Two-site Cluster Research Articles

Strategies to improve the recruitment and retention of underserved children and families in clinical trials: A case example of a school-supervised asthma therapy pilot

BackgroundDue to underrepresentation of racial/ethnic minority and low-income groups in clinical studies, there is a call to improve the recruitment and retention of these populations in research. Pilot studies can test recruitment and retention practices for better inclusion of medically underserved children and families in subsequent clinical trials. We examined this using a school-based asthma intervention, in preparation for a larger clinical trial in which our goal is to include an underserved study population. MethodsWe recruited children with poorly controlled asthma in a two-site pilot cluster randomized controlled trial of school-supervised asthma therapy versus enhanced usual care (receipt of an educational asthma workbook). We sought a study population with a high percentage of children and families from racial/ethnic minority and low-income groups. The primary outcome of the pilot trial was recruitment/retention over 12 months. Strategies used to facilitate recruitment/retention of this study population included engaging pre-trial multi-level stakeholders, selecting trial sites with high percentages of underserved children and families, training diverse medical providers to recruit participants, conducting remote trial assessments, and providing multi-lingual study materials. ResultsTwenty-six children [42.3% female, 11.5% Black, 30.8% Multiracial (Black & other), 76.9% Hispanic, and 92.3% with family income below $40,000] and their caregivers were enrolled in the study, which represents 55.3% of those initially referred by their provider, with 96.2%, 92.3%, and 96.2% retention at 3-, 6-, and 12-month follow-up, respectively. ConclusionTargeted strategies facilitated the inclusion of a medically underserved population of children and families in our pilot study, prior to expanding to a larger trial.

Estimation of biquadratic and bicubic Heisenberg effective couplings from multiorbital Hubbard models

We studied a multi-orbital Hubbard model at half-filling for two and three orbitals per site on a two-site cluster via full exact diagonalization, in a wide range for the onsite repulsion U, from weak to strong coupling, and multiple ratios of the Hund coupling J H to U. The hopping matrix elements among the orbitals were also varied extensively. At intermediate and large U, we mapped the results into a Heisenberg model. For two orbitals per site, the mapping is into a S = 1 Heisenberg model where by symmetry both nearest-neighbor (S i ⋅ S j ) and are allowed, with respective couplings J 1 and J 2. For the case of three orbitals per site, the mapping is into a S = 3/2 Heisenberg model with (S i ⋅ S j ), , and terms, and respective couplings J 1, J 2, and J 3. The strength of these coupling constants in the Heisenberg models depend on the U, J H, and hopping amplitudes of the underlying Hubbard model. Our study provides a first crude estimate to establish bounds on how large the ratios J 2/J 1 and J 3/J 1 can be. We show that those ratios appear rather limited and, as a qualitative guidance, we conclude that J 2/J 1 is less than 0.4 and J 3/J 1 is less than 0.2, establishing bounds on effective models for strongly correlated Hubbard systems. Moreover, the intermediate Hubbard U regime was found to be the most promising to enhance J 2/J 1 and J 3/J 1.

A knowledge broker facilitated intervention to improve the use of standardized assessment tools by physical therapists: A cluster randomized trial

Objective To compare two methods of knowledge broker support to improve standardized assessment use. Design Two-site cluster randomized trial. Setting Acute rehabilitation hospital. Participants 18 physical therapists. Intervention A 10-month intervention was collaboratively designed with an external knowledge broker and physical therapists to compare full and partial implementation support. The knowledge broker provided education and strategies for implementation to the fully supported group and recommended strategies to the partially supported group that they self-implemented. Measurement Chart audit data documenting frequency of use was extracted at four timepoints. Ten focus groups were conducted to describe factors that influenced use. Focus group data were coded using the Consolidated Framework for Implementation Research and rated as barriers and facilitators for standardized assessment use. Results For the fully supported group, standardized assessment use at initial examination increased from 0% to 58.3% at month 2 and decreased to 17.6% and 11.8% at months 4 and 8–10. For the partially supported group, standardized assessment use increased from 0% to 46% and 50% at month 2 and 4 and decreased to 2.8% at months 8–10. For both groups, early use was seen multiple facilitators. At month 10, barriers included organizational changes that impacted intervention fit. In addition, the fully supported group didn't value the selected standardized assessment and the partially supported group lacked space. Conclusions Knowledge broker support improved both groups standardized assessment use early on, but it was not sustained. The amount of support could not be isolated as factors that influenced use varied by groups.

Householder-transformed density matrix functional embedding theory

Quantum embedding based on the (one-electron reduced) density matrix is revisited by means of the unitary Householder transformation. While being exact and equivalent to (but formally simpler than) density matrix embedding theory (DMET) in the non-interacting case, the resulting Householder transformed density matrix functional embedding theory (Ht-DMFET) preserves, by construction, the single-particle character of the bath when electron correlation is introduced. In Ht-DMFET, the projected "impurity+bath" cluster's Hamiltonian (from which approximate local properties of the interacting lattice can be extracted) becomes an explicit functional of the density matrix. In the spirit of single-impurity DMET, we consider in this work a closed (two-electron) cluster constructed from the full-size non-interacting density matrix. When the (Householder transformed) interaction on the bath site is taken into account, per-site energies obtained for the half-filled one-dimensional Hubbard lattice match almost perfectly the exact Bethe Ansatz results in all correlation regimes. In the strongly correlated regime, the results deteriorate away from half-filling. This can be related to the electron number fluctuations in the (two-site) cluster which are not described neither in Ht-DMFET nor in regular DMET. As expected, the per-site energies dramatically improve when increasing the number of embedded impurities. Formal connections with density/density matrix functional theories have been briefly discussed and should be explored further. Work is currently in progress in this direction.

Theoretical study of network junction models for totally asymmetric exclusion processes with interacting particles

Biological transport phenomena frequently exhibit complex network behavior when several molecular fluxes converge to special junctions from which another fluxes move out in different directions. Similar behavior is also observed in vehicular transport. Stimulated by these observations, we developed a theoretical framework to investigate network junction models of totally asymmetric simple exclusion processes with interacting particles. Utilizing a two-site cluster mean field framework that takes into account some correlations in the system, stationary dynamic properties, such as phase diagrams, density profiles and correlations profiles, are explicitly evaluated. It is found that the number of stationary phases strongly depend on the number of segments that come and leave the network junction. The inter-particle interactions also have a strong effect of dynamic properties of the system. Our method can be extended to the systems with several junctions. All theoretical predictions are in good agreement with extensive Monte Carlo computer simulations.

The two gap transitions in Ge1−xSnx: Effect of non-substitutional complex defects

The existence of non-substitutional β-Sn defects in Ge1−xSnx alloys was confirmed by emission channeling experiments [Decoster et al., Phys. Rev. B 81, 155204 (2010)], which established that, although most Sn enters substitutionally (α-Sn) in the Ge lattice, a second significant fraction corresponds to the Sn-vacancy defect complex in the split-vacancy configuration (β-Sn), in agreement with our previous theoretical study [Ventura et al., Phys. Rev. B 79, 155202 (2009)]. Here, we present the electronic structure calculations for Ge1−xSnx, including the substitutional α-Sn as well as the non-substitutional β-Sn defects. To include the presence of the non-substitutional complex defects in the electronic structure calculation for this multi-orbital alloy problem, we extended the approach for the purely substitutional alloy by Jenkins and Dow [Phys. Rev. B 36, 7994 (1987)]. We employed an effective substitutional two-site cluster equivalent to the real non-substitutional β-Sn defect, which was determined by a Green's functions calculation. We then calculated the electronic structure of the effective alloy purely in terms of substitutional defects, embedding the effective substitutional clusters in the lattice. Our results describe the two transitions of the fundamental gap of Ge1−xSnx as a function of the total Sn-concentration: namely, from an indirect to a direct gap, first, and the metallization transition at a higher x. They also highlight the role of β-Sn in the reduction of the concentration range, which corresponds to the direct-gap phase of this alloy of interest for the optoelectronics applications.

A cluster randomized trial of a transition intervention for adolescents with congenital heart disease: rationale and design of the CHAPTER 2 study.

BackgroundThe population of adolescents and young adults with congenital heart disease (CHD) is growing exponentially. These survivors are at risk of late cardiac complications and require lifelong cardiology care. However, there is a paucity of data on how to prepare adolescents to assume responsibility for their health and function within the adult health care system. Evidence-based transition strategies are required.MethodsThe Congenital Heart Adolescents Participating in Transition Evaluation Research (CHAPTER 2) Study is a two-site cluster randomized clinical trial designed to evaluate the efficacy of a nurse-led transition intervention for 16–17 year olds with moderate or complex CHD. The primary endpoint is excess time to adult CHD care, defined as the time interval between the final pediatric cardiology appointment and the first adult CHD appointment, minus the recommended time interval between these appointments. Secondary endpoints include the MyHeart score (CHD knowledge), Transition Readiness Assessment Questionnaire score, and need for catheter or surgical re-intervention. Participants are enrolled in clusters based on week of attendance in the pediatric cardiology clinic. The intervention consists of two one-hour individualized sessions between a cardiology nurse and study participant. Session One focuses on knowledge of the participant’s CHD, review of their cardiac anatomy and prior interventions, and potential late cardiac complications. Session Two focuses on self-management and communication skills through review and discussion of videos and role-play. The study will recruit 120 participants.DiscussionMany adolescents and young adults experience a gap in care predisposing them to late cardiac complications. The CHAPTER 2 Study will investigate the impact of a nurse-led transition intervention among adolescents with CHD. Fidelity of the intervention is a major focus and priority. This study will build on our experience by (i) enrolling at two tertiary care programs, (ii) including a self-management intervention component, and (iii) evaluating the impact of the intervention on time to ACHD care, a clinically relevant outcome. The results of this study will inform pediatric cardiology programs, patients and policy makers in judging whether a structured intervention program provides clinically meaningful outcomes for adolescents and young adults living with CHD.Trial registrationClinicalTrials.gov ID NCT01723332

Thickness dependent Curie temperature and power-law behavior of layering transitions in ferromagnetic classical and quantum thin films described by Ising, XY and Heisenberg models

Ferromagnetic–paramagnetic phase transitions in classical and quantum thin films have been studied up to 50 mono-layers using effective field theory with two-site cluster approximation. Variation of the Curie temperature as a function of film thickness has been examined. The relative shift of the Curie temperature from the corresponding bulk value has been investigated in terms of the shift exponent λ. We have found that shift exponent λ clearly depends on the strength of the ferromagnetic exchange coupling of the surface. Moreover, we have not observed any significant difference between classical and quantum exponents for a particular model.

Chebyshev matrix product state impurity solver for dynamical mean-field theory

We compute the spectral functions for the two-site dynamical cluster theory and for the two-orbital dynamical mean-field theory in the density-matrix renormalization group (DMRG) framework using Chebyshev expansions represented with matrix product states (MPS). We obtain quantitatively precise results at modest computational effort through technical improvements regarding the truncation scheme and the Chebyshev rescaling procedure. We furthermore establish the relation of the Chebyshev iteration to real-time evolution, and discuss technical aspects as computation time and implementation in detail.

Two-particle correlations in a functional renormalization group scheme using a dynamical mean-field theory approach

We apply a recently introduced hybridization flow functional renormalization group scheme for Anderson-like impurity models as an impurity solver in a dynamical mean-field theory (DMFT) approach to lattice Hubbard models. We present how this scheme is capable of reproducing metallic and insulating solutions of the lattice model. Our setup also offers a numerically rather inexpensive method to calculate two-particle correlation functions. For the paramagnetic Hubbard model on the Bethe lattice in infinite dimensions we calculate the local two-particle vertex for the metallic and the insulating phase. Then we go to a two-site cluster DMFT scheme for the two-dimensional Hubbard model that includes short-range antiferromagnetic fluctuations and obtain the local and nonlocal two-particle vertex functions. We discuss the rich frequency structures of these vertices and compare with the vertex in the single-site solution.

Exact results in a slave boson saddle point approach for a strongly correlated electron model

We revisit the Kotliar-Ruckenstein (KR) slave boson saddle point evaluation for a two-site correlated electron model. As the model can be solved analytically, it is possible to compare the KR saddle point results with the exact many-particle levels. The considered two-site cluster mimics an infinite-$U$ single-impurity Anderson model with a nearest-neighbor Coulomb interaction: one site is strongly correlated with an infinite local Coulomb repulsion, which hybridizes with the second site, on which the local Coulomb repulsion vanishes. Making use of the flexibility of the representation, we introduce appropriate weight factors in the KR saddle point scheme. Ground-state and all excitation levels agree with the exact diagonalization results. Thermodynamics and correlation functions may be recovered in a suitably renormalized saddle point evaluation.

Cluster dual fermion approach to nonlocal correlations

We formulate a general cluster Dual Fermion Approach to nonlocal correlations in crystals. The scheme allows the treatment of long-range correlations beyond cluster DMFT and nonlocal effects in realistic calculations of multiorbital systems. We show that the the simplest approximation exactly corresponds to free cluster DMFT. We further consider the relation between the two-particle Green functions in real and dual variables. We apply this approach by calculating the Green function of the Hubbard model in one dimension starting from the two-site cluster DMFT solution. The result agrees well with the Green function obtained from a DMRG calculation.

Slave bosons in radial gauge: A bridge between path integral and Hamiltonian language

We establish a correspondence between the resummation of world lines and the diagonalization of the Hamiltonian for a strongly correlated electronic system. For this purpose, we analyze the functional integrals for the partition function and the correlation functions invoking a slave boson representation in the radial gauge. We show in the spinless case that the Green's function of the physical electron and the projected Green's function of the pseudofermion coincide. Correlation and Green's functions in the spinful case involve a complex entanglement of the world lines which, however, can be obtained through a strikingly simple extension of the spinless scheme. As a toy model we investigate the two-site cluster of the single impurity Anderson model which yields analytical results. All expectation values and dynamical correlation functions are obtained from the exact calculation of the relevant functional integrals. The hole density, the hole auto-correlation function and the Green's function are computed, and a comparison between spinless and spin 1/2 systems provides insight into the role of the radial slave boson field. In particular, the exact expectation value of the radial slave boson field is finite in both cases, and it is not related to a Bose condensate.

First-order phase transitions in classical lattice gas spin models

The present paper considers some classical ferromagnetic lattice-gas models, consisting of particles that carry $n$-component spins $(n=2,3)$ and associated with a $D$-dimensional lattice $(D=2,3)$; each site can host one particle at most, thus implicitly allowing for hard-core repulsion; the pair interaction, restricted to nearest neighbors, is ferromagnetic, and site occupation is also controlled by the chemical potential $\ensuremath{\mu}$. The models had previously been investigated by mean field and two-site cluster treatments (when $D=3$), as well as grand-canonical Monte Carlo simulation in the case $\ensuremath{\mu}=0$, for both $D=2$ and $D=3$; the obtained results showed the same kind of critical behavior as the one known for their saturated lattice counterparts, corresponding to one particle per site. Here we addressed by grand-canonical Monte Carlo simulation the case where the chemical potential is negative and sufficiently large in magnitude; the value $\ensuremath{\mu}=\ensuremath{-}D∕2$ was chosen for each of the four previously investigated counterparts, together with $\ensuremath{\mu}=\ensuremath{-}3D∕4$ in an additional instance. We mostly found evidence of first-order transitions, both for $D=2$ and $D=3$, and quantitatively characterized their behavior. Comparisons are also made with recent experimental results.

Pseudogap State of Underdoped Cuprate Hts as a Display of The Jahn–Teller Pseudoeffect

For underdoped quasi-two dimensional cuprate antiferromagnets within the framework of the two-component model of charge carriers (holes and Zhang–Rice polarons) it is considered two near-degenerate states of hole molecular orbitals of one-site cluster Cu2+O4 2− and two-site cluster Cu2+O4 2−+Cu2+O4 2 in CuO2 planes. It is shown that the vibronic mixing of these near-degenerate states with near energies separated by the energy barrier $$\Delta \varepsilon$$ , leads to transition of the system to the pseudogap state with new quasilocal and local states of charge carriers. The supposition that the pseudogap state is a consequence of the Jahn–Teller pseudoeffect and that barrier $$\Delta \varepsilon$$ is stipulated by magnetic interaction is discussed.

Two-dimensional lattice gas models with extremely anisotropic spin interactions

The effect of anisotropic magnetic interactions on the physical properties of lattice gases is considered in the framework of two simple models, consisting of particles that carry an $n$-component classical spin (unit vector, $n=2$ or 3), and associated with a two-dimensional square lattice; each site can host one particle at most, thus implicitly allowing for hard-core repulsion; the pair potential, restricted to nearest neighbors, is ferromagnetic and extremely anisotropic in spin space, in the sense that only one component is involved in the interaction; the models are rigorously known to support an orientational ordering transition in appropriate ranges of temperature and chemical potential. Thermodynamic properties and phase diagrams of both models have been studied by means of mean-field and two-site cluster treatments, and their tricritical points have been identified. The case of zero chemical potential has been investigated by Monte Carlo simulations, so as to obtain a quantitative test of the named approximations, as well as a more detailed physical characterization.

Nonperturbative approach to full Mott behavior

Though most fermionic Mott insulators order at low temperatures, ordering is ancillary to their insulating behaviour. Our emphasis here is on disentangling ordering from the intrinsic strongly correlated physics of a doped half-filled band. To this end, we focus on the 2D Hubbard model. Because the charge gap arises from on-site correlations, we implement a non-perturbative approach which incorporates local physics. Crucial to this method is a self-consistent two-site dynamical cluster expansion which builds in the nearest-neighbour energy scale, $J$. At half-filling, we find that the spectral function possesses a gap of order $U$ and is devoid of any coherent quasi-particle peaks. In the doped case, we find that the Fermi surface exceeds the Luttinger volume. Additionally in the underdoped regime, we find that a pseudogap opens in the single particle density of states.The pseudogap closes above optimal doping and hence our proposal is not inconsistent with that of Loram. In analogy with the Mott gap and antiferromagnetism, we propose that ordering may also accompany the formation of a pseudogap. We suggest a current pattern within a 1-band model that preserves translational but breaks time-reversal symmetry along the canonical x and y axes but not along $x=\pm y$ that is consistent with the experimental observations. Finally, we show that the Hall coefficient in a doped Mott insulator must change sign at a doping level $x<1/3$. The sign change is tied to a termination of strong correlation physics in the doped Mott state.

On the xy model and its generalizations

The simplest plane rotator model consists of two-component unit vectors, associated with a D-dimensional lattice (say Z D ), parameterized by polar angles ϕ j , and interacting via a ferromagnetic potential restricted to nearest neighbours U= U jk =− ϵcos( ϕ j − ϕ k ); here ϵ is a positive quantity setting energy and temperature scales (i.e., T ∗=k BT/ϵ ). On the other hand, the xy model involves three-component unit vectors, parameterized by polar angles ( θ k , φ k ), but with two components only coupled by the interaction, i.e., V= V jk =− ϵsin θ j sin θ k cos( φ j − φ k ). We consider here generalized xy models, where the interaction is defined by W= W jk =− ϵ(sin θ j sin θ k ) L cos( φ j − φ k ), L∈ N , L⩾1, and point out rigorous comparison inequalities holding for them; in turn, these can be used to prove existence and type of phase transitions when D⩾2; Mean Field and Two-Site Cluster estimates of the ordering transition temperatures are calculated as well, for D=3 and L⩽4.

Properties of the discotic-nematic to isotropic transition: influence of short range orientational order

The present investigation concerns the analysis of the influence of short range orientational correlation on the thermodynamic properties of discotic-nematic liquid crystals. Two-site cluster approximation is applied to the orientational molecular coordinates to include the short range orientational correlation. The role of short range orientational order, dispersion interaction, molecular length-to-width ratio and pressure on the thermodynamic and orientational behaviour of discotic nematogens close to the discotic-nematic to isotropic transition are analysed. It is observed that the short range orientational order has a strong influence on the thermodynamic properties and that the transition properties of both the calamitic and discotic mesogens exhibit quite similar behaviour.

Plane-rotator lattice gas in an external orienting field

We consider a lattice gas of particles that carry a two-component classical spin (i.e., a two-component unit vector). The pair interaction, restricted to nearest neighbors, implicitly includes hard-core repulsion, since each site can host one particle at most, and also contains ferromagnetic interaction between spins as well as nonmagnetic attraction between particles. We study thermodynamic properties and phase diagrams of the model by means of mean-field and two-site cluster approximations, and also by grand-canonical Monte Carlo simulations carried out for one value of the chemical potential; these aim at a quantitative check of the named approximations, as well as a more detailed description. Both mean-field and two-site cluster approximations were found to provide a qualitatively correct description for the thermodynamics of the model with nearest-neighbor interactions, and the predictions of the two-site cluster approximation were in satisfactory quantitative agreement with simulation results. According to both mean-field and two-site cluster treatments, the temperature-density phase diagrams of the model at zero external field are similar to those of the Ising lattice gas, but the effect of external field is quite different. In particular, at zero nonmagnetic attraction the field effect on the gas-liquid critical temperature becomes nonmonotonic. Having compared the field effects in the Ising, plane-rotator, and Heisenberg spin fluids, we conclude that the ability of the external field to decrease the gas-liquid critical temperature weakens with increasing number of spin components.