We present Keck/DEIMOS spectroscopy of the first complete sample of ultradiffuse galaxies (UDGs) in the Virgo cluster. We select all UDGs in Virgo that contain at least 10 globular cluster (GC) candidates and are more than 2.5σ outliers in scaling relations of size, surface brightness, and luminosity (a total of 10 UDGs). We use the radial velocity of their GC satellites to measure the velocity dispersion of each UDG. We find a mixed bag of galaxies, from one UDG that shows no signs of dark matter, to UDGs that follow the luminosity–dispersion relation of early-type galaxies, to the most extreme examples of heavily dark matter–dominated galaxies that break well-known scaling relations such as the luminosity–dispersion or U-shaped total mass-to-light ratio relations. This is indicative of a number of mechanisms at play forming these peculiar galaxies. Some of them may be the most extended version of dwarf galaxies, while others are so extreme that they seem to populate dark matter halos consistent with that of the Milky Way or even larger. Even though Milky Way stars and other GC interlopers contaminating our sample of GCs cannot be fully ruled out, our assessment of this potential problem and simulations indicate that the probability is low and, if present, unlikely to be enough to explain the extreme dispersions measured. Further confirmation from stellar kinematics studies in these UDGs would be desirable. The lack of such extreme objects in any of the state-of-the-art simulations opens an exciting avenue of new physics shaping these galaxies.

The application effect of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) based on the improved fuzzy C-mean clustering (GA-PFCM) algorithm in analyzing premenopausal and postmenopausal invasive breast carcinoma was discussed. 159 patients with breast carcinoma were selected and divided into the postmenopausal group (71 patients) and the premenopausal group (88 patients) according to their menstrual status. The magnetic resonance images of the two groups were processed and analyzed using GA-PFCM algorithm, and the imaging characteristics and relevant parameters of DCE-MRI examination of the two groups were analyzed. Besides, the sensitivity, specificity, and accuracy of the diagnosis of invasive breast carcinoma by DCE-MRI examination were investigated. The results showed that the percentage of patients with lobulated lumps, patients with burrs on lesion edge, and patients with uniformly enhanced tumors in the premenopausal group was larger than that in the postmenopausal group ( P < 0.05 ). In the postmenopausal group, TCI of 33 patients was shown as platform curves, and that of 34 patients was shown as outflow curves. In the premenopausal group, TCI of 39 patients was shown as platform curves, and that of 41 patients was shown as outflow curves with a high proportion. The number of patients with peak height time ranging between 130 s and 260 s and of patients with early signal enhancement rate ranging between 100% and 200% was large. In contrast, the number of patients with ADC value higher than 1.2 × 10 − 3 was the least. In this research, there were 128 patients with positive invasive breast carcinoma and 31 with negative invasive breast carcinoma by pathological examination. Based on DCE-MRI examination, there were 121 patients with positive invasive breast carcinoma and 38 with negative invasive breast carcinoma. The sensitivity, specificity, and accuracy of invasive breast carcinoma by DCE-MRI were 91.41%, 87.1%, and 90.57%, respectively. In addition, the positive and negative predictive values reached 96.69% and 71.05%, respectively. In summary, GA-PFCM algorithm can be applied in the processing and segmentation of DCE-MRI images, and DCE-MRI could better diagnose invasive breast carcinoma with positive guiding value.