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Symmetry-protected topological crystalline insulators (TCIs) have primarily been characterized by their gapless boundary states. However, in time-reversal- ($${{{{{{{\mathcal{T}}}}}}}}$$$T$-) invariant (helical) 3D TCIs—termed higher-order TCIs (HOTIs)—the boundary signatures can manifest as a sample-dependent network of 1D hinge states. We here introduce nested spin-resolved Wilson loops and layer constructions as tools to characterize the intrinsic bulk topological properties of spinful 3D insulators. We discover that helical HOTIs realize one of three spin-resolved phases with distinct responses that are quantitatively robust to large deformations of the bulk spin-orbital texture: 3D quantum spin Hall insulators (QSHIs), “spin-Weyl” semimetals, and$${{{{{{{\mathcal{T}}}}}}}}$$$T$-doubled axion insulator (T-DAXI) states with nontrivial partial axion angles indicative of a 3D spin-magnetoelectric bulk response and half-quantized 2D TI surface states originating from a partial parity anomaly. Using ab-initio calculations, we demonstrate thatβ-MoTe₂realizes a spin-Weyl state and thatα-BiBr hosts both 3D QSHI and T-DAXI regimes.

Islamophobia, a negative predilection towards the Muslim community, is present on social media platforms. In addition to causing harm to victims, it also hurts the reputation of social media platforms that claim to provide a safe online environment for all users. The volume of social media content is impossible to be manually reviewed, thus, it is important to find automated solutions to combat hate speech on social media platforms. Machine learning approaches have been used in the literature as a way to automate hate speech detection. In this paper, we use deep learning techniques to detect Islamophobia over Reddit and topic modeling to analyze the content and reveal topics from comments identified as Islamophobic. Some topics we identified include the Islamic dress code, religious practices, marriage, and politics. To detect Islamophobia, we used deep learning models. The highest performance was achieved with BERTbase+CNN, with an F1-Score of 0.92.

Previous research has documented the existence of both online echo chambers and hostile intergroup interactions. In this paper, we explore the relationship between these two phenomena by studying the activity of 5.97M Reddit users and 421M comments posted over 13 years. We examine whether users who are more engaged in echo chambers are more hostile when they comment on other communities. We then create a typology of relationships between political communities based on whether their users are toxic to each other, whether echo chamber-like engagement with these communities has a polarizing effect, and on the communities' political leanings. We observe both the echo chamber and hostile intergroup interaction phenomena, but neither holds universally across communities. Contrary to popular belief, we find that polarizing and toxic speech is more dominant between communities on the same, rather than opposing, sides of the political spectrum, especially on the left; however, this mostly points to the collective targeting of political outgroups.