Binary response experiments are common in scientific studies. However, the study of optimal designs in this area is in a very underdeveloped stage. Sitter and Torsney (1995a) studied optimal designs for binary response experiments with two design variables. In this paper, we consider a general situation with multiple design variables. A novel approach is proposed to identify optimal designs for the commonly used multi-factor logistic and probit models. We give explicit formulas for a large class of optimal designs, including D-, A-, and E-optimal designs. In addition, we identify the general structure of optimal designs, which has a relatively simple format. This property makes it feasible to solve seemingly intractable problems. This result can also be applied in a multi-stage approach.

Obesity is associated with a number of health problems, especial insulin resistance and Type 2 diabetes. Our previous study showed that obese males had decreased neural activity in the orbital frontal cortex (OFC) and increased activity in the left putamen (Zhang et al., 2015b), which could indicate altered eating behaviors in obesity related to a hyper-functioning striatum and hypo-functioning inhibitory control. Accordingly, our goal of the current study was to determine whether there are alterations in the brain structures within these two neural systems in obese individuals. Twenty obese men (age: 20–28 years) and 20 age-matched lean male subjects were involved in the current study. Plasma glucose and insulin were tested during hunger state, and homeostasis model assessment of insulin resistance (HOMA-IR) was based on the blood samples. In the study, we used structural MRI and a voxel-based morphometry (VBM) method to investigate regional structures in obese subjects and find out whether there are correlations between the insulin and the brain structures. We found that obese men only showed a significantly increased gray matter volume (GMV) in the left putamen and that the GMV of the left putamen was positively correlated with body mass index, plasma insulin and HOMA-IR. The putamen is a core region participating in insulin signal regulation, and our results showed an abnormal GMV of the putamen is a core alternation in aberrant insulin. Furthermore, the GMV of the OFC was negatively correlated with hunger rating, despite there being no significant difference between the two groups in the OFC. In conclusion, the altered structure and function of the putamen could play important roles in obesity and aberrant insulin.

Abstract:The periodic impulse feature is the most typical fault signature of the vibration signal from fault rolling element bearings (REBs). However, it is easily contaminated by noise and interference harmonics. In order to extract the incipient impulse feature from the fault vibration signal, this paper presented an autocorrelation function periodic impulse harmonic to noise ratio (ACFHNR) index based on the SVD-Teager energy operator (TEO) method. Firstly, the Hankel matrix is constructed based on the raw vibration fault signal of rolling bearing, and the SVD method is used to obtain the singular components. Afterwards, the ACFHNR index is employed to measure the abundance of the periodic impulse fault feature for the singular components, and the component with the largest ACFHNR index value is extracted. Moreover, the properties of the ACFHNR index are demonstrated by simulations and the full life cycle of the experiment, showing its superiority over the traditional kurtosis and root mean square (RMS) index for extracting and detecting incipient periodic impulse features. Finally, the Teager energy operator spectrum of the extracted informative signal is gained. The simulation and experimental results indicated that the proposed ACFHNR index based method can effectively detect the incipient fault feature of the rolling bearing, and it shows better performance than the kurtosis and RMS index based methods.Keywords: rolling element bearings (REBs); singular value decomposition (SVD); autocorrelation function impulse harmonic to noise ratio (ACFHNR); teager energy operator (TEO)

No abstract