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In this article, the collection of classes of matrices presented in [J. Garloff, M. Adm, ad J. Titi, A survey of classes of matrices possessing the interval property and related properties, Reliab. Comput. 22:1-14, 2016] is continued. That is, given an interval of matrices with respect to a certain partial order, it is desired to know whether a special property of the entire matrix interval can be inferred from some of its element matrices lying on the vertices of the matrix interval. The interval property of some matrix classes found in the literature is presented, and the interval property of further matrix classes including the ultrametric, the conditionally positive semidefinite, and the infinitely divisible matrices is given for the first time. For the inverse M-matrices the cardinality of the required set of vertex matrices known so far is significantly reduced.
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.
Matrix methods for the computation of bounds for the range of a complex polynomial and its modulus over a rectangular region in the complex plane are presented. The approach relies on the expansion of the given polynomial into Bernstein polynomials. The results are extended to multivariate complex polynomials and rational functions.
The class of square matrices of order n having a negative determinant and all their minors up to order n-1 nonnegative is considered. A characterization of these matrices is presented which provides an easy test based on the Cauchon algorithm for their recognition. Furthermore, the maximum allowable perturbation of the entry in position (2,2) such that the perturbed matrix remains in this class is given. Finally, it is shown that all matrices lying between two matrices of this class with respect to the checkerboard ordering are contained in this class, too.
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.
Das produzierende Gewerbe in Deutschland erlebt aufgrund von Technologiewandel im Automobilbau, der Anpassung von Lieferketten und der digitalen Transformation grundlegende Veränderungen. Diese als Chance für künftiges Wachstum zu begreifen ist essenziell und eine zwingende Voraussetzung für den Wirtschaftsstandort Deutschland. Anhand eines konkreten Unternehmensbeispiels werden hierfür zentrale Aspekte für Transformation eines mittelständischen produzierenden Blechbearbeitungsunternehmens hin zu einem netzwerkbasierten Geschäftsmodell betrachtet. Auf Basis der Analyse von Referenzbeispielen webbasierter Vertriebsplattformen in der Blechbearbeitung werden erfolgsrelevante Aspekte für die Ausgestaltung und die Umsetzung für ein Onlineplattformmodell beschrieben. Hierbei wird exemplarisch dargelegt, wie mittels digitaler Vertriebsplattformen in Verbindung mit digitalen Auftragsmanagementprozessen neue Wege für Wachstum ermöglicht werden können.
Im Zuge zunehmender Effizienzbestrebungen in produzierenden Unternehmen spielt auch die Optimierung von indirekten Wertschöpfungsprozessen eine immer größere Rolle. Neben einer ansteigenden Aufgabenvielfalt stellt ein parallel wachsender Kostendruck eine doppelte Herausforderung dar. Dies gilt insbesondere für Einkaufsbereiche entsprechender Organisationen, welche an der Schnittstelle zwischen der unternehmensinternen und -externen Wertschöpfungskette operieren und an dieser einen essenziellen Beitrag auch im Sinne des Informationsflusses zur Unterstützung eines integrierten Supply Chain Managements darstellen. Um diesen zu begegnen, ist es notwendig, die relevanten Kernprozesse der Einkaufsbereiche stetig im Blick zu halten und Verbesserungsmöglichkeiten zu identifizieren und umzusetzen. Dieser Beitrag will zu einem Überblick für die Prozessoptimierung mithilfe des Einsatzes digitaler Technologien speziell in Einkaufsbereichen beitragen. Es werden die Spezifika des Einkaufs vorgestellt, relevante Kernaufgaben beschrieben und exemplarisch technologische Ansätze zur Prozessoptimierung anhand von Process Mining, Robotic Process Automation und künstlicher Intelligenz aufgezeigt.
This paper presents a generic method to enhance performance and incorporate temporal information for cardiorespiratory-based sleep stage classification with a limited feature set and limited data. The classification algorithm relies on random forests and a feature set extracted from long-time home monitoring for sleep analysis. Employing temporal feature stacking, the system could be significantly improved in terms of Cohen’s κ and accuracy. The detection performance could be improved for three classes of sleep stages (Wake, REM, Non-REM sleep), four classes (Wake, Non-REM-Light sleep, Non-REM Deep sleep, REM sleep), and five classes (Wake, N1, N2, N3/4, REM sleep) from a κ of 0.44 to 0.58, 0.33 to 0.51, and 0.28 to 0.44 respectively by stacking features before and after the epoch to be classified. Further analysis was done for the optimal length and combination method for this stacking approach. Overall, three methods and a variable duration between 30 s and 30 min have been analyzed. Overnight recordings of 36 healthy subjects from the Interdisciplinary Center for Sleep Medicine at Charité-Universitätsmedizin Berlin and Leave-One-Out-Cross-Validation on a patient-level have been used to validate the method.
Probabilistic Short-Term Low-Voltage Load Forecasting using Bernstein-Polynomial Normalizing Flows
(2021)
The transition to a fully renewable energy grid requires better forecasting of demand at the low-voltage level. However, high fluctuations and increasing electrification cause huge forecast errors with traditional point estimates. Probabilistic load forecasts take future uncertainties into account and thus enables various applications in 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 363 smart meter customers, our density predictions compare favorably against Gaussian and Gaussian mixture densities and also outperform a non-parametric approach based on the pinball loss for 24h-ahead load forecasting for two different neural network architectures.