Post-critical set and non existence of preserved meromorphic two-forms

We present a family of birational transformations in $CP_2$ depending on two, or three, parameters which does not, generically, preserve meromorphic two-forms. With the introduction of the orbit of the critical set (vanishing condition of the Jacobian), also called ``post-critical set'', we get some new structures, some "non-analytic" two-form which reduce to meromorphic two-forms for particular subvarieties in the parameter space. On these subvarieties, the iterates of the critical set have a polynomial growth in the \emph{degrees of the parameters}, while one has an exponential growth out of these subspaces. The analysis of our birational transformation in $CP_2$ is first carried out using Diller-Favre criterion in order to find the complexity reduction of the mapping. The integrable cases are found. The identification between the complexity growth and the topological entropy is, one more time, verified. We perform plots of the post-critical set, as well as calculations of Lyapunov exponents for many orbits, confirming that generically no meromorphic two-form can be preserved for this mapping. These birational transformations in $CP_2$, which, generically, do not preserve any meromorphic two-form, are extremely similar to other birational transformations we previously studied, which do preserve meromorphic two-forms. We note that these two sets of birational transformations exhibit totally similar results as far as topological complexity is concerned, but drastically different results as far as a more ``probabilistic'' approach of dynamical systems is concerned (Lyapunov exponents). With these examples we see that the existence of a preserved meromorphic two-form explains most of the (numerical) discrepancy between the topological and probabilistic approach of dynamical systems.Comment: 34 pages, 7 figure

Quantum butterfly effect in weakly interacting diffusive metals

We study scrambling, an avatar of chaos, in a weakly interacting metal in the presence of random potential disorder. It is well known that charge and heat spread via diffusion in such an interacting disordered metal. In contrast, we show within perturbation theory that chaos spreads in a ballistic fashion. The squared anticommutator of the electron field operators inherits a light-cone like growth, arising from an interplay of a growth (Lyapunov) exponent that scales as the inelastic electron scattering rate and a diffusive piece due to the presence of disorder. In two spatial dimensions, the Lyapunov exponent is universally related at weak coupling to the sheet resistivity. We are able to define an effective temperature-dependent butterfly velocity, a speed limit for the propagation of quantum information, that is much slower than microscopic velocities such as the Fermi velocity and that is qualitatively similar to that of a quantum critical system with a dynamical critical exponent $z > 1$.Comment: 15 pages in two-column format, 7 figure

Time-and event-driven communication process for networked control systems: A survey

Copyright © 2014 Lei Zou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In recent years, theoretical and practical research topics on networked control systems (NCSs) have gained an increasing interest from many researchers in a variety of disciplines owing to the extensive applications of NCSs in practice. In particular, an urgent need has arisen to understand the effects of communication processes on system performances. Sampling and protocol are two fundamental aspects of a communication process which have attracted a great deal of research attention. Most research focus has been on the analysis and control of dynamical behaviors under certain sampling procedures and communication protocols. In this paper, we aim to survey some recent advances on the analysis and synthesis issues of NCSs with different sampling procedures (time-and event-driven sampling) and protocols (static and dynamic protocols). First, these sampling procedures and protocols are introduced in detail according to their engineering backgrounds as well as dynamic natures. Then, the developments of the stabilization, control, and filtering problems are systematically reviewed and discussed in great detail. Finally, we conclude the paper by outlining future research challenges for analysis and synthesis problems of NCSs with different communication processes.This work was supported in part by the National Natural Science Foundation of China under Grants 61329301, 61374127, and 61374010, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Consolidity: Mystery of inner property of systems uncovered

AbstractThis paper uncovers the mystery of consolidity, an inner property of systems that was amazingly hidden. Consolidity also reveals the secrecy of why strong stable and highly controllable systems are not invulnerable of falling and collapsing. Consolidity is measured by its Consolidity Index, defined as the ratio of overall changes of output parameters over combined changes of input and system parameters, all operating in fully fuzzy environment. Under this notion, systems are classified into consolidated, quasi-consolidated, neutrally consolidated, unconsolidated, quasi-unconsolidated and mixed types. The strategy for the implementation of consolidity is elaborated for both natural and man-made existing systems as well as the new developed ones. An important critique arises that the by-product consolidity of natural or built-as-usual system could lead to trapping such systems into a completely undesired unconsolidity. This suggests that the ample number of conventional techniques that do not take system consolidity into account should gradually be changed, and adjusted with improved consolidity-based techniques. Four Golden Rules are highlighted for handling system consolidity, and applied to several illustrative case studies. These case studies cover the consolidity analysis of the Drug Concentration problem, Predator-Prey Population problem, Spread of Infectious Disease problem, AIDS Epidemic problem and Arm Race model. It is demonstrated that consolidity changes are contrary (opposite in sign) to changes of both stability and controllability. This is a very significant result showing that our present practice of stressing on building strong stable and highly controllable systems could have already jeopardized the consolidity behavior of an ample family of existing real life systems. It is strongly recommended that the four Golden Rules of consolidity should be enforced as future strict regulations of systems modeling, analysis, design and building of different disciplines of sciences. It can be stated that with the mystery of consolidity uncovered, the door is now wide open towards the launching of a new generation of systems with superior consolidity in various sciences and disciplines. Examples of these disciplines are basic sciences, evolutionary systems, engineering, astronautics, astronomy, biology, ecology, medicine, pharmacology, economics, finance, commerce, political and management sciences, humanities, social sciences, literature, psychology, philosophy, mass communication, and education

Real-time predictive maintenance for wind turbines using Big Data frameworks

This work presents the evolution of a solution for predictive maintenance to a Big Data environment. The proposed adaptation aims for predicting failures on wind turbines using a data-driven solution deployed in the cloud and which is composed by three main modules. (i) A predictive model generator which generates predictive models for each monitored wind turbine by means of Random Forest algorithm. (ii) A monitoring agent that makes predictions every 10 minutes about failures in wind turbines during the next hour. Finally, (iii) a dashboard where given predictions can be visualized. To implement the solution Apache Spark, Apache Kafka, Apache Mesos and HDFS have been used. Therefore, we have improved the previous work in terms of data process speed, scalability and automation. In addition, we have provided fault-tolerant functionality with a centralized access point from where the status of all the wind turbines of a company localized all over the world can be monitored, reducing O&M costs

Characterisation of large changes in wind power for the day-ahead market using a fuzzy logic approach

Wind power has become one of the renewable resources with a major growth in the electricity market. However, due to its inherent variability, forecasting techniques are necessary for the optimum scheduling of the electric grid, specially during ramp events. These large changes in wind power may not be captured by wind power point forecasts even with very high resolution Numerical Weather Prediction (NWP) models. In this paper, a fuzzy approach for wind power ramp characterisation is presented. The main benefit of this technique is that it avoids the binary definition of ramp event, allowing to identify changes in power out- put that can potentially turn into ramp events when the total percentage of change to be considered a ramp event is not met. To study the application of this technique, wind power forecasts were obtained and their corresponding error estimated using Genetic Programming (GP) and Quantile Regression Forests. The error distributions were incorporated into the characterisation process, which according to the results, improve significantly the ramp capture. Results are presented using colour maps, which provide a useful way to interpret the characteristics of the ramp events