408 research outputs found
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 be points in , and let
be a one-parameter family of similitudes of : where
is our parameter. Then, as is well known, there exists a
unique self-similar attractor satisfying
. Each has
at least one address , i.e.,
.
We show that for sufficiently close to 1, each has different
addresses. If is not too close to 1, then we can still have an
overlap, but there exist 's which have a unique address. However, we
prove that almost every has addresses,
provided 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
supported on a discrete point set, generically of size . These sequences
are uniformly distributed with respect to the infinite Bernoulli convolution
measure , as tends to infinity. Numerical evidence suggests that for
a generic , 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
the behavior is totally different.Comment: 17 pages, 6 figure
Recommended from our members
EventiC: A Real-Time Unbiased Event Based Learning Technique for Complex Systems
European Unionâs 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
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