329 research outputs found
Phase transition in the Countdown problem
Here we present a combinatorial decision problem, inspired by the celebrated
quiz show called the countdown, that involves the computation of a given target
number T from a set of k randomly chosen integers along with a set of
arithmetic operations. We find that the probability of winning the game
evidences a threshold phenomenon that can be understood in the terms of an
algorithmic phase transition as a function of the set size k. Numerical
simulations show that such probability sharply transitions from zero to one at
some critical value of the control parameter, hence separating the algorithm's
parameter space in different phases. We also find that the system is maximally
efficient close to the critical point. We then derive analytical expressions
that match the numerical results for finite size and permit us to extrapolate
the behavior in the thermodynamic limit.Comment: Submitted for publicatio
Time series irreversibility: a visibility graph approach
We propose a method to measure real-valued time series irreversibility which
combines two differ- ent tools: the horizontal visibility algorithm and the
Kullback-Leibler divergence. This method maps a time series to a directed
network according to a geometric criterion. The degree of irreversibility of
the series is then estimated by the Kullback-Leibler divergence (i.e. the
distinguishability) between the in and out degree distributions of the
associated graph. The method is computationally effi- cient, does not require
any ad hoc symbolization process, and naturally takes into account multiple
scales. We find that the method correctly distinguishes between reversible and
irreversible station- ary time series, including analytical and numerical
studies of its performance for: (i) reversible stochastic processes
(uncorrelated and Gaussian linearly correlated), (ii) irreversible stochastic
pro- cesses (a discrete flashing ratchet in an asymmetric potential), (iii)
reversible (conservative) and irreversible (dissipative) chaotic maps, and (iv)
dissipative chaotic maps in the presence of noise. Two alternative graph
functionals, the degree and the degree-degree distributions, can be used as the
Kullback-Leibler divergence argument. The former is simpler and more intuitive
and can be used as a benchmark, but in the case of an irreversible process with
null net current, the degree-degree distribution has to be considered to
identifiy the irreversible nature of the series.Comment: submitted for publicatio
The shape of memory in temporal networks
Temporal networks are widely used models for describing the architecture of
complex systems. Network memory -- that is the dependence of a temporal
network's structure on its past -- has been shown to play a prominent role in
diffusion, epidemics and other processes occurring over the network, and even
to alter its community structure. Recent works have proposed to estimate the
length of memory in a temporal network by using high-order Markov models. Here
we show that network memory is inherently multidimensional and cannot be
meaningfully reduced to a single scalar quantity. Accordingly, we introduce a
mathematical framework for defining and efficiently estimating the microscopic
shape of memory, which fully characterises how the activity of each link
intertwines with the activities of all other links. We validate our methodology
on a wide range of synthetic models of temporal networks with tuneable memory,
and subsequently study the heterogeneous shapes of memory emerging in various
real-world networks.Comment: 35 pages (5 main, 30 supplementary), 14 figures (3 main, 11
supplementary), 3 tables (all supplementary), uses tikz-network.sty and
tikz_network.p
On the biological role of Fraunhofer lines of the Sun
The important role of Fraunhofer lines formed in the solar atmosphere in the spectrum of the Sun for the biological evolution on Earth has been discussed. In vitro, laboratory experiments have been accomplished to substantiate the concept of the role of Fraunhofer lines as drivers of the evolution via impact on molecules of biological significance. As a practical application of the concept,
successful results of clinical tests on humans have been obtained to demonstrate the possibility of non-medicinal means to be used for therapy in the cases of infectious
deceases such as HIV/AIDS. The importance for human health of blurring Fraunhofer lines due to increasing atmospheric pollution has been emphasized
Phase transition in a stochastic prime number generator
We introduce a stochastic algorithm that acts as a prime number generator.
The dynamics of such algorithm gives rise to a continuous phase transition
which separates a phase where the algorithm is able to reduce a whole set of
integers into primes and a phase where the system reaches a frozen state with
low prime density. We present both numerical simulations and an analytical
approach in terms of an annealed approximation, by means of which the data are
collapsed. A critical slowing down phenomenon is also outlined.Comment: accepted in PRE (Rapid Comm.
Predicting success in the worldwide start-up network
By drawing on large-scale online data we construct and analyze the
time-varying worldwide network of professional relationships among start-ups.
The nodes of this network represent companies, while the links model the flow
of employees and the associated transfer of know-how across companies. We use
network centrality measures to assess, at an early stage, the likelihood of the
long-term positive performance of a start-up, showing that the start-up network
has predictive power and provides valuable recommendations doubling the current
state of the art performance of venture funds. Our network-based approach not
only offers an effective alternative to the labour-intensive screening
processes of venture capital firms, but can also enable entrepreneurs and
policy-makers to conduct a more objective assessment of the long-term
potentials of innovation ecosystems and to target interventions accordingly
Number theoretic example of scale-free topology inducing self-organized criticality
In this work we present a general mechanism by which simple dynamics running
on networks become self-organized critical for scale free topologies. We
illustrate this mechanism with a simple arithmetic model of division between
integers, the division model. This is the simplest self-organized critical
model advanced so far, and in this sense it may help to elucidate the mechanism
of self-organization to criticality. Its simplicity allows analytical
tractability, characterizing several scaling relations. Furthermore, its
mathematical nature brings about interesting connections between statistical
physics and number theoretical concepts. We show how this model can be
understood as a self-organized stochastic process embedded on a network, where
the onset of criticality is induced by the topology.Comment: 4 pages, 3 figures. Physical Review Letters, in pres
Critical behavior of a Ginzburg-Landau model with additive quenched noise
We address a mean-field zero-temperature Ginzburg-Landau, or \phi^4, model
subjected to quenched additive noise, which has been used recently as a
framework for analyzing collective effects induced by diversity. We first make
use of a self-consistent theory to calculate the phase diagram of the system,
predicting the onset of an order-disorder critical transition at a critical
value {\sigma}c of the quenched noise intensity \sigma, with critical exponents
that follow Landau theory of thermal phase transitions. We subsequently perform
a numerical integration of the system's dynamical variables in order to compare
the analytical results (valid in the thermodynamic limit and associated to the
ground state of the global Lyapunov potential) with the stationary state of the
(finite size) system. In the region of the parameter space where metastability
is absent (and therefore the stationary state coincide with the ground state of
the Lyapunov potential), a finite-size scaling analysis of the order parameter
fluctuations suggests that the magnetic susceptibility diverges quadratically
in the vicinity of the transition, what constitutes a violation of the
fluctuation-dissipation relation. We derive an effective Hamiltonian and
accordingly argue that its functional form does not allow to straightforwardly
relate the order parameter fluctuations to the linear response of the system,
at odds with equilibrium theory. In the region of the parameter space where the
system is susceptible to have a large number of metastable states (and
therefore the stationary state does not necessarily correspond to the ground
state of the global Lyapunov potential), we numerically find a phase diagram
that strongly depends on the initial conditions of the dynamical variables.Comment: 8 figure
Impact of survey geometry and super-sample covariance on future photometric galaxy surveys
Photometric galaxy surveys probe the late-time Universe where the density field is highly non-Gaussian. A consequence is the emergence of the super-sample covariance (SSC), a non-Gaussian covariance term that is sensitive to fluctuations on scales larger than the survey window. In this work, we study the impact of the survey geometry on the SSC and, subsequently, on cosmological parameter inference. We devise a fast SSC approximation that accounts for the survey geometry and compare its performance to the common approximation of rescaling the results by the fraction of the sky covered by the survey, fSKY, dubbed ‘full-sky approximation’. To gauge the impact of our new SSC recipe, that we call ‘partial-sky’, we perform Fisher forecasts on the parameters of the (w0, wa)-CDM model in a 3 × 2 point analysis, varying the survey area, the geometry of the mask, and the galaxy distribution inside our redshift bins. The differences in the marginalised forecast errors –with the full-sky approximation performing poorly for small survey areas but excellently for stage-IV-like areas– are found to be absorbed by the marginalisation on galaxy bias nuisance parameters. For large survey areas, the unmarginalised errors are underestimated by about 10% for all probes considered. This is a hint that, even for stage-IV-like surveys, the partial-sky method introduced in this work will be necessary if tight priors are applied on these nuisance parameters. We make the partial-sky method public with a new release of the public code PySSC
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