Downdating of Szego polynomials and data fitting applications

Many algorithms for polynomial least squares approximation of real- valued function on a real interval determine polynomials that are orthogonal with respect to a suitable inner product defined on this interval. Analogously, it is convenient to computer Szego polynomials, i.e., polynomials that are orthogonal with respect to an inner product on the unit circle, when approximating a complex-valued function on the unit circle in the least squares sense. It may also be appropriate to determine Szego polynomials in algorithms for least squares approximation of real-valued periodic functions by trigonometric polynomials. This paper is concerned with Szego polynomials that are defined by a discrete inner product on the unit circle. We present a scheme for downdating the Szego polynomials and given least squares approximant when a node is deleted from the inner product. Our scheme uses the QR algorithm for unitary upper IIessenberg matrices. We describe a data-fitting application that illustrates how our scheme can be combined with the fast Fourier transform algorithm when the given nodes are not equidistant. Application to sliding windows is discussed alsohttp://archive.org/details/downdatingofszeg00gragN

Heterogeneity of patients with functional/dissociative seizures: three multidimensional profiles

Objective Current concepts highlight the neurological and psychological heterogeneity of functional/dissociative seizures (FDS). However, it remains uncertain whether it is possible to distinguish between a limited number of subtypes of FDS disorders. We aimed to identify profiles of distinct FDS subtypes by cluster analysis of a multidimensional dataset without any a priori hypothesis. Methods We conducted an exploratory, prospective multicenter study of 169 patients with FDS. We collected biographical, trauma (childhood and adulthood traumatic experiences), semiological (seizure characteristics), and psychopathological data (psychiatric comorbidities, dissociation, and alexithymia) through psychiatric interviews and standardized scales. Clusters were identified by the Partitioning Around Medoids method. The similarity of patients was computed using Gower distance. The clusters were compared using analysis of variance, chi-squared, or Fisher exact tests. Results Three patient clusters were identified in this exploratory, hypothesis-generating study and named on the basis of their most prominent characteristics: 1. A “No/Single Trauma” group (31.4%), with more male patients, intellectual disabilities, and nonhyperkinetic seizures, and a low level of psychopathology; 2. A “Cumulative Lifetime Traumas” group (42.6%), with clear female predominance, hyperkinetic seizures, relatively common comorbid epilepsy, and a high level of psychopathology; and 3. A “Childhood Traumas” group (26%), commonly with comorbid epilepsy, history of childhood sexual abuse (75%), and posttraumatic stress disorder, but also with a high level of anxiety and dissociation. Significance Although our cluster analysis was undertaken without any a priori hypothesis, the nature of the trauma history emerged as the most important differentiator between three common FDS disorder subtypes. This subdifferentiation of FDS disorders may facilitate the development of more specific therapeutic programs for each patient profile

Heterogeneous treatment effects of therapeutic-dose heparin in patients hospitalized for COVID-19

Importance Randomized clinical trials (RCTs) of therapeutic-dose heparin in patients hospitalized with COVID-19 produced conflicting results, possibly due to heterogeneity of treatment effect (HTE) across individuals. Better understanding of HTE could facilitate individualized clinical decision-making. Objective To evaluate HTE of therapeutic-dose heparin for patients hospitalized for COVID-19 and to compare approaches to assessing HTE. Design, Setting, and Participants Exploratory analysis of a multiplatform adaptive RCT of therapeutic-dose heparin vs usual care pharmacologic thromboprophylaxis in 3320 patients hospitalized for COVID-19 enrolled in North America, South America, Europe, Asia, and Australia between April 2020 and January 2021. Heterogeneity of treatment effect was assessed 3 ways: using (1) conventional subgroup analyses of baseline characteristics, (2) a multivariable outcome prediction model (risk-based approach), and (3) a multivariable causal forest model (effect-based approach). Analyses primarily used bayesian statistics, consistent with the original trial. Exposures Participants were randomized to therapeutic-dose heparin or usual care pharmacologic thromboprophylaxis. Main Outcomes and Measures Organ support–free days, assigning a value of −1 to those who died in the hospital and the number of days free of cardiovascular or respiratory organ support up to day 21 for those who survived to hospital discharge; and hospital survival. Results Baseline demographic characteristics were similar between patients randomized to therapeutic-dose heparin or usual care (median age, 60 years; 38% female; 32% known non-White race; 45% Hispanic). In the overall multiplatform RCT population, therapeutic-dose heparin was not associated with an increase in organ support–free days (median value for the posterior distribution of the OR, 1.05; 95% credible interval, 0.91-1.22). In conventional subgroup analyses, the effect of therapeutic-dose heparin on organ support–free days differed between patients requiring organ support at baseline or not (median OR, 0.85 vs 1.30; posterior probability of difference in OR, 99.8%), between females and males (median OR, 0.87 vs 1.16; posterior probability of difference in OR, 96.4%), and between patients with lower body mass index (BMI 90% for all comparisons). In risk-based analysis, patients at lowest risk of poor outcome had the highest propensity for benefit from heparin (lowest risk decile: posterior probability of OR >1, 92%) while those at highest risk were most likely to be harmed (highest risk decile: posterior probability of OR <1, 87%). In effect-based analysis, a subset of patients identified at high risk of harm (P = .05 for difference in treatment effect) tended to have high BMI and were more likely to require organ support at baseline. Conclusions and Relevance Among patients hospitalized for COVID-19, the effect of therapeutic-dose heparin was heterogeneous. In all 3 approaches to assessing HTE, heparin was more likely to be beneficial in those who were less severely ill at presentation or had lower BMI and more likely to be harmful in sicker patients and those with higher BMI. The findings illustrate the importance of considering HTE in the design and analysis of RCTs. Trial Registration ClinicalTrials.gov Identifiers: NCT02735707, NCT04505774, NCT04359277, NCT0437258

Effect of angiotensin-converting enzyme inhibitor and angiotensin receptor blocker initiation on organ support-free days in patients hospitalized with COVID-19

IMPORTANCE Overactivation of the renin-angiotensin system (RAS) may contribute to poor clinical outcomes in patients with COVID-19. Objective To determine whether angiotensin-converting enzyme (ACE) inhibitor or angiotensin receptor blocker (ARB) initiation improves outcomes in patients hospitalized for COVID-19. DESIGN, SETTING, AND PARTICIPANTS In an ongoing, adaptive platform randomized clinical trial, 721 critically ill and 58 non–critically ill hospitalized adults were randomized to receive an RAS inhibitor or control between March 16, 2021, and February 25, 2022, at 69 sites in 7 countries (final follow-up on June 1, 2022). INTERVENTIONS Patients were randomized to receive open-label initiation of an ACE inhibitor (n = 257), ARB (n = 248), ARB in combination with DMX-200 (a chemokine receptor-2 inhibitor; n = 10), or no RAS inhibitor (control; n = 264) for up to 10 days. MAIN OUTCOMES AND MEASURES The primary outcome was organ support–free days, a composite of hospital survival and days alive without cardiovascular or respiratory organ support through 21 days. The primary analysis was a bayesian cumulative logistic model. Odds ratios (ORs) greater than 1 represent improved outcomes. RESULTS On February 25, 2022, enrollment was discontinued due to safety concerns. Among 679 critically ill patients with available primary outcome data, the median age was 56 years and 239 participants (35.2%) were women. Median (IQR) organ support–free days among critically ill patients was 10 (–1 to 16) in the ACE inhibitor group (n = 231), 8 (–1 to 17) in the ARB group (n = 217), and 12 (0 to 17) in the control group (n = 231) (median adjusted odds ratios of 0.77 [95% bayesian credible interval, 0.58-1.06] for improvement for ACE inhibitor and 0.76 [95% credible interval, 0.56-1.05] for ARB compared with control). The posterior probabilities that ACE inhibitors and ARBs worsened organ support–free days compared with control were 94.9% and 95.4%, respectively. Hospital survival occurred in 166 of 231 critically ill participants (71.9%) in the ACE inhibitor group, 152 of 217 (70.0%) in the ARB group, and 182 of 231 (78.8%) in the control group (posterior probabilities that ACE inhibitor and ARB worsened hospital survival compared with control were 95.3% and 98.1%, respectively). CONCLUSIONS AND RELEVANCE In this trial, among critically ill adults with COVID-19, initiation of an ACE inhibitor or ARB did not improve, and likely worsened, clinical outcomes. TRIAL REGISTRATION ClinicalTrials.gov Identifier: NCT0273570

Constructing a unitary Hessenberg matrix from spectral data

We consider the numerical construction of a unitary Hessenberg matrix from spectral data using an inverse QR algorithm. Any unitary upper Hessenberg matrix H with nonnegative subdiagonal elements can be represented by 2n - 1 real parameters. This representation, which we refer to as the Schur parameterization of H, facilitates the development of efficient algorithms for this class of matrices. We show that a unitary upper Hessenberg matrix H with positive subdiagonal elements is determined by its eigenvalues and the eigenvalues of a rank-one unitary perturbation of H. The eigenvalues of the perturbation strictly interlace the eigenvalues of H on the unit circle. Inverse eigenvalue problem, Unitary matrix, Orthogonal polynomialprepared in conjunction with research conducted for the National Science Foundation and for the Naval Postgraduate School Research Council and funded by the Naval Postgraduate School Research Council.http://archive.org/details/constructingunit00gragO&MN, Direct fundingN

Emerging group C and group G streptococcal endocarditis: A Canadian perspective

Objectives: The aim of this study was to determine the incidence of infective endocarditis (IE) in patients with bacteremia caused by group C and group G streptococci (GCGS) and to characterize the burden of disease, clinical characteristics, and outcomes through a case series of patients with GCGS IE. Methods: Individuals with blood cultures growing GCGS in Manitoba, Canada, between January 2012 and December 2015 were included. Clinical and echocardiographic parameters were collected retrospectively. IE was suspected or confirmed according to the modified Duke criteria. Results: Two hundred and nine bacteremic events occurred in 198 patients. Transthoracic echocardiography (TTE) was performed in 33%. Suspected or confirmed IE occurred in 6% of all patients and in 18% of those with TTE. Native valve infection was more common than prosthetic valve and device-related infections (75%, 17%, and 8%, respectively). Metastatic infection was observed in 64%, primarily to the lungs (57%), skin (43%), osteoarticular system (29%), and central nervous system (29%). Sepsis occurred in 58% and streptococcal toxic shock syndrome in 50% of those with IE, with overall mortality of 17%. Conclusions: IE from GCGS bacteremia is common and is frequently associated with severe disease, embolic events, and mortality. In the appropriate clinical context, GCGS bacteremic events should prompt investigation for IE. Keywords: Streptococcus dysgalactiae, Group C streptococci, Group G streptococci, Bacteremia, Infective endocarditi

Dual-energy CT pulmonary angiography (DECTPA) quantifies vasculopathy in severe COVID-19 pneumonia

Background The role of dual energy computed tomographic pulmonary angiography (DECTPA) in revealing vasculopathy in coronavirus disease 2019 (COVID-19) has not been fully explored. Purpose To evaluate the relationship between DECTPA and disease duration, right ventricular dysfunction (RVD), lung compliance, D-dimer and obstruction index in COVID-19 pneumonia. Materials and Methods This institutional review board approved this retrospective study, and waived the informed consent requirement. Between March-May 2020, 27 consecutive ventilated patients with severe COVID-19 pneumonia underwent DECTPA to diagnose pulmonary thrombus (PT); 11 underwent surveillance DECTPA 14 ±11.6 days later. Qualitative and quantitative analysis of perfused blood volume (PBV) maps recorded: i) perfusion defect ‘pattern’ (wedge-shaped, mottled or amorphous), ii) presence of PT and CT obstruction index (CTOI) and iii) PBV relative to pulmonary artery enhancement (PBV/PAenh); PBV/PAenh was also compared with seven healthy volunteers and correlated with D-Dimer and CTOI. Results Amorphous (n=21), mottled (n=4), and wedge-shaped (n=2) perfusion defects were observed (M=20; mean age=56 ±8.7 years). Mean extent of perfusion defects=36.1%±17.2. Acute PT was present in 11/27(40.7%) patients. Only wedge-shaped defects corresponded with PT (2/27, 7.4%). Mean CTOI was 2.6±5.4 out of 40. PBV/PAenh (18.2 ±4.2%) was lower than in healthy volunteers (27 ±13.9%, p = 0.002). PBV/PAenh correlated with disease duration (β = 0.13, p = 0.04), and inversely correlated with RVD (β = -7.2, p = 0.001), persisting after controlling for confounders. There were no linkages between PBV/PAenh and D-dimer or CTOI. Conclusion Perfusion defects and decreased PBV/PAenh are prevalent in severe COVID-19 pneumonia. PBV/PAenh correlates with disease duration and inversely correlates with RVD. PBV/PAenh may be an important marker of vasculopathy in severe COVID-19 pneumonia even in the absence of arterial thrombus. Summary Significantly decreased (qualitative and quantitative) lung enhancement on dual-energy CT pulmonary angiography is an early feature of severe COVID-19 pneumonia and is associated with right ventricular dysfunction

The Transcription Factor ETV1 Induces Atrial Remodeling and Arrhythmia

Rationale: Structural and electrophysiological remodeling of the atria are recognized consequences of sustained atrial arrhythmias, such as atrial fibrillation. The identification of underlying key molecules and signaling pathways has been challenging because of the changing cell type composition during structural remodeling of the atria. Objective: Thus, the aims of our study were (1) to search for transcription factors and downstream target genes, which are involved in atrial structural remodeling, (2) to characterize the significance of the transcription factor ETV1 (E twenty-six variant 1) in atrial remodeling and arrhythmia, and (3) to identify ETV1-dependent gene regulatory networks in atrial cardiac myocytes. Methods and Results: The transcription factor ETV1 was significantly upregulated in atrial tissue from patients with permanent atrial fibrillation. Mice with cardiac myocyte-specific overexpression of ETV1 under control of the myosin heavy chain promoter developed atrial dilatation, fibrosis, thrombosis, and arrhythmia. Cardiac myocyte-specific ablation of ETV1 in mice did not alter cardiac structure and function at baseline. Treatment with Ang II (angiotensin II) for 2 weeks elicited atrial remodeling and fibrosis in control, but not in ETV1-deficient mice. To identify ETV1-regulated genes, cardiac myocytes were isolated and purified from mouse atrial tissue. Active cis-regulatory elements in mouse atrial cardiac myocytes were identified by chromatin accessibility (assay for transposase-accessible chromatin sequencing) and the active chromatin modification H3K27ac (chromatin immunoprecipitation sequencing). One hundred seventy-eight genes regulated by Ang II in an ETV1-dependent manner were associated with active cis-regulatory elements containing ETV1-binding sites. Various genes involved in Ca2+ handling or gap junction formation (Ryr2, Jph2, Gja5), potassium channels (Kcnh2, Kcnk3), and genes implicated in atrial fibrillation (Tbx5) were part of this ETV1-driven gene regulatory network. The atrial ETV1-dependent transcriptome in mice showed a significant overlap with the human atrial proteome of patients with permanent atrial fibrillation. Conclusions: This study identifies ETV1 as an important component in the pathophysiology of atrial remodeling associated with atrial arrhythmias