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Let A = [a_ij] be a real symmetric matrix. If f:(0,oo)-->[0,oo) is a Bernstein function, a sufficient condition for the matrix [f(a_ij)] to have only one positive eigenvalue is presented. By using this result, new results for a symmetric matrix with exactly one positive eigenvalue, e.g., properties of its Hadamard powers, are derived.
In this paper, rectangular matrices whose minors of a given order have the same strict sign are considered and sufficient conditions for their recognition are presented. The results are extended to matrices whose minors of a given order have the same sign or are allowed to vanish. A matrix A is called oscillatory if all its minors are nonnegative and there exists a positive integer k such that A^k has all its minors positive. As a generalization, a new type of matrices, called oscillatory of a specific order, is introduced and some of their properties are investigated.
Positive systems play an important role in systems and control theory and have found applications in multiagent systems, neural networks, systems biology, and more. Positive systems map the nonnegative orthant to itself (and also the non-positive orthant to itself). In other words, they map the set of vectors with zero sign variation to itself. In this article, discrete-time linear systems that map the set of vectors with up to k-1 sign variations to itself are introduced. For the special case k = 1 these reduce to discrete-time positive linear systems. Properties of these systems are analyzed using tools from the theory of sign-regular matrices. In particular, it is shown that almost every solution of such systems converges to the set of vectors with up to k-1 sign variations. It is also shown that these systems induce a positive dynamics of k-dimensional parallelotopes.
Short-Term Density Forecasting of Low-Voltage Load using Bernstein-Polynomial Normalizing Flows
(2023)
The transition to a fully renewable energy grid requires better forecasting of demand at the low-voltage level to increase efficiency and ensure reliable control. However, high fluctuations and increasing electrification cause huge forecast variability, not reflected in traditional point estimates. Probabilistic load forecasts take uncertainties into account and thus allow more informed decision-making for the planning and operation of low-carbon energy systems. We propose an approach for flexible conditional density forecasting of short-term load based on Bernstein polynomial normalizing flows, where a neural network controls the parameters of the flow. In an empirical study with 3639 smart meter customers, our density predictions for 24h-ahead load forecasting compare favorably against Gaussian and Gaussian mixture densities. Furthermore, they outperform a non-parametric approach based on the pinball loss, especially in low-data scenarios.
This study investigates the application of Force Sensing Resistor (FSR) sensors and machine learning algorithms for non-invasive body position monitoring during sleep. Although reliable, traditional methods like Polysomnography (PSG) are invasive and unsuited for extended home-based monitoring. Our approach utilizes FSR sensors placed beneath the mattress to detect body positions effectively. We employed machine learning techniques, specifically Random Forest (RF), K-Nearest Neighbors (KNN), and XGBoost algorithms, to analyze the sensor data. The models were trained and tested using data from a controlled study with 15 subjects assuming various sleep positions. The performance of these models was evaluated based on accuracy and confusion matrices. The results indicate XGBoost as the most effective model for this application, followed by RF and KNN, offering promising avenues for home-based sleep monitoring systems.
Cardiovascular diseases (CVD) are leading contributors to global mortality, necessitating advanced methods for vital sign monitoring. Heart Rate Variability (HRV) and Respiratory Rate, key indicators of cardiovascular health, are traditionally monitored via Electrocardiogram (ECG). However, ECG's obtrusiveness limits its practicality, prompting the exploration of Ballistocardiography (BCG) as a non-invasive alternative. BCG records the mechanical activity of the body with each heartbeat, offering a contactless method for HRV monitoring. Despite its benefits, BCG signals are susceptible to external interference and present a challenge in accurately detecting J-Peaks. This research uses advanced signal processing and deep learning techniques to overcome these limitations. Our approach integrates accelerometers for long-term BCG data collection during sleep, applying Discrete Wavelet Transforms (DWT) and Ensemble Empirical Mode Decomposition (EEMD) for feature extraction. The Bi-LSTM model, leveraging these features, enhances heartbeat detection, offering improved reliability over traditional methods. The study's findings indicate that the combined use of DWT, EEMD, and Bi-LSTM for J-Peak detection in BCG signals is effective, with potential applications in unobtrusive long-term cardiovascular monitoring. Our results suggest that this methodology could contribute to HRV monitoring, particularly in home settings, enhancing patient comfort and compliance.
Ein Holzhaus als Botschaft. Die erste diplomatische Vertretung des Deutschen Reiches in Ankara 1924
(2015)
Auf die Gründung der türkischen Republik und die Verlagerung der Hauptstadt nach Ankara reagierte das Deutsche Reich 1924 zeitnah mit der Errichtung eines Botschaftsgebäudes in Fertigteilbauweise. Dieses präfabrizierte Holzhaus wurde von der für den Holzbau der Moderne bedeutenden Firma Christoph & Unmack AG aus Niesky/Oberlausitz geliefert. Nach Errichtung eines größeren, massiven Botschaftsgebäudes in Ankara wurde das Holzhaus 1934 auf das Gelände des Atatürk Orman Çiftliği transloziert, wo es noch heute existiert. 2010 konnte es einer gründlichen Baudokumentation unterzogen werden. Im Rahmen von drei Einzelbeiträgen werden die Ergebnisse der Untersuchungen an diesem ebenso ungewöhnlichen wie bedeutenden Baudenkmal vorgestellt.
Reed-Muller (RM) codes have recently regained some interest in the context of low latency communications and due to their relation to polar codes. RM codes can be constructed based on the Plotkin construction. In this work, we consider concatenated codes based on the Plotkin construction, where extended Bose-Chaudhuri-Hocquenghem (BCH) codes are used as component codes. This leads to improved code parameters compared to RM codes. Moreover, this construction is more flexible concerning the attainable code rates. Additionally, new soft-input decoding algorithms are proposed that exploit the recursive structure of the concatenation and the cyclic structure of the component codes. First, we consider the decoding of the cyclic component codes and propose a low complexity hybrid ordered statistics decoding algorithm. Next, this algorithm is applied to list decoding of the Plotkin construction. The proposed list decoding approach achieves near-maximum-likelihood performance for codes with medium lengths. The performance is comparable to state-of-the-art decoders, whereas the complexity is reduced.