Polynomial identities of matrices with the symplectic involution: The low degrees - D'Amour, A.; Racine, M. (Communications in Algebra, 2004)
The *-polynomial identities of minimal degree of Mn(F) are determined for n = 2, 4, * the symplectic involution. Copyright © 2004 by Marcel Dekker, Inc.
6 citations (Crossref) [2023-10-31]
Keywords: *-Polynomial identity; Polynomial identity; Symplectic involution; dept.mat

Adaptive urn designs for estimating several percentiles of a dose–response curve - Mugno, Raymond; Zhus, Wei; Rosenberger, William F (Statistics in Medicine, 2004)
Dose-response experiments are crucial in biomedical studies. There are usually multiple objectives in such experiments and among the goals is the estimation of several percentiles on the dose-response curve. Here we present the first non-parametric adaptive design approach to estimate several percentiles simultaneously via generalized Pó lya urns. Theoretical properties of these designs are investigated and their performance is gaged by the locally compound optimal designs. As an example, we re-investigated a psychophysical experiment where one of the goals was to estimate the three quartiles. We show that these multiple-objective adaptive designs are more efficient than the original single-objective adaptive design targeting the median only. We also show that urn designs which target the optimal designs are slightly more efficient than those which target the desired percentiles directly. Guidelines are given as to when to use which type of design. Overall we are pleased with the efficiency results and hope compound adaptive designs proposed in this work or their variants may prove to be a viable non-parametric alternative in multiple-objective dose-response studies. Copyright © 2004 John Wiley & Sons, Ltd.
9 citations (Crossref) [2023-10-31] Citation Key Alias: lens.org/021-461-086-120-672 tex.type: [object Object]
Keywords: *Dose-Response Relationship; Drug; Adaptive design; Dose-Response Relationship; Drug; Dose-response experiment; Generalized Pólya urn; Guidelines; Guidelines as Topic; Likelihood Functions; Monte Carlo method; Non-parametric design; Psychophysics; United States; article; biostatistics; c-optimal design; cerebrovascular accident; clinical trial; dept.mat; dose response; experimental design; human; kinesthesia; maximum likelihood method; neurologic disease; nonparametric test; process optimization; psychophysics; sensory stimulation; statistical analysis; theoretical study; validation process

Dominating Sets for Outerplanar Graphs - Pinciu, Val (International Conference on Applied Mathematics, 2004)
Abstract:- We provide lower and upper bounds for the domination numbers and the connected domination numbers for outerplanar graphs. We also provide a recursive algorithm that finds a connected domination set for an outerplanar graph. Finally, we show that for outerplanar graphs where all bounded faces are 3-cycles, the problem of determining the connected domination number is equivalent to an art gallery problem, which is known to be NP-hard. Key-Words:- dominating sets, star forests, outerplanar graphs, art gallery 1
tex.type: Proceedings paper
Keywords: dept.mat; ⛔ No DOI found