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A theorem of single-sorted universal algebra asserts that every finite algebra can be represented as a product of a finite family of finite directly irreducible algebras. In this article, we show that the many-sorted counterpart of the above theorem is also true, but under the condition of requiring, in the definition of directly reducible many-sorted algebra, that the supports of the factors should be included in the support of the many-sorted algebra. Moreover, we show that the theorem of Birkhoff, according to which every single-sorted algebra is isomorphic to a subdirect product of subdirectly irreducible algebras, is also true in the field of many-sorted algebras.

The identification of a bacterial, viral, or even noninfectious cause is essential in the management of febrile syndrome in the emergency department (ED), especially in epidemic contexts such as flu or CoVID-19. The aim was to assess discriminative performances of two biomarkers, CD64 on neutrophils (nCD64) and CD169 on monocytes (mCD169), using a new flow cytometry procedure, in patients presenting with fever to the ED during epidemics. Eighty five adult patients presenting with potential infection were included during the 2019 flu season in the ED of La Timone Hospital. They were divided into four diagnostic outcomes according to their clinical records: no-infection, bacterial infection, viral infection and co-infection. Seventy six patients with confirmed SARS-CoV-2 infection were also compared to 48 healthy volunteers. For the first cohort, 38 (45%) patients were diagnosed with bacterial infections, 11 (13%) with viral infections and 29 (34%) with co-infections. mCD169 was elevated in patients with viral infections, with a majority of Flu A virus or Respiratory Syncytial Virus, while nCD64 was elevated in subjects with bacterial infections, with a majority of Streptococcus pneumoniae and Escherichia coli. nCD64 and mCD169 showed 90% and 80% sensitivity, and 78% and 91% specificity, respectively, for identifying patients with bacterial or viral infections. When studied in a second cohort, mCD169 was elevated in 95% of patients with SARS-CoV-2 infections and remained at normal level in 100% of healthy volunteers. nCD64 and mCD169 have potential for accurately distinguishing bacterial and acute viral infections. Combined in an easy and rapid flow cytometry procedure, they constitute a potential improvement for infection management in the ED, and could even help for triage of patients during emerging epidemics., (© 2021 International Society for Advancement of Cytometry.)

Aim: Management of patients with infections within the Emergency Department (ED) is challenging for practitioners, as the identification of infectious causes remains difficult with current techniques. A new combination of two biomarkers was tested with a new rapid flow cytometry technique. Materials & methods: Subjects from the ED were tested for their CD64 on neutrophils (nCD64) and CD169 on monocytes (mCD169) levels and results were compared to their clinical records. Results: Among 139 patients, 29% had confirmed bacterial infections and 5% viral infections. nCD64 and mCD169 respectively showed 88 and 86% sensitivity and 90 and 100% specificity for identifying subjects in bacterial or viral conditions. Conclusion: This point-of-care technique could allow better management of patients in the ED.