Abstract Identifying mouth breathing during sleep in a reliable, non-invasive way is challenging and currently not included in sleep studies. However, it has a high clinical relevance in pediatrics, as it can negatively impact the physical and mental health of children. Since mouth breathing is an anomalous condition in the general population with only 2% prevalence in our data set, we are facing an anomaly detection problem. This type of human medical data is commonly approached with deep learning methods. However, applying multiple supervised and unsupervised machine learning methods to this anomaly detection problem showed that classic machine learning methods should also be taken into account. This paper compared deep learning and classic machine learning methods on respiratory data during sleep using a leave-one-out cross validation. This way we observed the uncertainty of the models and their performance across participants with varying signal quality and prevalence of mouth breathing. The main contribution is identifying the model with the highest clinical relevance to facilitate the diagnosis of chronic mouth breathing, which may allow more affected children to receive appropriate treatment.

This paper introduces new techniques for the efficient computation of discrete Fourier transforms (DFTs) of Sn-k-invariant functions on the symmetric group Sn. We uncover diamond- and leaf-rake-like structures in Young's seminormal and orthogonal representations. Combining this with both a multiresolution scheme and an anticipation technique for saving scalar multiplications leads to linear time partial FFTs. Following the inductive version of Young's branching rule we obtain a global FFT that computes a DFT of Sn-k-invariant functions on Sn in at most ck...[Sn : Sn-k] scalar multiplications and additions, where ck denotes a positive constant depending only on k. This run-time, which is linear in [Sn : Sn-k], is order optimal and improves Maslen's algorithm. For example, it takes less than one second on a standard notebook to run our FFT algorithm for an Sn-2-invariant real-valued function on Sn, n=5000.

Recent digitization efforts have led to large music collections, which contain music documents of various modes comprising textual, visual and acoustic data. In this paper, we present a multimodal music player for presenting and browsing digitized music collections consisting of heterogeneous document types. In particular, we concentrate on music documents of two widely used types for representing a musical work, namely visual music representation (scanned images of sheet music) and associated interpretations (audio recordings). We introduce novel user interfaces for multimodal (audio-visual) music presentation as well as intuitive navigation and browsing. Our system offers high quality audio playback with time-synchronous display of the digitized sheet music associated to a musical work. Furthermore, our system enables a user to seamlessly crossfade between various interpretations belonging to the currently selected musical work.

The reuse of human motion capture data to create new, realistic motions by applying morphing and blending techniques has become an important issue in computer animation. This requires the identification and extraction of logically related motions scattered within some data set. Such content-based retrieval of motion capture data, which is the topic of this paper, constitutes a difficult and time-consuming problem due to significant spatio-temporal variations between logically related motions. In our approach, we introduce various kinds of qualitative features describing geometric relations between specified body points of a pose and show how these features induce a time segmentation of motion capture data streams. By incorporating spatio-temporal invariance into the geometric features and adaptive segments, we are able to adopt efficient indexing methods allowing for flexible and efficient content-based retrieval and browsing in huge motion capture databases. Furthermore, we obtain an efficient preprocessing method substantially accelerating the cost-intensive classical dynamic time warping techniques for the time alignment of logically similar motion data streams. We present experimental results on a test data set of more than one million frames, corresponding to 180 minutes of motion. The linearity of our indexing algorithms guarantees the scalability of our results to much larger data sets.

In this paper, we propose a unified approach to fast index-based music recognition. As an important area within the field of music information retrieval (MIR), the goal of music recognition is, given a database of musical pieces and a query document, to locate all occurrences of that document within the database, up to certain possible errors. In particular, the identification of the query with regard to the database becomes possible. The approach presented in this paper is based on a general algorithmic framework for searching complex patterns of objects in large databases. We describe how this approach may be applied to two important music recognition tasks: The polyphonic (musical score-based) search in polyphonic score data and the identification of pulse-code modulation audio material from a given acoustic waveform. We give an overview on the various aspects of our technology including fault-tolerant search methods. Several areas of application are suggested. We describe several prototypic systems we have developed for those applications including the notify! and the audentify! systems for score- and waveform-based music recognition, respectively.

For $2 \leqq c \leqq \infty $, the c-linear complexity $L_c (A)$ of a complex matrix A is defined as the minimal number of additions, subtractions, and multiplications by complex constants of absolute value $ \leqq c$, sufficient to evaluate A at a generic input vector. It is shown that if A is a Fourier transform on the finite group G, then $| L_\infty (A) - L_\infty (A^{ - 1} ) | \leqq | G |$. $L_c (G): = \min \{ L_c (A)|A{\text{ a Fourier transform for }}G\} $ is called the c-linear complexity of the finite group G. It is proved that $L_2 (G) > \frac{1}{4}| G |\log | G |$ for any finite group G, and two infinite classes of non-abelian groups G with $L_2 (G) \leqq 0.6| G |\log | G |$ and $L_2 (G) \leqq 0.8| G |\log | G |$, respectively, are presented. Thus there are non-abelian groups with even faster Fourier transforms than elementary abelian 2-groups (for which $L_2 (G) \leqq | G |\log | G |$)!

Let G be a finite group . Then $L_s (G)$, the minimal number of arithmetic operations to evaluate a Fourier transform corresponding to G, is smaller than $2 \cdot |G|^2 $. The fast Fourier transform algorithms improve this trivial upper bound by showing that for a cyclic group $G,L_s (G) \leqq c \cdot |G| \cdot \log |G|$. This last result is extended to metabelian groups, and it is shown that these groups also have fast inverse Fourier transforms. In particular there are fast algorithms for the (inverse) Fourier transforms for dihedral and generalized quaternion groups, as well as for all groups of square-free order.