131 research outputs found
Deep learning systems as complex networks
Thanks to the availability of large scale digital datasets and massive
amounts of computational power, deep learning algorithms can learn
representations of data by exploiting multiple levels of abstraction. These
machine learning methods have greatly improved the state-of-the-art in many
challenging cognitive tasks, such as visual object recognition, speech
processing, natural language understanding and automatic translation. In
particular, one class of deep learning models, known as deep belief networks,
can discover intricate statistical structure in large data sets in a completely
unsupervised fashion, by learning a generative model of the data using
Hebbian-like learning mechanisms. Although these self-organizing systems can be
conveniently formalized within the framework of statistical mechanics, their
internal functioning remains opaque, because their emergent dynamics cannot be
solved analytically. In this article we propose to study deep belief networks
using techniques commonly employed in the study of complex networks, in order
to gain some insights into the structural and functional properties of the
computational graph resulting from the learning process.Comment: 20 pages, 9 figure
Growth or Reproduction: Emergence of an Evolutionary Optimal Strategy
Modern ecology has re-emphasized the need for a quantitative understanding of
the original 'survival of the fittest theme' based on analyzis of the intricate
trade-offs between competing evolutionary strategies that characterize the
evolution of life. This is key to the understanding of species coexistence and
ecosystem diversity under the omnipresent constraint of limited resources. In
this work we propose an agent based model replicating a community of
interacting individuals, e.g. plants in a forest, where all are competing for
the same finite amount of resources and each competitor is characterized by a
specific growth-reproduction strategy. We show that such an evolution dynamics
drives the system towards a stationary state characterized by an emergent
optimal strategy, which in turn depends on the amount of available resources
the ecosystem can rely on. We find that the share of resources used by
individuals is power-law distributed with an exponent directly related to the
optimal strategy. The model can be further generalized to devise optimal
strategies in social and economical interacting systems dynamics.Comment: 10 pages, 5 figure
Early warning signs in social-ecological networks
Social ecological systems are often difficult to investigate and manage
because of their inherent complexity1. Small variations in external drivers can
lead to abrupt changes associated with instabilities and bifurcations in the
underlying dynamics2-4. Anticipating critical transitions and divergence from
the present state of the system is particularly crucial to the prevention or
mitigation of the effects of unwanted and irreversible changes5-10. Recent
research in ecology has focused on leading indicators of regime shift in
ecosystems characterized by one state variable5,7,11,12. The case of systems
with several mutually interacting components, however, has remained poorly
investigated13, while the connection between network stability and research on
indicators for loss of resilience has been elusive14. Here we develop a
theoretical framework to analyze early warning signs of instability and regime
shift in social ecological networks. We provide analytical expressions for a
set of precursors of instability in social ecological systems with additive
noise for a variety of network structures. In particular, we show that the
covariance matrix of the dynamics can effectively anticipate the emergence of
instability. We also compare signals of early warning based on the dynamics of
suitably selected nodes, to indicators based on the integrated behavior of the
whole network. We find that the performances of these indicators are affected
by the network structure and the type of interaction among nodes. These results
provide new advances in multidimensional early warning analysis and offer a
framework to evaluate the resilience of social ecological networks.Comment: 14 pages, 4 figures. Supplementary Information available upon reques
Species survival and scaling laws in hostile and disordered environments
In this work we study the likelihood of survival of single-species in the
context of hostile and disordered environments. Population dynamics in this
environment, as modeled by the Fisher equation, is characterized by negative
average growth rate, except in some random spatially distributed patches that
may support life. In particular, we are interested in the phase diagram of the
survival probability and in the critical size problem, i.e., the minimum patch
size required for surviving in the long time dynamics. We propose a measure for
the critical patch size as being proportional to the participation ratio (PR)
of the eigenvector corresponding to the largest eigenvalue of the linearized
Fisher dynamics. We obtain the (extinction-survival) phase diagram and the
probability distribution function (PDF) of the critical patch sizes for two
topologies, namely, the one-dimensional system and the fractal Peano basin. We
show that both topologies share the same qualitative features, but the fractal
topology requires higher spatial fluctuations to guarantee species survival. We
perform a finite-size scaling and we obtain the associated scaling exponents.
In addition, we show that the PDF of the critical patch sizes has an universal
shape for the 1D case in terms of the model parameters (diffusion, growth rate,
etc.). In contrast, the diffusion coefficient has a drastic effect on the PDF
of the critical patch sizes of the fractal Peano basin, and it does not obey
the same scaling law of the 1D case.Comment: 20 pages, 5 Figure
Neutral dynamics with environmental noise: age-size statistics and species lifetimes
Neutral dynamics, where taxa are assumed to be demographically equivalent and
their abundance is governed solely by the stochasticity of the underlying
birth-death process, has proved itself as an important minimal model that
accounts for many empirical datasets in genetics and ecology. However, the
restriction of the model to demographic [] noise yields
relatively slow dynamics that appears to be in conflict with both short-term
and long-term characteristics of the observed systems. Here we analyze two of
these problems - age size relationships and species extinction time - in the
framework of a neutral theory with both demographic and environmental
stochasticity. It turns out that environmentally induced variations of the
demographic rates control the long-term dynamics and modify dramatically the
predictions of the neutral theory with demographic noise only, yielding much
better agreement with empirical data. We consider two prototypes of "zero mean"
environmental noise, one which is balanced with regard to the arithmetic
abundance, another balanced in the logarithmic (fitness) space, study their
species lifetime statistics and discuss their relevance to realistic models of
community dynamics
Virtual water controlled demographic growth of nations
Population growth is in general constrained by food production, which in turn
depends on the access to water resources. At a country level, some populations
use more water than they control because of their ability to import food and
the virtual water required for its production. Here, we investigate the
dependence of demographic growth on available water resources for exporting and
importing nations. By quantifying the carrying capacity of nations based on
calculations of the virtual water available through the food trade network, we
point to the existence of a global water unbalance. We suggest that current
export rates will not be maintained and consequently we question the long-run
sustainability of the food trade system as a whole. Water rich regions are
likely to soon reduce the amount of virtual water they export, thus leaving
import-dependent regions without enough water to sustain their populations. We
also investigate the potential impact of possible scenarios that might mitigate
these effects through (1) cooperative interactions among nations whereby water
rich countries maintain a tiny fraction of their food production available for
export; (2) changes in consumption patterns; and (3) a positive feedback
between demographic growth and technological innovations. We find that these
strategies may indeed reduce the vulnerability of water-controlled societies.Comment: 11 pages, 3 figure
Reconciling cooperation, biodiversity and stability in complex ecological communities
Empirical observations show that ecological communities can have a huge
number of coexisting species, also with few or limited number of resources.
These ecosystems are characterized by multiple type of interactions, in
particular displaying cooperative behaviors. However, standard modeling of
population dynamics based on Lotka-Volterra type of equations predicts that
ecosystem stability should decrease as the number of species in the community
increases and that cooperative systems are less stable than communities with
only competitive and/or exploitative interactions. Here we propose a stochastic
model of population dynamics, which includes exploitative interactions as well
as cooperative interactions induced by cross-feeding. The model is exactly
solved and we obtain results for relevant macro-ecological patterns, such as
species abundance distributions and correlation functions. In the large system
size limit, any number of species can coexist for a very general class of
interaction networks and stability increases as the number of species grows.
For pure mutualistic/commensalistic interactions we determine the topological
properties of the network that guarantee species coexistence. We also show that
the stationary state is globally stable and that inferring species interactions
through species abundance correlation analysis may be misleading. Our
theoretical approach thus show that appropriate models of cooperation naturally
leads to a solution of the long-standing question about complexity-stability
paradox and on how highly biodiverse communities can coexist.Comment: 25 pages, 10 figure
Ecohydrological Footprints:Quantitative Response of Ecosystems to Changes in their Hydrological Drivers
Ecohydrological footprints are defined as the response of ecosystem functions or services to changes in their hydrologic drivers. In this thesis, several diverse footprints are addressed: noise-driven effects on storage-discharge relations and catchment streamflow distributions, that are important drivers of biodiversity; soil salinization and its ecohydrological implications; topological effects of the ecological interaction networks on living communities (e.g. on their species persistence); and form and function of the global virtual water trade network. The coherence of the conceptual framework is provided by the study of drivers and controls of ecohydrological variability using methodological approaches based on statistical mechanics. In fact, this thesis work outlines a significant portion of environmental statistical mechanics, an overarching discipline that is emerging in recent years, which applies mathematical tools from statistical mechanics to model several ecohydrological processes. The proposed relevance of this thesis lies in the major effects of hydrologic drivers on ecological process. The view that emerges from current research in ecohydrology, that this thesis supports, is that there exists a definite need for an integrated understanding of ecological and hydrological processes. Because stochasticity is intrinsic to environmental and ecohydrological variability, noise plays an important and constructive role in ecohydrological processes. In this thesis, a stochastic approach is applied to analyze different ecohydrological processes, ranging from green and blue water flows in river basins (part I), ecosystem dynamics affected by the directional dispersal provided by river networks (part II) to water footprints of human society (part III).Methods range from novel exact solutions to stochastic differential equations to random graph theory applications, and imply the analysis of suitable field data. An analytical framework for quantitative analysis is laid out to tackle complex problems and to estimate the effects of environmental change on the interaction of the hydrologic processes with the biota. The main results of this thesis are: i) the achievement of exact solutions for the probability distribution of catchment streamflow, that takes in account stochastic fluctuations in the storage-discharge relation and for the condition of a noise induced phenomena to the streamflows regimes; ii) the stationary solutions of soil salinity under stochastic hydrologic forcing; iii) a novel solution of the Ito-Stratonovich problem in multiplicative Poisson processes; iv) the proper framework for species' persistence time distributions, as a function of topological constraints on the ecosystem, and its connection with other important macroecological laws. A related length-bias sampling problem is also solved. v) A statistical analysis of the global virtual trade network and a semi-analytical model that is able to describe most of the observed properties
Testing the critical brain hypothesis using a phenomelogical renormalization group
We present a systematic study to test a recently introduced phenomenological
renormalization group, proposed to coarse-grain data of neural activity from
their correlation matrix. The approach allows, at least in principle, to
establish whether the collective behavior of the network of spiking neurons is
described by a non-Gaussian critical fixed point. We test this renormalization
procedure in a variety of models focusing in particular on the contact process,
which displays an absorbing phase transition at between a
silent and an active state. We find that the results of the coarse-graining do
not depend on the presence of long-range interactions, but some scaling
features persist in the super-critical system up to a distance of from
. Our results provide insights on the possible subtleties that one
needs to consider when applying such phenomenological approaches directly to
data to infer signatures of criticality.Comment: 9 pages, 8 figure
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