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Totally nonnegative matrices, i.e., matrices having all their minors nonnegative, and matrix intervals with respect to the checkerboard partial order are considered. It is proven that if the two bound matrices of such a matrix interval are totally nonnegative and satisfy certain conditions, then all matrices from this interval are also totally nonnegative and satisfy the same conditions.
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 thesis, the recognition problem and the properties of eigenvalues and eigenvectors of matrices which are strictly sign-regular of a given order, i.e., matrices whose minors of a given order have the same strict sign, are considered. The results are extended to matrices which are sign-regular of a given order, i.e., matrices whose minors of a given order have the same sign or are allowed to vanish. As a generalization, a new type of matrices called oscillatory of a specific order, are introduced. Furthermore, the properties for this type are investigated. Also, same applications to dynamic systems are given.
Forecasting is crucial for both system planning and operations in the energy sector. With increasing penetration of renewable energy sources, increasing fluctuations in the power generation need to be taken into account. Probabilistic load forecasting is a young, but emerging research topic focusing on the prediction of future uncertainties. However, the majority of publications so far focus on techniques like quantile regression, ensemble, or scenario-based methods, which generate discrete quantiles or sets of possible load curves. The conditioned probability distribution remains unknown and can only be estimated when the output is post-processed using a statistical method like kernel density estimation.
Instead, the proposed probabilistic deep learning model uses a cascade of transformation functions, known as normalizing flow, to model the conditioned density function from a smart meter dataset containing electricity demand information for over 4,000 buildings in Ireland. Since the whole probability density function is tractable, the parameters of the model can be obtained by minimizing the negative loglikelihood through the state of the art gradient descent. This leads to the model with the best representation of the data distribution.
Two different deep learning models have been compared, a simple three-layer fully connected neural network and a more advanced convolutional neural network for sequential data processing inspired by the WaveNet architecture. These models have been used to parametrize three different probabilistic models, a simple normal distribution, a Gaussian mixture model, and the normalizing flow model. The prediction horizon is set to one day with a resolution of 30 minutes, hence the models predict 48 conditioned probability distributions.
The normalizing flow model outperforms the two other variants for both architectures and proves its ability to capture the complex structures and dependencies causing the variations in the data. Understanding the stochastic nature of the task in such detail makes the methodology applicable for other use cases apart from forecasting. It is shown how it can be used to detect anomalies in the power grid or generate synthetic scenarios for grid planning.
Soft-input decoding of concatenated codes based on the Plotkin construction and BCH component codes
(2020)
Low latency communication requires soft-input decoding of binary block codes with small to medium block lengths.
In this work, we consider generalized multiple concatenated (GMC) codes based on the Plotkin construction. These codes are similar to Reed-Muller (RM) codes. In contrast to RM codes, BCH codes are employed as component codes. This leads to improved code parameters. Moreover, a decoding algorithm is proposed that exploits the recursive structure of the concatenation. This algorithm enables efficient soft-input decoding of binary block codes with small to medium lengths. The proposed codes and their decoding achieve significant performance gains compared with RM codes and recursive GMC decoding.
For a long time, the use of intermediate products in production has been growing more rapidly in most countries than domestic production. This is a strong indication of more interdependency in production. The main purpose of input-output analysis is to study the interdependency of industries in an economy. Often the term interindustry analysis is also used. Therefore, the exchange of intermediate products is a key issue of input-output analysis. We will use input–output data for this study that the author prepared for the new ‘Handbook on Supply, Use and Input–Output Tables with Extensions and Applications’ of the United Nations. The supply use and input–output tables contain separate valuation matrices for trade margins, transport margins, value added tax, other taxes on products and subsidies on products. For the study, two input–output models were developed to evaluate the impact of fuel subsidy and taxation reform on output, gross domestic product, inflation and trade. Six scenarios are discussed covering different aspects of the reform.
The evaluation of the effectiveness of different machine learning algorithms on a publicly available database of signals derived from wearable devices is presented with the goal of optimizing human activity recognition and classification. Among the wide number of body signals we choose a couple of signals, namely photoplethysmographic (optically detected subcutaneous blood volume) and tri-axis acceleration signals that are easy to be simultaneously acquired using commercial widespread devices (e.g. smartwatches) as well as custom wearable wireless devices designed for sport, healthcare, or clinical purposes. To this end, two widely used algorithms (decision tree and k-nearest neighbor) were tested, and their performance were compared to two new recent algorithms (particle Bernstein and a Monte Carlo-based regression) both in terms of accuracy and processing time. A data preprocessing phase was also considered to improve the performance of the machine learning procedures, in order to reduce the problem size and a detailed analysis of the compression strategy and results is also presented.
The transformation to an Industry 4.0, which is in general seen as a solution to increasing market challenges, is forcing companies to radically change their way of thinking and to be open to new forms of cooperation. In this context, the opening-up of the innovation process is widely seen as a necessity to meet these challenges, especially for small and medium enterprises (SMEs). The aim of the study therefore is to analyze how cooperation today can be characterized, how this character has changed since the establishment of the term Industry 4.0 at Hanover Fair in 2011 and which cooperation strategies have proven successful. The analysis consists of a quantitative, secondary data analysis that includes country-specific data from 35 European countries of 2010 and 2016 collected by the European Commission and the OECD. The research, focusing on the secondary sector, shows that multinational enterprises MNEs still tend to cooperate more than SMEs, with a slight overall trend towards protectionism. Nevertheless, there is a clear tendency towards the opening-up of SMEs. In this regard, especially universities, competitors and suppliers have become increasingly attractive as cooperation partners for SMEs.