A mathematical formalism for treating spacetime topology as a quantum observable is provided. We describe spacetime foam entirely in algebraic terms. To implement the correspondence principle we express the classical spacetime manifold of general relativity and the commutative coordinates of its events by means of appropriate limit constructions.

Cortisol is a steroid hormone that is involved in a broad range of physiological processes in human/animal organisms. Cortisol levels in biological samples are a valuable biomarker, e.g., of stress and stress-related diseases; thus, cortisol determination in biological fluids, such as serum, saliva and urine, is of great clinical value. Although cortisol analysis can be performed with chromatography-based analytical techniques, such as liquid chromatography–tandem mass spectrometry (LC-MS/MS), conventional immunoassays (radioimmunoassays (RIAs), enzyme-linked immunosorbent assays (ELISAs), etc.) are considered the “gold standard” analytical methodology for cortisol, due to their high sensitivity along with a series of practical advantages, such as low-cost instrumentation, an assay protocol that is fast and easy to perform, and high sample throughput. Especially in recent decades, research efforts have focused on the replacement of conventional immunoassays by cortisol immunosensors, which may offer further improvements in the field, such as real-time analysis at the point of care (e.g., continuous cortisol monitoring in sweat through wearable electrochemical sensors). In this review, most of the reported cortisol immunosensors, mainly electrochemical and also optical ones, are presented, focusing on their immunosensing/detection principles. Future prospects are also briefly discussed.

Protein detection and characterization based on Broad-band Mach-Zehnder Interferometry is analytically outlined and demonstrated through a monolithic silicon microphotonic transducer. Arrays of silicon light emitting diodes and monomodal silicon nitride waveguides forming Mach-Zehnder interferometers were integrated on a silicon chip. Broad-band light enters the interferometers and exits sinusoidally modulated with two distinct spectral frequencies characteristic of the two polarizations. Deconvolution in the Fourier transform domain makes possible the separation of the two polarizations and the simultaneous monitoring of the TE and the TM signals. The dual polarization analysis over a broad spectral band makes possible the refractive index calculation of the binding adlayers as well as the distinction of effective medium changes into cover medium or adlayer ones. At the same time, multi-analyte detection at concentrations in the pM range is demonstrated.

The consumption of water and milk contaminated with bacteria can lead to foodborne disease outbreaks. For this reason, the development of rapid and sensitive analytical methods for bacteria detection is of primary importance for public health protection. Here, a miniaturized immunosensor based on broadband Mach–Zehnder Interferometry for the simultaneous determination of S. typhimurium and E. coli O157:H7 in drinking water and milk is presented. For the assay, mixtures of bacteria solutions with anti-bacteria-specific antibodies were run over the chip, followed by solutions of biotinylated anti-species-specific antibody and streptavidin. The assay was fast (10 min for water, 15 min for milk), accurate, sensitive (LOD: 40 cfu/mL for S. typhimurium; 110 cfu/mL for E. coli) and reproducible. The analytical characteristics achieved combined with the small chip size make the proposed biosensor suitable for on-site bacteria determination in drinking water and milk samples.