Tensor Product Approximation (DMRG) and Coupled Cluster method in Quantum Chemistry

We present the Copupled Cluster (CC) method and the Density matrix Renormalization Grooup (DMRG) method in a unified way, from the perspective of recent developments in tensor product approximation. We present an introduction into recently developed hierarchical tensor representations, in particular tensor trains which are matrix product states in physics language. The discrete equations of full CI approximation applied to the electronic Schr\"odinger equation is casted into a tensorial framework in form of the second quantization. A further approximation is performed afterwards by tensor approximation within a hierarchical format or equivalently a tree tensor network. We establish the (differential) geometry of low rank hierarchical tensors and apply the Driac Frenkel principle to reduce the original high-dimensional problem to low dimensions. The DMRG algorithm is established as an optimization method in this format with alternating directional search. We briefly introduce the CC method and refer to our theoretical results. We compare this approach in the present discrete formulation with the CC method and its underlying exponential parametrization.Comment: 15 pages, 3 figure

Continuous heating of a giant X-ray flare on Algol

Giant flares can release large amounts of energy within a few days: X-ray emission alone can be up to ten percent of the star's bolometric luminosity. These flares exceed the luminosities of the largest solar flares by many orders of magnitude, which suggests that the underlying physical mechanisms supplying the energy are different from those on the Sun. Magnetic coupling between the components in a binary system or between a young star and an accretion disk has been proposed as a prerequisite for giant flares. Here we report X-ray observations of a giant flare on Algol B, a giant star in an eclipsing binary system. We observed a total X-ray eclipse of the flare, which demonstrates that the plasma was confined to Algol B, and reached a maximum height of 0.6 stellar radii above its surface. The flare occurred around the south pole of Algol B, and energy must have been released continously throughout its life. We conclude that a specific extrastellar environment is not required for the presence of a flare, and that the processes at work are therefore similar to those on the Sun.Comment: Nature, Sept. 2 199

Multimessenger measurements of the static structure of shock-compressed liquid silicon at 100 GPa

The ionic structure of high-pressure, high-temperature fluids is a challenging theoretical problem with applications to planetary interiors and fusion capsules. Here we report a multimessenger platform using velocimetry and in situ angularly and spectrally resolved x-ray scattering to measure the thermodynamic conditions and ion structure factor of materials at extreme pressures. We document the pressure, density, and temperature of shocked silicon near 100GPa with uncertainties of 6%, 2%, and 20%, respectively. The measurements are sufficient to distinguish between and rule out some ion screening models

Reduced clinical and postmortem measures of cardiac pathology in subjects with advanced Alzheimer's Disease

Background. Epidemiological studies indicate a statistical linkage between atherosclerotic vascular disease (ATH) and Alzheimer\u27s disease (AD). Autopsy studies of cardiac disease in AD have been few and inconclusive. In this report, clinical and gross anatomic measures of cardiac disease were compared in deceased human subjects with and without AD. Methods. Clinically documented cardiovascular conditions from AD (n = 35) and elderly non-demented control subjects (n = 22) were obtained by review of medical records. Coronary artery stenosis and other gross anatomical measures, including heart weight, ventricular wall thickness, valvular circumferences, valvular calcifications and myocardial infarct number and volume were determined at autopsy. Results. Compared to non-demented age-similar control subjects, those with AD had significantly fewer total diagnosed clinical conditions (2.91 vs 4.18), decreased coronary artery stenosis (70.8 vs 74.8%), heart weight (402 vs 489 g for males; 319 vs 412 g for females) and valvular circumferences. Carriage of the Apolipoprotein E-ε4 allele did not influence the degree of coronary stenosis. Group differences in heart weight remained significant after adjustment for age, gender, body mass index and apolipoprotein E genotype while differences in coronary artery stenosis were significantly associated with body mass index alone. Conclusions. The results are in agreement with an emerging understanding that, while midlife risk factors for ATH increase the risk for the later development of AD, once dementia begins, both risk factors and manifest disease diminish, possibly due to progressive weight loss with increasing dementia as well as disease involvement of the brain\u27s vasomotor centers. © 2011 Beach et al; licensee BioMed Central Ltd

Discourse or dialogue? Habermas, the Bakhtin Circle, and the question of concrete utterances

This is the author's accepted manuscript. The final publication is available at Springer via the link below.This article argues that the Bakhtin Circle presents a more realistic theory of concrete dialogue than the theory of discourse elaborated by Habermas. The Bakhtin Circle places speech within the “concrete whole utterance” and by this phrase they mean that the study of everyday language should be analyzed through the mediations of historical social systems such as capitalism. These mediations are also characterized by a determinate set of contradictions—the capital-labor contradiction in capitalism, for example—that are reproduced in unique ways in more concrete forms of life (the state, education, religion, culture, and so on). Utterances always dialectically refract these processes and as such are internal concrete moments, or concrete social forms, of them. Moreover, new and unrepeatable dialogic events arise in these concrete social forms in order to overcome and understand the constant dialectical flux of social life. But this theory of dialogue is different from that expounded by Habermas, who tends to explore speech acts by reproducing a dualism between repeatable and universal “abstract” discursive processes (commonly known as the ideal speech situation) and empirical uses of discourse. These critical points against Habermas are developed by focusing on six main areas: sentences and utterances; the lifeworld and background language; active versus passive understandings of language; validity claims; obligation and relevance in language; and dialectical universalism

Comparison of techniques for handling missing covariate data within prognostic modelling studies: a simulation study

Background: There is no consensus on the most appropriate approach to handle missing covariate data within prognostic modelling studies. Therefore a simulation study was performed to assess the effects of different missing data techniques on the performance of a prognostic model. Methods: Datasets were generated to resemble the skewed distributions seen in a motivating breast cancer example. Multivariate missing data were imposed on four covariates using four different mechanisms; missing completely at random (MCAR), missing at random (MAR), missing not at random (MNAR) and a combination of all three mechanisms. Five amounts of incomplete cases from 5% to 75% were considered. Complete case analysis (CC), single imputation (SI) and five multiple imputation (MI) techniques available within the R statistical software were investigated: a) data augmentation (DA) approach assuming a multivariate normal distribution, b) DA assuming a general location model, c) regression switching imputation, d) regression switching with predictive mean matching (MICE-PMM) and e) flexible additive imputation models. A Cox proportional hazards model was fitted and appropriate estimates for the regression coefficients and model performance measures were obtained. Results: Performing a CC analysis produced unbiased regression estimates, but inflated standard errors, which affected the significance of the covariates in the model with 25% or more missingness. Using SI, underestimated the variability; resulting in poor coverage even with 10% missingness. Of the MI approaches, applying MICE-PMM produced, in general, the least biased estimates and better coverage for the incomplete covariates and better model performance for all mechanisms. However, this MI approach still produced biased regression coefficient estimates for the incomplete skewed continuous covariates when 50% or more cases had missing data imposed with a MCAR, MAR or combined mechanism. When the missingness depended on the incomplete covariates, i.e. MNAR, estimates were biased with more than 10% incomplete cases for all MI approaches. Conclusion: The results from this simulation study suggest that performing MICE-PMM may be the preferred MI approach provided that less than 50% of the cases have missing data and the missing data are not MNAR

HERMES-24 Score Derivation and Validation for Simple and Robust Outcome Prediction After Large Vessel Occlusion Treatment

\ua9 2024 American Heart Association, Inc. BACKGROUND: Clinicians need simple and highly predictive prognostic scores to assist practical decision-making. We aimed to develop a simple outcome prediction score applied 24 hours after anterior circulation acute ischemic stroke treatment with endovascular thrombectomy and validate it in patients treated both with and without endovascular thrombectomy. METHODS: Using the HERMES (Highly Effective Reperfusion Evaluated in Multiple Endovascular Stroke Trials) collaboration data set (n=1764), patients in the endovascular thrombectomy arm were divided randomly into a derivation cohort (n=430) and a validation cohort (n=441). From a set of candidate predictors, logistic regression modeling using forward variable selection was used to select a model that was both parsimonious and highly predictive for modified Rankin Scale (mRS) ≤2 at 90 days. The score was validated in validation cohort, control arm (n=893), and external validation cohorts from the ESCAPE-NA1 (Efficacy and Safety of Nerinetide for the Treatment of Acute Ischaemic Stroke; n=1066) and INTERRSeCT (Identifying New Approaches to Optimize Thrombus Characterization for Predicting Early Recanalization and Reperfusion With IV Alteplase and Other Treatments Using Serial CT Angiography; n=614). RESULTS: In the derivation cohort, we selected 2 significant predictors of mRS ≤2 (National Institutes of Health Stroke Scale score at 24 hours and age [β-coefficient, 0.34 and 0.06]) and derived the HERMES-24 score: age (years)/10+National Institutes of Health Stroke Scale score at 24 hours. The HERMES-24 score was highly predictive for mRS ≤2 (c-statistic 0.907 [95% CI, 0.879–0.935]) in the derivation cohort. In the validation cohort and the control arm, the HERMES-24 score predicts mRS ≤2 (c-statistic, 0.914 [95% CI, 0.886–0.944] and 0.909 [95% CI, 0.887–0.930]). Observed provability of mRS ≤2 ranged between 3.1% and 3.4% when HERMES-24 score ≥25, while it ranged between 90.6% and 93.0% when HERMES-24 score <10 in the derivation cohort, validation cohort, and control arm. The HERMES-24 score also showed c-statistics of 0.894 and 0.889 for mRS ≤2 in the ESCAPE-NA1 and INTERRSeCT populations. CONCLUSIONS: The post-treatment HERMES-24 score is a simple validated score that predicts a 3-month outcome after anterior circulation large vessel occlusion stroke regardless of intervention, which helps prognostic discussion with families on day 2