Quadtrees constitute a hierarchical data structure which permits fast access to multidimensional data. This paper presents the analysis of the expected cost of various types of searches in quadtrees--fully specified and partial-match queries. The data model assumes random points with independently drawn coordinate values.The analysis leads to a class of "full-history" divide-and-conquer recurrences. These recurrences are solved using generating functions, either exactly for dimension d = 2, or asymptotically for higher dimensions. The exact solutions involve hypergeometric functions. The general asymptotic solutions rely on the classification of singularities of linear differential equations with analytic coefficients, and on singularity analysis techniques.These methods are applicable to the asymptotic solution of a wide range of linear recurrences, as may occur in particular in the analysis of multidimensional searching problems.
SUMMARY Lorazepam was compared with diazepam for the treatment of acute convulsions and status epilepticus in 102 children in a prospective, open, ‘odd and even dates’ trial. Convulsions were controlled in 76 per cent of patients treated with a single dose of lorazepam and 51 per cent of patients treated with a single dose of diazepam. Significantly fewer patients treated with lorazepam required additional anticonvulsants to terminate the seizure. Respiratory depression occurred in 3 per cent of lorazepam‐treated patients and 15 per cent of diazepam‐treated patients. No patient who received lorazepam required admission to the intensive care unit for either respiratory depression or persisting status epilepticus. Rectally administered lorazepam appeared to be particularly valuable (100 per cent efficacy) when venous access was not possible. RÉSUMÉ Lorazepam vs diazepam dans le Tretirement aigu des crises comitiales el de L'étal de mat épileptique Le lorazepam a été comparé au diazepam dans lc traitement aigu de convulsions et de L'et at de mal épileptique chcz 102 enfants, dans une étude prospective, ouverte, en essais ‘jours pairs et impairs.’ Les convulsions furent eontrolées chez 76 pour cent des patients tradés par lorazepam et 51 pour cent des patients traités par diazepam. Significativement moins de patients traités par lorazepam exigérent des anticomitiaux complémentaires pour terminer la crise. Une dépression respiratoire se manifesta chez 3 pour cent des patients traités par lorazepam et 15 pour cent des patients traités par diazepam. Aucun des patients traités par lorazepam n'exigércnt une admission dans une unité de soins intensifs pour dépression respiratoire ou persistance d'un etal de mal. Le lorazepam administré par voic rectalc semble particuliércment efficace (100 pour cent d'efficacité) lorsqul'il n'y a pas les conditions d'une injection intra‐veincusc. ZUSAMMENFASSUNG Lorazepam versus Diazepam bei der Akutversorung von epileptischen Anjâilen mid Status epilepticus Bei 102 Kindern wurde in einer prospektiven offenen ‘odd and even dates’ Studie Lorazepam mit Diazepam bei der Behandlung von akulen Anfällen und des Status epilepticus verglichen. Bei 76 Prozent der mit Lorazepam und bei 51 Prozent der mit Diazepam bchandelten Patientcn konnten die Anfälle untcr Kontrolle gebracht werden. Von den mit Lorazepam behandelten Patienten brauchten signifikant weniger zusätzlichc Antikonvulsiva, urn die Anfälle zu stoppen. Eine Atemdepression wurde unter Lorazepam nur bei 3 Prozent unter Diazepam bei 15 Prozent der Patienten beobachtet. Kein Patient, der mit Lorazepam behandelt wurde, mußte weder wegen einer Atemdepression noch wegen eines anhaltenden Status epilepticus auf die Intensivstation aufgenommen werden. Rcktal verabreichtes Lorazepam schien besonders geeignet (100 Prozent Wirksamkeit), wenn ein venöser Zugang nicht möglich war. RESUMEN Lorazepam versus diazepam en el tratamiento agudo de crisis epilepsias y ‘status epilepticus’ Se comparó el lorazepam con el diazepam en el tratamiento de las conv...
Abstract. It is well-known that the question of whether a given finite region can be tiled with a given set of tiles is NP-complete. We show that the same is true for the right tromino and square tetromino on the square lattice, or for the right tromino alone. In the process, we show that Monotone 1-in-3 Satisfiability is NP-complete for planar cubic graphs. In higher dimensions, we show NP-completeness for the domino and straight tromino for general regions on the cubic lattice, and for simplyconnected regions on the four-dimensional hypercubic lattice.
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