Pierre S Youssef

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We extend to the matrix setting a recent result of Srivastava-Vershynin [21] about estimating the covariance matrix of a random vector. The result can be interpreted as a quantified version of the law of large numbers for positive semi-definite matrices which verify some regularity assumption. Beside giving examples, we discuss the notion of log-concave(More)
Let Dn,d be the set of all d-regular directed graphs on n vertices. Let G be a graph chosen uniformly at random from Dn,d and M be its adjacency matrix. We show that M is invertible with probability at least 1 − C ln d/ √ d for C ≤ d ≤ cn/ ln n, where c, C are positive absolute constants. To this end, we establish a few properties of d-regular directed(More)
Let Dn,d be the set of all directed d-regular graphs on n vertices. Let G be a graph chosen uniformly at random from Dn,d and M be its adjacency matrix. We show that M is invertible with probability at least 1−C ln d/ √ d for C ≤ d ≤ cn/ ln n, where c, C are positive absolute constants. To this end, we establish a few properties of directed d-regular(More)
Given a matrix U , using a deterministic method, we extract a "large" submatrix of Ũ (whose columns are obtained by normalizing those of U ) and estimate its smallest and largest singular value. We apply this result to the study of contact points of the unit ball with its maximal volume ellipsoid. We consider also the paving problem and give a deterministic(More)
A reusable Robertshaw red rubber double-lumen endotracheal tube (DLT) was placed to facilitate lung isolation for thoracoscopy in a 49-year-old atopic patient. In spite of its smooth insertion, it was then not possible to remove the DLT. Direct laryngoscopy showed severe laryngeal edema. After 48 hours of medical treatment with steroids, the trachea was(More)
OBJECTIVE Current problems in gastric cancer surgery concern the extent of gastric resection, the need for abdominal evisceration, the degree of lymphadenectomy, and an optimal preoperative tumor staging procedure. METHODS A retrospective clinical trial of 284 patients who underwent surgery at Ernst-Moritz-Arndt-University, Greifswald, Germany for gastric(More)
We derive a lower bound on the smallest singular value of a random d-regular matrix, that is, the adjacency matrix of a random d-regular directed graph. More precisely, let C1 < d < c1n/ log 2 n and let Mn,d be the set of all 0/1-valued square n × n matrices such that each row and each column of a matrix M ∈ Mn,d has exactly d ones. Let M be uniformly(More)
Benign cystic lymphangioma is a relatively rare tumor of the human body. It's more frequent in young patients. It is usually localized in the neck but may have mediastinal or intra-abdominal localization. It's usually asymptomatic with good prognosis after total excision. We report in this article the case of a young man with a huge mediastinal cystic(More)