A toral diffeomorphism with a non-polygonal rotation set

We construct a diffeomorphism of the two-dimensional torus which is isotopic to the identity and whose rotation set is not a polygon

Difficulty Classification of Mountainbike Downhill Trails utilizing Deep Neural Networks

The difficulty of mountainbike downhill trails is a subjective perception. However, sports-associations and mountainbike park operators attempt to group trails into different levels of difficulty with scales like the Singletrail-Skala (S0-S5) or colored scales (blue, red, black, ...) as proposed by The International Mountain Bicycling Association. Inconsistencies in difficulty grading occur due to the various scales, different people grading the trails, differences in topography, and more. We propose an end-to-end deep learning approach to classify trails into three difficulties easy, medium, and hard by using sensor data. With mbientlab Meta Motion r0.2 sensor units, we record accelerometer- and gyroscope data of one rider on multiple trail segments. A 2D convolutional neural network is trained with a stacked and concatenated representation of the aforementioned data as its input. We run experiments with five different sample- and five different kernel sizes and achieve a maximum Sparse Categorical Accuracy of 0.9097. To the best of our knowledge, this is the first work targeting computational difficulty classification of mountainbike downhill trails.Comment: 11 pages, 5 figure

Using an Indoor Localization System for Activity Recognition

Recognizing the activity performed by users is importantin many application domains, from e-health to home automation. Thispaper explores the use of a fine-grained indoor localization system, basedon ultra-wideband, for activity recognition. The user is supposed to weara number of active tags. The position of active tags is first determinedwith respect to the space where the user is moving, then some position-independent metrics are estimated and given as input to a previouslytrained system. Experimental results show that accuracy values as highas∼95% can be obtained when using a personalized model

Rotation set and Entropy

In 1991 Llibre and MacKay proved that if $f$ is a 2-torus homeomorphism isotopic to identity and the rotation set of $f$ has a non empty interior then $f$ has positive topological entropy. Here, we give a converselike theorem. We show that the interior of the rotation set of a 2-torus $C^{1+ \alpha}$ diffeomorphism isotopic to identity of positive topological entropy is not empty, under the additional hypotheses that $f$ is topologically transitive and irreducible. We also give examples that show that these hypotheses are necessary.Comment: 15 pages, 2 figures, references adde

Harmonic analysis of iterated function systems with overlap

In this paper we extend previous work on IFSs without overlap. Our method involves systems of operators generalizing the more familiar Cuntz relations from operator algebra theory, and from subband filter operators in signal processing.Comment: 37 page

Aperiodic order and pure point diffraction

We give a leisurely introduction into mathematical diffraction theory with a focus on pure point diffraction. In particular, we discuss various characterisations of pure point diffraction and common models arising from cut and project schemes. We finish with a list of open problems.Comment: 14 page

Ethical Surveillance: Applying Deep Learning and Contextual Awareness for the Benefit of Persons Living with Dementia

A significant proportion of the population has become used to sharing private information on the internet with their friends. This information can leak throughout their social network and the extent that personal information propagates can depend on the privacy policy of large corporations. In an era of artificial intelligence, data mining, and cloud computing, is it necessary to share personal information with unidentified people? Our research shows that deep learning is possible using relatively low capacity computing. When applied, this demonstrates promising results in spatio-temporal positioning of subjects, in prediction of movement, and assessment of contextual risk. A private surveillance system is particularly suitable in the care of those who may be considered vulnerable

Modelling Patient Behaviour Using IoT Sensor Data: a Case Study to Evaluate Techniques for Modelling Domestic Behaviour in Recovery from Total Hip Replacement Surgery

The UK health service sees around 160,000 total hip or knee replacements every year and this number is expected to rise with an ageing population. Expectations of surgical outcomes are changing alongside demographic trends, whilst aftercare may be fractured as a result of resource limitations. Conventional assessments of health outcomes must evolve to keep up with these changing trends. Health outcomes may be assessed largely by self-report using Patient Reported Outcome Measures (PROMs), such as the Oxford Hip or Oxford Knee Score, in the months up to and following surgery. Though widely used, many PROMs have methodological limitations and there is debate about how to interpret results and definitions of clinically meaningful change. With the development of a home-monitoring system, there is opportunity to characterise the relationship between PROMs and behaviour in a natural setting and to develop methods of passive monitoring of outcome and recovery after surgery. In this paper, we discuss the motivation and technology used in long-term continuous observation of movement, sleep and domestic routine for healthcare applications, such as the HEmiSPHERE project for hip and knee replacement patients. In this case study, we evaluate trends evident in data of two patients, collected over a 3-month observation period post-surgery, by comparison with scores from PROMs for sleep and movement quality, and by comparison with a third control home. We find that accelerometer and indoor localisation data correctly highlight long-term trends in sleep and movement quality and can be used to predict sleep and wake times and measure sleep and wake routine variance over time, whilst indoor localisation provides context for the domestic routine and mobility of the patient. Finally, we discuss a visual method of sharing findings with healthcare professionals