Edge of chaos as critical local symmetry breaking in dissipative nonautonomous systems

The fully nonlinear notion of resonance -$\textit{geometrical resonance}$- in the general context of dissipative systems subjected to $\textit{nonsteady}$ potentials is discussed. It is demonstrated that there is an exact local invariant associated with each geometrical resonance solution which reduces to the system's energy when the potential is steady. The geometrical resonance solutions represent a \textit{local symmetry} whose critical breaking leads to a new analytical criterion for the order-chaos threshold. This physical criterion is deduced in the co-moving frame from the local energy conservation over the shortest significant timescale. Remarkably, the new criterion for the onset of chaos is shown to be valid over large regions of parameter space, thus being useful beyond the perturbative regime and the scope of current mathematical techniques

Drastic disorded-induced reduction of signal amplification in scale-free networks

Understanding information transmission across a network is a fundamental task for controlling and manipulating both biological and man-made information processing systems. Here, we show how topological resonant-like amplification effects in scale-free networks of signaling devices are drastically reduced when phase disorder in the external signals is considered. This is demonstrated theoretically by means of a star-like network of overdamped bistable systems, and confirmed numerically by simulations of scale-free networks of such systems. The taming effect of the phase disorder is found to be sensitive to the amplification's strength, while the topology-induced amplification mechanism is robust against this kind of quenched disorder in the sense that it does not significantly change the values of the coupling strength where amplification is maximum in its absence.Comment: 5 pages, 4 (double) figure

Criticality-induced universitality in ratchets

Conclusive mathematical arguments are presented supporting the ratchet conjecture [R. Chacón,J. Phys. A 40, F413 (2007)], i.e., the existence of a universal force wave form which optimally enhances directed transport by symmetry breaking. Specifically, such a particular waveform is shown to be “unique” for both temporal and spatial biharmonic forces, and general (non-perturbative) laws providing the dependence of the strength of directed transport on the force parameters are deduced for these forces. The theory explains previous results for a great diversity of systems subjected to such biharmonic forces and provides a universal quantitative criterion to optimize “any” application of the ratchet effect induced by symmetry breaking of temporal and spatial biharmonic forces.notPeerReviewe

Prediction of tropospheric ozone concentration at urban locations using machine learning algorithms. Application to Barcelona, Spain

In the last decades, the interest in predicting tropospheric ozone levels (O₃) has increased due to its detrimental effect on population health and vegetation. Although certain factors such as solar radiation are well known to have an influence on ozone levels, the effect of other variables is less clear. In this study, several regression models based on the Random Forest (RF) algorithm are generated to predict the daily maximum hourly ozone concentration level (1hO₃) and the daily maximum 8-hours average ozone concentration level (8hO₃) one day ahead in Barcelona, using air quality data, meteorological data and time variables as inputs. Two versions of the model are considered: taking information from the whole year and focusing only on summer months (May to September). In addition, classification models are created, based on thresholds inspired by current regulations for both outputs. RF regression models capture the time variation of tropospheric ozone through the year and they generate accurate estimations with acceptable deviation between the observations and predictions. In general, the categorical models of 1hO₃ show suitable and lower error rates than 8hO₃. However, the categories, which gather the most of the tropospheric ozone values have high accuracy and the categories with few values inside them have low accuracy. Consequently, these categorical models are not useful as a tool to alert the population about a specific ozone event. The analysis of RF models shows that the tropospheric ozone level (1hO₃ or 8hO₃ according to the model) of the previous day to the prediction has the strongest association to the output. The importance of other inputs varies between the models considered; while solar radiation and day of the year are the main variables after O₃ for the whole year models, relative humidity, average dew-point deficit and weekday are also relevant in the summer models

Impulse-induced optimum signal amplification in scale-free networks

Optimizing information transmission across a network is an essential task for controlling and manipulating generic information-processing systems. Here, we show how topological amplification effects in scale-free networks of signaling devices are optimally enhanced when the impulse transmitted by periodic external signals (time integral over two consecutive zeros) is maximum. This is demonstrated theoretically by means of a star-like network of overdamped bistable systems subjected to generic zero-mean periodic signals and confirmed numerically by simulations of scale-free networks of such systems. Our results show that the enhancer effect of increasing values of the signal's impulse is due to a correlative increase of the energy transmitted by the periodic signals, while it is found to be resonant-like with respect to the topology-induced amplification mechanism.P.J.M. and R.C. acknowledge financial support from the Ministerio de Economía y Competitividad (Spain) through the FIS2014-55867-P and FIS2012-34902 projects, respectively. P.J.M. acknowledges financial support from the Gobierno de Aragon (Spain, E19-Grupo FENOL) and European Social Funds. R.C. acknowledges financial support from the Junta de Extremadura (JEx, Spain) through project GR15146.Peer Reviewe

Drastic disorder-induced reduction of signal amplification in scale-free networks

Understanding information transmission across a network is a fundamental task for controlling and manipulating both biological and manmade information-processing systems. Here we show how topological resonant-like amplification effects in scale-free networks of signaling devices are drastically reduced when phase disorder in the external signals is considered. This is demonstrated theoretically by means of a starlike network of overdamped bistable systems, and confirmed numerically by simulations of scale-free networks of such systems. The taming effect of the phase disorder is found to be sensitive to the amplification's strength, while the topology-induced amplification mechanism is robust against this kind of quenched disorder in the sense that it does not significantly change the values of the coupling strength where amplification is maximum in its absence.R. C. and P. J. M. acknowledge financial support from the Ministerio de Economía y Competitividad (Mineco, Spain) through FIS2012-34902 and FIS2011-25167 projects, respectively. R.C. acknowledges financial support from the Junta de Extremadura (JEx, Spain) through project GR10045.Peer Reviewe