Grain size analysis in permanent magnets from Kerr microscopy images using machine learning techniques

Understanding the relationships between composition, structure, processing and properties helps in the development of improved materials for known applications as well as for new applications. Materials scientists, chemists and physicists have researched these relationships for many years, until the recent past, by characterizing the bulk properties of functional materials and describing them with theoretical models. Magnets are widly used in electric vehicles (EV), hybrid electric vehicles (HEV), data storage, power generation and transmission, sensors etc. The search for novel magnetic phases requires an efficient quantitative microstructure analysis of microstructural information like phases, grain distribution and micromagnetic structural information like domain patterns, and correlating the information with intrinsic magnetic parameters of magnet samples. The information out of micromagnetic domains helps in obtaining the optimized microstructures in magnets that have good intrinsic magnetic properties. This paper is aimed at introducing the use of a traditional machine learning (ML) model with a higher dimensional feature set and a deep learning (DL) model to classify various regions in sintered NdFeB magnets based on Kerr-microscopy images. The obtained results are compared against reference data, which is generated manually by subject experts. Additionally, the results were compared against the approach for grain analysis, which is based on the electron backscatter diffraction (EBSD) technique. Further, the challenges faced by the traditional machine learning model for classifying microstructures in Kerr micrographs are discussed

Modeling Statistical Properties of Written Text

Written text is one of the fundamental manifestations of human language, and the study of its universal regularities can give clues about how our brains process information and how we, as a society, organize and share it. Among these regularities, only Zipf's law has been explored in depth. Other basic properties, such as the existence of bursts of rare words in specific documents, have only been studied independently of each other and mainly by descriptive models. As a consequence, there is a lack of understanding of linguistic processes as complex emergent phenomena. Beyond Zipf's law for word frequencies, here we focus on burstiness, Heaps' law describing the sublinear growth of vocabulary size with the length of a document, and the topicality of document collections, which encode correlations within and across documents absent in random null models. We introduce and validate a generative model that explains the simultaneous emergence of all these patterns from simple rules. As a result, we find a connection between the bursty nature of rare words and the topical organization of texts and identify dynamic word ranking and memory across documents as key mechanisms explaining the non trivial organization of written text. Our research can have broad implications and practical applications in computer science, cognitive science and linguistics

Automatic summarization of voicemail messages using lexical and prosodic features

This article presents trainable methods for extracting principal content words from voicemail messages. The short text summaries generated are suitable for mobile messaging applications. The system uses a set of classifiers to identify the summary words with each word described by a vector of lexical and prosodic features. We use an ROC-based algorithm, Parcel, to select input features (and classifiers). We have performed a series of objective and subjective evaluations using unseen data from two different speech recognition systems as well as human transcriptions of voicemail speech

O-regularly varying functions in approximation theory

For O-regularly varying functions a growth relation is introduced and characterized which gives an easy tool in the comparison of the rate of growth of two such functions at the limit point. In particular, methods based on this relation provide necessary and sufficient conditions in establishing chains of inequalities between functions and their geometric, harmonic, and integral means, in both directions. For periodic functions, for example, it is shown how this growth relation can be used in approximation theory in order to establish equivalence theorems between the best approximation and moduli of smoothness from prescribed inequalities of Jackson and Bernstein type. (orig.)SIGLEAvailable from TIB Hannover: RN 2414(459) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

The exponential sampling theorem of signal analysis

The Shannon sampling theory of signal analysis, which can be established by methods of Fourier analysis, plays an essential role in many fields. The aim of this paper is to establish the so-called exponential sampling theorem of optical physics and engineering in which the samples are not equally spaced apart as in the Shannon case but exponentially spaced, using the Mellin transform methods presented by the authors in earlier papers. Such spacing is needed for those applications where independent pieces of information accumulate near time t=0. The proof will make use of Mellin-bandlimited functions, apparently not studied seriously so far, a Bernstein-type inequality in the Mellin setting, and especially the Mellin-Poisson-summation formula introduced by the authors recently; it connects the classical Mellin transform with the finite Mellin transform. The exponential sampling results will not only be established for Mellin-bandlimited functions but for a less-restrictive class; namely functions which are only approximately Mellin-bandlimited. (orig.)Available from TIB Hannover: RN 2414(480) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

The finite Mellin transform, Mellin-fourier series, and the Mellin-poisson summation formula

The aim of this paper is to present the counterpart of the theory of Fourier series in the Mellin setting in a systematic form, independently of the Fourier theory, under natural and minimal assumption upon the functions in question. Such Mellin (Fourier) series will be definited for functions f:R_+#->#C for which f(x)=e"2"#pi#"cf(e"2"#pi#x) for c element of R and all x element of R_+, to be called c-recurrent functions, the counterpart of the periodic functions if c=0. The coefficients of the Mellin series or the finite Mellin transform will be connected with the classical Mellin transform on R_+ by our Mellin-Poisson summation formula; it is the analogue of the famous Poisson summation formula connecting the Fourier transform on R with the Fourier-coefficients or the finite Fourier transform. This summation formula will be used to give another proof of the Jacobi transformation formula for the Jacobi theta function. In a forthcoming paper the Mellin summation formula will be of basic importance in studying the Shannon sampling theorem of signal analysis in the Mellin setting, called the exponential sampling theory in optical circles. (orig.)Available from TIB Hannover: RN 2414(472) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Mellin transform theory and the role of its differential and integral operators

The purpose of this overview paper is to present an approach to Mellin transform theory that is fully independent of Laplace or Fourier transform results, in a unified systematic form, one that contains the transform properties and results under natural, minimal assumptions upon the functions in question. Cornerstones are two definitions of the Mellin transform, a local and a global transform, the Mellin inversion theory, established by approximation theoretical methods connected with the Mellin convolution singular integral of Gauss-Weierstrass-type, and especially the Mellin operators of differentiation and anti-differentiation. (orig.)Available from TIB Hannover: RN 2414(468) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

A direct approach to the Mellin transform

The aim of this paper is to present an approach to the Mellin transform that is fully independent of Laplace or Fourier transform theory, in a systematic, unified form, containing the basic properties and major results under natural, minimal hypotheses upon the functions in questions. Cornerstones of the approach are two definitions of the transform, a local and global Mellin transform, the Mellin translation and convolution structure, in particular approximation-theoretical methods connected with the Mellin convolution singular integral enabling one to establish the Mellin inversion theory. Of special intrest are the Mellin operators of differentiation and integration, more correctly of anti-differentiation, enabling one to establish the fundamental theorem of the differential and integral calculus in the Mellin frame. These two operators are different to those considered so far and more general. They are particular importance in solving differential and integral equations. As applications, the wave equation on R_+ x R_+ and the heat equation in a semi-infinite rod are considered in detail. The paper is written in part form an historical, survey-type perspective. (orig.)Available from TIB Hannover: RN 2414(467) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Mellin-fourier series and the classical Mellin transform

The aim of this paper is to present the counterpart of the theory of Fourier series in the Mellin setting, thus to consider a finite Mellin transform, or Mellin-Fourier coefficients, together with the associated Mellin-Fourier series. The presentation, in a systematic and overview form, is independent to the Fourier theory (of Laplace transform theory) and follows under natural and minimal assumption upon the functions in question. This material is put into connection with classical Mellin transform theory /bbfR_+ via the Mellin-Poisson summation formula, also in the form of two tables, as well as with Fourier transform theory. A highlight is an application to a new Kramer-type form of the exponential sampling theory of signal analysis. (orig.)Available from TIB Hannover: RN 2414(481) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman