discrete subgroups
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2021 ◽  
Vol 26 (Supplement_1) ◽  
pp. e58-e59
Author(s):  
Jordan Yeo ◽  
Caitlyn Gudmundsen ◽  
Sajjad Fazel ◽  
Alex Corrigan ◽  
Madison Fullerton ◽  
...  

Abstract Primary Subject area Public Health and Preventive Medicine Background As Canada embarks on its rollout of the COVID-19 vaccine, vaccine hesitancy has the potential to hamper success of the vaccination campaign. Multiple surveys show that the number of Canadians willing to take the vaccine is insufficient to achieve herd immunity. Therefore, governments and health agencies are looking for solutions to increase vaccination uptake. Obtaining a better understanding of the perspective of those who are vaccine-hesitant is critical to developing successful implementation strategies for COVID-19 vaccination. Objectives To explore COVID-19 vaccination determinants among hesitant caregivers and describe categories of COVID-19 vaccine hesitancy. Design/Methods We conducted 23 semi-structured telephone interviews with parents recruited from a tertiary pediatric care centre. Seventeen participants had previously attended a specialty clinic to discuss vaccine hesitancy; the remaining were recruited from an infectious diseases follow-up clinic. The interview guide was structured around the Theoretical Domains Framework, assessing 14 behavioural constructs to identify specific determinants that guide behaviour change. Interviews were audio-recorded, transcribed, and analyzed by two independent data coders using a pragmatic inductive approach. Recurring themes were noted among subgroups of participants, who were subsequently divided into categories based on their underlying concerns. Results Five archetypes of vaccine-hesitant caregivers emerged in our data (Table 1). 1). “Bubble Dwellers” perceive themselves to be safe by following public health recommendations, and distinguish themselves from higher-risk groups to whom the vaccine should first be offered. 2). “Worriers and Delayers” identify the pandemic as a threat and are generally supportive of vaccines, but are concerned about side effects and issues surrounding vaccine development and prefer to delay vaccination. 3). “Need-for-Normals” are more concerned about social isolation and the economy than the direct effects of the COVID-19 virus, but express that the idea of a “return to normal” may sway their opinions regarding the vaccine. 4). “Exceptionalists” hold personal misperceptions of vaccine contraindications due to comorbidities or previous experiences with vaccination, and are concerned that the current rollout invokes a “one size fits all” model that does not apply to their circumstances. 5. “Freedom Fighters” view the pandemic as a hoax, are anti-establishment, and believe the information they have been provided is not convincing for them to adopt the vaccine. Conclusion The evolving pandemic provides a unique opportunity to understand determinants of vaccination intention in the vaccine hesitant population. Our qualitative study is unique in that we were able to draw upon pre-identified vaccine hesitant individuals to explore their perspectives around COVID-19 immunization. We propose that rather than viewing these individuals as one homogenous group, policymakers and health professionals address these discrete subgroups with specific communication tools and information. We are hopeful that our results will help tailor implementation strategies that are targeted to different vaccine hesitancy archetypes, as the vaccine is made available to the general public in the coming year.


2021 ◽  
Author(s):  
Rosaleena Mohanty ◽  
Daniel Ferreira ◽  
Agneta Nordberg ◽  
Eric Westman

INTRODUCTION: Different subtypes/patterns have been defined using tau-PET and structural-MRI in Alzheimer's disease (AD), but the relationship between tau pathology and atrophy remains unclear. Our goals were twofold: (a) investigate the association between baseline tau-PET patterns and longitudinal atrophy in the AD continuum; (b) characterize heterogeneity as a continuous phenomenon over the conventional notion using discrete subgroups. METHODS: In 366 individuals (amyloid-beta-positive: cognitively normal, prodromal AD, AD dementia; amyloid-beta-negative healthy), we examined the association between tau-PET patterns (operationalized as a continuous phenomenon and a discrete phenomenon) and longitudinal sMRI. RESULTS: We observed a differential association between tau-PET patterns and longitudinal atrophy. Heterogeneity, measured continuously, may offer an alternative characterization, sharing correspondence with the conventional subgrouping. DISCUSSION: Site and the rate of atrophy are modulated differentially by tau-PET patterns in the AD continuum. We postulate that heterogeneity be treated as a continuous phenomenon for greater sensitivity over the current/conventional discrete subgrouping.


Author(s):  
JOHN HOPFENSPERGER

Abstract Suppose G is an amenable locally compact group with lattice subgroup $\Gamma $ . Grosvenor [‘A relation between invariant means on Lie groups and invariant means on their discrete subgroups’, Trans. Amer. Math. Soc.288(2) (1985), 813–825] showed that there is a natural affine injection $\iota : {\text {LIM}}(\Gamma )\to {\text {TLIM}}(G)$ and that $\iota $ is a surjection essentially in the case $G={\mathbb R}^d$ , $\Gamma ={\mathbb Z}^d$ . In the present paper it is shown that $\iota $ is a surjection if and only if $G/\Gamma $ is compact.


Author(s):  
G. Margulis ◽  
G. Soifer

We prove the discreteness of small deformations of a discrete cocompact subgroup of isometries of a locally compact metric space under some natural restrictions.


Author(s):  
CHRISTOPHER LUTSKO

Abstract We prove a theorem describing the limiting fine-scale statistics of orbits of a point in hyperbolic space under the action of a discrete subgroup. Similar results have been proved only in the lattice case with two recent infinite-volume exceptions by Zhang for Apollonian circle packings and certain Schottky groups. Our results hold for general Zariski dense, non-elementary, geometrically finite subgroups in any dimension. Unlike in the lattice case orbits of geometrically finite subgroups do not necessarily equidistribute on the whole boundary of hyperbolic space. But rather they may equidistribute on a fractal subset. Understanding the behavior of these orbits near the boundary is central to Patterson–Sullivan theory and much further work. Our theorem characterises the higher order spatial statistics and thus addresses a very natural question. As a motivating example our work applies to sphere packings (in any dimension) which are invariant under the action of such discrete subgroups. At the end of the paper we show how this statistical characterization can be used to prove convergence of moments and to write down the limiting formula for the two-point correlation function and nearest neighbor distribution. Moreover we establish a formula for the 2 dimensional limiting gap distribution (and cumulative gap distribution) which also applies in the lattice case.


Circulation ◽  
2020 ◽  
Vol 142 (Suppl_3) ◽  
Author(s):  
Carolyn Lam ◽  
Karen S Sliwa ◽  
Anna Giczewska ◽  
Kevin Anstrom ◽  
Frank Edelmann ◽  
...  

Introduction: The VICTORIA (Vericiguat Global Study in Subjects with HF with Reduced EF) trial included 5050 patients in 3 discrete subgroups reflecting their index worsening heart failure (HF) event: <3 months after HF hospitalization (HFH) (n=3366), 3-6 months after HFH (n=871), and those requiring IV diuretic therapy without HFH within the prior 3 months (n=813). We evaluated clinical characteristics, outcomes and treatment response to vericiguat across these index event subgroups in VICTORIA. Methods: We compared primary composite (CV death and HFH) and secondary (all-cause death and HFH) outcomes across index event subgroups, both before and after adjusting for clinical covariates (HF duration, NYHA class, medical history, heart rate, HF medications and laboratory values including baseline NT-proBNP), as well as their response to vericiguat. Results: Baseline characteristics were balanced between treatment arms within each subgroup. Over a median follow up of 10.8 months, the absolute primary event rates were high in all subgroups (20.5 - 42.5 per 100 patient-years, Figure). Compared to the IV diuretic group highest relative risk was in HFH <3 months (HR 1.69, 95% CI 1.46-1.95), followed by HFH 3-6 months (HR 1.26, 95% CI 1.06-1.50). After multivariable adjustment, this difference remained significant only in HFH <3 months (adjusted HR [vs IV diuretic] 1.47, 95% CI 1.26-1.72). Vericiguat was associated with reduced risk of the primary outcome overall (HR 0.90, 95% CI 0.82-0.98) and in all 3 subgroups, with no evidence of treatment heterogeneity. Similar results were evident for the secondary composite outcome. Conclusions: Among patients with worsening chronic HF, those within a 3 month window of HFH had almost a 1.5 times risk of CV death or HFH compared to those requiring IV diuretics but not HFH , irrespective of age or clinical risk factors. Vericiguat added to standard therapy was associated with similar benefit across the spectrum of risk in worsening HF.


2020 ◽  
pp. 1-30
Author(s):  
YVES BENOIST

Abstract The topic of this course is the discrete subgroups of semisimple Lie groups. We discuss a criterion that ensures that such a subgroup is arithmetic. This criterion is a joint work with Sébastien Miquel, which extends previous work of Selberg and Hee Oh and solves an old conjecture of Margulis. We focus on concrete examples like the group $\mathrm {SL}(d,{\mathbb {R}})$ and we explain how classical tools and new techniques enter the proof: the Auslander projection theorem, the Bruhat decomposition, the Mahler compactness criterion, the Borel density theorem, the Borel–Harish-Chandra finiteness theorem, the Howe–Moore mixing theorem, the Dani–Margulis recurrence theorem, the Raghunathan–Venkataramana finite-index subgroup theorem and so on.


2020 ◽  
Vol 126 (3) ◽  
pp. 540-558
Author(s):  
Jacopo Bassi

Dynamical conditions that guarantee stability for discrete transformation group $C^*$-algebras are determined. The results are applied to the case of some discrete subgroups of $\operatorname{SL} (2,\mathbb{R} )$ acting on the punctured plane by means of matrix multiplication of vectors. In the case of cocompact subgroups, further properties of such crossed products are deduced from properties of the $C^*$-algebra associated to the horocycle flow on the corresponding compact homogeneous space of $\operatorname{SL} (2,\mathbb{R} )$.


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