510 Mathematik
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510 Mathematik
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- 511 Allgemeine mathematische Prinzipien
- 512 Algebra
- 513 Arithmetik
- 514 Topologie
- 515 Analysis
- 516 Geometrie
- 518 Numerische Analysis
- 519 Wahrscheinlichkeiten, angewandte Mathematik
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We investigate how the potential burden of processing ever more knowledge has affected the careers and research output of researchers in mathematics over the past 64 years. We construct a panel dataset of 48.851 researchers who published in ten top-ranking journals in mathematics. For this population of researchers, we supplement the dataset with years of birth from public sources. Our results show a significant increase of the average age of researchers at their first publication in one of our top-ranking journals, of the number of references of single-author articles, and of the number of coauthors that contribute to an article. Our findings extend earlier empirical findings on patents, as well as on researchers in economics, and hint at a burden of knowledge pervading different areas of human development. Moreover, our results indicate that researchers develop strategies like the division of labor to deal with this burden.
This paper introduces DANSEN, the hardware accelerator component for neoDBMS, a full-stack computational storage system designed to manage on-device execution of database queries/transactions as a Near-Data Processing (NDP)-operation. The proposed system enables Database Management Systems (DBMS) to oload NDP-operations to the storage while maintaining control over data through a native storage interface. DANSEN provides an NDP-engine that enables DBMS to perform both low-level database tasks, such as performing database administration, as well as high-level tasks like executing SQL, on the smart storage device while observing the DBMS concurrency control. Furthermore, DANSEN enables the incorporation of custom accelerators as an NDP-operation, e.g., to perform hardware-accelerated ML inference directly on the stored data. We built the DANSEN storage prototype and interface on an Ultrascale+HBM FPGA and fully integrated it with PostgreSQL 12. Experimental results demonstrate that the proposed NDP approach outperforms software-only PostgreSQL using a fast of-the-shelf NVMe drive, and signiicantly improves the end-to-end execution time of an aggregation operation (similar to Q6 from CH-benCHmark, 150 million records) by ≈10.6×. The versatility of the proposed approach is also validated by integrating a compute-intensive data analytics application with multi-row results, outperforming PostgreSQL by ≈1.5×.
Wave-like differential equations occur in many engineering applications. Here the engineering setup is embedded into the framework of functional analysis of modern mathematical physics. After an overview, the –Hilbert space approach to free Euler–Bernoulli bending vibrations of a beam in one spatial dimension is investigated. We analyze in detail the corresponding positive, selfadjoint differential operators of 4-th order associated to the boundary conditions in statics. A comparison with free string wave swinging is outlined.
Online-Portal "MINTFabrik"
(2023)
Das browserbasierte Online-Portal "MINTFabrik" entstand im Zuge der Maßnahmen zur Minderung von Lernrückständen mit der Idee, eine Lücke zu schließen, die es oft bei großen Online-Brückenkursen gibt: Ein Mangel an Übungsaufgaben, die schnell zugänglich sind, einfach ausgesucht werden können und gut auf bestimmte Lehrveranstaltungen und deren Anforderungen zugeschnitten sind. Die Entwicklung erfolgte in einer Kooperation der Hochschule Reutlingen mit der Tübinger Softwarefirma "Let´s Make Sense GmbH". Das Portal verzichtet bewusst auf eine Lektionsstruktur und besteht ausschließlich aus einzelnen Lernbausteinen (Items), d.h. Video-Tutorials, VisuApps und Aufgaben, die über eine komfortable Suche mit Filtern erreichbar sind und direkt bearbeitet werden können. Ein besonderes Merkmal der MINTFabrik sind Mikrokurse, die von Lehrenden und Studierenden erstellt werden können. Das sind kleine Einheiten aus einigen wenigen Items, die beliebig miteinander kombinierbar sind.
The aim of this article is to establish a stochastic search algorithm for neural networks based on the fractional stochastic processes {𝐵𝐻𝑡,𝑡≥0} with the Hurst parameter 𝐻∈(0,1). We define and discuss the properties of fractional stochastic processes, {𝐵𝐻𝑡,𝑡≥0}, which generalize a standard Brownian motion. Fractional stochastic processes capture useful yet different properties in order to simulate real-world phenomena. This approach provides new insights to stochastic gradient descent (SGD) algorithms in machine learning. We exhibit convergence properties for fractional stochastic processes.
Geometry of music perception
(2022)
Prevalent neuroscientific theories are combined with acoustic observations from various studies to create a consistent geometric model for music perception in order to rationalize, explain and predict psycho-acoustic phenomena. The space of all chords is shown to be a Whitney stratified space. Each stratum is a Riemannian manifold which naturally yields a geodesic distance across strata. The resulting metric is compatible with voice-leading satisfying the triangle inequality. The geometric model allows for rigorous studies of psychoacoustic quantities such as roughness and harmonicity as height functions. In order to show how to use the geometric framework in psychoacoustic studies, concepts for the perception of chord resolutions are introduced and analyzed.
The aim of this work is to establish and generalize a relationship between fractional partial differential equations (fPDEs) and stochastic differential equations (SDEs) to a wider class of stochastic processes, including fractional Brownian motions and sub-fractional Brownian motions with Hurst parameter H ∈ (1/2,1). We start by establishing the connection between a fPDE and SDE via the Feynman-Kac Theorem, which provides a stochastic representation of a general Cauchy problem. In hindsight, we extend this connection by assuming SDEs with fractional and sub-fractional Brownian motions and prove the generalized Feynman-Kac formulas under a (sub-)fractional Brownian motion. An application of the theorem demonstrates, as a by-product, the solution of a fractional integral, which has relevance in probability theory.
This study empirically analyzes and compares return data from developed and emerging market data based on the Fama French five-factor model and compares it to previous results from the Fama French three-factor model by Kostin, Runge and Adams (2021). It researches whether the addition of the profitability and investment pattern factors show superior results in the assessment of emerging markets during the COVID-19 pandemic compared to developed markets. We use panel data covering eight indices of developed and emerging countries as well as a selection of eight companies from these markets, covering a period from 2000 to 2020. Our findings suggest that emerging markets do not generally outperform developed markets. The results underscore the need to reconsider the assumption that adding more factors to regression models automatically yields results that are more reliable. Our study contributes to the extant literature by broadening this research area. It is the first study to compare the performance of the Fama French three-factor model and the Fama French five-factor model in the cost of equity calculation for developed and emerging countries during the COVID-19 pandemic and other crisis events of the past two decades.
In this note we look at anisotropic approximation of smooth functions on bounded domains with tensor product splines. The main idea is to extend such functions and then use known approximation techniques on Rd. We prove an error estimate for domains for which bounded extension operators exist. This obvious approach has some limitations. It is not applicable without restrictions on the chosen coordinate degree even if the domain is as simple as the unit disk. Further for approximation on Rd there are error estimates in which the grid widths and directional derivatives are paired in an interesting way. It seems impossible to maintain this property using extension operators.
In this article feedback linearization for control-affine nonlinear systems is extended to systems where linearization is not feasible in the complete state space by combining state feedback linearization and homotopy numerical continuation in subspaces of the phase space where feedback linearization fails. Starting from the conceptual simplicity of feedback linearization, this new method expands the scope of their applicability to irregular systems with poorly expressed relative degree. The method is illustrated on a simple SISO–system and by controlling the speed and the rotor flux linkage in a three phase induction machine.
