The Maximum Order of Adjacency Matrices With a Given Rank

AMS Subject Classification: 05B20, 05C50.Graph;Adjacency matrix

The Maximum Order of Reduced Square(0, 1)-Matrices with a Given Rank

We look for the maximum order of a square (0, 1)-matrix A with a fixed rank r, provided A has no repeated rows or columns. If A is the adjacency matrix of a graph, Kotlov and Lovász [J. Graph Theory 23, 1996] proved that the maximum order equals Θ(2r/2). In this note we show that this result remains correct if A is symmetric, but becomes false if symmetry is not required.(0;1)-matrix;rank;graph

Wavelength dependence of light diffusion in strongly scattering macroporous gallium phosphide

We present time-resolved measurements of light transport through strongly scattering macroporous gallium phosphide at various vacuum wavelengths between 705 nm and 855 nm. Within this range the transport mean free path is strongly wavelength dependent, whereas the observed energy velocity is shown to be independent of the wavelength. We conclude that microscopic resonances, which can strongly slow down the diffusion process in, e.g., granular TiO2, are absent in macroporous gallium phosphide in the wavelength region of concern

The Maximum Order of Adjacency Matrices With a Given Rank

AMS Subject Classification: 05B20, 05C50.

Population dynamics of free-swimming Annelida in four Dutch wastewater treatment plants in relation to process characteristics

Free-swimming Annelida occasionally occur in very high densities in WWTPs (WasteWater Treatment Plants) and are nowadays applied for waste sludge reduction, but their growth is uncontrollable. In order to get more insight in the population dynamics of these free-swimming Annelida, and relate their presence to process characteristics, nine ATs (Aeration Tanks) of four Dutch WWTPs were regularly sampled over a 2.5-year period. For each species, peak periods in worm population growth were defined and population doubling times and half-lives calculated. Peak periods and doubling times were compared to those in natural systems. Process characteristics were obtained from the plant operators and related to the worm populations by multivariate analysis for the first time in large-scale WWTPs. The species composition in the WWTPs was limited and the most abundant free-swimming Annelida were in decreasing order Nais spp., Aeolosoma hemprichi, Pristina aequiseta, Aeolosoma variegatum, Chaetogaster diastrophus, and Aeolosoma tenebrarum.This latter species had never been found before in WWTPs. Worm absence sometimes coincided with the presence of anoxic zones, but this was possibly overcome by higher temperatures in the WWTPs. Worms were present all year round, even in winter, but no yearly recurrences of population peaks were observed, probably as a result of stable food supply and temperature, and the lack of predation in the WWTPs. Peak periods were similar between the ATs of each WWTP. The duration of the peak periods was on average 2¿3 months for each species and the population doubling times in the peak periods were short (on average 2¿6 days), which also corresponds to a stable favorable environment. The disappearance of worm populations from the WWTPs was presumably caused by declining asexual reproduction and subsequent removal with the waste sludge. Multivariate analysis indicated that 36% of the variability in worm populations was due to spatial and temporal patterns only. In addition, no more than 4% of the variability in worm populations was related to variations in process characteristics only and worm presence was usually associated with better sludge settleability. In conclusion, our data from large-scale WWTPs suggest that growth of free-swimming Annelida still seems uncontrollable and that their effects on treatment processes are unclear, which makes stable application in wastewater treatment for sludge reduction difficult

Wearables measuring electrodermal activity to assess perceived stress in care:A scoping review

Background:Chronic stress responses can lead to physical and behavioural health problems, often experienced and observed in the care of people with intellectual disabilities or people with dementia. Electrodermal activity (EDA) is a bio-signal for stress, which can be measured by wearables and thereby support stress management. However, the how, when and to what extent patients and healthcare providers can benefit is unclear. This study aims to create an overview of available wearables enabling the detection of perceived stress by using EDA.Methods:Following the PRISMA-SCR protocol for scoping reviews, four databases were included in the search of peer-reviewed studies published between 2012 and 2022, reporting detection of EDA in relation to self-reported stress or stress-related behaviours. Type of wearable, bodily location, research population, context, stressor type and the reported relationship between EDA and perceived stress were extracted.Results:Of the 74 included studies, the majority included healthy subjects in laboratory situations. Field studies and studies using machine learning (ML) to predict stress have increased in the last years. EDA is most often measured on the wrist, with offline data processing. Studies predicting perceived stress or stress-related behaviour using EDA features, reported accuracies between 42% and 100% with an average of 82.6%. Of these studies, the majority used ML.Conclusion:Wearable EDA sensors are promising in detecting perceived stress. Field studies with relevant populations in a health or care context are lacking. Future studies should focus on the application of EDA-measuring wearables in real-life situations to support stress management

Engineering of two-photon quantum correlation behind a double slit

Quantum Matter and Optic

Magnetic field dependence of the exciton energy in a quantum disk

The groundstate energy and binding energy of an exciton, confined in a^M quantum disk, are calculated as a function of an external magnetic field. The confinement potential is a hard wall of finite height. The diamagnetic shift is investigated for magnetic fields up to 40$T$. Our results are applied to $In_{y}Al_{1-y}As/Al_{x}Ga_{1-x}As$ self-assembled quantum dots and very good agreement with experiments is obtained. Furthermore, we investigated the influence of the dot size on the diamagnetic shift by changing the disk radius. The exciton excited states are found as a function of the magnetic field. The relative angular momentum is not a quantum number and changes with the magnetic field strength.Comment: 10 pages, 17 figure