yields to large transmission times hindering any
possible infection, group conversations translate into an
FIG. 1. (color online) Schematic view of communications
events around individual i: each horizontal segment indicates
an event between i ! j (top) and ⇤ ! i (bottom). At each
t↵ in the ⇤ ! i time series, ⇥ij is the time elapsed to the next
i ! j event, which is di erent from the inter-event time tij
in the i ! j time series. The red shaded area represents the
recover time window Ti after t↵.
10
-6
10
-4
10
-2
10
0
10
210
-4
10
-2
10
0
10
-4
10
-2
10
0
10
2
10
-6
10
-3
10
0
10
3
⇥ij / tij
P(⇥ij/tij)
P(tij/tij)
FIG. 2. (color online) Distribution of the relay time inter-
vals ⇥ij (main) and of the inter-event times tij (inset) in the
i ! j tie rescaled by tij. The black circles correspond to
the real data, while the red squares is the overall-shu⇥ed re-
sult. Blue diamonds correspond to the case in which only the
⇤ ! i sequence is randomized. Only ties with wij 10 are
considered. In both graphs the dashed line correspond to the
e x
function.
tional reasons we consider the latter case. Nodes remain
infected during a time Ti until they decay into the re-
covered state. For the sake of simplicity we simulate the
Tij ⇥ 1 P0
ij
Long waiting times (bursts)
make transmissibility smaller
Tij ⇥ 1 P0
ij
Tij
˜Tij
' 1 ) 1 (1 )n
' 1 for n > 0
39. @estebanmoro
- =-
•
• Probability of no event
P0
ij = P(nij = 0; T) =
Z 1
T
P( ij)d ij
3
1
1.2
1.4
1.6
1.8
1 10
1
1.05
1.1
1.15
0.05 0.10 0.15 0.20
0.6
0.8
1.0
1.2
1.4
nij⇥/˜nij⇥P0/˜P0
s⇥/˜s⇥
a
b
c
,R1/˜R1
T (in days)
icking Eq. (1) and ii) when the whole CDR time-stamps
are shu⌅ed thus destroying both tie temporal patterns
and correlation between ties. Both shu⌅ings preserve the
tie intensity wij [18], i.e. the number of calls and their
duration and also the circadian rhythms of human com-
munication [15]. The result for P( tij) shows that small
and large inter-event times are more probable for the real
series than for the shu⌅ed ones, where the pdf is almost
exponential as in a Poissonian process, apart from a small
deviation due to the circadian rhythms. This bursty pat-
tern of activity has been found in numerous examples
of human behavior [6] and seems to be universal in the
way a single individual schedules tasks. Here we see that
it also happens at the level of two individuals interac-
tion confirming recent results in mobile [15] and online
communities [7] dynamics. The pdf for ⇤ij is also heavy-
tailed but displays a larger number of short ⇤ij compared
to the shu⌅ed one. The abundance of short ⇤ij suggests
that receiving an information (⇥ ⇤ i) triggers commu-
nication with other people (i ⇤ j), a manifestation of
group conversations [11–13]. While the fat-tail of P(⇤ij)
is accurately described by Eq. (1), i.e. large transmission
intervals ⇤ij are mostly due to large inter-event commu-
nication times in the i ⇤ j tie, the behavior of P(⇤ij) is
not only due to the bursty patterns of tij, but also to the
temporal correlation between the i ⇤ j and the ⇥ ⇤ i
events. In fact, if the correlation between the i ⇤ j and
the ⇥ ⇤ i series is destroyed, the probability of short-
time intervals decreases and approaches the Poissonian
case (Fig. 2). In summary, relay times depend on two
main properties of human communication that compete
to one another. While the bursty nature of human ac-
tivity yields to large transmission times hindering any
possible infection, group conversations translate into an
FIG. 1. (color online) Schematic view of communications
events around individual i: each horizontal segment indicates
an event between i ! j (top) and ⇤ ! i (bottom). At each
t↵ in the ⇤ ! i time series, ⇥ij is the time elapsed to the next
i ! j event, which is di erent from the inter-event time tij
in the i ! j time series. The red shaded area represents the
recover time window Ti after t↵.
10
-6
10
-4
10
-2
10
0
10
210
-4
10
-2
10
0
10
-4
10
-2
10
0
10
2
10
-6
10
-3
10
0
10
3
⇥ij / tij
P(⇥ij/tij)
P(tij/tij)
FIG. 2. (color online) Distribution of the relay time inter-
vals ⇥ij (main) and of the inter-event times tij (inset) in the
i ! j tie rescaled by tij. The black circles correspond to
the real data, while the red squares is the overall-shu⇥ed re-
sult. Blue diamonds correspond to the case in which only the
⇤ ! i sequence is randomized. Only ties with wij 10 are
considered. In both graphs the dashed line correspond to the
e x
function.
tional reasons we consider the latter case. Nodes remain
infected during a time Ti until they decay into the re-
covered state. For the sake of simplicity we simulate the
Tij ⇥ 1 P0
ij
Long waiting times (bursts)
make transmissibility smaller
Tij ⇥ 1 P0
ij
Tij
˜Tij
' 1 ) 1 (1 )n
' 1 for n > 0
40. @estebanmoro
- =-
•
• Probability of no event
P0
ij = P(nij = 0; T) =
Z 1
T
P( ij)d ij
3
1
1.2
1.4
1.6
1.8
1 10
1
1.05
1.1
1.15
0.05 0.10 0.15 0.20
0.6
0.8
1.0
1.2
1.4
nij⇥/˜nij⇥P0/˜P0
s⇥/˜s⇥
a
b
c
,R1/˜R1
T (in days)
icking Eq. (1) and ii) when the whole CDR time-stamps
are shu⌅ed thus destroying both tie temporal patterns
and correlation between ties. Both shu⌅ings preserve the
tie intensity wij [18], i.e. the number of calls and their
duration and also the circadian rhythms of human com-
munication [15]. The result for P( tij) shows that small
and large inter-event times are more probable for the real
series than for the shu⌅ed ones, where the pdf is almost
exponential as in a Poissonian process, apart from a small
deviation due to the circadian rhythms. This bursty pat-
tern of activity has been found in numerous examples
of human behavior [6] and seems to be universal in the
way a single individual schedules tasks. Here we see that
it also happens at the level of two individuals interac-
tion confirming recent results in mobile [15] and online
communities [7] dynamics. The pdf for ⇤ij is also heavy-
tailed but displays a larger number of short ⇤ij compared
to the shu⌅ed one. The abundance of short ⇤ij suggests
that receiving an information (⇥ ⇤ i) triggers commu-
nication with other people (i ⇤ j), a manifestation of
group conversations [11–13]. While the fat-tail of P(⇤ij)
is accurately described by Eq. (1), i.e. large transmission
intervals ⇤ij are mostly due to large inter-event commu-
nication times in the i ⇤ j tie, the behavior of P(⇤ij) is
not only due to the bursty patterns of tij, but also to the
temporal correlation between the i ⇤ j and the ⇥ ⇤ i
events. In fact, if the correlation between the i ⇤ j and
the ⇥ ⇤ i series is destroyed, the probability of short-
time intervals decreases and approaches the Poissonian
case (Fig. 2). In summary, relay times depend on two
main properties of human communication that compete
to one another. While the bursty nature of human ac-
tivity yields to large transmission times hindering any
possible infection, group conversations translate into an
FIG. 1. (color online) Schematic view of communications
events around individual i: each horizontal segment indicates
an event between i ! j (top) and ⇤ ! i (bottom). At each
t↵ in the ⇤ ! i time series, ⇥ij is the time elapsed to the next
i ! j event, which is di erent from the inter-event time tij
in the i ! j time series. The red shaded area represents the
recover time window Ti after t↵.
10
-6
10
-4
10
-2
10
0
10
210
-4
10
-2
10
0
10
-4
10
-2
10
0
10
2
10
-6
10
-3
10
0
10
3
⇥ij / tij
P(⇥ij/tij)
P(tij/tij)
FIG. 2. (color online) Distribution of the relay time inter-
vals ⇥ij (main) and of the inter-event times tij (inset) in the
i ! j tie rescaled by tij. The black circles correspond to
the real data, while the red squares is the overall-shu⇥ed re-
sult. Blue diamonds correspond to the case in which only the
⇤ ! i sequence is randomized. Only ties with wij 10 are
considered. In both graphs the dashed line correspond to the
e x
function.
tional reasons we consider the latter case. Nodes remain
infected during a time Ti until they decay into the re-
covered state. For the sake of simplicity we simulate the
Tij ⇥ 1 P0
ij
Long waiting times (bursts)
make transmissibility smaller
Tij ⇥ 1 P0
ij
Tij
˜Tij
' 1 ) 1 (1 )n
' 1 for n > 0
41. @estebanmoro
- =-
•
• Average number of events
• If there is no correlation between
tie activity
• Correlation makes
and thus ( )
⌧ 1 ) 1 (1 )n
' n
hnijit↵
h˜nijit↵
h˜nijit↵
= wij
T
T0
hnijit↵
h˜nijit↵
Tij
˜Tij
Tij ⇥nij⇤t↵
1!10
5
2!10
5
a
smax
1
1.2
1.4
1.6
1.8
1.1
1.15
nij⇥/˜nij⇥0
a
b
Real
Shuffled
Poisson
2
events and in particular, the possible heavy-tail proper-
ties of P( tij) are directly inherited by P(⇤ij). Fig. 2
shows our (rescaled) results for P( tij) and P(⇤ij). For
comparison, we also show the results obtained when i)
the time-stamps of the ⇥ ⇤ i events are randomly se-
lected from the complete CDR, thus destroying any possi-
ble temporal correlation with i ⇤ j and e ectively mim-
icking Eq. (1) and ii) when the whole CDR time-stamps
are shu⌅ed thus destroying both tie temporal patterns
and correlation between ties. Both shu⌅ings preserve the
tie intensity wij [18], i.e. the number of calls and their
duration and also the circadian rhythms of human com-
munication [15]. The result for P( tij) shows that small
and large inter-event times are more probable for the real
series than for the shu⌅ed ones, where the pdf is almost
exponential as in a Poissonian process, apart from a small
deviation due to the circadian rhythms. This bursty pat-
tern of activity has been found in numerous examples
of human behavior [6] and seems to be universal in the
way a single individual schedules tasks. Here we see that
it also happens at the level of two individuals interac-
tion confirming recent results in mobile [15] and online
communities [7] dynamics. The pdf for ⇤ij is also heavy-
tailed but displays a larger number of short ⇤ij compared
to the shu⌅ed one. The abundance of short ⇤ij suggests
that receiving an information (⇥ ⇤ i) triggers commu-
i j
⇥ i
t t
t
ij tij
FIG. 1. (color online) Schematic view of communications
events around individual i: each horizontal segment indicates
an event between i ! j (top) and ⇤ ! i (bottom). At each
t↵ in the ⇤ ! i time series, ⇥ij is the time elapsed to the next
i ! j event, which is di erent from the inter-event time tij
in the i ! j time series. The red shaded area represents the
recover time window Ti after t↵.
-4
10
-2
10
0
10
-4
10
-2
10
0
10
2
10
-6
10
-3
10
0
10
3
P(⇥ij/tij)
P(tij/tij)
T0
T
42. @estebanmoro
- =-
• Smaller transmissibility =
• Slower propagation
• Smaller propagation
• Transmissibility can be used to
predict the dynamical percolation
transition
0
50
100
150
0 20 40 60 80 100
0
1
2
3
4
0.05 0.1 0.15 0.2
1!10
5
2!10
5
a
c
t (in days)
s(t)⇥ b
a
b
smax
FIG. 3. (color online) Average size dynamics for a large (a)
and a small (b) value of (left) and maximum size (right)
of the infection outbreaks (over 104
realizations) for the real
data (black lines) and shu ed data (red lines) for T = 2
days. The dashed line shows the critical point estimation
of the percolation transition given by R1[ , T] = 1 with R1
calculated using Eq. (6).
), where the causality between ⇥ ⌅ i and the i ⌅ j
series can make P0 even smaller in the real case.
o give a more quantitative analysis of the observed
vior we investigate the percolation process in a so-
network in which links have transmissibility Tij. The
ortant quantity is the secondary reproductive num-
R1, that is the average number of secondary infec-
s produced by an infectious individual. R1 gives in-
ation about percolation transition in the SIR process
ch happens at R1 = 1 [17]), but also about the speed
usion (which is proportional to R1 [20]) and of the
of the cascades (which is a growing function of R1
. Assuming that the Tij are given and that the so-
network is random in any other respect, R1 can be
oximated as
R1[ , T] =
⌥(
⇥
j Tij)2
i ⌥
⇥
j T 2
ij i
⌥
⇥
j Tij i
. (6)
that in the homogeneous case in which Tij = T
ecover the common result in random networks R1 =
2
i /⌥ki 1) [17]. Figs. 3 and 4 show the accuracy
he approximations used to get Eq.(6) to predict the
[3] C. Castellano, S. Fortunat
Phys. 81, 591 (2009).
[4] M. E. J. Newman, SIAM R
[5] A.-L. Barab´asi, Nature 435
[6] A. V´azquez et al., Phys. R
[7] D. Rybski et al., Proc. Natl
(2009).
[8] L. Isella et al., arXiv:1006.
[9] G. Kossinets, D. J. Watts,
[10] C. A. Hidalgo and C. Rodr
3017 (2008).
[11] J.-P. Eckmann, E. Moses, a
Sci. U.S.A. 101, 14333 (20
[12] Q. Zhao, and N. Oliver, Co
Approach to Characterize M
Mob2010.
[13] Y. Wu et al., Proc. Natl. A
(2010).
[14] J. L. Iribarren and E. Moro,
(2009).
[15] M. Karsai et al., arXiv:100
[16] A. Gautreau, A. Barrat, an
Acad. Sci. U.S.A. 106, 884
[17] M. E. J. Newman, Phys.
Kenah and J. M. Robins, Ph
[18] J.-P. Onnela et al, Proc. N
43. @estebanmoro
- =-
• Thus, in general
Property effect on spreading
Bursty tie acitivity Slows down
Conversations (correlated
contact patterns)
Accelerates
45. @estebanmoro
- =-
• Some data/models shows that burstiness accelerates contagion
Figure 1A, we see that an infection spreads much more slowly in
the RD network model, reaching fewer than 50% of the
individuals compared to more than 60% in the original network.
Thus, correlations in the order in which the contacts occur speed
up disease spread. More concretely, one such tendency is that
individuals tend to be intensely active over a period of time
followed by idle periods. When the time stamps are randomized
(RD model), this tendency disappears such that the presence of
individuals in the system is now, on average, longer and the
contacts less frequent. The average time, between an individual’s
first and last active period of, increases from 170.960.1 days in the
original network to 337.560.1 days after randomization. In
addition to correlations in the temporal order of contacts, the
randomized network yields more rapid a
(Figure 1B). The more rapid initial epidem
network results from the high clustering o
Finally, considering both the temporal and
randomized (RDT model), the curve (evol
Figure 1C) is in between those of Figure 1
fraction of infected vertices increases slowl
days, but not more slowly than in the RD
Later it increases more rapidly and by th
period reaches about 70% of the individual
RT scenario in Figure 1B, but still, larg
network).
The limit of high transmission probabili
Figure 1. Temporal and topological correlations effect on epidemics. In A–C, we plot the time evolution of the fra
ÆVæ. The curves correspond to SI epidemics in the original network (full line) and in its randomized versions: panel A represen
(RD); B shows rewiring of the edges and keeping the sellers’ time correlations (RT); and panel C depicts simultaneous rando
and edges (RDT).
doi:10.1371/journal.pcbi.1001109.g001
Simulated Epidemics in Real
0
0.2
0.4
0.6
0.8
1
10
1
10
3
10
5
〈Ii〉
(a) original
randomized
0
0.1
0.2
0.3
0.4
0.5
101
103
105
(b)
0.6
(c)
0.4
(d)
0
0.2
0.4
0.6
0.8
1
10
1
10
3
10
5
〈Ii〉
(a) original
randomized
0
0.1
0.2
0.3
0.4
0.5
101
(b)
0
0.2
0.4
0.6
10
3
10
5
10
7
〈Ii〉
(c)
τd
0
0.1
0.2
0.3
0.4
103
1
(d)
Figure 3: Average final infection size ⟨Ii⟩ for (a, b) Conference
Squares and circles correspond to the original and randomized tem
We set (a) v = 5, (b) v = 20, (c) v = 3, and (d) v = 10.
Rocha, L., Liljeros, F. & Holme, P., 2011.
Simulated epidemics in an empirical
spatiotemporal network of 50,185
sexual contacts. PLoS Computational
Biology, 7(3), p.e1001109.
Takaguchi, T., Masuda, N. & Holme, P., 2012.
Bursty communication patterns facilitate
spreading in a threshold-based epidemic
dynamics. PLoS ONE, 8(7), pp.e68629–
e68629.
46. 2Effect of tie dynamics
form/decay
t1 t2 t3
Tie activity
is bursty t
Groups of
conversation
t1 t1+dt
Ties
Communities
form/change/decay
t1 t2
Communities
Networks
form/change/decay
t1 t2
Network
47. @estebanmoro
= -
• Real data
• Shuffled data (1)
• Shuffled data (2)
P(dt) heavy tailed
Correlated bursts
Correlated tie activity
Temporal motifs
Tie dynamics
P(dt) exponential
Uncorrelated bursts
Uncorrelated tie activity
No temporal motifs
No tie dynamics
⌦
⌦
⌦
P(dt) exponential
Uncorrelated bursts
Uncorrelated tie activity
Temporal motifs ?
Tie dynamics
48. @estebanmoro
-
• Burstiness + conservation of ties
• Half of the slowing effect comes from destroying tie dynamics in the shuffling
a dynamical model of human interactions 115
0 50 100 150 200 250
0
200
400
600
800
t (in days)
hs(t)i
real-time data
overall shuffled data
intra-tie shuffled data
Average fraction of infected nodes (over 104
realizations) as a function of time for
nd T=7 days obtained for real-time data (solid curve), shuffled-time data (dashed
huffled tie creation/removal data (pointed curve). The effect of tie creation/removal
⌦
⌦
⌦
Miritello, G. (2013). Temporal Patterns
of Communication in Social Networks.
Springer.
52. @estebanmoro
1
2
3
-1 0 1 2 3 4 5
0.00003511
0.00007296
0.00015161
0.00031503
0.00065460
0.00136021
0.00282641
0.00587305
0.01220371
3.5e-5
2.8e-3
3.1e-4
1
2
3
4
-1 0 1 2 3 4 5
3.5e-05
7.3e-05
1.5e-04
3.2e-04
6.6e-04
1.4e-03
2.8e-03
5.9e-03
1.2e-02
2.5e-02
by communicating with them permanently, while older people use communica
wander around the social network.
x
x n ,i
ki = 10
ki = 20
ki = 50
i
0.2 0.5 1.0 2.0
-0.50.00.51.0
gamma
tiempomediodeinfección
tinf
Figure 6. Time of infection: Di↵erence of infection time as a function
for each of the iso-connectivity groups in figure 5. The relative di↵erence is w
average infection time for each of the groups.
build out systems of generalized reciprocity, connectivity
commons-based production. This is in contrast both t
earlier network im- agery that emphasized self-interest
Social keepers received
information before
Miritello, G. et al., 2013. Limited communication capacity unveils
strategies for human interaction. Scientific Reports, 3.
keepers explorers-
• Do strategies give an information
awareness advantage?
53. @estebanmoro
- =- -
• Thus, in general
Property Effect on spreading
Bursty tie acitivity Slows down
Conversations (correlated
contact patterns)
Accelerates
Tie dynamics Slows down
54. 3Models for temporal/dynamical networks
form/decay
t1 t2 t3
Tie activity
is bursty t
Groups of
conversation
t1 t1+dt
Ties
Communities
form/change/decay
t1 t2
Communities
Networks
form/change/decay
t1 t2
Network
55. @estebanmoro
-
• Activity driven model
• Each node is assigned an activity ai
from a probability distribution P(a)
• At each time step t the node is
activated and create m links with other
nodes
• At next time step t+∆t all edges are
removed
• With memory:
Perra, N. et al., 2012. Activity driven
modeling of time varying networks.
Scientific Reports, 2.
Karsai, M., Perra, N. & Vespignani, A., 2013.
Time varying networks and the weakness of
strong ties. Scientific Reports, 4, pp.4001–
4001.
56. @estebanmoro
-
FIG. 1 (color online). Schematic representation of t
struction procedure: a weighted directed graph G can
garded as a superposition of paths. Unfolding these path
results in itineraries (of variable characteristics) that ge
temporal network N .
PRL 110, 158702 (2013) P H Y S I C A
• Random itinearies
• Given an aggregated graph with
egde weights
• Generate random walk paths
through the network
• Decrease the weights of the path
• If edge is discarded
• Repeat until all edges are discarded
wij
wij ! wij 1
wij = 0
Barrat, A. et al., 2013. Modeling
Temporal Networks Using Random
Itineraries. Physical Review Letters,
110
57. 3Outlook
form/decay
t1 t2 t3
Tie activity
is bursty t
Groups of
conversation
t1 t1+dt
Ties
Communities
form/change/decay
t1 t2
Communities
Networks
form/change/decay
t1 t2
Network
58. @estebanmoro
=
• How universal is temporal/dynamical evolution of the network?
• Burstiness
• Tie evolution
• Motifs
• Community evolution
• Network birth and death
• How those process impact the way we observe the network?
• What are the Erdos-Renyi / Preferential attachement model in temporal/dynamical
networks? We need simple generative models
59. @estebanmoro
=
• Other human networks: mobility networks
untry movements
flows (comprising
t than country-to-
further investiga-
146 million geo-
gh the public API
in and from 29th
we consider that
user has tweeted
those transitions
the same day. We
ns and keep only
1km (see SI XX).
different users are
Tij between mu-
n our database in
nation lies within
conomical infor-
Statistics Institute
raph based on the
database, one can
, the elapsed time
mong many other
istribution with a
constraint of con-
tination checkins
part of the distri-
tion based on activity and geography and v) it is consistent when a
percentage p of links are randomly removed. All these considera-
tions, make natural consider the Infomap communities as functional
divisions of the country, where every community is connected (there
is no isolated municipality, see SI for further details). Communities
are plotted in the underlying blue scale colors in figure .
Fig. 1. Mobility graph and communities
61. @estebanmoro
• How two people communicate
• Detect link decay
• How people allocate their time
across their social relationships
• Find your “best” friends
• How people manage their
sociability? Social strategies?
• Detect social behaviors
SpringerTheses
Recognizing Outstanding Ph.D. Research
Physics
ISBN 978-3-319-00109-8
TemporalPatterns
ofCommunication
inSocialNetworks
MiritelloTemporalPatternsofCommunicationinSocialNetworks
SpringerTheses
Giovanna Miritello
Temporal Patterns of Communication in Social Networks
The main interest of this research has been in understanding and char-
acterizing large networks of human interactions as continuously chang-
ing objects. In fact, although many real social networks are dynamic
networks whose elements and properties continuously change over time,
traditional approaches to social network analysis are essentially static,
thus neglecting all temporal aspects. Specifically, we have investigated the
role that temporal patterns of human interaction play in three main fields
of social network analysis and data mining: characterization of time (or
attention) allocation in social networks, prediction of link decay/persist-
ence, and information spreading. In order to address this we analyzed
large anonymized data sets of phone call communication traces over long
periods of time. Access to these observations was granted by Telefonica
Research, Spain. The findings that emerge from our research indicate that
the observed heterogeneities and correlations of human temporal patterns
of interaction significantly affect the traditional view of social networks,
shifting from a very steady to a highly complex entity. Since structure and
dynamics are tightly coupled, they cannot be disentangled in the analysis
and modeling of human behavior, though traditional models seek to do
so. Our results impact not only the way in which social network are tradi-
tionally characterized, but more importantly also the understanding and
modeling phenomena such as group formation, spread of epidemics, and
the dissemination of ideas, opinions and information.
Giovanna Miritello
312485_Print.indd 1312485_Print.indd 1 3/5/2013 3:54:14 PM3/5/2013 3:54:14 PM