25 research outputs found
Generalized Markov stability of network communities
We address the problem of community detection in networks by introducing a
general definition of Markov stability, based on the difference between the
probability fluxes of a Markov chain on the network at different time scales.
The specific implementation of the quality function and the resulting optimal
community structure thus become dependent both on the type of Markov process
and on the specific Markov times considered. For instance, if we use a natural
Markov chain dynamics and discount its stationary distribution -- that is, we
take as reference process the dynamics at infinite time -- we obtain the
standard formulation of the Markov stability. Notably, the possibility to use
finite-time transition probabilities to define the reference process naturally
allows detecting communities at different resolutions, without the need to
consider a continuous-time Markov chain in the small time limit. The main
advantage of our general formulation of Markov stability based on dynamical
flows is that we work with lumped Markov chains on network partitions, having
the same stationary distribution of the original process. In this way the form
of the quality function becomes invariant under partitioning, leading to a
self-consistent definition of community structures at different aggregation
scales
Non-mean-field Critical Exponent in a Mean-field Model : Dynamics versus Statistical Mechanics
The mean-field theory tells that the classical critical exponent of
susceptibility is the twice of that of magnetization. However, the linear
response theory based on the Vlasov equation, which is naturally introduced by
the mean-field nature, makes the former exponent half of the latter for
families of quasistationary states having second order phase transitions in the
Hamiltonian mean-field model and its variances. We clarify that this strange
exponent is due to existence of Casimir invariants which trap the system in a
quasistationary state for a time scale diverging with the system size. The
theoretical prediction is numerically confirmed by -body simulations for the
equilibrium states and a family of quasistationary states.Comment: 6 pages, 3 figure
The scientific influence of nations on global scientific and technological development
Determining how scientific achievements influence the subsequent process of
knowledge creation is a fundamental step in order to build a unified ecosystem
for studying the dynamics of innovation and competitiveness. Relying separately
on data about scientific production on one side, through bibliometric
indicators, and about technological advancements on the other side, through
patents statistics, gives only a limited insight on the key interplay between
science and technology which, as a matter of fact, move forward together within
the innovation space. In this paper, using citation data of both research
papers and patents, we quantify the direct influence of the scientific outputs
of nations on further advancements in science and on the introduction of new
technologies. Our analysis highlights the presence of geo-cultural clusters of
nations with similar innovation system features, and unveils the heterogeneous
coupled dynamics of scientific and technological advancements. This study
represents a step forward in the buildup of an inclusive framework for
knowledge creation and innovation
Universal Database for Economic Complexity
We present an integrated database suitable for the investigations of the
Economic development of countries by using the Economic Fitness and Complexity
framework. Firstly, we implement machine learning techniques to reconstruct the
database of Trade of Services and we integrate it with the database of the
Trade of the physical Goods, generating a complete view of the International
Trade and denoted the Universal database. Using this data, we derive a
statistically significant network of interaction of the Economic activities,
where preferred paths of development and clusters of High-Tech industries
naturally emerge. Finally, we compute the Economic Fitness, an algorithmic
assessment of the competitiveness of countries, removing the unexpected
misbehaviour of Economies under-represented by the sole consideration of the
Trade of the physical Goods
Linear response theory for long-range interacting systems in quasistationary states
Long-range interacting systems, while relaxing to equilibrium, often get
trapped in long-lived quasistationary states which have lifetimes that diverge
with the system size. In this work, we address the question of how a long-range
system in a quasistationary state (QSS) responds to an external perturbation.
We consider a long-range system that evolves under deterministic Hamilton
dynamics. The perturbation is taken to couple to the canonical coordinates of
the individual constituents. Our study is based on analyzing the Vlasov
equation for the single-particle phase space distribution. The QSS represents
stable stationary solution of the Vlasov equation in the absence of the
external perturbation. In the presence of small perturbation, we linearize the
perturbed Vlasov equation about the QSS to obtain a formal expression for the
response observed in a single-particle dynamical quantity. For a QSS that is
homogeneous in the coordinate, we obtain an explicit formula for the response.
We apply our analysis to a paradigmatic model, the Hamiltonian mean-field
model, that involves particles moving on a circle under Hamilton dynamics. Our
prediction for the response of three representative QSSs in this model (the
water-bag QSS, the Fermi-Dirac QSS, and the Gaussian QSS) is found to be in
good agreement with -particle simulations for large . We also show the
long-time relaxation of the water-bag QSS to the Boltzmann-Gibbs equilibrium
state.Comment: 13 pages, 4 figures; v2: typos fixed; v3: small changes, close to the
published versio
Geography of science: competitiveness and inequality
We characterize the temporal dynamics of Scientific Fitness, as defined by the Economic Fitness and Complexity (EFC) framework, and R&D expenditures at the geographic scale of nations. Our analysis highlights common patterns across similar research systems, and shows how develop-ing nations (China in particular) are quickly catching up with the developed world. This paints the picture of a general growth of scientific and technical capabilities of nations induced by the spreading of information typical of the scientific environment. Shifting the focus of the analysis to the regional level, we find that even developed nations display a considerable level of inequal-ity in the Scientific Fitness of their internal regions. Further, we assess comparatively how the competitiveness of each geographic region is distributed over the spectrum of research sectors. Overall, the Scientific Fitness represents the first high quality estimation of the scientific strength of nations and regions, opening new policy-making applications for better allocating resources, filling inequality gaps and ultimately promoting innovation
The scientific impact of nations on scientific and technological development
Determining how scientific achievements influence the subsequent process of knowledge creation is a fundamental step in order to build a unified ecosystem for studying the dynamics of innovation and competitiveness. Yet, relying separately on data about scientific production on one side, through bibliometric indicators, and about technological advancements on the other side, through patents statistics, gives only a limited insight on the key interplay between science and technology which, as a matter of fact, move forward together within the innovation space. In this paper, using citation data of both scientific papers and patents, we quantify the direct impact of the scientific outputs of nations on further advancements in science and on the introduction of new technologies. Our analysis highlights the presence of geo-cultural clusters of nations with similar innovation system features, and unveils the heterogeneous coupled dynamics of scientific and technological success. This study represents a first step in the buildup of a comprehensive framework for knowledge creation and innovation
Ranking species in complex ecosystems through nestedness maximization
Identifying the rank of species in a social or ecological network is a
difficult task, since the rank of each species is invariably determined by
complex interactions stipulated with other species. Simply put, the rank of a
species is a function of the ranks of all other species through the adjacency
matrix of the network. A common system of ranking is to order species in such a
way that their neighbours form maximally nested sets, a problem called nested
maximization problem (NMP). Here we show that the NMP can be formulated as an
instance of the Quadratic Assignment Problem, one of the most important
combinatorial optimization problem widely studied in computer science,
economics, and operations research. We tackle the problem by Statistical
Physics techniques: we derive a set of self-consistent nonlinear equations
whose fixed point represents the optimal rankings of species in an arbitrary
bipartite mutualistic network, which generalize the Fitness-Complexity
equations widely used in the field of economic complexity. Furthermore, we
present an efficient algorithm to solve the NMP that outperforms
state-of-the-art network-based metrics and genetic algorithms. Eventually, our
theoretical framework may be easily generalized to study the relationship
between ranking and network structure beyond pairwise interactions, e.g. in
higher-order networks.Comment: 28 pages; 2 figure