nn-body Correlation of Tonks-Girardeau Gas

For the well-known exponential complexity it is a giant challenge to calculate the correlation function for general many-body wave function. We investigate the ground state $n$th-order correlation functions of the Tonks-Girardeau (TG) gases. Basing on the wavefunction of free fermions and Bose-Fermi mapping method we obtain the exact ground state wavefunction of TG gases. Utilizing the properties of Vandermonde determinant and Toeplitz matrix, the $n$th-order correlation function is formulated as $(N-n)$-order Toeplitz determinant, whose element is the integral dependent on 2$(N-n)$ sign functions and can be computed analytically. By reducing the integral on domain $[0,2\pi]$ into the summation of the integral on several independent domains, we obtain the explicit form of the Toeplitz matrix element ultimately. As the applications we deduce the concise formula of the reduced two-body density matrix and discuss its properties. The corresponding natural orbitals and their occupation distribution are plotted. Furthermore, we give a concise formula of the reduced three-body density matrix and discuss its properties. It is shown that in the successive second measurements, atoms appear in the regions where atoms populate with the maximum probability in the first measurement.Comment: 8 pages, 7 figure

A Differentially Private Weighted Empirical Risk Minimization Procedure and its Application to Outcome Weighted Learning

It is commonplace to use data containing personal information to build predictive models in the framework of empirical risk minimization (ERM). While these models can be highly accurate in prediction, results obtained from these models with the use of sensitive data may be susceptible to privacy attacks. Differential privacy (DP) is an appealing framework for addressing such data privacy issues by providing mathematically provable bounds on the privacy loss incurred when releasing information from sensitive data. Previous work has primarily concentrated on applying DP to unweighted ERM. We consider an important generalization to weighted ERM (wERM). In wERM, each individual's contribution to the objective function can be assigned varying weights. In this context, we propose the first differentially private wERM algorithm, backed by a rigorous theoretical proof of its DP guarantees under mild regularity conditions. Extending the existing DP-ERM procedures to wERM paves a path to deriving privacy-preserving learning methods for individualized treatment rules, including the popular outcome weighted learning (OWL). We evaluate the performance of the DP-wERM application to OWL in a simulation study and in a real clinical trial of melatonin for sleep health. All empirical results demonstrate the viability of training OWL models via wERM with DP guarantees while maintaining sufficiently useful model performance. Therefore, we recommend practitioners consider implementing the proposed privacy-preserving OWL procedure in real-world scenarios involving sensitive data.Comment: 24 pages and 2 figures for the main manuscript, 5 pages and 2 figures for the supplementary material

Novel hybrid vacuum/triple glazing units with pressure equalisation design

AbstractVacuum glazing units (VGUs) are thought to be a type of glazing system with superior effective insulation performance. However, the differential pressure between the outside and the inner spaces and the supporting pillars create a high pre-existing stress field in the constituent glass during fabrication and hence make the units highly susceptible to breakage, even under small applied loads. In order to address this problem, a novel hybrid vacuum/triple glazing system with a pressure equalisation design has been devised and is reported in this paper. In this system, a VGU is enclosed by two glass panels to form a triple glazing unit system. This new design creates an equalised air pressure on both sides of the VGU hence subjects the VGU to no additional loads apart from the inherent fabrication stresses. This results in a high thermal and sound insulation as well as a more durable safety performance of the hybrid glazing component. Pressure tests were undertaken on the novel glazing system to confirm its reliability. Results show that under various loading levels, the stresses and deflections in the VGU of this novel glazing system always remain at a marginal level, and hence the likelihood of breakage for VGUs can be reduced significantly

Spine surgeon specialty differences in single-level percutaneous kyphoplasty

Background Percutaneous kyphoplasty (PKP) is a procedure performed by a spine surgeon who undergoes either orthopedic or neurosurgical training. The relationship between short-term adverse outcomes and spine specialty is presently unknown. To compare short-term adverse outcomes of single-level PKP when performed by neurosurgeons and orthopedic surgeons in order to develop more concretely preventive strategies for patients under consideration for single-level PKP. Methods We evaluated patients who underwent single-level PKP from 2012 to 2014 through the American College of Surgeons National Surgical Quality Improvement Program (ACS NSQIP). We used univariate analysis and multivariate logistic regression to assess the association between spine surgeon specialty and short-term adverse events, including postoperative complication and unplanned readmission, and to identify different independent risk predictors between two specialties. Results Of 2248 patients who underwent single-level PKP procedure, 1229 patients (54.7%) had their operations completed by a neurosurgeon. There were no significant differences in the development of the majority of postoperative complications and the occurrence of unplanned readmission between the neurosurgical cohort (NC) and the orthopedic cohort (OC). A difference in the postoperative blood transfusion rate (0.7% NS vs. 1.7% OC, P = 0.039) was noted and may due to the differences in comorbidities between patients. Multivariate regression analysis revealed different independent predictors of postoperative adverse events for the two spine specialties. Conclusions By comparing a large range of demographic feature, preoperative comorbidities, and intraoperative factors, we find that short-term adverse events in single-level PKP patients does not affect by spine surgeon specialty, except that the OC had higher postoperative blood transfusion rate. In addition, the different perioperative predictors of postoperative complications and unplanned readmissions were identified between the two specialties. These findings can lead to better evidence-based patient counseling and provide valuable information for medical evaluation and potentially devise methods to reduce patients’ risk

Vertex Combination Method for Heat Transfer Analysis of Structures with Uncertain Parameters

Uncertainty is wide-spreads in practical projects which can be solved by interval method. Regarding the temperature field prediction of structures with uncertain parameters, a vertex combination method is presented on the basis of the sampling according to the vertex combinations of interval parameters and monotonic relationship of objective function which can effectively reduce the number of boundary combined samples. A numerical example of heat transfer problems of a panel without thermal resource is used to verify the effectiveness of the proposed method

Vertex Combination Method for Heat Transfer Analysis of Structures with Uncertain Parameters

Uncertainty is wide-spreads in practical projects which can be solved by interval method. Regarding the temperature field prediction of structures with uncertain parameters, a vertex combination method is presented on the basis of the sampling according to the vertex combinations of interval parameters and monotonic relationship of objective function which can effectively reduce the number of boundary combined samples. A numerical example of heat transfer problems of a panel without thermal resource is used to verify the effectiveness of the proposed method

The Alternating Direction Implicit Body of Revolution Multiresolution Time Domain Method with Convolution Perfect Matched Layer

Overmuch memory and time of CPU have been taken by multiresolution time domain (MRTD) method in three-dimension issues. In order to solve this problem, the alternating direction implicit body of revolution multiresolution time domain (ADI-BOR-MRTD) scheme is presented. Firstly, based on body of revolution finite difference time domain (BOR-FDTD) method, equations of body of revolution multiresolution time domain (BOR-MRTD) method are implemented. Then alternating direction implicit (ADI) is introduced into BOR-MRTD method. Lastly, convolution perfect matched layer (CPML) is applied for ADI-BOR-MRTD method. Numerical results demonstrate that ADI-BOR-MRTD method saves more memory and time of CPU than FDTD and MRTD methods