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In this work, we study foliations of arbitrary codimension
with integrable normal bundles on complete Riemannian manifolds. We obtain a necessary and sufficient condition for
to be totally geodesic. For this, we introduce a special number
that measures when the foliation ceases to be totally geodesic. Furthermore, applying some maximum principle we deduce geometric properties for
. We conclude with a geometrical version of Novikov’s theorem (Trans. Moscow Math. Soc. (1965), 268–304), for Riemannian compact manifolds of arbitrary dimension.
Despite the multitude of clinical manifestations of post-acute sequelae of SARS-CoV-2 infection (PASC), studies applying statistical methods to directly investigate patterns of symptom co-occurrence and their biological correlates are scarce.
We assessed 30 symptoms pertaining to different organ systems in 749 adults (age = 55 ± 14 years; 47% female) during in-person visits conducted at 6–11 months after hospitalization due to coronavirus disease 2019 (COVID-19), including six psychiatric and cognitive manifestations. Symptom co-occurrence was initially investigated using exploratory factor analysis (EFA), and latent variable modeling was then conducted using Item Response Theory (IRT). We investigated associations of latent variable severity with objective indices of persistent physical disability, pulmonary and kidney dysfunction, and C-reactive protein and D-dimer blood levels, measured at the same follow-up assessment.
The EFA extracted one factor, explaining 64.8% of variance; loadings were positive for all symptoms, and above 0.35 for 16 of them. The latent trait generated using IRT placed fatigue, psychiatric, and cognitive manifestations as the most discriminative symptoms (coefficients > 1.5, p < 0.001). Latent trait severity was associated with decreased body weight and poorer physical performance (coefficients > 0.240; p ⩽ 0.003), and elevated blood levels of C-reactive protein (coefficient = 0.378; 95% CI 0.215–0.541; p < 0.001) and D-dimer (coefficient = 0.412; 95% CI 0.123–0.702; p = 0.005). Results were similar after excluding subjects with pro-inflammatory comorbidities.
Different symptoms that persist for several months after moderate or severe COVID-19 may unite within one latent trait of PASC. This trait is dominated by fatigue and psychiatric symptoms, and is associated with objective signs of physical disability and persistent systemic inflammation.
A variety of subjective experiences have been reported to be associated with the symptom expression of obsessive-compulsive disorder (OCD) and Tourette syndrome (TS). First described in TS patients, these subjective experiences have been defined in different ways. There is no consensus in the literature on how to best define subjective experiences. This lack of consensus may hinder the understanding of study results and prevents the possibility of including them in the search for etiological factors associated with OCD and TS.
The objective of this article was to review the descriptions of subjective experiences in the English-language literature from 1980–2007. This meta-analytic review was carried out using the English-language literature from 1980–2007 available on MEDLINE, PsyclNFO, and the Cochrane Library databases using the following search terms: premonitory urges, sensory tics, “just-right” perceptions, sensory phenomena, sensory experiences, incompleteness, “not just-right” phenomena, obsessive-compulsive disorder and TS, including OCD and/or TS, in all combination searches. We also searched for the references cited in each article previously found that referred to the aforementioned terms. Thirtyone articles were included in the study.
Subjective experiences, in particular, the sensory phenomena, were important phenotypic variables in the characterization of the tic-related OCD subtype and were more frequent in the early-onset OCD subtype. There is a paucity of studies using structured interviews to assess sensory phenomena, their epidemiology and the etiological mechanisms associated with sensory phenomena.
The current review provides some evidence that sensory phenomena can be useful to identify more homogenous subgroups of OCD and TS patients and should be included as important phenotypic variables in future clinical, genetic, neuroimaging, and treatment-response studies.
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