Finite to infinite steady state solutions, bifurcations of an integro-differential equation

We consider a bistable integral equation which governs the stationary solutions of a convolution model of solid--solid phase transitions on a circle. We study the bifurcations of the set of the stationary solutions as the diffusion coefficient is varied to examine the transition from an infinite number of steady states to three for the continuum limit of the semi--discretised system. We show how the symmetry of the problem is responsible for the generation and stabilisation of equilibria and comment on the puzzling connection between continuity and stability that exists in this problem

Inborn errors of OAS-RNase L in SARS-CoV-2-related multisystem inflammatory syndrome in children

Multisystem inflammatory syndrome in children (MIS-C) is a rare and severe condition that follows benign COVID-19. We report autosomal recessive deficiencies of OAS1, OAS2, or RNASEL in five unrelated children with MIS-C. The cytosolic double-stranded RNA (dsRNA)-sensing OAS1 and OAS2 generate 2'-5'-linked oligoadenylates (2-5A) that activate the single-stranded RNA-degrading ribonuclease L (RNase L). Monocytic cell lines and primary myeloid cells with OAS1, OAS2, or RNase L deficiencies produce excessive amounts of inflammatory cytokines upon dsRNA or severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) stimulation. Exogenous 2-5A suppresses cytokine production in OAS1-deficient but not RNase L-deficient cells. Cytokine production in RNase L-deficient cells is impaired by MDA5 or RIG-I deficiency and abolished by mitochondrial antiviral-signaling protein (MAVS) deficiency. Recessive OAS-RNase L deficiencies in these patients unleash the production of SARS-CoV-2-triggered, MAVS-mediated inflammatory cytokines by mononuclear phagocytes, thereby underlying MIS-C

Local bifurcation at the second eigenvalue of the Laplacian in a square

In this work we study local bifurcation from the branch of trivial solutions for a class of semilinear elliptic equations, at the second eigenvalue λ 2 \lambda _2 of a square. We find that the bifurcation set can be locally described as the union of exactly four bifurcation branches of nontrivial solutions which cross the bifurcation point ( λ 2 , 0 ) (\lambda _2,0) . We also compute the Morse index of the solutions in the four branches