Exploring the Optimal Choice for Generative Processes in Diffusion Models: Ordinary vs Stochastic Differential Equations

The diffusion model has shown remarkable success in computer vision, but it remains unclear whether ODE-based probability flow or SDE-based diffusion models are superior and under what circumstances. Comparing the two is challenging due to dependencies on data distribution, score training, and other numerical factors. In this paper, we examine the problem mathematically by examining two limiting scenarios: the ODE case and the large diffusion case. We first introduce a pulse-shape error to perturb the score function and analyze error accumulation, with a generalization to arbitrary error. Our findings indicate that when the perturbation occurs at the end of the generative process, the ODE model outperforms the SDE model (with a large diffusion coefficient). However, when the perturbation occurs earlier, the SDE model outperforms the ODE model, and we demonstrate that the error of sample generation due to pulse-shape error can be exponentially suppressed as the diffusion term's magnitude increases to infinity. Numerical validation of this phenomenon is provided using toy models such as Gaussian, Gaussian mixture models, and Swiss roll. Finally, we experiment with MNIST and observe that varying the diffusion coefficient can improve sample quality even when the score function is not well trained

Standard metabolic rate predicts growth trajectory of juvenile Chinese crucian carp (Carassius auratus) under changing food availability

Phenotypic traits vary greatly within populations and can have a significant influence on aspects of performance. The present study aimed to investigate the effects of individual variation in standard metabolic rate (SMR) on growth rate and tolerance to food-deprivation in juvenile crucian carp (Carassius auratus) under varying levels of food availability. To address this issue, 19 high and 16 low SMR (individuals were randomly assigned to a satiation diet for 3 weeks, whereas another 20 high and 16 low SMR individuals were assigned to a restricted diet (approximately 50% of satiation) for the same period. Then, all fish were completely food-deprived for another 3 weeks. High SMR individuals showed a higher growth rate when fed to satiation, but this advantage of SMR did not exist in food-restricted fish. This result was related to improved feeding efficiency with decreased food intake in low SMR individuals, due to their low food processing capacity and maintenance costs. High SMR individuals experienced more mass loss during food-deprivation as compared to low SMR individuals. Our results here illustrate context-dependent costs and benefits of intraspecific variation in SMR whereby high SMR individuals show increased growth performance under high food availability but had a cost under stressful environments (i.e., food shortage)

An Improved Direct Torque Control for a Single-Winding Bearingless Switched Reluctance Motor

The direct torque control (DTC) and direct force control (DFC) method were introduced to reduce the torque and levitation force ripple in single-winding bearingless switched reluctance motors (SWBSRMs). However, it still has some disadvantages. Firstly, the flux-linkage control is not suitable for the DTC method in SWBSRMs. On the one hand, it can increase the torque ripple. On the other hand, the RMS current can be increased and then the torque-ampere ratio is decreased. Secondly, the vectors selection is also unreasonable, which can increase the torque ripple further. In order to solve these problems, an improved control method based on DTC and DFC method for SWBSRMs is proposed in this paper, which can obtain high torque-ampere ratio and low torque ripple simultaneously. In the proposed method, the flux-linkage loop control is not needed and the space voltage vector table is improved. The experimental results show that the torque ripple is reduced by 66.7%, the torque-ampere ratio is increased by 200% and the switching times in one electrical period are reduced by 47.3%

Hyperon polarization and its correlation with directed flow in high-energy nuclear collisions

We investigate the hyperon polarization and its correlation with the directed flow of the quark-gluon plasma (QGP) in non-central Au+Au collisions at $\sqrt{s_{\textrm{NN}}} = 27$ GeV. A modified 3-dimensional (3D) Glauber model is developed and coupled to a (3+1)-D viscous hydrodynamic evolution of the QGP. Within this framework, we obtain a satisfactory simultaneous description of the directed flow of identified particles and $\Lambda$ polarization, and show sensitivity of polarization to both the tilted geometry and the longitudinal flow profile of the QGP. A non-monotonic transverse momentum dependence of the $\Lambda$ polarization is found in our calculation, which is absent from hydrodynamic simulation using other initialization methods and can be tested by future experimental data with higher precision. A strong correlation (or anti-correlation) is found between the global polarization and directed flow of $\Lambda$ when the longitudinal flow field (or medium deformation) varies, indicating the common origin of these two quantities. Therefore, a combination of these observables may provide a more stringent constraint on the initial condition of the QGP.Comment: 15 pages, 12 figures, any comments are welcom

Prevalence and Associated Factors of Elder Mistreatment in a Rural Community in People's Republic of China: A Cross-Sectional Study

Background: Current knowledge about elder mistreatment is mainly derived from studies done in Western countries, which indicate that this problem is related to risk factors such as a shared living situation, social isolation, disease burden, and caregiver strain. We know little about prevalence and risk factors for elder mistreatment and mistreatment subtypes in rural China where the elder population is the most vulnerable. Methods: In 2010, we conducted a cross-sectional survey among older adults aged 60 or older in three rural communities in Macheng, a city in Hubei province, China. Of 2245 people initially identified, 2039 were available for interview and this was completed in 2000. A structured questionnaire was used to collect data regarding mistreatment and covariates. Logistic regression analysis was used to identify factors related to elder mistreatment and subtypes of mistreatment. Results: Elder mistreatment was reported by 36.2 % (95 % CI: 34.1%–38.3%) of the participants. Prevalence rates of psychological mistreatment, caregiver neglect, physical mistreatment, and financial mistreatment were 27.3 % (95 % CI