Approximate Recovery and Relative Entropy I: General von Neumann Subalgebras

We prove the existence of a universal recovery channel that approximately recovers states on a von Neumann subalgebra when the change in relative entropy, with respect to a fixed reference state, is small. Our result is a generalization of previous results that applied to type-I von Neumann algebras by Junge at al. [arXiv:1509.07127]. We broadly follow their proof strategy but consider here arbitrary von Neumann algebras, where qualitatively new issues arise. Our results hinge on the construction of certain analytic vectors and computations/estimations of their Araki–Masuda $$L_p$$ L p norms. We comment on applications to the quantum null energy condition.

Impact of a Vibrotactile Belt on Emotionally Challenging Everyday Situations of the Blind

Spatial orientation and navigation depend primarily on vision. Blind people lack this critical source of information. To facilitate wayfinding and to increase the feeling of safety for these people, the “feelSpace belt” was developed. The belt signals magnetic north as a fixed reference frame via vibrotactile stimulation. This study investigates the effect of the belt on typical orientation and navigation tasks and evaluates the emotional impact. Eleven blind subjects wore the belt daily for seven weeks. Before, during and after the study period, they filled in questionnaires to document their experiences. A small sub-group of the subjects took part in behavioural experiments before and after four weeks of training, i.e., a straight-line walking task to evaluate the belt’s effect on keeping a straight heading, an angular rotation task to examine effects on egocentric orientation, and a triangle completion navigation task to test the ability to take shortcuts. The belt reduced subjective discomfort and increased confidence during navigation. Additionally, the participants felt safer wearing the belt in various outdoor situations. Furthermore, the behavioural tasks point towards an intuitive comprehension of the belt. Altogether, the blind participants benefited from the vibrotactile belt as an assistive technology in challenging everyday situations.

Automated Medical Care: Bradycardia Detection and Cardiac Monitoring of Preterm Infants

Background and Objectives: Prematurity of birth occurs before the 37th week of gestation and affects up to 10% of births worldwide. It is correlated with critical outcomes; therefore, constant monitoring in neonatal intensive care units or home environments is required. The aim of this work was to develop solutions for remote neonatal intensive supervision systems, which should assist medical diagnosis of premature infants and raise alarm at cardiac abnormalities, such as bradycardia. Additionally, the COVID-19 pandemic has put a worldwide stress upon the medical staff and the management of healthcare units. Materials and Methods: A traditional medical diagnosing scheme was set up, implemented with the aid of powerful mathematical operators. The algorithm was tailored to the infants’ personal ECG characteristics and was tested on real ECG data from the publicly available PhysioNet database “Preterm Infant Cardio-Respiratory Signals Database”. Different processing problems were solved: noise filtering, baseline drift removal, event detection and compression of medical data using the à trous wavelet transform. Results: In all 10 available clinical cases, the bradycardia events annotated by the physicians were correctly detected using the RR intervals. Compressing the ECG signals for remote transmission, we obtained compression ratios (CR) varying from 1.72 to 7.42, with the median CR value around 3. Conclusions: We noticed that a significant amount of noise can be added to a signal while monitoring using standard clinical sensors. We tried to offer solutions for these technical problems. Recent studies have shown that persons infected with the COVID-19 disease are frequently reported to develop cardiovascular symptoms and cardiac arrhythmias. An automatic surveillance system (both for neonates and adults) has a practical medical application. The proposed algorithm is personalized, no fixed reference value being applied, and the algorithm follows the neonate’s cardiac rhythm changes. The performance depends on the characteristics of the input ECG. The signal-to-noise ratio of the processed ECG was improved, with a value of up to 10 dB.

Investigation of localization accuracy in UWB relative ranging system

The hybrid combination of a traditional positioning system with fixed reference points and a relative positioning system based on the relative position of network subscribers on the basis of measuring the distances between them increases the availability of the positioning system for moving objects in harsh environment and the accuracy of their positioning. Depending on the operating conditions, the cascade measurement of the distances between the nodes expands the working area with an acceptable positioning accuracy with the same number of fixed anchors.

Mirau-Based CSI with Oscillating Reference Mirror for Vibration Compensation in In-Process Applications

We present a Mirau-type coherence scanning interferometer (CSI) with an oscillating reference mirror and an integrated interferometric distance sensor (IDS) sharing the optical path with the CSI. The IDS works simultaneously with the CSI and measures the distance changes during the depth scanning process with high temporal resolution. The additional information acquired by the IDS is used to correct the CSI data disturbed by unwanted distance changes due to environmental vibrations subsequent to the measurement. Due to the fixed reference mirror in commercial Mirau objectives, a Mirau attachment (MA) comprising an oscillating reference mirror is designed and built. Compared to our previous systems based on the Michelson and the Linnik interferometer, the MA represents a novel solution that completes the range of possible applications. Due to its advantages, the Mirau setup is the preferred and most frequently used interferometer type in industry. Therefore, the industrial use is ensured by this development. We investigate the functioning of the system and the capability of the vibration compensation by several measurements on various surface topographies.

Compositional Data Analysis of Microbiome and Any-Omics Datasets: A Validation of the Additive Logratio Transformation

Microbiome and omics datasets are, by their intrinsic biological nature, of high dimensionality, characterized by counts of large numbers of components (microbial genes, operational taxonomic units, RNA transcripts, etc.). These data are generally regarded as compositional since the total number of counts identified within a sample is irrelevant. The central concept in compositional data analysis is the logratio transformation, the simplest being the additive logratios with respect to a fixed reference component. A full set of additive logratios is not isometric, that is they do not reproduce the geometry of all pairwise logratios exactly, but their lack of isometry can be measured by the Procrustes correlation. The reference component can be chosen to maximize the Procrustes correlation between the additive logratio geometry and the exact logratio geometry, and for high-dimensional data there are many potential references. As a secondary criterion, minimizing the variance of the reference component's log-transformed relative abundance values makes the subsequent interpretation of the logratios even easier. On each of three high-dimensional omics datasets the additive logratio transformation was performed, using references that were identified according to the abovementioned criteria. For each dataset the compositional data structure was successfully reproduced, that is the additive logratios were very close to being isometric. The Procrustes correlations achieved for these datasets were 0.9991, 0.9974, and 0.9902, respectively. We thus demonstrate, for high-dimensional compositional data, that additive logratios can provide a valid choice as transformed variables, which (a) are subcompositionally coherent, (b) explain 100% of the total logratio variance and (c) come measurably very close to being isometric. The interpretation of additive logratios is much simpler than the complex isometric alternatives and, when the variance of the log-transformed reference is very low, it is even simpler since each additive logratio can be identified with a corresponding compositional component.

Horizontal/vertical displacements and their rates

This chapter widens our scope towards translation and rotation. These displacements are critical in tectonic studies along with distortion, which has so far been the main subject of this book. Note that a translation needs a fixed reference to be defined. Consider, for example, the glide of the lithosphere over the asthenosphere with respect to the mid-Atlantic ridge. On a spherical surface, a translation is also a rotation, where the horizontal displacement of a plate is governed by a rotation axis (or pole) and an angular velocity. Vertical displacements of the Earth’s surface are one order of magnitude less (on the order of mm per year) than horizontal displacements. Lots of studies, performed in the frame of a discipline called neotectonics, attempt to determine uplift rates through different techniques, such as fission track and radioactive decay. They will be briefly presented in this chapter. The main reference for vertical displacements is the sea level, which itself is mobile through time. This mobility is obviously sensitive when processes such as erosion or post-glacial rebound are considered, but much less significant when exhumation of deep-seated rocks may reach kilometres during an orogeny.

An approach to drastically reduce the required legs DOFs for bipedal robots and lower-limb exoskeletons

We present a method to drastically reduce the required number of degrees-of-freedom (DOFs) needed for walking for each leg of bipedal robots and lower-limb exoskeletons. This approach releases more legs DOFs in the null space to do other tasks, instead of unnecessarily constraining them. It uses relative reference frames to control relative motion between the two feet, instead of the usual method of controlling foot movement with respect to fixed reference frames. In its basic form, it controls the bipedal walking holistically using two controllers: (1) world space control using relative feet motion and (2) null-space control of the legs posture.

Temporal integration of partial loudness of helicopter-like sounds

When developing new vehicles that are to be operated in existing background noise, such as electric vertical take-off and landing aircraft (eVTOLs) in cities, a sound design goal should be to minimize the loudness in the given background noise. Rotorcraft sounds are characterised by their pulses, and the choice of rotor size and number allows to vary the temporal characteristics. We asked participants to compare the loudness of pulse trains with pulse durations of 1, 2, 5, 10 and 20 ms and a pulse rate of 20 Hz in a two-interval, two-alternatives forced choice task and a 1-up/1-down procedure. Street noise was presented simultaneously with the pulse trains, and had the same root-mean-square (RMS) level as the fixed reference pulse train of about 65 dB SPL. First results indicate that the sounds with a short pulse duration need considerably less RMS level to result in the same loudness as a long pulse duration, i.e. the partial loudness of shorter pulses is higher at the same equivalent sound pressure level.