The Grover algorithm with large nuclear spins in semiconductors

We show a possible way to implement the Grover algorithm in large nuclear spins 1/2<I<9/2 in semiconductors. The Grover sequence is performed by means of multiphoton transitions that distribute the spin amplitude between the nuclear spin states. They are distinguishable due to the quadrupolar splitting, which makes the nuclear spin levels non-equidistant. We introduce a generalized rotating frame for an effective Hamiltonian that governs the non-perturbative time evolution of the nuclear spin states for arbitrary spin lengths I. The larger the quadrupolar splitting, the better the agreement between our approximative method using the generalized rotating frame and exact numerical calculations.Comment: 11 pages, 18 EPS figures, REVTe

Neurologic Involvement in Children and Adolescents Hospitalized in the United States for COVID-19 or Multisystem Inflammatory Syndrome

This article is made available for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.Importance Coronavirus disease 2019 (COVID-19) affects the nervous system in adult patients. The spectrum of neurologic involvement in children and adolescents is unclear. Objective To understand the range and severity of neurologic involvement among children and adolescents associated with COVID-19. Setting, Design, and Participants Case series of patients (age <21 years) hospitalized between March 15, 2020, and December 15, 2020, with positive severe acute respiratory syndrome coronavirus 2 test result (reverse transcriptase-polymerase chain reaction and/or antibody) at 61 US hospitals in the Overcoming COVID-19 public health registry, including 616 (36%) meeting criteria for multisystem inflammatory syndrome in children. Patients with neurologic involvement had acute neurologic signs, symptoms, or diseases on presentation or during hospitalization. Life-threatening involvement was adjudicated by experts based on clinical and/or neuroradiologic features. Exposures Severe acute respiratory syndrome coronavirus 2. Main Outcomes and Measures Type and severity of neurologic involvement, laboratory and imaging data, and outcomes (death or survival with new neurologic deficits) at hospital discharge. Results Of 1695 patients (909 [54%] male; median [interquartile range] age, 9.1 [2.4-15.3] years), 365 (22%) from 52 sites had documented neurologic involvement. Patients with neurologic involvement were more likely to have underlying neurologic disorders (81 of 365 [22%]) compared with those without (113 of 1330 [8%]), but a similar number were previously healthy (195 [53%] vs 723 [54%]) and met criteria for multisystem inflammatory syndrome in children (126 [35%] vs 490 [37%]). Among those with neurologic involvement, 322 (88%) had transient symptoms and survived, and 43 (12%) developed life-threatening conditions clinically adjudicated to be associated with COVID-19, including severe encephalopathy (n = 15; 5 with splenial lesions), stroke (n = 12), central nervous system infection/demyelination (n = 8), Guillain-Barré syndrome/variants (n = 4), and acute fulminant cerebral edema (n = 4). Compared with those without life-threatening conditions (n = 322), those with life-threatening neurologic conditions had higher neutrophil-to-lymphocyte ratios (median, 12.2 vs 4.4) and higher reported frequency of D-dimer greater than 3 μg/mL fibrinogen equivalent units (21 [49%] vs 72 [22%]). Of 43 patients who developed COVID-19–related life-threatening neurologic involvement, 17 survivors (40%) had new neurologic deficits at hospital discharge, and 11 patients (26%) died. Conclusions and Relevance In this study, many children and adolescents hospitalized for COVID-19 or multisystem inflammatory syndrome in children had neurologic involvement, mostly transient symptoms. A range of life-threatening and fatal neurologic conditions associated with COVID-19 infrequently occurred. Effects on long-term neurodevelopmental outcomes are unknown

Von Mises condition revisited

It is shown that the rate of convergence in the von Mises conditions of extreme value theory determines the distance of the underlying distribution function F from a generalized Pareto distribution. The distance is measured in terms of the pertaining densities with the limit being ultimately attained if and only if F is ultimately a generalized Pareto distribution. Consequently, the rate of convergence of the extremes in an lid sample, whether in terms of the distribution of the largest order statistics or of corresponding empirical truncated point processes, is determined by the rate of convergence in the von Mises condition. We prove that the converse is also true

Laws of small numbers : Some applications to conditional curve estimation

No abstract availabl

Asymptotically optimal tests for conditional distributions

No abstract availabl

On the Loss of Information Due to Nonrandom Truncation

It is assumed that observations among an iid sample falling into certain subsets of the sample space cannot be observed directly, but only through their frequencies. Bounds for the corresponding loss of information are established, which are based on the Hellinger distance between the empirical point process Nn of the complete set of observations and an empirical process N*n that aims at restoring Nn. An application of these bounds to parametric models generalizes and quantifies results for locally asymptotically Gaussian experiments. When applied to extreme value models, this approach generalizes the peaks-over-threshold method for modeling the exceedances over high thresholds in an iid sample.point process, Hellinger distance, statistical experiment, deficiency distance, Blackwell sufficiency, local asymptotic normality, extreme value models, peaks-over-threshold method

A First Course on Time Series Analysis : Examples with SAS

The analysis of real data by means of statistical methods with the aid of a software package common in industry and administration usually is not an integral part of mathematics studies, but it will certainly be part of a future professional work. The present book links up elements from time series analysis with a selection of statistical procedures used in general practice including the statistical software package SAS Statistical Analysis System). Consequently this book addresses students of statistics as well as students of other branches such as economics, demography and engineering, where lectures on statistics belong to their academic training. But it is also intended for the practician who, beyond the use of statistical tools, is interested in their mathematical background. Numerous problems illustrate the applicability of the presented statistical procedures, where SAS gives the solutions. The programs used are explicitly listed and explained. No previous experience is expected neither in SAS nor in a special computer system so that a short training period is guaranteed. This book is meant for a two semester course (lecture, seminar or practical training) where the first two chapters can be dealt with in the first semester. They provide the principal components of the analysis of a time series in the time domain. Chapters 3, 4 and 5 deal with its analysis in the frequency domain and can be worked through in the second term. In order to understand the mathematical background some terms are useful such as convergence in distribution, stochastic convergence, maximum likelihood estimator as well as a basic knowledge of the test theory, so that work on the book can start after an introductory lecture on stochastics. Each chapter includes exercises. An exhaustive treatment is recommended. This book is consecutively subdivided in a statistical part and an SAS-specific part. For better clearness the SAS-specific part, including the diagrams generated with SAS, always starts with a computer symbol, representing the beginning of a session at the computer, and ends with a printer symbol for the end of this session. This book is an open source project under the GNU Free Documentation License

A First Course on Time Series Analysis : Examples with SAS

The analysis of real data by means of statistical methods with the aid of a software package common in industry and administration usually is not an integral part of mathematics studies, but it will certainly be part of a future professional work. The present book links up elements from time series analysis with a selection of statistical procedures used in general practice including the statistical software package SAS. Consequently this book addresses students of statistics as well as students of other branches such as economics, demography and engineering, where lectures on statistics belong to their academic training. But it is also intended for the practician who, beyond the use of statistical tools, is interested in their mathematical background. Numerous problems illustrate the applicability of the presented statistical procedures, where SAS gives the solutions. The programs used are explicitly listed and explained. No previous experience is expected neither in SAS nor in a special computer system so that a short training period is guaranteed. This book is meant for a two semester course (lecture, seminar or practical training) where the first three chapters can be dealt within the first semester. They provide the principal components of the analysis of a time series in the time domain. Chapters 4, 5 and 6 deal with its analysis in the frequency domain and can be worked through in the second term. In order to understand the mathematical background some terms are useful such as convergence in distribution, stochastic convergence, maximum likelihood estimator as well as a basic knowledge of the test theory, so that work on the book can start after an introductory lecture on stochastics. Each chapter includes exercises. An exhaustive treatment is recommended. Chapter 7 (case study) deals with a practical case and demonstrates the presented methods. It is possible to use this chapter independent in a seminar or practical training course, if the concepts of time series analysis are already well understood. This book is consecutively subdivided in a statistical part and an SAS-specific part. For better clearness the SAS-specific parts are highlighted. This book is an open source project under the GNU Free Documentation License