Three-dimensional Self-similar Fractal Light in Canonical Resonators

Unstable canonical resonators can possess eigenmodes with a fractal intensity structure [Karman et al., Nature 402, 138(1999)]. In one particular transverse plane, the intensity is not merely statistically fractal, but self-similar [Courtial and Padgett, PRL 85, 5320 (2000)]. This can be explained using a combination of diffraction and imaging with magnification greater than one. Here we show that the same mechanism also shapes the intensity cross-section in the longitudinal direction into a self-similar fractal, but with a different magnification. This results in three-dimensional, self-similar, fractal intensity structure in the eigenmodes

Analyzing Visual Mappings of Traditional and Alternative Music Notation

In this paper, we postulate that combining the domains of information visualization and music studies paves the ground for a more structured analysis of the design space of music notation, enabling the creation of alternative music notations that are tailored to different users and their tasks. Hence, we discuss the instantiation of a design and visualization pipeline for music notation that follows a structured approach, based on the fundamental concepts of information and data visualization. This enables practitioners and researchers of digital humanities and information visualization, alike, to conceptualize, create, and analyze novel music notation methods. Based on the analysis of relevant stakeholders and their usage of music notation as a mean of communication, we identify a set of relevant features typically encoded in different annotations and encodings, as used by interpreters, performers, and readers of music. We analyze the visual mappings of musical dimensions for varying notation methods to highlight gaps and frequent usages of encodings, visual channels, and Gestalt laws. This detailed analysis leads us to the conclusion that such an under-researched area in information visualization holds the potential for fundamental research. This paper discusses possible research opportunities, open challenges, and arguments that can be pursued in the process of analyzing, improving, or rethinking existing music notation systems and techniques.Comment: 5 pages including references, 3rd Workshop on Visualization for the Digital Humanities, Vis4DH, IEEE Vis 201

Investigating Machine Learning Clustering Methods to Replicate the Human Idea of Structure to Documents

Anyone trying to maintain a set of text documents in an information retrieval system will run into problems keeping it relevant and up to date as the amount of data increases. This thesis investigates how a collection of documents can be clustered in a way that resembles how a human would organize it. It also assesses how difficult it is to implement this into an existing information retrieval system with current programming libraries, and in what practical ways this can be useful. The text data in this project is represented by a TF-IDF model. A K-Means clustering algorithm generates one clustering, and a Support Vector Machine is trained with minimal user data to provide another clustering. These two are then evaluated and compared using a set of metrics. This project takes a practical approach to the problem, focusing on what can be implemented using existing programming libraries and what will actually work in a production environment. Software for visualizing the corpus and calculating similar documents, are implemented as well. The supervised method SVM greatly surpasses the unsupervised method K-Means in being able to replicate the given ground truth, but both models are in themselves useful. With a relatively simple understanding of machine learning, any company could set up a similar system. It does, however, take some deeper mathematical knowledge and fine tuning to get the most out of it and tailor it to the dataset

Spectral projections and resolvent bounds for partially elliptic quadratic differential operators

We study resolvents and spectral projections for quadratic differential operators under an assumption of partial ellipticity. We establish exponential-type resolvent bounds for these operators, including Kramers-Fokker-Planck operators with quadratic potentials. For the norms of spectral projections for these operators, we obtain complete asymptotic expansions in dimension one, and for arbitrary dimension, we obtain exponential upper bounds and the rate of exponential growth in a generic situation. We furthermore obtain a complete characterization of those operators with orthogonal spectral projections onto the ground state.Comment: 60 pages, 3 figures. J. Pseudo-Differ. Oper. Appl., to appear. Revised according to referee report, including minor changes to Corollary 1.8. The final publication will be available at link.springer.co

A primer on computational statistics for ordinal models with applications to survey data

The analysis of survey data is a frequently arising issue in clinical trials, particularly when capturing quantities which are difficult to measure using, e.g., a technical device or a biochemical procedure. Typical examples are questionnaires about patient's well-being, pain, anxiety, quality of life or consent to an intervention. Data is captured on a discrete scale containing only a limited (usually three to ten) number of possible answers, of which the respondent has to pick the answer which fits best his personal opinion to the question. This data is generally located on an ordinal scale as answers can usually be arranged in an increasing order, e.g., "bad", "neutral", "good" for well-being or "none", "mild", "moderate", "severe" for pain. Since responses are often stored numerically for data processing purposes, analysis of survey data using ordinary linear regression (OLR) models seems to be natural. However, OLR assumptions are often not met as linear regression requires a constant variability of the response variable and can yield predictions out of the range of response categories. Moreover, in doing so, one only gains insights about the mean response which might, depending on the response distribution, not be very representative. In contrast, ordinal regression models are able to provide probability estimates for all response categories and thus yield information about the full response scale rather than just the mean. Although these methods are well described in the literature, they seem to be rarely applied to biomedical or survey data. In this paper, we give a concise overview about fundamentals of ordinal models, applications to a real data set, outline usage of state-of-the-art-software to do so and point out strengths, limitations and typical pitfalls. This article is a companion work to a current vignette-based structured interview study in paediatric anaesthesia

Tuning of Kilopixel Transition Edge Sensor Bolometer Arrays with a Digital Frequency Multiplexed Readout System

A digital frequency multiplexing (DfMUX) system has been developed and used to tune large arrays of transition edge sensor (TES) bolometers read out with SQUID arrays for mm-wavelength cosmology telescopes. The DfMUX system multiplexes the input bias voltages and output currents for several bolometers on a single set of cryogenic wires. Multiplexing reduces the heat load on the camera's sub-Kelvin cryogenic detector stage. In this paper we describe the algorithms and software used to set up and optimize the operation of the bolometric camera. The algorithms are implemented on soft processors embedded within FPGA devices operating on each backend readout board. The result is a fully parallelized implementation for which the setup time is independent of the array size.Comment: 5 pages, 4 figure

On the way to DSM-V

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Fractal light from lasers

Fractals, complex shapes with structure at multiple scales, have long been observed in Nature: as symmetric fractals in plants and sea shells, and as statistical fractals in clouds, mountains and coastlines. With their highly polished spherical mirrors, laser resonators are almost the precise opposite of Nature, and so it came as a surprise when, in 1998, transverse intensity cross-sections of the eigenmodes of unstable canonical resonators were predicted to be fractals [Karman et al., Nature 402, 138 (1999)]. Experimental verification has so far remained elusive. Here we observe a variety of fractal shapes in transverse intensity cross-sections through the lowest-loss eigenmodes of unstable canonical laser resonators, thereby demonstrating the controlled generation of fractal light inside a laser cavity. We also advance the existing theory of fractal laser modes, first by predicting 3D self-similar fractal structure around the centre of the magnified self-conjugate plane, second by showing, quantitatively, that intensity cross-sections are most self-similar in the magnified self-conjugate plane. Our work offers a significant advance in the understanding of a fundamental symmetry of Nature as found in lasers