309 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
Arrow of time across five centuries of classical music
The concept of time series irreversibility—the degree by which the statistics of signals are not invariant under time reversal—naturally appears in nonequilibrium physics in stationary systems which operate away from equilibrium and produce entropy. This concept has not been explored to date in the realm of musical scores as these are typically short sequences whose time reversibility estimation could suffer from strong finite size effects which preclude interpretability. Here we show that the so-called horizontal visibility graph method—which recently was shown to quantify such statistical property even in nonstationary signals—is a method that can estimate time reversibility of short symbolic sequences, thus unlocking the possibility of exploring such properties in the context of musical compositions. Accordingly, we analyze over 8000 musical pieces ranging from the Renaissance to the early Modern period and show that, indeed, most of them display clear signatures of time irreversibility. Since by construction stochastic processes with a linear correlation structure (such as
1
/
f
noise) are time reversible, we conclude that musical compositions have a considerably richer structure, that goes beyond the traditional properties retrieved by the power spectrum or similar approaches. We also show that musical compositions display strong signs of nonlinear correlations, that nonlinearity is correlated to irreversibility, and that these are also related to asymmetries in the abundance of musical intervals, which we associate to the narrative underpinning a musical composition. These findings provide tools for the study of musical periods and composers, as well as criteria related to music appreciation and cognition
Feigenbaum graphs: a complex network perspective of chaos
The recently formulated theory of horizontal visibility graphs transforms
time series into graphs and allows the possibility of studying dynamical
systems through the characterization of their associated networks. This method
leads to a natural graph-theoretical description of nonlinear systems with
qualities in the spirit of symbolic dynamics. We support our claim via the case
study of the period-doubling and band-splitting attractor cascades that
characterize unimodal maps. We provide a universal analytical description of
this classic scenario in terms of the horizontal visibility graphs associated
with the dynamics within the attractors, that we call Feigenbaum graphs,
independent of map nonlinearity or other particulars. We derive exact results
for their degree distribution and related quantities, recast them in the
context of the renormalization group and find that its fixed points coincide
with those of network entropy optimization. Furthermore, we show that the
network entropy mimics the Lyapunov exponent of the map independently of its
sign, hinting at a Pesin-like relation equally valid out of chaos.Comment: Published in PLoS ONE (Sep 2011
Monensin and forskolin inhibit the transcription rate of sucrase-isomaltase but not the stability of its mRNA in Caco-2 cells
AbstractTreatment of Caco-2 cells with forskolin (25 ÎĽM) or monensin (1 ÎĽM) has previously been shown to cause a marked decrease in the level of sucrase-isomaltase (SI) mRNA, without any effect on the expression of dipeptidylpeptidase IV (DPP-IV). In the present work, we report that there is no significant difference in the stability of SI mRNA between control and treated cells. On the other hand, we demonstrate a decrease in the transcription rate of SI mRNA which is sufficient to account for the decrease in the steady-state level of SI mRNA both in forskolin- and monensin-treated Caco-2 cells
Phase transitions in number theory: from the birthday problem to Sidon sets
In this work, we show how number theoretical problems can be fruitfully approached with the tools of statistical physics. We focus on g-Sidon sets, which describe sequences of integers whose pairwise sums are different, and propose a random decision problem which addresses the probability of a random set of k integers to be g-Sidon. First, we provide numerical evidence showing that there is a crossover between satisfiable and unsatisfiable phases which converts to an abrupt phase transition in a properly defined thermodynamic limit. Initially assuming independence, we then develop a mean-field theory for the g-Sidon decision problem. We further improve the mean-field theory, which is only qualitatively correct, by incorporating deviations from independence, yielding results in good quantitative agreement with the numerics for both finite systems and in the thermodynamic limit. Connections between the generalized birthday problem in probability theory, the number theory of Sidon sets and the properties of q-Potts models in condensed matter physics are briefly discusse
Informe sobre la enseñanza secundaria agrĂcola en Inglaterra y Gales
The author tries to give a whole idea of the organization and character of the agricultural secondary teaching in England and Wales, its principal direction being contained in the rapport drawn by the Loveday Commision in 1945. It is to be noted the English trend to suppress the exclusively technical or professiontal secondary schools in a strict sense. The agricultural secondary teaching tries to prepare those wo will later on occupy positions of responsibility in the agricultural industry so that they may be clever, useful members in the rural community. In the first place the Loveday Commision studied the adaptation of a plan of agricultural studies to the existing schools: Secondary Grammar School, Secondary Technical School and Secondary Modern School and in second place the creation of two types of agricultural technical secondary Schools: Agricultural Technical School and Rural Junior Polytechnic
Description of stochastic and chaotic series using visibility graphs
Nonlinear time series analysis is an active field of research that studies
the structure of complex signals in order to derive information of the process
that generated those series, for understanding, modeling and forecasting
purposes. In the last years, some methods mapping time series to network
representations have been proposed. The purpose is to investigate on the
properties of the series through graph theoretical tools recently developed in
the core of the celebrated complex network theory. Among some other methods,
the so-called visibility algorithm has received much attention, since it has
been shown that series correlations are captured by the algorithm and
translated in the associated graph, opening the possibility of building
fruitful connections between time series analysis, nonlinear dynamics, and
graph theory. Here we use the horizontal visibility algorithm to characterize
and distinguish between correlated stochastic, uncorrelated and chaotic
processes. We show that in every case the series maps into a graph with
exponential degree distribution P (k) ~ exp(-{\lambda}k), where the value of
{\lambda} characterizes the specific process. The frontier between chaotic and
correlated stochastic processes, {\lambda} = ln(3/2), can be calculated
exactly, and some other analytical developments confirm the results provided by
extensive numerical simulations and (short) experimental time series
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