On Variable Ordination of Modified Cholesky Decomposition for Sparse Covariance Matrix Estimation

Estimation of large sparse covariance matrices is of great importance for statistical analysis, especially in the high-dimensional settings. The traditional approach such as the sample covariance matrix performs poorly due to the high dimensionality. The modified Cholesky decomposition (MCD) is a commonly used method for sparse covariance matrix estimation. However, the MCD method relies on the order of variables, which is often not available or cannot be pre-determined in practice. In this work, we solve this order issue by obtaining a set of covariance matrix estimates under different orders of variables used in the MCD. Then we consider an ensemble estimator as the "center" of such a set of covariance matrix estimates with respect to the Frobenius norm. The proposed method not only ensures the estimator to be positive definite, but also can capture the underlying sparse structure of the covariance matrix. Under some weak regularity conditions, we establish both algorithmic convergence and asymptotical convergence of the proposed method. The merits of the proposed method are illustrated through simulation studies and one real data example

On Block Cholesky Decomposition for Sparse Inverse Covariance Estimation

The modified Cholesky decomposition is popular for inverse covariance estimation, but often needs pre-specification on the full information of variable ordering. In this work, we propose a block Cholesky decomposition (BCD) for estimating inverse covariance matrix under the partial information of variable ordering, in the sense that the variables can be divided into several groups with available ordering among groups, but variables within each group have no orderings. The proposed BCD model provides a unified framework for several existing methods including the modified Cholesky decomposition and the Graphical lasso. By utilizing the partial information on variable ordering, the proposed BCD model guarantees the positive definiteness of the estimated matrix with statistically meaningful interpretation. Theoretical results are established under regularity conditions. Simulation and case studies are conducted to evaluate the proposed BCD model

Optimization of the Fermentation Process of Actinomycete Strain Hhs.015T

Strain Hhs.015T (Saccharothrix yanglingensis sp. nov.), an antagonistic endophytic Saccharothrix actinomycete isolated from roots of cucumber plants, exhibited a broad antimicrobial spectrum in vitro and was active as a biocontrol against plant diseases in field trials. The SSY medium was used for production of antimicrobial metabolites by strain Hhs.015T. However, this medium is too expensive for large-scale production. In this study, an alternative culture medium, based on agricultural waste products (e.g., apple pomace), was optimized. The results showed that the alternative medium contained 15 g apple pomace, 4 g rapeseed meal, 0.1 g KH2PO4, and 0.6 g MgSO4·7H2O in 1 L distilled water. This medium reduced the material costs by 91.5% compared to SSY medium. Response surface methodology (RSM) was used to investigate the influence of environmental variables on production of compounds of antimicrobial metabolites. The optimal conditions achieved were initial pH 7.0, medium volume of 90 mL in 250 mL flasks, rotary speed of 100 rpm, temperature 25°C, and inoculation volume of 15.8%. The antimicrobial activity was increased by 20% by optimizing the environmental parameters. The results obtained allow an efficient production of components with antimicrobial activity by strain Hhs.015T on a large scale at low costs

Real-Time Track Reallocation for Emergency Incidents at Large Railway Stations

After track capacity breakdowns at a railway station, train dispatchers need to generate appropriate track reallocation plans to recover the impacted train schedule and minimize the expected total train delay time under stochastic scenarios. This paper focuses on the real-time track reallocation problem when tracks break down at large railway stations. To represent these cases, virtual trains are introduced and activated to occupy the accident tracks. A mathematical programming model is developed, which aims at minimizing the total occupation time of station bottleneck sections to avoid train delays. In addition, a hybrid algorithm between the genetic algorithm and the simulated annealing algorithm is designed. The case study from the Baoji railway station in China verifies the efficiency of the proposed model and the algorithm. Numerical results indicate that, during a daily and shift transport plan from 8:00 to 8:30, if five tracks break down simultaneously, this will disturb train schedules (result in train arrival and departure delays)

Multistage Force Amplification of Piezoelectric Stacks

Embodiments of the disclosure include an apparatus and methods for using a piezoelectric device, that includes an outer flextensional casing, a first cell and a last cell serially coupled to each other and coupled to the outer flextensional casing such that each cell having a flextensional cell structure and each cell receives an input force and provides an output force that is amplified based on the input force. The apparatus further includes a piezoelectric stack coupled to each cell such that the piezoelectric stack of each cell provides piezoelectric energy based on the output force for each cell. Further, the last cell receives an input force that is the output force from the first cell and the last cell provides an output apparatus force In addition, the piezoelectric energy harvested is based on the output apparatus force. Moreover, the apparatus provides displacement based on the output apparatus force

A novel traveling-wave-based protection scheme for LCC-HVDC systems using Teager Energy Operator

Line Commutated Converter (LCC) based High-Voltage Direct Current (HVDC) technology has been in operation with a high level reliability and little maintenance requirements for more than thirty years. The current-source based or classical LCC-HVDC systems are being considered for buried cable transmission as well as overhead transmission. The fault analysis and protection of LCC-HVDC system is a very important aspect in terms of power system stability. This paper proposes a novel protection scheme for LCC-HVDC systems, in which the difference between propagation processes of traveling wave under internal and external faults is used as a criterion for detection of fault incidents in HVDC transmission lines. In order to quantify and intensify this difference, Teager Energy Operator (TEO) is used which has the ability to reflect the instantaneous energy of a signal. The main feature of the proposed scheme in comparison with the existing ones is that it operates faster, since it does not require to extract any harmonic or high frequency component; moreover, a 2-ms sampling window is sufficient for its algorithm which only deals with simple calculations. In order to validate the effectiveness of the proposed protection scheme, several fault events under different fault resistances and fault locations were simulated on a test network using PSCAD/EMTDC software. Also, the performance of the proposed scheme under real fault events was tested using four field data cases. Both simulation data and field data test results indicated that the proposed protection strategy has the ability to accurately discriminate between internal and external faults and detect the faulted pole in the bipolar systems even under high-impedance fault conditions