A greedy algorithm for computing eigenvalues of a symmetric matrix

We present a greedy algorithm for computing selected eigenpairs of a large sparse matrix $H$ that can exploit localization features of the eigenvector. When the eigenvector to be computed is localized, meaning only a small number of its components have large magnitudes, the proposed algorithm identifies the location of these components in a greedy manner, and obtains approximations to the desired eigenpairs of $H$ by computing eigenpairs of a submatrix extracted from the corresponding rows and columns of $H$. Even when the eigenvector is not completely localized, the approximate eigenvectors obtained by the greedy algorithm can be used as good starting guesses to accelerate the convergence of an iterative eigensolver applied to $H$. We discuss a few possibilities for selecting important rows and columns of $H$ and techniques for constructing good initial guesses for an iterative eigensolver using the approximate eigenvectors returned from the greedy algorithm. We demonstrate the effectiveness of this approach with examples from nuclear quantum many-body calculations, many-body localization studies of quantum spin chains and road network analysis.Comment: 19 pages, 9 figures, 1 tabl

Managing Hypertension, Diabetes, and Cardiovascular Disease Risk via Short-Term Medical Trips: A Retrospective Longitudinal Study in Santo Domingo

Background: Short-term medical trips (STMTs) from high-resource countries frequently provide care in low and middle-income countries. Little existing literature objectively tracks the long-term outcomes of these interventions on the receiving populations over time to assess potential benefits and to ensure no harm is being done. Objectives: The purpose of this study was to objectively analyze the outcomes of a biannual STMT to Santo Domingo, Dominican Republic on hypertension (HTN), diabetes mellitus type 2 (DM2), and cardiovascular disease (CVD) risk over a five-year period (2015-2019). Methods: Data from 1655 patients was extracted from the electronic medical record. In patients who received treatment and had more than one visit, a linear mixed model was used to analyze effects on systolic blood pressure (SBP) and hemoglobin A1C (HbA1C) values over time. In patients with high CVD risk based on a non-laboratory-based assessment, provider compliance with prescribing an aspirin and statin was calculated and tracked over time. Results: In patients with HTN who received treatment, average SBP was 148.83 mmHg (SD = 23.96) at initial visit and demonstrated no change over time (Estimate: 0.68 mmHg/year increase, p = 0.46). HbA1C data was insufficient for analysis. Treatment for patients with high CVD risk with an aspirin and statin improved from 41.46% in 2015 to 70.51% in 2019. Conclusion: SBP in patients with HTN treated by this STMT demonstrated no significant change over time. Possible contributing factors included patient education, access and adherence to medications, and documentation of data. Provider compliance with appropriate prescribing was high for patients with HTN and DM2 and improved over time for patients with high CVD risk, serving as an indirect measure for potential long-term benefits on these populations. All STMTs should objectively track outcomes of their interventions to assess risks and benefits to the communities being served

Anomalous elasticity of cellular tissue vertex model

Vertex Models, as used to describe cellular tissue, have an energy controlled by deviations of each cell area and perimeter from target values. The constrained nonlinear relation between area and perimeter leads to new mechanical response. Here we provide a mean-field treatment of a highly simplified model: a uniform network of regular polygons with no topological rearrangements. Since all polygons deform in the same way, we only need to analyze the ground states and the response to deformations of a single polygon (cell). The model exhibits the known transition between a fluid/compatible state, where the cell can accommodate both target area and perimeter, and a rigid/incompatible state. %The rigid solid-like state has a single gapped ground state. We calculate and measure the mechanical resistance to various deformation protocols and discover that at the onset of rigidity, where a single zero-energy ground-state exists, %We show that in the incompatible state, where a single frustrated ground-state exists, linear elasticity fails to describe the mechanical response to even infinitesimal deformations. In particular we identify a breakdown of reciprocity expressed via different moduli for compressive and tensile loads, implying non-analyticity of the energy functional. We give a pictorial representation in configuration space that reveals that the complex elastic response of the Vertex Model arises from the presence of two distinct sets of reference states (associated with target area and target perimeter)

The role of non-affine deformations in the elastic behavior of the cellular vertex model

The vertex model of epithelia describes the apical surface of a tissue as a tiling of polygonal cells, with a mechanical energy governed by deviations in cell shape from preferred, or target, area, $A_0$, and perimeter, $P_0$. The model exhibits a rigidity transition driven by geometric incompatibility as tuned by the target shape index, $p_0 = P_0 / \sqrt{A_0}$. For $p_0 > p_*(6) = \sqrt{8 \sqrt{3}} \approx 3.72$, with $p_*(6)$ the perimeter of a regular hexagon of unit area, a cell can simultaneously attain both the preferred area and preferred perimeter. As a result, the tissue is in a mechanically soft compatible state, with zero shear and Young's moduli. For $p_0 < p_*(6)$, it is geometrically impossible for any cell to realize the preferred area and perimeter simultaneously, and the tissue is in an incompatible rigid solid state. Using a mean-field approach, we present a complete analytical calculation of the linear elastic moduli of an ordered vertex model. We analyze a relaxation step that includes non-affine deformations, leading to a softer response than previously reported. The origin of the vanishing shear and Young's moduli in the compatible state is the presence of zero-energy deformations of cell shape. The bulk modulus exhibits a jump discontinuity at the transition and can be lower in the rigid state than in the fluid-like state. The Poisson's ratio can become negative which lowers the bulk and Young's moduli. Our work provides a unified treatment of linear elasticity for the vertex model and demonstrates that this linear response is protocol-dependent

Resident and Facility Factors Associated with Rehospitalization from Skilled Nursing Facilities

ABSTRACT Older adults often require short-term nursing home care after an acute hospital stay to receive skilled nursing or rehabilitation services. Rehospitalization after a skilled nursing facility (SNF) admission is a potential indicator of poor nursing home quality that is associated with substantial risks of complications and increased costs of care. This study examined resident and facility factors associated with 30-day rehospitalizations during a one-year study period from SNFs in New Mexico. The Minimum Data Set 3.0 was used to explore resident factors and Nursing Home Compare data was used for facility factors. Among residents admitted to the SNF from an acute care hospital for 30-days or fewer (n = 2,370), 317 (13.4%) were rehospitalized. In bivariate analyses, several resident characteristics during their SNF stay were associated with significantly increased probability of rehospitalization, including an unhealed pressure ulcer, delirium, shortness of breath, and oxygen use. In multivariable models, the relative odds of rehospitalization were increased in those who identified as American Indian or Alaska Native, residents who rejected care, those with symptoms of delirium, and those who required greater mobility assistance with activities of daily living. The relative odds of rehospitalization were decreased in women and in residents with dementia. However, overall, none of the models improved prediction of rehospitalization. The Nursing Home Compare 5-star rating showed a decline in nurse staff ratings from 2015 to 2016. Policy implications include value-based penalties linked to high SNF rehospitalization rates and policies focused on reducing Medicare costs, while improving nursing home quality

Comparison of ESTs from juvenile and adult phases of the giant unicellular green alga Acetabularia acetabulum

BACKGROUND: Acetabularia acetabulum is a giant unicellular green alga whose size and complex life cycle make it an attractive model for understanding morphogenesis and subcellular compartmentalization. The life cycle of this marine unicell is composed of several developmental phases. Juvenile and adult phases are temporally sequential but physiologically and morphologically distinct. To identify genes specific to juvenile and adult phases, we created two subtracted cDNA libraries, one adult-specific and one juvenile-specific, and analyzed 941 randomly chosen ESTs from them. RESULTS: Clustering analysis suggests virtually no overlap between the two libraries. Preliminary expression data also suggests that we were successful at isolating transcripts differentially expressed between the two developmental phases and that many transcripts are specific to one phase or the other. Comparison of our EST sequences against publicly available sequence databases indicates that ESTs from the adult and the juvenile libraries partition into different functional classes. Three conserved sequence elements were common to several of the ESTs and were also found within the genomic sequence of the carbonic anhydrase1 gene from A. acetabulum. To date, these conserved elements are specific to A. acetabulum. CONCLUSIONS: Our data provide strong evidence that adult and juvenile phases in A. acetabulum vary significantly in gene expression. We discuss their possible roles in cell growth and morphogenesis as well as in phase change. We also discuss the potential role of the conserved elements found within the EST sequences in post-transcriptional regulation, particularly mRNA localization and/or stability

Effect of substrate thermal resistance on space-domain microchannel

In recent years, Fluorescent Melting Curve Analysis (FMCA) has become an almost ubiquitous feature of commercial quantitative PCR (qPCR) thermal cyclers. Here a micro-fluidic device is presented capable of performing FMCA within a microchannel. The device consists of modular thermally conductive blocks which can sandwich a microfluidic substrate. Opposing ends of the blocks are held at differing temperatures and a linear thermal gradient is generated along the microfluidic channel. Fluorescent measurements taken from a sample as it passes along the micro-fluidic channel permits fluorescent melting curves to be generated. In this study we measure DNA melting temperature from two plasmid fragments. The effects of flow velocity and ramp-rate are investigated, and measured melting curves are compared to those acquired from a commercially available PCR thermocycler

Tapping Environmental History to Recreate America’s Colonial Hydrology

To properly remediate, improve, or predict how hydrological systems behave, it is vital to establish their histories. However, modern-style records, assembled from instrumental data and remote sensing platforms, hardly exist back more than a few decades. As centuries of data is preferable given multidecadal fluxes of both meteorology/climatology and demographics, building such a history requires resources traditionally considered only useful in the social sciences and humanities. In this Feature, Pastore et al. discuss how they have undertaken the synthesis of historical records and modern techniques to understand the hydrology of the Northeastern U.S. from Colonial times to modern day. Such approaches could aid studies in other regions that may require heavier reliance on qualitative narratives. Further, a better insight as to how historical changes unfolded could provide a “past is prologue” methodology to increase the accuracy of predictive environmental models