Coexistence of superconductivity with partially filled stripes in the Hubbard model.

The Hubbard model is an iconic model in quantum many-body physics and has been intensely studied, especially since the discovery of high-temperature cuprate superconductors. Combining the complementary capabilities of two computational methods, we found superconductivity in both the electron- and hole-doped regimes of the two-dimensional Hubbard model with next-nearest-neighbor hopping. In the electron-doped regime, superconductivity was weaker and was accompanied by antiferromagnetic Néel correlations at low doping. The strong superconductivity on the hole-doped side coexisted with stripe order, which persisted into the overdoped region with weaker hole-density modulation. These stripe orders varied in fillings between 0.6 and 0.8. Our results suggest the applicability of the Hubbard model with next-nearest hopping for describing cuprate high-transition temperature (Tc) superconductivity.

Nested gausslet basis sets.

We introduce nested gausslet bases, an improvement on previous gausslet bases that can treat systems containing atoms with much larger atomic numbers. We also introduce pure Gaussian distorted gausslet bases, which allow the Hamiltonian integrals to be performed analytically, as well as hybrid bases in which the gausslets are combined with standard Gaussian-type bases. All these bases feature the diagonal approximation for the electron-electron interactions so that the Hamiltonian is completely defined by two Nb × Nb matrices, where Nb ≈ 104 is small enough to permit fast calculations at the Hartree-Fock level. In constructing these bases, we have gained new mathematical insight into the construction of one-dimensional diagonal bases. In particular, we have proved an important theorem relating four key basis set properties: completeness, orthogonality, zero-moment conditions, and diagonalization of the coordinate operator matrix. We test our basis sets on small systems with a focus on high accuracy, obtaining, for example, an accuracy of 2 × 10-5 Ha for the total Hartree-Fock energy of the neon atom in the complete basis set limit.

Validating Phase-Space Methods with Tensor Networks in Two-Dimensional Spin Models with Power-Law Interactions.

Using a recently developed extension of the time-dependent variational principle for matrix product states, we evaluate the dynamics of 2D power-law interacting XXZ models, implementable in a variety of state-of-the-art experimental platforms. We compute the spin squeezing as a measure of correlations in the system, and compare to semiclassical phase-space calculations utilizing the discrete truncated Wigner approximation (DTWA). We find the latter efficiently and accurately captures the scaling of entanglement with system size in these systems, despite the comparatively resource-intensive tensor network representation of the dynamics. We also compare the steady-state behavior of DTWA to thermal ensemble calculations with tensor networks. Our results open a way to benchmark dynamical calculations for two-dimensional quantum systems, and allow us to rigorously validate recent predictions for the generation of scalable entangled resources for metrology in these systems.

Effectiveness of a Bundled Payments for Care Improvement Program for Chronic Obstructive Pulmonary Disease.

BACKGROUND: The Medicare Bundled Payments for Care Improvement (BPCI) program reimburses 90-day care episodes post-hospitalization. COPD is a leading cause of early readmissions making it a target for value-based payment reform. OBJECTIVE: Evaluate the financial impact of a COPD BPCI program. DESIGN, PARTICIPANTS, INTERVENTIONS: A single-site retrospective observational study evaluated the impact of an evidence-based transitions of care program on episode costs and readmission rates, comparing patients hospitalized for COPD exacerbations who received versus those who did not receive the intervention. MAIN MEASURES: Mean episode costs and readmissions. KEY RESULTS: Between October 2015 and September 2018, 132 received and 161 did not receive the program, respectively. Mean episode costs were below target for six out of eleven quarters for the intervention group, as opposed to only one out of twelve quarters for the control group. Overall, there were non-significant mean savings of $2551 (95% CI: - $811 to $5795) in episode costs relative to target costs for the intervention group, though results varied by index admission diagnosis-related group (DRG); there were additional costs of $4184 per episode for the least-complicated cohort (DRG 192), but savings of $1897 and $1753 for the most complicated index admissions (DRGs 191 and 190, respectively). A significant mean decrease of 0.24 readmissions per episode was observed in 90-day readmission rates for intervention relative to control. Readmissions and hospital discharges to skilled nursing facilities were factors of higher costs (mean increases of $9098 and $17,095 per episode respectively). CONCLUSIONS: Our COPD BPCI program had a non-significant cost-saving effect, although sample size limited study power. The differential impact of the intervention by DRG suggests that targeting interventions to more clinically complex patients could increase the financial impact of the program. Further evaluations are needed to determine if our BPCI program decreased care variation and improved quality of care. PRIMARY SOURCE OF FUNDING: This research was supported by NIH NIA grant #5T35AG029795-12.

Where is the Quantum Spin Nematic?

We provide strong evidence of the spin-nematic state in a paradigmatic ferro-antiferromagnetic J_{1}-J_{2} model using analytical and density-matrix renormalization group methods. In zero field, the attraction of spin-flip pairs leads to a first-order transition and no nematic state, while pair repulsion at larger J_{2} stabilizes the nematic phase in a narrow region near the pair-condensation field. A devil's staircase of multipair condensates is conjectured for weak pair attraction. A suppression of the spin-flip gap by many-body effects leads to an order-of-magnitude contraction of the nematic phase compared to naïve expectations. The proposed phase diagram should be broadly valid.

Treating asthma in the time of COVID.

The Precision Interventions for Severe and/or Exacerbation-Prone Asthma clinical trials network is actively assessing novel treatments for severe asthma during the coronavirus disease (COVID-19) pandemic and has needed to adapt to various clinical dilemmas posed by the COVID-19 pandemic. Pharmacologic interactions between established asthma therapies and novel drug interventions for COVID-19 infection, including antivirals, biologics, and vaccines, have emerged as a critical and unanticipated issue in the clinical care of asthma. In particular, impaired metabolism of some long-acting beta-2 agonists by the cytochrome P4503A4 enzyme in the setting of antiviral treatment using ritonavir-boosted nirmatrelvir (NVM/r, brand name Paxlovid) may increase risk for adverse cardiovascular events. Although available data have documented the potential for such interactions, these issues are largely unappreciated by clinicians who treat asthma, or those dispensing COVID-19 interventions in patients who happen to have asthma. Because these drug-drug interactions have not previously been relevant to patient care, clinicians have had no guidance on management strategies to reduce potentially serious interactions between treatments for asthma and COVID-19. The Precision Interventions for Severe and/or Exacerbation-Prone Asthma network considered the available literature and product information, and herein share our considerations and plans for treating asthma within the context of these novel COVID-19-related therapies.

Discerning asthma endotypes through comorbidity mapping.

Asthma is a heterogeneous, complex syndrome, and identifying asthma endotypes has been challenging. We hypothesize that distinct endotypes of asthma arise in disparate genetic variation and life-time environmental exposure backgrounds, and that disease comorbidity patterns serve as a surrogate for such genetic and exposure variations. Here, we computationally discover 22 distinct comorbid disease patterns among individuals with asthma (asthma comorbidity subgroups) using diagnosis records for >151 M US residents, and re-identify 11 of the 22 subgroups in the much smaller UK Biobank. GWASs to discern asthma risk loci for individuals within each subgroup and in all subgroups combined reveal 109 independent risk loci, of which 52 are replicated in multi-ancestry meta-analysis across different ethnicity subsamples in UK Biobank, US BioVU, and BioBank Japan. Fourteen loci confer asthma risk in multiple subgroups and in all subgroups combined. Importantly, another six loci confer asthma risk in only one subgroup. The strength of association between asthma and each of 44 health-related phenotypes also varies dramatically across subgroups. This work reveals subpopulations of asthma patients distinguished by comorbidity patterns, asthma risk loci, gene expression, and health-related phenotypes, and so reveals different asthma endotypes.

DNA methylation signatures in airway cells from adult children of asthmatic mothers reflect subtypes of severe asthma.

Maternal asthma (MA) is among the most consistent risk factors for asthma in children. Possible mechanisms for this observation are epigenetic modifications in utero that have lasting effects on developmental programs in children of mothers with asthma. To test this hypothesis, we performed differential DNA methylation analyses of 398,186 individual CpG sites in primary bronchial epithelial cells (BECs) from 42 nonasthma controls and 88 asthma cases, including 56 without MA (NMA) and 32 with MA. We used weighted gene coexpression network analysis (WGCNA) of 69 and 554 differentially methylated CpGs (DMCs) that were specific to NMA and MA cases, respectively, compared with controls. WGCNA grouped 66 NMA-DMCs and 203 MA-DMCs into two and five comethylation modules, respectively. The eigenvector of one MA-associated module (turquoise) was uniquely correlated with 85 genes expressed in BECs and enriched for 36 pathways, 16 of which discriminated between NMA and MA using machine learning. Genes in all 16 pathways were decreased in MA compared with NMA cases (P = 7.1 × 10−3), a finding that replicated in nasal epithelial cells from an independent cohort (P = 0.02). Functional interpretation of these pathways suggested impaired T cell signaling and responses to viral and bacterial pathogens. The MA-associated turquoise module eigenvector was additionally correlated with clinical features of severe asthma and reflective of type 2 (T2)-low asthma (i.e., low total serum immunoglobulin E, fractional exhaled nitric oxide, and eosinophilia). Overall, these data suggest that MA alters diverse epigenetically mediated pathways that lead to distinct subtypes of severe asthma in adults, including hard-to-treat T2-low asthma.

Genome-wide association study identifies kallikrein 5 in type 2 inflammation-low asthma.

BACKGROUND: Clinical studies of type 2 (T2) cytokine-related neutralizing antibodies in asthma have identified a substantial subset of patients with low levels of T2 inflammation who do not benefit from T2 cytokine neutralizing antibody treatment. Non-T2 mechanisms are poorly understood in asthma but represent a redefined unmet medical need. OBJECTIVE: We sought to gain a better understanding of genetic contributions to T2-low asthma. METHODS: We utilized an unbiased genome-wide association study of patients with moderate to severe asthma stratified by T2 serum biomarker periostin. We also performed additional expression and biological analysis for the top genetic hits. RESULTS: We identified a novel protective single nucleotide polymorphism at chr19q13.41, which is selectively associated with T2-low asthma and establishes Kallikrein-related peptidase 5 (KLK5) as the causal gene mediating this association. Heterozygous carriers of the single nucleotide polymorphisms have reduced KLK5 expression. KLK5 is secreted by human bronchial epithelial cells and elevated in asthma bronchial alveolar lavage. T2 cytokines IL-4 and IL-13 downregulate KLK5 in human bronchial epithelial cells. KLK5, dependent on its catalytic function, induces epithelial chemokine/cytokine expression. Finally, overexpression of KLK5 in airway or lack of an endogenous KLK5 inhibitor, SPINK5, leads to spontaneous airway neutrophilic inflammation. CONCLUSION: Our data identify KLK5 to be the causal gene at a novel locus at chr19q13.41 associated with T2-low asthma.

Beyond the Lung: Geriatric Conditions Afflict Community-Dwelling Older Adults With Self-Reported Chronic Obstructive Pulmonary Disease.

RATIONALE: Chronic obstructive pulmonary disease (COPD) predominantly affects older adults. However, the co-morbid occurrence of geriatric conditions has been understudied. OBJECTIVE: Characterize the prevalence of geriatric conditions among community-dwelling U.S. older adults with self-reported COPD. METHODS: We conducted a nationally representative, cross-sectional study of 3,005 U.S. community-dwelling older adults (ages 57-85 years) from the National Social Life, Health, and Aging Project (NSHAP). We evaluated the prevalence of select geriatric conditions (multimorbidity, functional disability, impaired physical function, low physical activity, modified frailty assessment, falls, polypharmacy, and urinary incontinence) and psychosocial measures (frequency of socializing, sexual activity in the last year, loneliness, cognitive impairment, and depressive symptoms) among individuals with self-reported COPD as compared to those without. Using multivariate logistic and linear regressions, we investigated the relationships between COPD and these geriatric physical and psychosocial conditions. MAIN RESULTS: Self-reported COPD prevalence was 10.7%, similar to previous epidemiological studies. Individuals with COPD had more multimorbidity [modified Charlson score 2.6 (SD 1.9) vs. 1.6 (SD 1.6)], more functional disability (58.1 vs. 29.6%; adjusted OR 3.1, 95% CI 2.3, 4.3), falls in the last year (28.4 vs. 20.8%; adjusted OR 1.4, 95% CI 1.01, 2.0), impaired physical function (75.8 vs. 56.6%; adjusted OR 2.1, 95% CI 1.1, 3.7), more frequently reported extreme low physical activity (18.7 vs. 8.1%; adjusted OR 2.3, 95% CI 1.5, 3.5) and higher frailty prevalence (16.0 vs. 2.7%; adjusted OR 6.3, 95% CI 3.0,13.0) than those without COPD. They experienced more severe polypharmacy (≥10 medications, 37.5 vs. 16.1%; adjusted OR 2.9, 95% CI 2.0, 4.2). They more frequently reported extreme social disengagement and were lonelier, but the association with social measures was eliminated when relationship status was accounted for, as those with COPD were less frequently partnered. They more frequently endorsed depressive symptoms (32.0 vs. 18.9%, adjusted OR 1.9, 95% CI 1.4, 2.7). There was no noted difference in cognitive impairment between the two populations. CONCLUSIONS: Geriatric conditions are common among community-dwelling older adults with self-reported COPD. A "beyond the lung" approach to COPD care should center on active management of geriatric conditions, potentially leading to improved COPD management, and quality of life.

Hybrid gausslet/Gaussian basis sets.

We introduce hybrid gausslet/Gaussian basis sets, where a standard Gaussian basis is added to a gausslet basis in order to increase accuracy near the nuclei while keeping the spacing of the grid of gausslets relatively large. The Gaussians are orthogonalized to the gausslets, which are already orthonormal, and approximations are introduced to maintain the diagonal property of the two electron part of the Hamiltonian so that it continues to scale as the second power of the number of basis functions rather than the fourth. We introduce several corrections to the Hamiltonian designed to enforce certain exact properties, such as the values of certain two-electron integrals. We also introduce a simple universal energy correction that compensates for the incompleteness of the basis stemming from the electron-electron cusps based on the measured double occupancy of each basis function. We perform a number of Hartree Fock and full configuration interaction (full-CI) test calculations on two electron systems and Hartree Fock on a ten-atom hydrogen chain to benchmark these techniques. The inclusion of the cusp correction allows us to obtain complete basis set full-CI results for the two electron cases at the level of several micro-Hartrees, and we see similar apparent accuracy for Hartree Fock on the ten-atom hydrogen chain.

Pharmacogenetic studies of long-acting beta agonist and inhaled corticosteroid responsiveness in randomised controlled trials of individuals of African descent with asthma.

BACKGROUND: Pharmacogenetic studies in asthma cohorts, primarily made up of White people of European descent, have identified loci associated with response to inhaled beta agonists and corticosteroids (ICSs). Differences exist in how individuals from different ancestral backgrounds respond to long-acting beta agonist (LABA) and ICSs. Therefore, we sought to understand the pharmacogenetic mechanisms regulating therapeutic responsiveness in individuals of African descent. METHODS: We did ancestry-based pharmacogenetic studies of children (aged 5-11 years) and adolescents and adults (aged 12-69 years) from the Best African Response to Drug (BARD) trials, in which participants with asthma uncontrolled with low-dose ICS (fluticasone propionate 50 µg in children, 100 µg in adolescents and adults) received different step-up combination therapies. The hierarchal composite outcome of pairwise superior responsiveness in BARD was based on asthma exacerbations, a 31-day difference in annualised asthma-control days, or a 5% difference in percentage predicted FEV1. We did whole-genome admixture mapping of 15 159 ancestral segments within 312 independent regions, stratified by the two age groups. The two co-primary outcome comparisons were the step up from low-dose ICS to the quintuple dose of ICS (5 × ICS: 250 µg twice daily in children and 500 µg twice daily in adolescents and adults) versus double dose (2-2·5 × ICS: 100 µg twice daily in children, 250 µg twice daily in adolescents and adults), and 5 × ICS versus 100 µg fluticasone plus a LABA (salmeterol 50 µg twice daily). We used a genome-wide significance threshold of p<1·6 × 10-4, and tested for replication using independent cohorts of individuals of African descent with asthma. FINDINGS: We included 249 unrelated children and 267 unrelated adolescents and adults in the BARD pharmacogenetic analysis. In children, we identified a significant admixture mapping peak for superior responsiveness to 5 × ICS versus 100 µg fluticasone plus salmeterol on chromosome 12 (odds ratio [ORlocal African] 3·95, 95% CI 2·02-7·72, p=6·1 × 10-5) fine mapped to a locus adjacent to RNFT2 and NOS1 (rs73399224, ORallele dose 0·17, 95% CI 0·07-0·42, p=8·4 × 10-5). In adolescents and adults, we identified a peak for superior responsiveness to 5 × ICS versus 2·5 × ICS on chromosome 22 (ORlocal African 3·35, 1·98-5·67, p=6·8 × 10-6) containing a locus adjacent to TPST2 (rs5752429, ORallele dose 0·21, 0·09-0·52, p=5·7 × 10-4). We replicated rs5752429 and nominally replicated rs73399224 in independent African American cohorts. INTERPRETATION: BARD is the first genome-wide pharmacogenetic study of LABA and ICS response in clinical trials of individuals of African descent to detect and replicate genome-wide significant loci. Admixture mapping of the composite BARD trial outcome enabled the identification of novel pharmacogenetic variation accounting for differential therapeutic responses in people of African descent with asthma. FUNDING: National Institutes of Health, National Heart, Lung, and Blood Institute.

Asthma-associated genetic variants induce IL33 differential expression through an enhancer-blocking regulatory region.

Genome-wide association studies (GWAS) have implicated the IL33 locus in asthma, but the underlying mechanisms remain unclear. Here, we identify a 5 kb region within the GWAS-defined segment that acts as an enhancer-blocking element in vivo and in vitro. Chromatin conformation capture showed that this 5 kb region loops to the IL33 promoter, potentially regulating its expression. We show that the asthma-associated single nucleotide polymorphism (SNP) rs1888909, located within the 5 kb region, is associated with IL33 gene expression in human airway epithelial cells and IL-33 protein expression in human plasma, potentially through differential binding of OCT-1 (POU2F1) to the asthma-risk allele. Our data demonstrate that asthma-associated variants at the IL33 locus mediate allele-specific regulatory activity and IL33 expression, providing a mechanism through which a regulatory SNP contributes to genetic risk of asthma.

Ground-state phase diagram of the t-t'-J model.

We report results of large-scale ground-state density matrix renormalization group (DMRG) calculations on t-[Formula: see text]-J cylinders with circumferences 6 and 8. We determine a rough phase diagram that appears to approximate the two-dimensional (2D) system. While for many properties, positive and negative [Formula: see text] values ([Formula: see text]) appear to correspond to electron- and hole-doped cuprate systems, respectively, the behavior of superconductivity itself shows an inconsistency between the model and the materials. The [Formula: see text] (hole-doped) region shows antiferromagnetism limited to very low doping, stripes more generally, and the familiar Fermi surface of the hole-doped cuprates. However, we find [Formula: see text] strongly suppresses superconductivity. The [Formula: see text] (electron-doped) region shows the expected circular Fermi pocket of holes around the [Formula: see text] point and a broad low-doped region of coexisting antiferromagnetism and d-wave pairing with a triplet p component at wavevector [Formula: see text] induced by the antiferromagnetism and d-wave pairing. The pairing for the electron low-doped system with [Formula: see text] is strong and unambiguous in the DMRG simulations. At larger doping another broad region with stripes in addition to weaker d-wave pairing and striped p-wave pairing appears. In a small doping region near [Formula: see text] for [Formula: see text], we find an unconventional type of stripe involving unpaired holes located predominantly on chains spaced three lattice spacings apart. The undoped two-leg ladder regions in between mimic the short-ranged spin correlations seen in two-leg Heisenberg ladders.

Weak Handgrip at Index Admission for Acute Exacerbation of COPD Predicts All-Cause 30-Day Readmission.

Rationale: Identifying patients hospitalized for acute exacerbations of COPD (AECOPD) who are at high risk for readmission is challenging. Traditional markers of disease severity such as pulmonary function have limited utility in predicting readmission. Handgrip strength, a component of the physical frailty phenotype, may be a simple tool to help predict readmission. Objective(s): To investigate if handgrip strength, a component of the physical frailty phenotype and surrogate for weakness, is a predictive biomarker of COPD readmission. Methods: This was a prospective, observational study of patients admitted to the inpatient general medicine unit at the University of Chicago Medicine, US. This study evaluated age, sex, ethnicity, degree of obstructive lung disease by spirometry (FEV1 percent predicted), and physical frailty phenotype (components include handgrip strength and walk speed). The primary outcome was all-cause hospital readmission within 30 days of discharge. Results: Of 381 eligible patients with AECOPD, 70 participants agreed to consent to participate in this study. Twelve participants (17%) were readmitted within 30 days of discharge. Weak grip at index hospitalization, defined as grip strength lower than previously established cut-points for sex and body mass index (BMI), was predictive of readmission (OR 11.2, 95% CI 1.3, 93.2, p = 0.03). Degree of airway obstruction (FEV1 percent predicted) did not predict readmission (OR 1.0, 95% CI 0.95, 1.1, p = 0.7). No non-frail patients were readmitted. Conclusions: At a single academic center weak grip strength was associated with increased 30-day readmission. Future studies should investigate whether geriatric measures can help risk-stratify patients for likelihood of readmission after admission for AECOPD.

Publisher's Note: Sliced Basis Density Matrix Renormalization Group for Electronic Structure [Phys. Rev. Lett. 119, 046401 (2017)].

This corrects the article DOI: 10.1103/PhysRevLett.119.046401.

A-to-I editing of miR-200b-3p in airway cells is associated with moderate-to-severe asthma.

BACKGROUND: Asthma is a chronic lung disease characterised by persistent airway inflammation. Altered microRNA (miRNA)-mediated gene silencing in bronchial epithelial cells (BECs) has been reported in asthma, yet adenosine deaminase acting on RNA (ADAR)-mediated miRNA editing in asthma remains unexplored. METHODS: We first identified adenosine to inosine (A-to-I) edited sites in miRNAs in BECs from 142 adult asthma cases and controls. A-to-I edited sites were tested for associations with asthma severity and clinical measures of asthma. Paired RNA sequencing data were used to perform pathway enrichments and test for associations with bioinformatically predicted target genes of the unedited and edited miRNAs. RESULTS: Of 19 A-to-I edited sites detected in these miRNAs, one site at position 5 of miR-200b-3p was edited less frequently in cases compared with controls (pcorrected=0.013), and especially compared with cases with moderate (pcorrected=0.029) and severe (pcorrected=3.9×10-4), but not mild (pcorrected=0.38), asthma. Bioinformatic prediction revealed 232 target genes of the edited miR-200b-3p, which were enriched for both interleukin-4 and interferon-γ signalling pathways, and included the SOCS1 (suppressor of cytokine signalling 1) gene. SOCS1 was more highly expressed in moderate (pcorrected=0.017) and severe (pcorrected=5.4×10-3) asthma cases compared with controls. Moreover, both miR-200b-3p editing and SOCS1 were associated with bronchoalveolar lavage eosinophil levels. CONCLUSIONS: Reduced A-to-I editing of position 5 of miR-200b-3p in lower airway cells from moderate-to-severe asthmatic subjects may lead to overexpression of SOCS1 and impaired cytokine signalling. We propose ADAR-mediated editing as an epigenetic mechanism contributing to features of moderate-to-severe asthma in adulthood.

Altered transcriptional and chromatin responses to rhinovirus in bronchial epithelial cells from adults with asthma.

There is a life-long relationship between rhinovirus (RV) infection and the development and clinical manifestations of asthma. In this study we demonstrate that cultured primary bronchial epithelial cells from adults with asthma (n = 9) show different transcriptional and chromatin responses to RV infection compared to those without asthma (n = 9). Both the number and magnitude of transcriptional and chromatin responses to RV were muted in cells from asthma cases compared to controls. Pathway analysis of the transcriptionally responsive genes revealed enrichments of apoptotic pathways in controls but inflammatory pathways in asthma cases. Using promoter capture Hi-C we tethered regions of RV-responsive chromatin to RV-responsive genes and showed enrichment of these regions and genes at asthma GWAS loci. Taken together, our studies indicate a delayed or prolonged inflammatory state in cells from asthma cases and highlight genes that may contribute to genetic risk for asthma.

The precision interventions for severe and/or exacerbation-prone asthma (PrecISE) adaptive platform trial: statistical considerations.

The Precision Interventions for Severe and/or Exacerbation-prone Asthma (PrecISE) study is an adaptive platform trial designed to investigate novel interventions to severe asthma. The study is conducted under a master protocol and utilizes a crossover design with each participant receiving up to five interventions and at least one placebo. Treatment assignments are based on the patients' biomarker profiles and precision health methods are incorporated into the interim and final analyses. We describe key elements of the PrecISE study including the multistage adaptive enrichment strategy, early stopping of an intervention for futility, power calculations, and the primary analysis strategy.