Enhancing Population Persistence by a Protection Zone in a Reaction-Diffusion Model with Strong Allee Effect

Protecting endangered species has been an important issue in ecology. We derive a reaction-diffusion model for a population in a one-dimensional bounded habitat, where the population is subjected to a strong Allee effect in its natural domain but obeys a logistic growth in a protection zone. We establish the conditions for population persistence and extinction via the principal eigenvalue of an associated eigenvalue problem and investigate the dependence of this principal eigenvalue on the location (i.e., the starting point and the length) of the protection zone. The results are used to design the optimal protection zone under different boundary conditions, that is, to suggest the starting point and length of the protection zone with respect to different population growth rate in the protection zone, in order for the population to persist in a long term

破裂颅内动脉瘤的超早期血管内介入治疗

Objective: To explore the clinic significance of endovascular treatment of  ruptured intracranial aneurysms in super-early stage. Methods: Endovascular treatment of 53 cases of ruptured intracranial aneurysms,including first ruptured in 42 cases and 11 cases of ruptured twice, were performed using GDC and stent assisted GDC embolization, 29 cases in 2 days and 24 cases in more than two days after ruptured. And it was divided into the ultra-early group and the non-ultra-early group. The locations of aneurysms were as following: 20 cases in posterior communicating artery, 15 cases in anterior communicating artery, 3 cases in Ophthalmic artery, 4 cases in internal carotid artery, 6 cases in vertebral artery, and 3 cases in posterior inferior cerebellar artery; Hess-Hunt grade was as follows: 9 cases of gradeⅠ, 25 cases of grade Ⅱ,13 cases of grade Ⅲ, 6 cases of grade Ⅳ.Results:  According to the investigation among 59 aneurysms from 6 months to 60 months after operation, good recovery rate of the ultra-early group and the non-ultra-early group were respectively 96.55% and 79.17%.There was a significant difference between the two groups, and non-ultra-early group is worse, P value is less than 0.05.Conclusion: Endovascular embolization is an effective treatment for ruptured intracranial aneurysms in super-early stage.目的 探讨破裂颅内动脉瘤超早期血管内栓塞治疗的临床意义。方法 通过对53 例以自发性蛛网膜下腔出血急诊入院，包括首次破裂42例，2次破裂11例，确诊为颅内动脉瘤破裂病例采用GDC或支架辅助GDC的血管内栓塞治疗，29例于2天内、24例于2天及2天以上治疗，并分为超早期组29例和非超早期组24例。其中后交通动脉瘤20枚，前交通动脉瘤15枚，大脑中动脉瘤5枚，大脑前动脉瘤3枚，眼动脉瘤3枚，颈内动脉瘤4枚，椎动脉瘤6枚，小脑后下动脉瘤3枚；按Hess-Hunt分级：Ⅰ级9例，Ⅱ级25例，Ⅲ级13例，Ⅳ级6例。结果 随访6～60个月，超早期组和非超早期组恢复良好率分别为：96.55%，79.17%，非超早期组预后较差，两组之间比较差异有统计学意义（P＜0.05）。结论 采用超早期血管内栓塞是一种治疗破裂颅内动脉瘤的有效方法。

Continuum field theory of 3D topological orders with emergent fermions and braiding statistics

Universal topological data of topologically ordered phases can be captured by topological quantum field theory in continuous space time by taking the limit of low energies and long wavelengths. While previous continuum field-theoretical studies of topological orders in $3$D real space focus on either self-statistics, braiding statistics, shrinking rules, fusion rules or quantum dimensions, it is yet to systematically put all topological data together in a unified continuum field-theoretical framework. Here, we construct the topological $BF$ field theory with twisted terms (e.g., $AAdA$ and $AAB$) as well as a $K$-matrix $BB$ term, in order to simultaneously explore all such topological data and reach anomaly-free topological orders. Following the spirit of the famous $K$-matrix Chern-Simons theory of $2$D topological orders, we present general formulas and systematically show how the $K$-matrix $BB$ term confines topological excitations, and how self-statistics of particles is transmuted between bosonic one and fermionic one. In order to reach anomaly-free topological orders, we explore, within the present continuum field-theoretical framework, how the principle of gauge invariance fundamentally influences possible realizations of topological data. More concretely, we present the topological actions of (i) particle-loop braidings with emergent fermions, (ii) multiloop braidings with emergent fermions, and (iii) Borromean-Rings braidings with emergent fermions, and calculate their universal topological data. Together with the previous efforts, our work paves the way toward a more systematic and complete continuum field-theoretical analysis of exotic topological properties of $3$D topological orders. Several interesting future directions are also discussed