Average R\'{e}nyi Entropy of a Subsystem in Random Pure State

In this paper we examine the average R\'{e}nyi entropy $S_{\alpha}$ of a subsystem $A$ when the whole composite system $AB$ is a random pure state. We assume that the Hilbert space dimensions of $A$ and $AB$ are $m$ and $m n$ respectively. First, we compute the average R\'{e}nyi entropy analytically for $m = \alpha = 2$. We compare this analytical result with the approximate average R\'{e}nyi entropy, which is shown to be very close. For general case we compute the average of the approximate R\'{e}nyi entropy $\widetilde{S}_{\alpha} (m,n)$ analytically. When $1 \ll n$, $\widetilde{S}_{\alpha} (m,n)$ reduces to $\ln m - \frac{\alpha}{2 n} (m - m^{-1})$, which is in agreement with the asymptotic expression of the average von Neumann entropy. Based on the analytic result of $\widetilde{S}_{\alpha} (m,n)$ we plot the $\ln m$-dependence of the quantum information derived from $\widetilde{S}_{\alpha} (m,n)$. It is remarkable to note that the nearly vanishing region of the information becomes shorten with increasing $\alpha$, and eventually disappears in the limit of $\alpha \rightarrow \infty$. The physical implication of the result is briefly discussed.Comment: 14 pages, 3 figure

Strengthening deep-learning models for intracranial hemorrhage detection: strongly annotated computed tomography images and model ensembles

Background and purposeMultiple attempts at intracranial hemorrhage (ICH) detection using deep-learning techniques have been plagued by clinical failures. We aimed to compare the performance of a deep-learning algorithm for ICH detection trained on strongly and weakly annotated datasets, and to assess whether a weighted ensemble model that integrates separate models trained using datasets with different ICH improves performance.MethodsWe used brain CT scans from the Radiological Society of North America (27,861 CT scans, 3,528 ICHs) and AI-Hub (53,045 CT scans, 7,013 ICHs) for training. DenseNet121, InceptionResNetV2, MobileNetV2, and VGG19 were trained on strongly and weakly annotated datasets and compared using independent external test datasets. We then developed a weighted ensemble model combining separate models trained on all ICH, subdural hemorrhage (SDH), subarachnoid hemorrhage (SAH), and small-lesion ICH cases. The final weighted ensemble model was compared to four well-known deep-learning models. After external testing, six neurologists reviewed 91 ICH cases difficult for AI and humans.ResultsInceptionResNetV2, MobileNetV2, and VGG19 models outperformed when trained on strongly annotated datasets. A weighted ensemble model combining models trained on SDH, SAH, and small-lesion ICH had a higher AUC, compared with a model trained on all ICH cases only. This model outperformed four deep-learning models (AUC [95% C.I.]: Ensemble model, 0.953[0.938–0.965]; InceptionResNetV2, 0.852[0.828–0.873]; DenseNet121, 0.875[0.852–0.895]; VGG19, 0.796[0.770–0.821]; MobileNetV2, 0.650[0.620–0.680]; p < 0.0001). In addition, the case review showed that a better understanding and management of difficult cases may facilitate clinical use of ICH detection algorithms.ConclusionWe propose a weighted ensemble model for ICH detection, trained on large-scale, strongly annotated CT scans, as no model can capture all aspects of complex tasks

Visuomotor anomalies in achiasmatic mice expressing a transfer-defective Vax1 mutant

Vision: bringing the two sides togetherA protein regulating gene expression called Vax1 is essential for building the optic chiasm (OC), a brain structure where nerves from the left and right eyes cross to the other side of the brain. Signals from both eyes must be integrated for space and depth perception. Although some cues guiding optic nerve growth are known, those for the OC are not. Jin Woo Kim at the Korea Advanced Institute of Science and Technology, Daejeon, South Korea, and co-workers investigated visual development in mice expressing a mutant Vax1. They found that the mutant Vax1 could not support the optic nerve, which grew slowly and failed to connect to the other side of the brain. Consequently, the mice had impaired depth perception and low vision. These results show the importance of Vax1 for the development of binocular vision. In binocular animals that exhibit stereoscopic visual responses, the axons of retinal ganglion cells (RGCs) connect to brain areas bilaterally by forming a commissure called the optic chiasm (OC). Ventral anterior homeobox 1 (Vax1) contributes to the formation of the OC, acting endogenously in optic pathway cells and exogenously in growing RGC axons. Here, we generated Vax1(AA/AA) mice expressing the Vax1(AA) mutant, which is incapable of intercellular transfer. We found that RGC axons cannot take up Vax1(AA) protein from the Vax1(AA/AA) mouse optic stalk (OS) and grow slowly to arrive at the hypothalamus at a late stage. The RGC axons of Vax1(AA/AA) mice connect exclusively to ipsilateral brain areas after failing to access the midline, resulting in reduced visual acuity and abnormal oculomotor responses. Overall, our study provides physiological evidence for the necessity of intercellular transfer of Vax1 and the importance of the bilateral RGC axon projection in proper visuomotor responses.11Nsciescopuskc