Secretary Matching Meets Probing with Commitment

We consider the online bipartite matching problem within the context of stochastic probing with commitment. This is the one-sided online bipartite matching problem where edges adjacent to an online node must be probed to determine if they exist based on edge probabilities that become known when an online vertex arrives. If a probed edge exists, it must be used in the matching. We consider the competitiveness of online algorithms in the adversarial order model (AOM) and the secretary/random order model (ROM). More specifically, we consider an unknown bipartite stochastic graph G = (U,V,E) where U is the known set of offline vertices, V is the set of online vertices, G has edge probabilities (p_{e})_{e ? E}, and G has edge weights (w_{e})_{e ? E} or vertex weights (w_u)_{u ? U}. Additionally, G has a downward-closed set of probing constraints (?_{v})_{v ? V}, where ?_v indicates which sequences of edges adjacent to an online vertex v can be probed. This model generalizes the various settings of the classical bipartite matching problem (i.e. with and without probing). Our contributions include the introduction and analysis of probing within the random order model, and our generalization of probing constraints which includes budget (i.e. knapsack) constraints. Our algorithms run in polynomial time assuming access to a membership oracle for each ?_v. In the vertex weighted setting, for adversarial order arrivals, we generalize the known 1/2 competitive ratio to our setting of ?_v constraints. For random order arrivals, we show that the same algorithm attains an asymptotic competitive ratio of 1-1/e, provided the edge probabilities vanish to 0 sufficiently fast. We also obtain a strict competitive ratio for non-vanishing edge probabilities when the probing constraints are sufficiently simple. For example, if each ?_v corresponds to a patience constraint ?_v (i.e., ?_v is the maximum number of probes of edges adjacent to v), and any one of following three conditions is satisfied (each studied in previous papers), then there is a conceptually simple greedy algorithm whose competitive ratio is 1-1/e. - When the offline vertices are unweighted. - When the online vertex probabilities are "vertex uniform"; i.e., p_{u,v} = p_v for all (u,v) ? E. - When the patience constraint ?_v satisfies ?_v ? {[1,|U|} for every online vertex; i.e., every online vertex either has unit or full patience. Finally, in the edge weighted case, we match the known optimal 1/e asymptotic competitive ratio for the classic (i.e. without probing) secretary matching problem

Rare association between cystic fibrosis, Chiari I malformation, and hydrocephalus in a baby: a case report and review of the literature

<p>Abstract</p> <p>Introduction</p> <p>Cystic fibrosis, an epithelial cell transport disorder caused by mutations of the cystic fibrosis transmembrane conductance regulator gene, is not generally associated with malformations of the central nervous system. We review eight previously published reports detailing an infrequent association between cystic fibrosis and Chiari I malformation.</p> <p>Case presentation</p> <p>To the best of our knowledge, our report describes only the ninth case of a baby presenting with a new diagnosis of cystic fibrosis and Chiari I malformation, in this case in a 10-month-old, full-term Caucasian baby boy from the United States of America. Neurosurgical consultation was obtained for associated developmental delay, macrocephaly, bulging anterior fontanel, and papilledema. An MRI scan demonstrated an extensive Chiari I malformation with effacement of the fourth ventricle, obliteration of the outlets of the fourth ventricle and triventricular hydrocephalus without aqueductal stenosis. Our patient was taken to the operating room for ventriculoperitoneal shunt placement.</p> <p>Conclusions</p> <p>It is possible that the cystic fibrosis transmembrane conductance regulator gene may play a previously unrecognized role in central nervous system development; alternatively, this central nervous system abnormality may have been acquired due to constant valsalva from recurrent coughing or wheezing or metabolic and electrolyte imbalances that occur characteristically in cystic fibrosis.</p