111 research outputs found
A new matroid lift construction and an application to group-labeled graphs
A well-known result of Brylawski constructs an elementary lift of a matroid M from a linear class of circuits of M. We generalize this result by constructing a rank-k lift of M from a rank-k matroid on the set of circuits of M. We conjecture that every lift of M arises via this construction. We then apply this result to group-labeled graphs, generalizing a construction of Zaslavsky. Given a graph G with edges labeled by a group, Zaslavsky\u27s lift matroid K is an elementary lift of the graphic matroid M(G) that respects the group-labeling; specifically, the cycles of G that are circuits of K coincide with the cycles that are balanced with respect to the group-labeling. For k 2, when does there exist a rank-k lift of M(G) that respects the group-labeling in this same sense? For abelian groups, we show that such a matroid exists if and only if the group is isomorphic to the additive group of a non-prime finite field
Matroid lifts and representability
A 1965 result of Crapo shows that every elementary lift of a matroid can
be constructed from a linear class of circuits of . In a recent paper, Walsh
generalized this construction by defining a rank- lift of a matroid
given a rank- matroid on the set of circuits of , and conjectured
that all matroid lifts can be obtained in this way. In this sequel paper we
simplify Walsh's construction and show that this conjecture is true for
representable matroids but is false in general. This gives a new way to certify
that a particular matroid is non-representable, which we use to construct new
classes of non-representable matroids.
Walsh also applied the new matroid lift construction to gain graphs over the
additive group of a non-prime finite field, generalizing a construction of
Zaslavsky for these special groups. He conjectured that this construction is
possible on three or more vertices only for the additive group of a non-prime
finite field. We show that this conjecture holds for four or more vertices, but
fails for exactly three
Planar Tur\'an number of the 7-cycle
The of a
graph is the maximum number of edges in an -vertex planar graph without
as a subgraph. Let denote the cycle of length . The planar
Tur\'an number behaves differently for
and for , and it is known when .
We prove that for all , and show that equality holds for infinitely
many integers
Dense circuit graphs and the planar Tur\'an number of a cycle
The of a
graph is the maximum number of edges in an -vertex planar graph without
as a subgraph. Let denote the cycle of length . The planar Tur\'an
number is known for . We show that
dense planar graphs with a certain connectivity property (known as circuit
graphs) contain large near triangulations, and we use this result to obtain
consequences for planar Tur\'an numbers. In particular, we prove that there is
a constant so that for all . When this bound is tight up to
the constant and proves a conjecture of Cranston, Lidick\'y, Liu, and
Shantanam
Extended formulations for a class of polyhedra with bimodular cographic constraint matrices
We are motivated by integer linear programs (ILPs) defined by constraint
matrices with bounded determinants. Such matrices generalize the notion of
totally-unimodular matrices. When the determinants are bounded by , the
matrix is called bimodular. Artmann et al. give a polynomial-time algorithm for
solving any ILP defined by a bimodular constraint matrix. Complementing this
result, Conforti et al. give a compact extended formulation for a particular
class of bimodular-constrained ILPs, namely those that model the stable set
polytope of a graph with odd cycle packing number . We demonstrate that
their compact extended formulation can be modified to hold for polyhedra such
that (1) the constraint matrix is bimodular, (2) the row-matroid generated by
the constraint matrix is cographic and (3) the right-hand side is a linear
combination of the columns of the constraint matrix. This generalizes the
important special case from Conforti et al. concerning 4-connected graphs with
odd cycle transversal number at least four. Moreover, our results yield compact
extended formulations for a new class of polyhedra
Frequency of cannabis and illicit opioid use among people who use drugs and report chronic pain: A longitudinal analysis.
BACKGROUND:Ecological research suggests that increased access to cannabis may facilitate reductions in opioid use and harms, and medical cannabis patients describe the substitution of opioids with cannabis for pain management. However, there is a lack of research using individual-level data to explore this question. We aimed to investigate the longitudinal association between frequency of cannabis use and illicit opioid use among people who use drugs (PWUD) experiencing chronic pain. METHODS AND FINDINGS:This study included data from people in 2 prospective cohorts of PWUD in Vancouver, Canada, who reported major or persistent pain from June 1, 2014, to December 1, 2017 (n = 1,152). We used descriptive statistics to examine reasons for cannabis use and a multivariable generalized linear mixed-effects model to estimate the relationship between daily (once or more per day) cannabis use and daily illicit opioid use. There were 424 (36.8%) women in the study, and the median age at baseline was 49.3 years (IQR 42.3-54.9). In total, 455 (40%) reported daily illicit opioid use, and 410 (36%) reported daily cannabis use during at least one 6-month follow-up period. The most commonly reported therapeutic reasons for cannabis use were pain (36%), sleep (35%), stress (31%), and nausea (30%). After adjusting for demographic characteristics, substance use, and health-related factors, daily cannabis use was associated with significantly lower odds of daily illicit opioid use (adjusted odds ratio 0.50, 95% CI 0.34-0.74, p < 0.001). Limitations of the study included self-reported measures of substance use and chronic pain, and a lack of data for cannabis preparations, dosages, and modes of administration. CONCLUSIONS:We observed an independent negative association between frequent cannabis use and frequent illicit opioid use among PWUD with chronic pain. These findings provide longitudinal observational evidence that cannabis may serve as an adjunct to or substitute for illicit opioid use among PWUD with chronic pain
Recommended from our members
Cannabis use to manage opioid cravings among people who use unregulated opioids during a drug toxicity crisis.
BACKGROUND: Accumulating evidence has indicated that cannabis substitution is often used as a harm reduction strategy among people who use unregulated opioids (PWUO) and people living with chronic pain. We sought to investigate the association between cannabis use to manage opioid cravings and self-reported changes in opioid use among structurally marginalized PWUO. METHODS: The data were collected from a cross-sectional questionnaire administered to PWUO in Vancouver, Canada. Binary logistic regression was used to analyze the association between cannabis use to manage opioid cravings and self-reported changes in unregulated opioid use. RESULTS: A total of 205 people who use cannabis and opioids were enrolled in the present study from December 2019 to November 2021. Cannabis use to manage opioid cravings was reported by 118 (57.6%) participants. In the multivariable analysis, cannabis use to manage opioid cravings (adjusted Odds Ratio [aOR] = 2.13, 95% confidence interval [CI]: 1.07, 4.27) was significantly associated with self-reported reductions in opioid use. In the sub-analyses of pain, cannabis use to manage opioid cravings was only associated with self-assessed reductions in opioid use among people living with moderate to severe pain (aOR = 4.44, 95% CI: 1.52, 12.97). In the sub-analyses of males and females, cannabis use to manage opioid cravings was only associated with self-assessed reductions in opioid use among females (aOR = 8.19, 95% CI: 1.20, 55.81). CONCLUSIONS: These findings indicate that cannabis use to manage opioid cravings is a prevalent motivation for cannabis use among PWUO and is associated with self-assessed reductions in opioid use during periods of cannabis use. Increasing the accessibility of cannabis products for therapeutic use may be a useful supplementary strategy to mitigate exposure to unregulated opioids and associated harm during the ongoing drug toxicity crisis
The Grizzly, February 18, 2010
Every Ending Starts with a Beginning • Record-Breaking Blizzard Evokes Varied Reactions • Could Watching the Super Bowl Damage Your Heart? • Snow Storm Photos • Senior Class Gift Drive • SPINTfest \u2710 Brings New Themes for Houses • UC Goes Red to Raise Awareness About the Risks of Heart Disease • Opinion: Teenage Pregnancy TV Shows are a Big Hit, But What\u27s the Effect? • Tragedy Strikes in Early Hours of Winter Olympics • Men\u27s Basketball Shuts Down McDanielhttps://digitalcommons.ursinus.edu/grizzlynews/1806/thumbnail.jp
The Grizzly, February 12, 2010
Main Street Renovation Improves Safety • Community Brings Down Crime at Ursinus College • Annual Scottish Irish Festival This Weekend • Bonner Leaders Hold Fair in Lower Wismer • What You Should Really Expect from Study Abroad • New Member Education Starts Up Again and Looks Forward to Positive Change • UC Gymnastics is Flipping Through 2010 Season • Moliken Named New Athletic Directorhttps://digitalcommons.ursinus.edu/grizzlynews/1805/thumbnail.jp
- …