Event tracking for real-time unaware sensitivity analysis (EventTracker)

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.This paper introduces a platform for online Sensitivity Analysis (SA) that is applicable in large scale real-time data acquisition (DAQ) systems. Here we use the term real-time in the context of a system that has to respond to externally generated input stimuli within a finite and specified period. Complex industrial systems such as manufacturing, healthcare, transport, and finance require high quality information on which to base timely responses to events occurring in their volatile environments. The motivation for the proposed EventTracker platform is the assumption that modern industrial systems are able to capture data in real-time and have the necessary technological flexibility to adjust to changing system requirements. The flexibility to adapt can only be assured if data is succinctly interpreted and translated into corrective actions in a timely manner. An important factor that facilitates data interpretation and information modelling is an appreciation of the affect system inputs have on each output at the time of occurrence. Many existing sensitivity analysis methods appear to hamper efficient and timely analysis due to a reliance on historical data, or sluggishness in providing a timely solution that would be of use in real-time applications. This inefficiency is further compounded by computational limitations and the complexity of some existing models. In dealing with real-time event driven systems, the underpinning logic of the proposed method is based on the assumption that in the vast majority of cases changes in input variables will trigger events. Every single or combination of events could subsequently result in a change to the system state. The proposed event tracking sensitivity analysis method describes variables and the system state as a collection of events. The higher the numeric occurrence of an input variable at the trigger level during an event monitoring interval, the greater is its impact on the final analysis of the system state. Experiments were designed to compare the proposed event tracking sensitivity analysis method with a comparable method (that of Entropy). An improvement of 10% in computational efficiency without loss in accuracy was observed. The comparison also showed that the time taken to perform the sensitivity analysis was 0.5% of that required when using the comparable Entropy based method.EPSR

Combinatorics of linear iterated function systems with overlaps

Let $\bm p_0,...,\bm p_{m-1}$ be points in ${\mathbb R}^d$, and let $\{f_j\}_{j=0}^{m-1}$ be a one-parameter family of similitudes of ${\mathbb R}^d$: $$f_j(\bm x) = \lambda\bm x + (1-\lambda)\bm p_j, j=0,...,m-1,$$ where $\lambda\in(0,1)$ is our parameter. Then, as is well known, there exists a unique self-similar attractor $S_\lambda$ satisfying $S_\lambda=\bigcup_{j=0}^{m-1} f_j(S_\lambda)$. Each $\bm x\in S_\lambda$ has at least one address $(i_1,i_2,...)\in\prod_1^\infty\{0,1,...,m-1\}$, i.e., $\lim_n f_{i_1}f_{i_2}... f_{i_n}({\bf 0})=\bm x$. We show that for $\lambda$ sufficiently close to 1, each $\bm x\in S_\lambda\setminus\{\bm p_0,...,\bm p_{m-1}\}$ has $2^{\aleph_0}$ different addresses. If $\lambda$ is not too close to 1, then we can still have an overlap, but there exist $\bm x$'s which have a unique address. However, we prove that almost every $\bm x\in S_\lambda$ has $2^{\aleph_0}$ addresses, provided $S_\lambda$ contains no holes and at least one proper overlap. We apply these results to the case of expansions with deleted digits. Furthermore, we give sharp sufficient conditions for the Open Set Condition to fail and for the attractor to have no holes. These results are generalisations of the corresponding one-dimensional results, however most proofs are different.Comment: Accepted for publication in Nonlinearit

Spacings and pair correlations for finite Bernoulli convolutions

We consider finite Bernoulli convolutions with a parameter $1/2 < r < 1$ supported on a discrete point set, generically of size $2^N$. These sequences are uniformly distributed with respect to the infinite Bernoulli convolution measure $\nu_r$, as $N$ tends to infinity. Numerical evidence suggests that for a generic $r$, the distribution of spacings between appropriately rescaled points is Poissonian. We obtain some partial results in this direction; for instance, we show that, on average, the pair correlations do not exhibit attraction or repulsion in the limit. On the other hand, for certain algebraic $r$ the behavior is totally different.Comment: 17 pages, 6 figure

EventiC: A Real-Time Unbiased Event Based Learning Technique for Complex Systems

European Union’s Horizon 2020 Research and Innovation Program

Analysis of a Japan government intervention on the domestic agriculture market

We investigate an economic system in which one large agent - the Japan government changes the environment of numerous smaller agents - the Japan agriculture producers by indirect regulation of prices of agriculture goods. The reason for this intervention was that before the oil crisis in 1974 Japan agriculture production prices exhibited irregular and large amplitude changes. By means of analysis of correlations and a combination of singular spectrum analysis (SSA), principal component analysis (PCA), and time delay phase space construction (TDPSC) we study the influence of the government measures on the domestic piglet prices and production in Japan. We show that the government regulation politics was successful and leaded (i) to a decrease of the nonstationarities and to increase of predictability of the piglet price; (ii) to a coupling of the price and production cycles; (iii) to increase of determinism of the dynamics of the fluctuations of piglet price around the year average price. The investigated case is an example confirming the thesis that a large agent can change in a significant way the environment of the small agents in complex (economic or financial) systems which can be crucial for their survival or extinction.Comment: 10 pages, 6 figures presented at APFA5, Torino, Italy, 29.06-01.07.200

Enlarged scaling ranges for the KS-entropy and the information dimension

Numerical estimates of the Kolmogorov-Sinai entropy based on a finite amount of data decay towards zero in the relevant limits. Rewriting differences of block entropies as averages over decay rates, and ignoring all parts of the sample where these rates are uncomputable because of the lack of neighbours, yields improved entropy estimates. In the same way, the scaling range for estimates of the information dimension can be extended considerably. The improvement is demonstrated for experimental data.Comment: 5 pages, 6 figure

Golden gaskets: variations on the Sierpi\'nski sieve

We consider the iterated function systems (IFSs) that consist of three general similitudes in the plane with centres at three non-collinear points, and with a common contraction factor \la\in(0,1). As is well known, for \la=1/2 the invariant set, \S_\la, is a fractal called the Sierpi\'nski sieve, and for \la<1/2 it is also a fractal. Our goal is to study \S_\la for this IFS for 1/2<\la<2/3, i.e., when there are "overlaps" in \S_\la as well as "holes". In this introductory paper we show that despite the overlaps (i.e., the Open Set Condition breaking down completely), the attractor can still be a totally self-similar fractal, although this happens only for a very special family of algebraic \la's (so-called "multinacci numbers"). We evaluate \dim_H(\S_\la) for these special values by showing that \S_\la is essentially the attractor for an infinite IFS which does satisfy the Open Set Condition. We also show that the set of points in the attractor with a unique ``address'' is self-similar, and compute its dimension. For ``non-multinacci'' values of \la we show that if \la is close to 2/3, then \S_\la has a nonempty interior and that if \la<1/\sqrt{3} then \S_\la$ has zero Lebesgue measure. Finally we discuss higher-dimensional analogues of the model in question.Comment: 27 pages, 10 figure

A dynamical approach to the spatiotemporal aspects of the Portevin-Le Chatelier effect: Chaos,turbulence and band propagation

Experimental time series obtained from single and poly-crystals subjected to a constant strain rate tests report an intriguing dynamical crossover from a low dimensional chaotic state at medium strain rates to an infinite dimensional power law state of stress drops at high strain rates. We present results of an extensive study of all aspects of the PLC effect within the context a model that reproduces this crossover. A study of the distribution of the Lyapunov exponents as a function of strain rate shows that it changes from a small set of positive exponents in the chaotic regime to a dense set of null exponents in the scaling regime. As the latter feature is similar to the GOY shell model for turbulence, we compare our results with the GOY model. Interestingly, the null exponents in our model themselves obey a power law. The configuration of dislocations is visualized through the slow manifold analysis. This shows that while a large proportion of dislocations are in the pinned state in the chaotic regime, most of them are at the threshold of unpinning in the scaling regime. The model qualitatively reproduces the different types of deformation bands seen in experiments. At high strain rates where propagating bands are seen, the model equations are reduced to the Fisher-Kolmogorov equation for propagative fronts. This shows that the velocity of the bands varies linearly with the strain rate and inversely with the dislocation density, consistent with the known experimental results. Thus, this simple dynamical model captures the complex spatio-temporal features of the PLC effect.Comment: 17 pages, 18 figure

Optimal neural network feature selection for spatial-temporal forecasting

In this paper, we show empirical evidence on how to construct the optimal feature selection or input representation used by the input layer of a feedforward neural network for the propose of forecasting spatial-temporal signals. The approach is based on results from dynamical systems theory, namely the non-linear embedding theorems. We demonstrate it for a variety of spatial-temporal signals, with one spatial and one temporal dimensions, and show that the optimal input layer representation consists of a grid, with spatial/temporal lags determined by the minimum of the mutual information of the spatial/temporal signals and the number of points taken in space/time decided by the embedding dimension of the signal. We present evidence of this proposal by running a Monte Carlo simulation of several combinations of input layer feature designs and show that the one predicted by the non-linear embedding theorems seems to be optimal or close of optimal. In total we show evidence in four unrelated systems: a series of coupled Henon maps; a series of couple Ordinary Differential Equations (Lorenz-96) phenomenologically modelling atmospheric dynamics; the Kuramoto-Sivashinsky equation, a partial differential equation used in studies of instabilities in laminar flame fronts and finally real physical data from sunspot areas in the Sun (in latitude and time) from 1874 to 2015.Comment: 11 page