On the trace of the antipode and higher indicators

We introduce two kinds of gauge invariants for any finite-dimensional Hopf algebra H. When H is semisimple over C, these invariants are respectively, the trace of the map induced by the antipode on the endomorphism ring of a self-dual simple module, and the higher Frobenius-Schur indicators of the regular representation. We further study the values of these higher indicators in the context of complex semisimple quasi-Hopf algebras H. We prove that these indicators are non-negative provided the module category over H is modular, and that for a prime p, the p-th indicator is equal to 1 if, and only if, p is a factor of dim H. As an application, we show the existence of a non-trivial self-dual simple H-module with bounded dimension which is determined by the value of the second indicator.Comment: additional references, fixed some typos, minor additions including a questions and some remark

Solar System Processes Underlying Planetary Formation, Geodynamics, and the Georeactor

Only three processes, operant during the formation of the Solar System, are responsible for the diversity of matter in the Solar System and are directly responsible for planetary internal-structures, including planetocentric nuclear fission reactors, and for dynamical processes, including and especially, geodynamics. These processes are: (i) Low-pressure, low-temperature condensation from solar matter in the remote reaches of the Solar System or in the interstellar medium; (ii) High-pressure, high-temperature condensation from solar matter associated with planetary-formation by raining out from the interiors of giant-gaseous protoplanets, and; (iii) Stripping of the primordial volatile components from the inner portion of the Solar System by super-intense solar wind associated with T-Tauri phase mass-ejections, presumably during the thermonuclear ignition of the Sun. As described herein, these processes lead logically, in a causally related manner, to a coherent vision of planetary formation with profound implications including, but not limited to, (a) Earth formation as a giant gaseous Jupiter-like planet with vast amounts of stored energy of protoplanetary compression in its rock-plus-alloy kernel; (b) Removal of approximately 300 Earth-masses of primordial gases from the Earth, which began Earth's decompression process, making available the stored energy of protoplanetary compression for driving geodynamic processes, which I have described by the new whole-Earth decompression dynamics and which is responsible for emplacing heat at the mantle-crust-interface at the base of the crust through the process I have described, called mantle decompression thermal-tsunami; and, (c)Uranium accumulations at the planetary centers capable of self-sustained nuclear fission chain reactions.Comment: Invited paper for the Special Issue of Earth, Moon and Planets entitled Neutrino Geophysics Added final corrections for publicatio

Multimodal Analgesic Effectiveness on Acute Postoperative Pain Management After Adult Cardiac Surgery

Background Many patients report moderate to severe pain in the acute postoperative period. Enhanced recovery protocols recommend multimodal analgesics, but the optimal combination of these is unknown. Purpose The aim of this study was to synthesize the best available evidence about effectiveness of multimodal analgesics on pain after adult cardiac surgery. Methods A systematic review to determine the effect of multimodal postoperative analgesics is proposed (International Prospective Register of Systematic Reviews Registration CRD42022355834). Multiple databases including the Cochrane Library, Cochrane Central Register of Controlled Trials, Cumulative Index to Nursing and Allied Health Literature, American Psychological Association, the Education Resources Information Centre, the Excerpta Medica database, the Medical Literature Analysis and Retrieval System Online, Scopus, Web of Science, and clinical trials databases will be searched. Screening in Covidence and quality assessment will be conducted by 2 authors. A grading of recommendations, assessment, development, and evaluation summary of findings will be presented if meta-analysis is possible

Development of a Non-invasive Device for Swallow Screening in Patients at Risk of Oropharyngeal Dysphagia : Results from a Prospective Exploratory Study

Oropharyngeal dysphagia is prevalent in several at-risk populations, including post-stroke patients, patients in intensive care and the elderly. Dysphagia contributes to longer hospital stays and poor outcomes, including pneumonia. Early identification of dysphagia is recommended as part of the evaluation of at-risk patients, but available bedside screening tools perform inconsistently. In this study, we developed algorithms to detect swallowing impairment using a novel accelerometer-based dysphagia detection system (DDS). A sample of 344 individuals was enrolled across seven sites in the United States. Dual-axis accelerometry signals were collected prospectively with simultaneous videofluoroscopy (VFSS) during swallows of liquid barium stimuli in thin, mildly, moderately and extremely thick consistencies. Signal processing classifiers were trained using linear discriminant analysis and 10,000 random training-test data splits. The primary objective was to develop an algorithm to detect impaired swallowing safety with thin liquids with an area under receiver operating characteristic curve (AUC) > 80% compared to the VFSS reference standard. Impaired swallowing safety was identified in 7.2% of the thin liquid boluses collected. At least one unsafe thin liquid bolus was found in 19.7% of participants, but participants did not exhibit impaired safety consistently. The DDS classifier algorithms identified participants with impaired thin liquid swallowing safety with a mean AUC of 81.5%, (sensitivity 90.4%, specificity 60.0%). Thicker consistencies were effective for reducing the frequency of penetration-aspiration. This DDS reached targeted performance goals in detecting impaired swallowing safety with thin liquids. Simultaneous measures by DDS and VFSS, as performed here, will be used for future validation studies.Peer reviewe

Historical Missionary Activity, Schooling, and the Reversal of Fortunes: Evidence from Nigeria

This paper shows that historical missionary activity has had a persistent effect on schooling outcomes, and contributed to a reversal of fortunes wherein historically richer ethnic groups are poorer today. Combining contemporary individual-level data with a newly constructed dataset on mission stations in Nigeria, we find that individuals whose ancestors were exposed to greater missionary activity have higher levels of schooling. This effect is robust to omitted heterogeneity, ethnicity fixed effects, and reverse causation. We find inter-generational factors and the persistence of early advantages in educational infrastructure to be key channels through which the effect has persisted. Consistent with theory, the effect of missions on current schooling is larger for population subgroups that have historically suffered disadvantages in access to education