113 research outputs found
Axiomization of the center function on trees.
We give a new, short proof that four certain axiomatic properties uniquely define the center of a tree.
Generalized centrality in trees
In 1982, Slater defined path subgraph analogues to the center, median, and (branch or branchweight) centroid of a tree. We define three families of central substructures of trees, including three types of central subtrees of degree at most D that yield the center, median, and centroid for D = 0 and Slater's path analogues for D = 2. We generalize these results concerning paths and include proofs that each type of generalized center and generalized centroid is unique. We also present algorithms for finding one or all generalized central substructures of each type.
Plurality preference digraphs realized by trees, II: on realization numbers
AbstractA digraph D with vertex set X = {x1, x2,…, xn} is realizable by a connected graph G if there exists a subset C = {c1, c2,…, cn} of vertices of G so that for all distinct i and j in {1, 2,…, n}, xixj is an arc of D if and only if more vertices of G are closer to ci than to cj. For a positive integer n, let Fn denote the family of digraphs of order n which are realizable by trees. For a fixed D∈Fn, the realization number of D, denoted α(itD), is the smallest order of a tree which realizes D. Let α(Fn)=max{α(D):D∈Fn}. In this paper α(Fn) is determined explicitly
Axiomization of the center function on trees.
We give a new, short proof that four certain axiomatic properties uniquely define the center of a tree
Generalized centrality in trees
In 1982, Slater defined path subgraph analogues to the center, median, and (branch or branchweight) centroid of a tree. We define three families of central substructures of trees, including three types of central subtrees of degree at most D that yield the center, median, and centroid for D = 0 and Slater's path analogues for D = 2. We generalize these results concerning paths and include proofs that each type of generalized center and generalized centroid is unique. We also present algorithms for finding one or all generalized central substructures of each type
Orbital Separation Amplification in Fragile Binaries with Evolved Components
The secular stellar mass-loss causes an amplification of the orbital
separation in fragile, common proper motion, binary systems with separations of
the order of 1000 A.U. In these systems, companions evolve as two independent
coeval stars as they experience negligible mutual tidal interactions or mass
transfer. We present models for how post-main sequence mass-loss statistically
distorts the frequency distribution of separations in fragile binaries. These
models demonstrate the expected increase in orbital seapration resulting from
stellar mass-loss, as well as a perturbation of associated orbital parameters.
Comparisons between our models and observations resulting from the Luyten
survey of wide visual binaries, specifically those containing MS and
white-dwarf pairs, demonstrate a good agreement between the calculated and the
observed angular separation distribution functions.Comment: 37 pages, 13 figure
Feedback Vertex Sets in Tournaments
We study combinatorial and algorithmic questions around minimal feedback
vertex sets in tournament graphs.
On the combinatorial side, we derive strong upper and lower bounds on the
maximum number of minimal feedback vertex sets in an n-vertex tournament. We
prove that every tournament on n vertices has at most 1.6740^n minimal feedback
vertex sets, and that there is an infinite family of tournaments, all having at
least 1.5448^n minimal feedback vertex sets. This improves and extends the
bounds of Moon (1971).
On the algorithmic side, we design the first polynomial space algorithm that
enumerates the minimal feedback vertex sets of a tournament with polynomial
delay. The combination of our results yields the fastest known algorithm for
finding a minimum size feedback vertex set in a tournament
Gaussian quantum operator representation for bosons
We introduce a Gaussian quantum operator representation, using the most general possible multimode Gaussian operator basis. The representation unifies and substantially extends existing phase-space representations of density matrices for Bose systems and also includes generalized squeezed-state and thermal bases. It enables first-principles dynamical or equilibrium calculations in quantum many-body systems, with quantum uncertainties appearing as dynamical objects. Any quadratic Liouville equation for the density operator results in a purely deterministic time evolution. Any cubic or quartic master equation can be treated using stochastic methods
Collaborative International Research in Clinical and Longitudinal Experience Study in NMOSD
OBJECTIVE: To develop a resource of systematically collected, longitudinal clinical data and biospecimens for assisting in the investigation into neuromyelitis optica spectrum disorder (NMOSD) epidemiology, pathogenesis, and treatment. METHODS: To illustrate its research-enabling purpose, epidemiologic patterns and disease phenotypes were assessed among enrolled subjects, including age at disease onset, annualized relapse rate (ARR), and time between the first and second attacks. RESULTS: As of December 2017, the Collaborative International Research in Clinical and Longitudinal Experience Study (CIRCLES) had enrolled more than 1,000 participants, of whom 77.5% of the NMOSD cases and 71.7% of the controls continue in active follow-up. Consanguineous relatives of patients with NMOSD represented 43.6% of the control cohort. Of the 599 active cases with complete data, 84% were female, and 76% were anti-AQP4 seropositive. The majority were white/Caucasian (52.6%), whereas blacks/African Americans accounted for 23.5%, Hispanics/Latinos 12.4%, and Asians accounted for 9.0%. The median age at disease onset was 38.4 years, with a median ARR of 0.5. Seropositive cases were older at disease onset, more likely to be black/African American or Hispanic/Latino, and more likely to be female. CONCLUSION: Collectively, the CIRCLES experience to date demonstrates this study to be a useful and readily accessible resource to facilitate accelerating solutions for patients with NMOSD
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