A baby steps/giant steps Monte Carlo algorithm for computing roadmaps in smooth compact real hypersurfaces

International audienceWe consider the problem of constructing roadmaps of real algebraic sets. The problem was introduced by Canny to answer connectivity questions and solve motion planning problems. Given $s$ polynomial equations with rational coefficients, of degree $D$ in $n$ variables, Canny's algorithm has a Monte Carlo cost of $s^n\log(s) D^{O(n^2)}$ operations in $\mathbb{Q}$; a deterministic version runs in time $s^n \log(s) D^{O(n^4)}$. The next improvement was due to Basu, Pollack and Roy, with an algorithm of deterministic cost $s^{d+1} D^{O(n^2)}$ for the more general problem of computing roadmaps of semi-algebraic sets ($d \le n$ is the dimension of an associated object). We give a Monte Carlo algorithm of complexity $(nD)^{O(n^{1.5})}$ for the problem of computing a roadmap of a compact hypersurface $V$ of degree $D$ in $n$ variables; we also have to assume that $V$ has a finite number of singular points. Even under these extra assumptions, no previous algorithm featured a cost better than $D^{O(n^2)}$

Inherited p40phox deficiency differs from classic chronic granulomatous disease

Biallelic loss-of-function (LOF) mutations of the NCF4 gene, encoding the p40phox subunit of the phagocyte NADPH oxidase, have been described in only 1 patient. We report on 24 p40phox-deficient patients from 12 additional families in 8 countries. These patients display 8 different in-frame or out-of-frame mutations of NCF4 that are homozygous in 11 of the families and compound heterozygous in another. When overexpressed in NB4 neutrophil-like cells and EBV-transformed B cells in vitro, the mutant alleles were found to be LOF, with the exception of the p.R58C and c.120_134del alleles, which were hypomorphic. Particle-induced NADPH oxidase activity was severely impaired in the patients' neutrophils, whereas PMA-induced dihydrorhodamine-1,2,3 (DHR) oxidation, which is widely used as a diagnostic test for chronic granulomatous disease (CGD), was normal or mildly impaired in the patients. Moreover, the NADPH oxidase activity of EBV-transformed B cells was also severely impaired, whereas that of mononuclear phagocytes was normal. Finally, the killing of Candida albicans and Aspergillus fumigatus hyphae by neutrophils was conserved in these patients, unlike in patients with CGD. The patients suffer from hyperinflammation and peripheral infections, but they do not have any of the invasive bacterial or fungal infections seen in CGD. Inherited p40phox deficiency underlies a distinctive condition, resembling a mild, atypical form of CGD.info:eu-repo/semantics/publishedVersio

Para-infectious brain injury in COVID-19 persists at follow-up despite attenuated cytokine and autoantibody responses

To understand neurological complications of COVID-19 better both acutely and for recovery, we measured markers of brain injury, inflammatory mediators, and autoantibodies in 203 hospitalised participants; 111 with acute sera (1–11 days post-admission) and 92 convalescent sera (56 with COVID-19-associated neurological diagnoses). Here we show that compared to 60 uninfected controls, tTau, GFAP, NfL, and UCH-L1 are increased with COVID-19 infection at acute timepoints and NfL and GFAP are significantly higher in participants with neurological complications. Inflammatory mediators (IL-6, IL-12p40, HGF, M-CSF, CCL2, and IL-1RA) are associated with both altered consciousness and markers of brain injury. Autoantibodies are more common in COVID-19 than controls and some (including against MYL7, UCH-L1, and GRIN3B) are more frequent with altered consciousness. Additionally, convalescent participants with neurological complications show elevated GFAP and NfL, unrelated to attenuated systemic inflammatory mediators and to autoantibody responses. Overall, neurological complications of COVID-19 are associated with evidence of neuroglial injury in both acute and late disease and these correlate with dysregulated innate and adaptive immune responses acutely