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Nonunique UPGMA clusterings of microsatellite markers
Natàlia Segura-Alabart, Francesc Serratosa, Sergio Gómez and Alberto Fernández
Briefings in Bioinformatics 23(5) (2022) bbac312
(pdf
+
suppl)
(doi)
(OUP)
Agglomerative hierarchical clustering has become a common tool for the analysis and visualization of data,
thus being present in a large amount of scientific research and predating all areas of bioinformatics and
computational biology. In this work, we focus on a critical problem, the nonuniqueness of the clustering
when there are tied distances, for which several solutions exist but are not implemented in most
hierarchical clustering packages. We analyze the magnitude of this problem in one particular setting: the
clustering of microsatellite markers using the Unweighted Pair-Group Method with Arithmetic Mean. To do so,
we have calculated the fraction of publications at the Scopus database in which more than one hierarchical
clustering is possible, showing that about 46% of the articles are affected. Additionally, to show the
problem from a practical point of view, we selected two opposite examples of articles that have multiple
solutions: one with two possible dendrograms, and the other with more than 2.5 million different possible
hierarchical clusterings.
Multiple abrupt phase transitions in urban transport congestion
Aniello Lampo, Javier Borge-Holthoefer, Sergio Gómez and Albert Solé-Ribalta
Physical Review Research 3 (2021) 013267
(pdf
+
suppl)
(doi)
(APS open access)
During the last decades, the study of cities has been transformed by new approaches combining
engineering and complexity sciences. Network theory is playing a central role, facilitating the
quantitative analysis of crucial urban dynamics, such as mobility, city growth or urban planning.
In this work, we focus on the spatial aspects of congestion. Analyzing a large amount of real
city networks, we show that the location of the onset of congestion changes according to the
considered urban area, defining, in turn, a set of congestion regimes separated by abrupt
transitions. To help unveiling these spatial dependencies of congestion (in terms of network
betweenness analysis), we introduce a family of planar road network models composed of a dense
urban center connected to an arboreal periphery. These models, coined as GT and DT-MST models,
allow us to analytically, numerically and experimentally describe how and why congestion emerges
in particular geographical areas of monocentric cities and, subsequently, to describe the
congestion regimes and the factors that promote the appearance of their abrupt transitions. We
show that the fundamental ingredient behind the observed abrupt transitions is the spatial
separation between the urban center and the periphery, and the number of separate areas that
form the periphery. Elaborating on the implications of our results, we show that they may have
an influence on the design and optimization of road networks regarding urban growth and the
management of daily traffic dynamics.
Modeling the spatiotemporal epidemic spreading of COVID-19 and the impact of mobility and social distancing interventions
Alex Arenas, Wesley Cota, Jesús Gómez-Gardeñes, Sergio Gómez, Clara Granell,
Joan T. Matamalas, David Soriano-Paños and Benjamin Steinegger
Physical Review X 10 (2020) 041055
(pdf
+
suppl)
(doi)
(APS open access)
Code
(MMCAcovid19.jl)
On 31 December, 2019, an outbreak of a novel coronavirus, SARS-CoV-2, that causes the COVID-19
disease, was first reported in Hubei, mainland China. This epidemics� health threat is probably
one of the biggest challenges faced by our interconnected modern societies. According to the
epidemiological reports, the large basic reproduction number R0∼3.0,
together with a huge fraction of asymptomatic infections, paved the way for a major crisis of
the national health capacity systems. Here, we develop an age-stratified mobility-based
metapopulation model that encapsulates the main particularities of the spreading of COVID-19
regarding (i) its transmission among individuals, (ii) the specificities of certain demographic
groups with respect to the impact of COVID-19, and (iii) the human mobility patterns inside and
among regions. The full dynamics of the epidemic is formalized in terms of a microscopic Markov
chain approach that incorporates the former elements and the possibility of implementing
containment measures based on social distancing and confinement. With this model, we study the
evolution of the effective reproduction number R(t), the key epidemiological parameter
to track the evolution of the transmissibility and the effects of containment measures, as it
quantifies the number of secondary infections generated by an infected individual. The
suppression of the epidemic is directly related to this value and is attained when
R<1. We find an analytical expression connecting R with nonpharmacological
interventions, and its phase diagram is presented. We apply this model at the municipality
level in Spain, successfully forecasting the observed incidence and the number of fatalities
in the country at each of its regions. The expression for R should assist policymakers
to evaluate the epidemics� response to actions, such as enforcing or relaxing confinement and
social distancing.
Effective approach to epidemic containment using link equations in complex networks
Joan T. Matamalas, Alex Arenas and Sergio Gómez
Science Advances 4 (2018) eaau4212
(pdf
+
suppl)
(doi)
(AAAS open access)
Data
(AAAS)
Epidemic containment is a major concern when confronting large-scale infections in complex
networks. Many studies have been devoted to analytically understand how to restructure the
network to minimize the impact of major outbreaks of infections at large scale. In many cases,
the strategies are based on isolating certain nodes, while less attention has been paid to
interventions on the links. In epidemic spreading, links inform about the probability of
carrying the contagion of the disease from infected to susceptible individuals. Note that
these states depend on the full structure of the network, and its determination is not
straightforward from the knowledge of nodes� states. Here, we confront this challenge and
propose a set of discrete-time governing equations that can be closed and analyzed, assessing
the contribution of links to spreading processes in complex networks. Our approach allows a
scheme for the containment of epidemics based on deactivating the most important links in
transmitting the disease. The model is validated in synthetic and real networks, yielding an
accurate determination of epidemic incidence and critical thresholds. Epidemic containment
based on link deactivation promises to be an effective tool to maintain functionality of
networks while controlling the spread of diseases, such as disease spread through air
transportation networks.
Congestion induced by the structure of multiplex networks
Albert Solé-Ribalta, Sergio Gómez and Alex Arenas
Physical Review Letters 116 (2016) 108701
(pdf
+
suppl)
(doi)
(APS)
Multiplex networks are representations of multilayer interconnected complex networks where
the nodes are the same at every layer. They turn out to be good abstractions of the intricate
connectivity of multimodal transportation networks, among other types of complex systems. One
of the most important critical phenomena arising in such networks is the emergence of
congestion in transportation flows. Here, we prove analytically that the structure of
multiplex networks can induce congestion for flows that otherwise would be decongested
if the individual layers were not interconnected. We provide explicit equations for the
onset of congestion and approximations that allow us to compute this onset from individual
descriptors of the individual layers. The observed cooperative phenomenon is reminiscent
of Braess' paradox in which adding extra capacity to a network when the moving entities
selfishly choose their route can in some cases reduce overall performance. Similarly, in
the multiplex structure, the efficiency in transportation can unbalance the transportation
loads resulting in unexpected congestion.
Bond percolation on multiplex networks
Adam Hackett, Davide Cellai, Sergio Gómez, Alex Arenas and James P. Gleeson
Physical Review X 6 (2016) 021002
(pdf)
(doi)
(APS open access)
We present an analytical approach for bond percolation on multiplex networks and use it to
determine the expected size of the giant connected component and the value of the critical
bond occupation probability in these networks. We advocate the relevance of these tools to
the modeling of multilayer robustness and contribute to the debate on whether any benefit is
to be yielded from studying a full multiplex structure as opposed to its monoplex projection,
especially in the seemingly irrelevant case of a bond occupation probability that does not
depend on the layer. Although we find that in many cases the predictions of our theory for
multiplex networks coincide with previously derived results for monoplex networks, we also
uncover the remarkable result that for a certain class of multiplex networks, well described
by our theory, new critical phenomena occur as multiple percolation phase transitions are
present. We provide an instance of this phenomenon in a multiplex network constructed from
London rail and European air transportation data sets.
Ranking in interconnected multilayer networks reveals versatile nodes
Manlio De Domenico, Albert Solé-Ribalta, Elisa Omodei, Sergio Gómez and Alex Arenas
Nature Communications 6 (2015) 6868
(pdf
+
suppl)
(doi)
(Springer Nature)
Code
(MuxViz)
The determination of the most central agents in complex networks is important because
they are responsible for a faster propagation of information, epidemics, failures and
congestion, among others. A challenging problem is to identify them in networked systems
characterized by different types of interactions, forming interconnected multilayer
networks. Here we describe a mathematical framework that allows us to calculate centrality
in such networks and rank nodes accordingly, finding the ones that play the most central
roles in the cohesion of the whole structure, bridging together different types of
relations. These nodes are the most versatile in the multilayer network. We investigate
empirical interconnected multilayer networks and show that the approaches based on
aggregating—or neglecting—the multilayer structure lead to a wrong
identification of the most versatile nodes, overestimating the importance of more marginal
agents and demonstrating the power of versatility in predicting their role in diffusive
and congestion processes.
Emergence of assortative mixing between clusters of cultured neurons
Sara Teller, Clara Granell, Manlio De Domenico, Jordi Soriano, Sergio Gómez and Alex Arenas
PLOS Computational Biology 10(9) (2014) e1003796
(pdf
+ suppl)
(doi)
(PLOS open access)
The analysis of the activity of neuronal cultures is considered to be a good proxy of the
functional connectivity of in vivo neuronal tissues. Thus, the functional complex network
inferred from activity patterns is a promising way to unravel the interplay between
structure and functionality of neuronal systems. Here, we monitor the spontaneous
self-sustained dynamics in neuronal cultures formed by interconnected aggregates of
neurons (clusters). Dynamics is characterized by the fast activation of groups of clusters
in sequences termed bursts. The analysis of the time delays between clusters' activations
within the bursts allows the reconstruction of the directed functional connectivity of
the network. We propose a method to statistically infer this connectivity and analyze the
resulting properties of the associated complex networks. Surprisingly enough, in contrast
to what has been reported for many biological networks, the clustered neuronal cultures
present assortative mixing connectivity values, as well as a rich-club core, meaning
that there is a preference for clusters to link to other clusters that share similar
functional connectivity, which shapes a 'connectivity backbone' in the network. These
results point out that the grouping of neurons and the assortative connectivity between
clusters are intrinsic survival mechanisms of the culture.
Navigability of interconnected networks under random failures
Manlio De Domenico, Albert Solé-Ribalta, Sergio Gómez and Alex Arenas
Proceedings of the National Academy of Sciences USA 111 (2014) 8351-8356
(pdf
+
suppl)
(doi)
(PNAS open access)
Assessing the navigability of interconnected networks (transporting information, people,
or goods) under eventual random failures is of utmost importance to design and protect
critical infrastructures. Random walks are a good proxy to determine this navigability,
specifically the coverage time of random walks, which is a measure of the dynamical
functionality of the network. Here, we introduce the theoretical tools required to
describe random walks in interconnected networks accounting for structure and dynamics
inherent to real systems. We develop an analytical approach for the covering time of
random walks in interconnected networks and compare it with extensive Monte Carlo
simulations. Generally speaking, interconnected networks are more resilient to random
failures than their individual layers per se, and we are able to quantify this effect.
As an application —which we illustrate by considering the public transport of London—
we show how the efficiency in exploring the multiplex critically depends on layers' topology,
interconnection strengths, and walk strategy. Our findings are corroborated by data-driven
simulations, where the empirical distribution of check-ins and checks-out is considered
and passengers travel along fastest paths in a network affected by real disruptions.
These findings are fundamental for further development of searching and navigability
strategies in real interconnected systems.
Mathematical formulation of multilayer networks
Manlio De Domenico, Albert Solé-Ribalta, Emanuele Cozzo, Mikko Kivelä, Yamir Moreno, Mason A. Porter, Sergio Gómez and Alex Arenas
Physical Review X 3 (2013) 041022
(pdf)
(doi)
(APS open access)
A network representation is useful for describing the structure of a large variety of complex systems.
However, most real and engineered systems have multiple subsystems and layers of connectivity, and the
data produced by such systems are very rich. Achieving a deep understanding of such systems necessitates
generalizing “traditional” network theory, and the newfound deluge of data now makes it possible to test
increasingly general frameworks for the study of networks. In particular, although adjacency matrices are
useful to describe traditional single-layer networks, such a representation is insufficient for the analysis
and description of multiplex and time-dependent networks. One must therefore develop a more general
mathematical framework to cope with the challenges posed by multilayer complex systems. In this paper,
we introduce a tensorial framework to study multilayer networks, and we discuss the generalization of
several important network descriptors and dynamical processes —including degree centrality, clustering
coefficients, eigenvector centrality, modularity, von Neumann entropy, and diffusion— for this framework.
We examine the impact of different choices in constructing these generalizations, and we illustrate how to
obtain known results for the special cases of single-layer and multiplex networks. Our tensorial approach
will be helpful for tackling pressing problems in multilayer complex systems, such as inferring who is
influencing whom (and by which media) in multichannel social networks and developing routing
techniques for multimodal transportation systems.
Dynamical interplay between awareness and epidemic spreading in multiplex networks
Clara Granell, Sergio Gómez and Alex Arenas
Physical Review Letters 111 (2013) 128701
(pdf
+
suppl)
(doi)
(APS)
We present the analysis of the interrelation between two processes accounting for
the spreading of an epidemics, and the information awareness to prevent its infection,
on top of multiplex networks. This scenario is representative of an epidemic process
spreading on a network of persistent real contacts, and a cyclic information awareness
process diffusing in the network of virtual social contacts between the same individuals.
The topology corresponds to a multiplex network where two diffusive processes are
interacting affecting each other. The analysis using a Microscopic Markov Chain
Approach (MMCA) reveals the phase diagram of the incidence of the epidemics and allows
to capture the evolution of the epidemic threshold depending on the topological structure
of the multiplex and the interrelation with the awareness process. Interestingly,
the critical point for the onset of the epidemics has a critical value (meta-critical
point) defined by the awareness dynamics and the topology of the virtual network, from
which the onset increases and the epidemics incidence decreases.
Diffusion dynamics on multiplex networks
Sergio Gómez, Albert Díaz-Guilera, Jesús Gómez-Gardeñes, Conrad J. Pérez-Vicente, Yamir Moreno and Alex Arenas
Physical Review Letters 110 (2013) 028701
(pdf
+
suppl)
(doi)
(APS)
We study the time scales associated with diffusion processes that take place on multiplex
networks, i.e., on a set of networks linked through interconnected layers. To this end,
we propose the construction of a supra-Laplacian matrix, which consists of a dimensional
lifting of the Laplacian matrix of each layer of the multiplex network. We use
perturbative analysis to reveal analytically the structure of eigenvectors and
eigenvalues of the complete network in terms of the spectral properties of the
individual layers. The spectrum of the supra-Laplacian allows us to understand
the physics of diffusionlike processes on top of multiplex networks.
Explosive synchronization transitions in scale-free networks
Jesús Gómez-Gardeñes, Sergio Gómez, Alex Arenas and Yamir Moreno
Physical Review Letters 106 (2011) 128701
(pdf
+
suppl)
(doi)
(APS)
Explosive collective phenomena have attracted much attention since the discovery
of an explosive percolation transition. In this Letter, we demonstrate how an
explosive transition shows up in the synchronization of scale-free networks by
incorporating a microscopic correlation between the structural and the dynamical
properties of the system. The characteristics of the explosive transition are
analytically studied in a star graph reproducing the results obtained in
synthetic networks. Our findings represent the first abrupt synchronization
transition in complex networks and provide a deeper understanding of the
microscopic roots of explosive critical phenomena.
Discrete-time Markov chain approach to contact-based disease spreading in complex networks
Sergio Gómez, Alex Arenas, Javier Borge-Holthoefer, Sandro Meloni and Yamir Moreno
Europhysics Letters 89 (2010) 38009
(pdf)
(doi)
(IOP)
Many epidemic processes in networks spread by stochastic contacts among their
connected vertices. There are two limiting cases widely analyzed in the physics literature, the
so-called contact process (CP) where the contagion is expanded at a certain rate from an infected
vertex to one neighbor at a time, and the reactive process (RP) in which an infected individual
effectively contacts all its neighbors to expand the epidemics. However, a more realistic
scenario is obtained from the interpolation between these two cases, considering a certain number of
stochastic contacts per unit time. Here we propose a discrete-time formulation of the problem of
contact-based epidemic spreading. We resolve a family of models, parameterized by the number
of stochastic contact trials per unit time, that range from the CP to the RP. In contrast to the
common heterogeneous mean-field approach, we focus on the probability of infection of individual
nodes. Using this formulation, we can construct the whole phase diagram of the different infection
models and determine their critical properties.
Solving non-uniqueness in agglomerative hierarchical clustering using multidendrograms
Alberto Fernández and Sergio Gómez
Journal of Classification 25 (2008) 43-65
(view)
(pdf)
(doi)
(Springer Nature)
Code
(mdendro)
(MultiDendrograms)
(Radatools)
In agglomerative hierarchical clustering, pair-group methods suffer from
a problem of non-uniqueness when two or more distances between different clusters
coincide during the amalgamation process. The traditional approach for solving
this drawback has been to take any arbitrary criterion in order to break ties between
distances, which results in different hierarchical classifications depending on the criterion
followed. In this article we propose a variable-group algorithm that consists
in grouping more than two clusters at the same time when ties occur. We give a tree
representation for the results of the algorithm, which we call a multidendrogram, as
well as a generalization of the Lance and Williams' formula which enables the implementation
of the algorithm in a recursive way.
Analysis of the structure of complex networks at different resolution levels
Alex Arenas, Alberto Fernández and Sergio Gómez
New Journal of Physics 10 (2008) 053039
(pdf)
(doi)
(IOP open access)
Code
(Radatools)
Modular structure is ubiquitous in real-world complex networks, and
its detection is important because it gives insights into the structure-functionality
relationship. The standard approach is based on the optimization of a quality
function, modularity, which is a relative quality measure for the partition of a
network into modules. Recently, some authors (Fortunato and Barthélemy 2007
Proc. Natl Acad. Sci. USA 104 36 and Kumpula et al 2007 Eur. Phys. J. B
56 41) have pointed out that the optimization of modularity has a fundamental
drawback: the existence of a resolution limit beyond which no modular structure
can be detected even though these modules might have their own entity.
The reason is that several topological descriptions of the network coexist at
different scales, which is, in general, a fingerprint of complex systems. Here, we
propose a method that allows for multiple resolution screening of the modular
structure. The method has been validated using synthetic networks, discovering
the predefined structures at all scales. Its application to two real social networks
allows us to find the exact splits reported in the literature, as well as the
substructure beyond the actual split.
Portfolio selection using neural networks
Alberto Fernández and Sergio Gómez
Computers & Operations Research 34 (2007) 1177-1191
(pdf)
(doi)
(Elsevier)
In this paper we apply a heuristic method based on artificial neural
networks (NN) in order to trace out the efficient frontier associated
to the portfolio selection problem. We consider a generalization of
the standard Markowitz mean-variance model which includes cardinality
and bounding constraints. These constraints ensure the investment in
a given number of different assets and limit the amount of capital to
be invested in each asset. We present some experimental results
obtained with the NN heuristic and we compare them to those obtained
with three previous heuristic methods.
