2,455 research outputs found
Throttling for the game of Cops and Robbers on graphs
We consider the cop-throttling number of a graph for the game of Cops and
Robbers, which is defined to be the minimum of , where
is the number of cops and is the minimum number of
rounds needed for cops to capture the robber on over all possible
games. We provide some tools for bounding the cop-throttling number, including
showing that the positive semidefinite (PSD) throttling number, a variant of
zero forcing throttling, is an upper bound for the cop-throttling number. We
also characterize graphs having low cop-throttling number and investigate how
large the cop-throttling number can be for a given graph. We consider trees,
unicyclic graphs, incidence graphs of finite projective planes (a Meyniel
extremal family of graphs), a family of cop-win graphs with maximum capture
time, grids, and hypercubes. All the upper bounds on the cop-throttling number
we obtain for families of graphs are .Comment: 22 pages, 4 figure
Six Years Observation After Successful Treatment of Bacterial Vaginosis
Objective: The cure rate after treatment of bacterial vaginosis (BV) differs in various investigations, but most studies report a cure rate of 70% after 1 month
Optimizing the trade-off between number of cops and capture time in Cops and Robbers
The cop throttling number of a graph for the game of Cops and
Robbers is the minimum of , where is the number of cops and
is the minimum number of rounds needed for cops to capture the
robber on over all possible games in which both players play optimally. In
this paper, we construct a family of graphs having ,
establish a sublinear upper bound on the cop throttling number, and show that
the cop throttling number of chordal graphs is . We also introduce
the product cop throttling number as a parameter that
minimizes the person-hours used by the cops. This parameter extends the notion
of speed-up that has been studied in the context of parallel processing and
network decontamination. We establish bounds on the product cop throttling
number in terms of the cop throttling number, characterize graphs with low
product cop throttling number, and show that for a chordal graph ,
.Comment: 19 pages, 3 figure
Constructions of cospectral graphs with different zero forcing numbers
Several researchers have recently explored various graph parameters that can
or cannot be characterized by the spectrum of a matrix associated with a graph.
In this paper we show that several NP-hard zero forcing numbers are not
characterized by the spectra of several types of associated matrices with a
graph. In particular, we consider standard zero forcing, positive semidefinite
zero forcing, and skew zero forcing, and provide constructions of infinite
families of pairs of cospectral graphs which have different values for these
numbers. We explore several methods for obtaining these cospectral graphs
including using graph products, graph joins, and graph switching. Among these,
we provide a construction involving regular adjacency cospectral graphs; the
regularity of this construction also implies cospectrality with respect to
several other matrices including the Laplacian, signless Laplacian, and
normalized Laplacian. We also provide a construction where pairs of cospectral
graphs can have an arbitrarily large difference between their zero forcing
numbers
Improving Melanoma Classification by Integrating Genetic and Morphologic Features
Boris Bastian and colleagues present a refined morphological classification of primary melanomas that can be used to improve existing melanoma classifications by defining genetically homogeneous subgroups
Cop throttling number: Bounds, values, and variants
The cop throttling number thc(G) of a graph G for the game of Cops and Robbers is the minimum of k+captk(G), where k is the number of cops and captk(G) is the minimum number of rounds needed for k cops to capture the robber on G over all possible games in which both players play optimally. In this paper, we answer in the negative a question from [Breen et al., Throttling for the game of Cops and Robbers on graphs, {\em Discrete Math.}, 341 (2018) 2418--2430.] about whether the cop throttling number of any graph is O(n−−√) by constructing a family of graphs having thc(G)=Ω(n2/3). We establish a sublinear upper bound on the cop throttling number and show that the cop throttling number of chordal graphs is O(n−−√). We also introduce the product cop throttling number th×c(G) as a parameter that minimizes the person-hours used by the cops. We establish bounds on the product cop throttling number in terms of the cop throttling number, characterize graphs with low product cop throttling number, and show that for a chordal graph G, th×c(G)=1+rad(G)
Association of blood lead levels with onset of puberty in Russian boys
BACKGROUND: Epidemiologic studies suggest a temporal trend of earlier onset and longer duration of puberty, raising concerns regarding the potential impact of environmental factors on pubertal development. Lead exposure has been associated with delayed pubertal onset in girls; however, epidemiologic data in boys are limited.
METHODS: We used multivariable logistic regression models to explore the cross-sectional association of blood lead levels with growth and pubertal onset based on physician-assessed testicular volume (TV) and pubertal staging in 489 boys 8-9 years of age from Chapaevsk, Russia. We used multivariable linear regression models to assess associations of blood lead levels with somatic growth at the study entry visit.
RESULTS: The median (25th-75th percentile) blood lead level was 3 microg/dL (2-5 microg/dL). Height, weight, body mass index, birth weight, and gestational age were predictive of the onset of puberty as assessed either by TV (\u3e 3 mL), genitalia stage (G2), or both. Blood lead level was inversely associated with height (p \u3c 0.001) and weight (p = 0.06) after adjustment for birth weight, gestational age, and age at examination. In multivariable adjusted analyses, boys with blood lead levels \u3e or = 5 microg/dL had 43% reduced odds of having entered G2 compared with those with lower levels (odds ratio = 0.57; 95% confidence interval, 0.34-0.95, p = 0.03).
CONCLUSIONS: Relatively low environmental blood lead levels were associated with decreased growth and differences in pubertal onset in periadolescent Russian boys. Future analyses of this prospective cohort will address pubertal onset and progression in relation to lead and other environmental chemicals
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Association of Blood Lead Levels with Onset of Puberty in Russian Boys
Background: Epidemiologic studies suggest a temporal trend of earlier onset and longer duration of puberty, raising concerns regarding the potential impact of environmental factors on pubertal development. Lead exposure has been associated with delayed pubertal onset in girls; however, epidemiologic data in boys are limited. Methods: We used multivariable logistic regression models to explore the cross-sectional association of blood lead levels with growth and pubertal onset based on physician-assessed testicular volume (TV) and pubertal staging in 489 boys 8–9 years of age from Chapaevsk, Russia. We used multivariable linear regression models to assess associations of blood lead levels with somatic growth at the study entry visit. Results: The median (25th–75th percentile) blood lead level was 3 μg/dL (2–5 μg/dL). Height, weight, body mass index, birth weight, and gestational age were predictive of the onset of puberty as assessed either by TV (greater than 3 mL), genitalia stage (G2), or both. Blood lead level was inversely associated with height (p less than 0.001) and weight (p = 0.06) after adjustment for birth weight, gestational age, and age at examination. In multivariable adjusted analyses, boys with blood lead levels ≥ 5 μg/dL had 43% reduced odds of having entered G2 compared with those with lower levels (odds ratio = 0.57; 95% confidence interval, 0.34–0.95, p = 0.03). Conclusions: Relatively low environmental blood lead levels were associated with decreased growth and differences in pubertal onset in periadolescent Russian boys. Future analyses of this prospective cohort will address pubertal onset and progression in relation to lead and other environmental chemicals
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