Approximation of Markov Processes by Lower Dimensional Processes via Total Variation Metrics

The aim of this paper is to approximate a finite-state Markov process by another process with fewer states, called herein the approximating process. The approximation problem is formulated using two different methods. The first method, utilizes the total variation distance to discriminate the transition probabilities of a high dimensional Markov process and a reduced order Markov process. The approximation is obtained by optimizing a linear functional defined in terms of transition probabilities of the reduced order Markov process over a total variation distance constraint. The transition probabilities of the approximated Markov process are given by a water-filling solution. The second method, utilizes total variation distance to discriminate the invariant probability of a Markov process and that of the approximating process. The approximation is obtained via two alternative formulations: (a) maximizing a functional of the occupancy distribution of the Markov process, and (b) maximizing the entropy of the approximating process invariant probability. For both formulations, once the reduced invariant probability is obtained, which does not correspond to a Markov process, a further approximation by a Markov process is proposed which minimizes the Kullback-Leibler divergence. These approximations are given by water-filling solutions. Finally, the theoretical results of both methods are applied to specific examples to illustrate the methodology, and the water-filling behavior of the approximations.Comment: 38 pages, 17 figures, submitted to IEEE-TA

Towards better regulation : Luhmannian autopoeisis and the politics of morphosis

EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Automatic inspection of cultural monuments using deep and tensor-based learning on hyperspectral imagery

In Cultural Heritage, hyperspectral images are commonly used since they provide extended information regarding the optical properties of materials. Thus, the processing of such high-dimensional data becomes challenging from the perspective of machine learning techniques to be applied. In this paper, we propose a Rank-$R$ tensor-based learning model to identify and classify material defects on Cultural Heritage monuments. In contrast to conventional deep learning approaches, the proposed high order tensor-based learning demonstrates greater accuracy and robustness against overfitting. Experimental results on real-world data from UNESCO protected areas indicate the superiority of the proposed scheme compared to conventional deep learning models.Comment: Accepted for presentation in IEEE International Conference on Image Processing (ICIP 2022

Tensor-Based Learning for Detecting Abnormalities on Digital Mammograms

In this study, we propose a tensor-based learning model to efficiently detect abnormalities on digital mammograms. Due to the fact that the availability of medical data is limited and often restricted by GDPR (general data protection regulation) compliance, the need for more sophisticated and less data-hungry approaches is urgent. Accordingly, our proposed artificial intelligence framework utilizes the canonical polyadic decomposition to decrease the trainable parameters of the wrapped Rank-R FNN model, leading to efficient learning using small amounts of data. Our model was evaluated on the open source digital mammographic database INBreast and compared with state-of-the-art models in this domain. The experimental results show that the proposed solution performs well in comparison with the other deep learning models, such as AlexNet and SqueezeNet, achieving 90% ± 4% accuracy and an F1 score of 84% ± 5%. Additionally, our framework tends to attain more robust performance with small numbers of data and is computationally lighter for inference purposes, due to the small number of trainable parameters

Association of Lp-PLA2 with digital reactive hyperemia, coronary flow reserve, carotid atherosclerosis and arterial stiffness in coronary artery disease

BACKGROUND: Lipoprotein-associated Phospholipase A2 (Lp-PLA2), has a powerful inflammatory and atherogenic action in the vascular wall and is an independent marker of poor prognosis in coronary artery disease (CAD). We investigate the association of Lp-PLA2 with markers of vascular dysfunction and atherosclerosis with proven prognostic value in CAD. METHODS: In 111 patients with angiographically documented chronic CAD, we measured 1) carotid intima-media thickness (CIMT), 2) reactive hyperemia using fingertip peripheral arterial tonometry (RH-PAT), 3) coronary flow reserve (CFR), by Doppler echocardiography 4) pulse wave velocity (PWV) and 5) blood levels of Lp-PLA2. RESULTS: Patients with Lp-PLA2 concentration >234.5 ng/ml (50th percentile) had higher CIMT (1.44 +/- 0.07 vs. 1.06 +/- 0.06 mm), PWV (11.0 +/- 2.36 vs. 9.7 +/- 2.38 m/s) and lower RH-PAT(1.24 +/- 0.25 vs. 1.51 +/- 0.53) and CFR (2.39 +/- 0.75 vs. 2.9 +/- 0.86) compared to those with lower Lp-PLA (p < 0.05 for all comparisons). Lp-PLA2 was positively associated with CIMT (regression coefficient b: 0.30 per unit of Lp-PLA2, p = 0.02), PWV (b:0.201, p = 0.04) and inversely with RHI-PAT (b: -0.371, p < 0.001) and CFR (b:-0.32, p = 0.002). In multivariate analysis, Lp-PLA2 was an independent determinant of RHI-PAT, CFR, CIMT and PWV in a model including age, sex, smoking, diabetes, dyslipidemia and hypertension (p < 0.05 for all vascular markers). Lp-PLA2, RHI-PAT and CFR were independent predictors of cardiac events during a 3-year follow-up. CONCLUSIONS: Elevated Lp-PLA2 concentration is related with endothelial dysfunction, carotid atherosclerosis, impaired coronary flow reserve and increased arterial stiffness and adverse outcome in CAD patients. These findings suggest that the prognostic role of Lp-PLA2 in chronic CAD may be explained by a generalized detrimental effect of this lipase on endothelial function and arterial wall properties. (C) 2014 Elsevier Ireland Ltd. All rights reserve