Search results for "Piecewise"
showing 10 items of 108 documents
Lyapunov exponent and topological entropy plateaus in piecewise linear maps
2013
We consider a two-parameter family of piecewise linear maps in which the moduli of the two slopes take different values. We provide numerical evidence of the existence of some parameter regions in which the Lyapunov exponent and the topological entropy remain constant. Analytical proof of this phenomenon is also given for certain cases. Surprisingly however, the systems with that property are not conjugate as we prove by using kneading theory.
Statistics of return times for weighted maps of the interval
2000
For non markovian, piecewise monotonic maps of the interval associated to a potential, we prove that the law of the entrance time in a cylinder, when renormalized by the measure of the cylinder, converges to an exponential law for almost all cylinders. Thanks to this result, we prove that the fluctuations of Rn, first return time in a cylinder, are lognormal.
Testing with a nuisance parameter present only under the alternative: a score-based approach with application to segmented modelling
2016
ABSTRACTWe introduce a score-type statistic to test for a non-zero regression coefficient when the relevant term involves a nuisance parameter present only under the alternative. Despite the non-regularity and complexity of the problem and unlike the previous approaches, the proposed test statistic does not require the nuisance to be estimated. It is simple to implement by relying on the conventional distributions, such as Normal or t, and it justified in the setting of probabilistic coherence. We focus on testing for the existence of a breakpoint in segmented regression, and illustrate the methodology with an analysis on data of DNA copy number aberrations and gene expression profiles from…
Escape Times in Fluctuating Metastable Potential and Acceleration of Diffusion in Periodic Fluctuating Potentials
2004
The problems of escape from metastable state in randomly flipping potential and of diffusion in fast fluctuating periodic potentials are considered. For the overdamped Brownian particle moving in a piecewise linear dichotomously fluctuating metastable potential we obtain the mean first-passage time (MFPT) as a function of the potential parameters, the noise intensity and the mean rate of switchings of the dichotomous noise. We find noise enhanced stability (NES) phenomenon in the system investigated and the parameter region of the fluctuating potential where the effect can be observed. For the diffusion of the overdamped Brownian particle in a fast fluctuating symmetric periodic potential w…
Quantitative ergodicity for some switched dynamical systems
2012
International audience; We provide quantitative bounds for the long time behavior of a class of Piecewise Deterministic Markov Processes with state space Rd × E where E is a finite set. The continuous component evolves according to a smooth vector field that switches at the jump times of the discrete coordinate. The jump rates may depend on the whole position of the process. Under regularity assumptions on the jump rates and stability conditions for the vector fields we provide explicit exponential upper bounds for the convergence to equilibrium in terms of Wasserstein distances. As an example, we obtain convergence results for a stochastic version of the Morris-Lecar model of neurobiology.
Efficient change point detection in genomic sequences of continuous measurements
2010
Abstract Motivation: Knowing the exact locations of multiple change points in genomic sequences serves several biological needs, for instance when data represent aCGH profiles and it is of interest to identify possibly damaged genes involved in cancer and other diseases. Only a few of the currently available methods deal explicitly with estimation of the number and location of change points, and moreover these methods may be somewhat vulnerable to deviations of model assumptions usually employed. Results: We present a computationally efficient method to obtain estimates of the number and location of the change points. The method is based on a simple transformation of data and it provides re…
PIECEWISE ANOMALY DETECTION USING MINIMAL LEARNING MACHINE FOR HYPERSPECTRAL IMAGES
2021
Abstract. Hyperspectral imaging, with its applications, offers promising tools for remote sensing and Earth observation. Recent development has increased the quality of the sensors. At the same time, the prices of the sensors are lowering. Anomaly detection is one of the popular remote sensing applications, which benefits from real-time solutions. A real-time solution has its limitations, for example, due to a large amount of hyperspectral data, platform’s (drones or a cube satellite) constraints on payload and processing capability. Other examples are the limitations of available energy and the complexity of the machine learning models. When anomalies are detected in real-time from the hyp…
High-accuracy approximation of piecewise smooth functions using the Truncation and Encode approach
2017
Abstract In the present work, we analyze a technique designed by Geraci et al. in [1,11] named the Truncate and Encode (TE) strategy. It was presented as a non-intrusive method for steady and non-steady Partial Differential Equations (PDEs) in Uncertainty Quantification (UQ), and as a weakly intrusive method in the unsteady case. We analyze the TE algorithm applied to the approximation of functions, and in particular its performance for piecewise smooth functions. We carry out some numerical experiments, comparing the performance of the algorithm when using different linear and non-linear interpolation techniques and provide some recommendations that we find useful in order to achieve a hig…
Mixed l-/l1 fault detection observer design for positive switched systems with time-varying delay via delta operator approach
2014
Published version of an article in the journal: International Journal of Control, Automation and Systems. Also available from the publisher at: http://dx.doi.org/10.1007/s12555-013-0466-1 This paper investigates the problem of fault detection observer design for positive switched systems with time-varying delay via delta operator approach. A new fault sensitivity measure, called l-index, is proposed. The l- fault detection observer design and multi-objective l -/l1 fault detection observer design problems are addressed. Based on the average dwell time approach and the piecewise copositive type Lyapunov-Krasovskii functional method in delta domain, sufficient conditions for the existence of …
Estimating the temperature evolution of foodstuffs during freezing with a 3D meshless numerical method
2015
Abstract Freezing processes are characterised by sharp changes in specific heat capacity and thermal conductivity for temperatures close to the freezing point. This leads to strong nonlinearities in the governing PDE that may be difficult to resolve using traditional numerical methods. In this work we present a meshless numerical method, based on a local Hermite radial basis function collocation approach in finite differencing mode, to allow the solution of freezing problems. By introducing a Kirchhoff transformation and solving the governing equations in Kirchhoff space, the strength of nonlinearity is reduced while preserving the structure of the heat equation. In combination with the hig…