Browsing by Subject "Continuous time systems"
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Item Unknown On compact solution vectors in Kronecker-based Markovian analysis(Elsevier, 2017) Buchholz, P.; Dayar T.; Kriege, J.; Orhan, M. C.State based analysis of stochastic models for performance and dependability often requires the computation of the stationary distribution of a multidimensional continuous-time Markov chain (CTMC). The infinitesimal generator underlying a multidimensional CTMC with a large reachable state space can be represented compactly in the form of a block matrix in which each nonzero block is expressed as a sum of Kronecker products of smaller matrices. However, solution vectors used in the analysis of such Kronecker-based Markovian representations require memory proportional to the size of the reachable state space. This implies that memory allocated to solution vectors becomes a bottleneck as the size of the reachable state space increases. Here, it is shown that the hierarchical Tucker decomposition (HTD) can be used with adaptive truncation strategies to store the solution vectors during Kronecker-based Markovian analysis compactly and still carry out the basic operations including vector–matrix multiplication in Kronecker form within Power, Jacobi, and Generalized Minimal Residual methods. Numerical experiments on multidimensional problems of varying sizes indicate that larger memory savings are obtained with the HTD approach as the number of dimensions increases. © 2017 Elsevier B.V.Item Unknown A robust system for counting people using an infrared sensor and a camera(Elsevier BV, 2015) Erden, F.; Alkar, A. Z.; Çetin, A. EnisIn this paper, a multi-modal solution to the people counting problem in a given area is described. The multi-modal system consists of a differential pyro-electric infrared (PIR) sensor and a camera. Faces in the surveillance area are detected by the camera with the aim of counting people using cascaded AdaBoost classifiers. Due to the imprecise results produced by the camera-only system, an additional differential PIR sensor is integrated to the camera. Two types of human motion: (i) entry to and exit from the surveillance area and (ii) ordinary activities in that area are distinguished by the PIR sensor using a Markovian decision algorithm. The wavelet transform of the continuous-time real-valued signal received from the PIR sensor circuit is used for feature extraction from the sensor signal. Wavelet parameters are then fed to a set of Markov models representing the two motion classes. The affiliation of a test signal is decided as the class of the model yielding higher probability. People counting results produced by the camera are then corrected by utilizing the additional information obtained from the PIR sensor signal analysis. With the proof of concept built, it is shown that the multi-modal system can reduce false alarms of the camera-only system and determines the number of people watching a TV set in a more robust manner.