Galois Correspondence and Fourier Analysis on Local Discrete Subfactors

Discrete subfactors include a particular class of infinite index subfactors and all finite index ones. A discrete subfactor is called local when it is braided and it fulfills a commutativity condition motivated by the study of inclusion of Quantum Field Theories in the algebraic Haag–Kastler setting. In Bischoff et al. (J Funct Anal 281(1):109004, 2021), we proved that every irreducible local discrete subfactor arises as the fixed point subfactor under the action of a canonical compact hypergroup. In this work, we prove a Galois correspondence between intermediate von Neumann algebras and closed subhypergroups, and we study the subfactor theoretical Fourier transform in this context. Along the way, we extend the main results concerning α-induction and σ-restriction for braided subfactors previously known in the finite index case

Geotechnology Allows Construction of Two Cohabirating Projects

The following case history presents innovative geotechnical solutions which allowed the simultaneous construction of two overlapping projects, by two different contractors, sponsored by different governmental agencies under tight project schedules. A settlement sensitive Light Rail Transit (LRT) line was to cohabitate the same alignment as a new freeway with embankment heights of 27 feet; both of which are on compressible and weak subgrade soils. Construction activities could not impinge on one or anothers project. The geotechnical concepts used allowed the two projects to proceed simultaneously and minimized the impacts of embankment induced settlement on the two LRT tracks. Field monitoring confirmed the expected soil movements were not greater than the tolerable limits for either project

Optically probing symmetry breaking in the chiral magnet Cu2OSeO3

We report on the linear optical properties of the chiral magnet Cu2OSeO3, specifically associated with the absence of inversion symmetry, the chiral crystallographic structure, and magnetic order. Through spectroscopic ellipsometry, we observe local crystal-field excitations below the charge-transfer gap. These crystal-field excitations are optically allowed due to the lack of inversion symmetry at the Cu sites. Optical polarization rotation measurements were used to study the structural chirality and magnetic order. The temperature dependence of the natural optical rotation, originating in the chiral crystal structure, provides evidence for a finite magneto-electric effect in the helimagnetic phase. We find a large magneto-optical susceptibility on the order of V(540nm)~10^4 rad/(T*m) in the helimagnetic phase and a maximum Faraday rotation of ~165deg/mm in the ferrimagnetic phase. The large value of V can be explained by considering spin cluster formation and the relative ease of domain reorientation in this metamagnetic material. The magneto-optical activity allows us to map the magnetic phase diagram, including the skyrmion lattice phase. In addition to this, we probe and discuss the nature of the various magnetic phase transitions in Cu2OSeO3.Comment: 9 pages, 10 figure

First Season QUIET Observations: Measurements of Cosmic Microwave Background Polarization Power Spectra at 43 GHz in the Multipole Range 25 ≤ ℓ ≤ 475

The Q/U Imaging ExperimenT (QUIET) employs coherent receivers at 43 GHz and 94 GHz, operating on the Chajnantor plateau in the Atacama Desert in Chile, to measure the anisotropy in the polarization of the cosmic microwave background (CMB). QUIET primarily targets the B modes from primordial gravitational waves. The combination of these frequencies gives sensitivity to foreground contributions from diffuse Galactic synchrotron radiation. Between 2008 October and 2010 December, over 10,000 hr of data were collected, first with the 19 element 43 GHz array (3458 hr) and then with the 90 element 94 GHz array. Each array observes the same four fields, selected for low foregrounds, together covering ≈1000 deg^2. This paper reports initial results from the 43 GHz receiver, which has an array sensitivity to CMB fluctuations of 69 μK√s. The data were extensively studied with a large suite of null tests before the power spectra, determined with two independent pipelines, were examined. Analysis choices, including data selection, were modified until the null tests passed. Cross-correlating maps with different telescope pointings is used to eliminate a bias. This paper reports the EE, BB, and EB power spectra in the multipole range ℓ = 25-475. With the exception of the lowest multipole bin for one of the fields, where a polarized foreground, consistent with Galactic synchrotron radiation, is detected with 3σ significance, the E-mode spectrum is consistent with the ΛCDM model, confirming the only previous detection of the first acoustic peak. The B-mode spectrum is consistent with zero, leading to a measurement of the tensor-to-scalar ratio of r = 0.35^(+1.06)_(–0.87). The combination of a new time-stream "double-demodulation" technique, side-fed Dragonian optics, natural sky rotation, and frequent boresight rotation leads to the lowest level of systematic contamination in the B-mode power so far reported, below the level of r = 0.1

Bessere Verlaufsdokumentation bei Patienten mit lumboradikulären Schmerzsyndromen: Der modifizierte NASS-Fragebogen

Zusammenfassung: Hintergrund: Zweck dieser Studie war es, ein zuverlässiges und einfach anzuwendendes Instrument zur Erfassung des Krankheitsverlaufs und des Therapieerfolgs bei Rückenschmerzpatienten mit lumboradikulären Syndromen vorzustellen. Methodik: Es wurden Daten von Patienten, welche sich einer Mikrodiskektomie wegen lumboradikulärem Syndrom unterzogen, in die Studie eingeschlossen und mittels des 17-teiligen NASS-Fragebogens (North American Spine Society) in Form eines Interviews vor und nach dem operativen therapeutischen Eingriff befragt. Außerdem wurden die demographischen Daten und Komorbiditäten erhoben. Über die Auswertung der Effektstärke bzw. Standardized Response Mean konnten die Fragen mit der stärksten Veränderung (vorher/nachher) für das Behandlungsergebnis ausgewählt werden. Ergebnisse: Es konnten die Datensätze von 139Patienten ausgewertet werden. Aus den 3Dimensionen Schmerz, neurologische Symptome und Beeinträchtigung im Alltag wurden jeweils diejenigen Fragen mit der höchsten Veränderung ausgewählt (hohe E.S. bzw. S.R.M.). In Abstimmung mit der klinischen Relevanz ergab sich schließlich die Auswahl von 8Fragen als konzentrierte Kurzform des NASS-Fragebogens. Schlussfolgerung: In dem von uns vorgestellten Instrument eines kurzen und aussagekräftigen Fragebogens sehen wir eine nützliche und in der Klinik einfach einzusetzende Möglichkeit zur verbesserten Dokumentation bei Patienten mit lumboradikulären Syndromen, insbesondere auch zur Effektmessung therapeutischer Interventionen im Sinne einer patientenorientierten Ergänzung der klinischen Befunderhebung und Diagnostik. Dieses neue Instrument könnte helfen, die Qualitätssicherung bei der konservativen und interventionellen Schmerzbehandlung der Patienten mit lumboradikulären Schmerzsyndromen zu verbesser