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Metric Spaces Of Non Positive Curvature

This paper presents an opportunity for the uncertainty that has plagued the novel's criticism to appear as absences in the body of historical knowledge, particularly regarding the notion of life after death. Taking appearance (eg. proof of existence), as opposed to disappearance, as a universally accepted value allows this analysis to interrogate the novel's logic in relation to a variety of conventional systems whose very existence depends on the reproduction of their systems. The ineffectuality of Foucauldian disciplinary institutions in the novel establishes the threat of nonexistence. A significant relationship to Dante's Inferno is rendered, lending the appearance of language an 'enchanted' value through allusions to Dante's intentional invocation of Augustinian corporeal vision. The novel's metalanguage appears enchanted by the body of historical knowledge, particularly as the product of capitalism, discipline and Judeo-Christianity, and programmed by literary precursors William S. Burroughs, Gertrude Stein and Ernest Hemingway. Foregrounded by this complex network, an analysis of the novel’s first chapter demonstrates how an attention to appearance brings the language to life and draws the narrator, equally invested in appearance, into its realm of representation.

Will To Appear

Bounded cohomology of subgroups of mapping class groups (双曲空間及び離散群の研究 研究集会報告集)

As demonstrated by Croke and Kleiner, the visual boundary of a CAT(0) group is not well-defined since quasi-isometric CAT(0) spaces can have non-homeomorphic boundaries. We introduce a new type of boundary for a CAT(0) space, called the contracting boundary, made up rays satisfying one of five hyperbolic-like properties. We prove that these properties are all equivalent and that the contracting boundary is a quasi-isometry invariant. We use this invariant to distinguish the quasi-isometry classes of certain right-angled Coxeter groups.

Contracting boundaries of CAT(0) spaces

Background: The mental health impact of the COVID-19 crisis may differ from previously studied stressful events in terms of psychological reactions, specific risk factors, and symptom severity across geographic regions worldwide. Objective: To assess the impact of COVID-19 on a wide range of mental health symptoms, to identify relevant risk factors, to identify the effect of COVID-19 country impact on mental health, and to evaluate regional differences in psychological responses to COVID-19 compared to other stressful events. Method: 7034 respondents (74% female) participated in the worldwide Global Psychotrauma Screen - Cross-Cultural responses to COVID-19 study (GPS-CCC), reporting on mental health symptoms related to COVID-19 (n = 1838) or other stressful events (n = 5196) from April to November 2020. Results: Events related to COVID-19 were associated with more mental health symptoms compared to other stressful events, especially symptoms of PTSD, anxiety, depression, insomnia, and dissociation. Lack of social support, psychiatric history, childhood trauma, additional stressful events in the past month, and low resilience predicted more mental health problems for COVID-19 and other stressful events. Higher COVID-19 country impact was associated with increased mental health impact of both COVID-19 and other stressful events. Analysis of differences across geographic regions revealed that in Latin America more mental health symptoms were reported for COVID-19 related events versus other stressful events, while the opposite pattern was seen in North America. Conclusions: The mental health impact of COVID-19-related stressors covers a wide range of symptoms and is more severe than that of other stressful events. This difference was especially apparent in Latin America. The findings underscore the need for global screening for a wide range of mental health problems as part of a public health approach, allowing for targeted prevention and intervention programs.

https://www.tandfonline.com/doi/pdf/10.1080/20008198.2021.1929754

Mental health responses to COVID-19 around the world.

Turning wounds into wisdom: Posttraumatic growth over the course of two types of trauma-focused psychotherapy in patients with PTSD

To every Gromov hyperbolic space X one can associate a space at infinity called the Gromov boundary of X. Gromov showed that quasi-isometries of hyperbolic metric spaces induce homeomorphisms on their boundaries, thus giving rise to a well-defined notion of the boundary of a hyperbolic group. Croke and Kleiner showed that the visual boundary of non-positively curved (CAT(0)) groups is not well-defined, since quasi-isometric CAT(0) spaces can have non-homeomorphic boundaries. For any sublinear function $\kappa$, we consider a subset of the visual boundary called the $\kappa$-Morse boundary and show that it is QI-invariant and metrizable. This is to say, the $\kappa$-Morse boundary of a CAT(0) group is well-defined. In the case of Right-angled Artin groups, it is shown in the Appendix that the Poisson boundary of random walks is naturally identified with the $\sqrt{t \log t}$--boundary.

Sublinearly Morse Boundary I: CAT(0) Spaces

Subspace intersection graphs

We build an analogue of the Gromov boundary for any proper geodesic metric space, hence for any finitely generated group. More precisely, for any proper geodesic metric space $X$ and any sublinear function $\kappa$, we construct a boundary for $X$, denoted $\mathcal{\partial}_{\kappa} X$, that is quasi-isometrically invariant and metrizable. As an application, we show that when $G$ is the mapping class group of a finite type surface, or a relatively hyperbolic group, then with minimal assumptions the Poisson boundary of $G$ can be realized on the $\kappa$-Morse boundary of $G$ equipped the word metric associated to any finite generating set.

Yulan Qing

Papers

Mental health responses to COVID-19 around the world.

Turning wounds into wisdom: Posttraumatic growth over the course of two types of trauma-focused psychotherapy in patients with PTSD

Sublinearly Morse Boundary I: CAT(0) Spaces

Subspace intersection graphs

Sublinearly Morse Boundary II: Proper geodesic spaces