The world problem: on the computability of the topology of 4-manifolds

Topological classification of the 4-manifolds bridges computation theory and physics. A proof of the undecidability of the homeomorphy problem for 4-manifolds is outlined here in a clarifying way. It is shown that an arbitrary Turing machine with an arbitrary input can be encoded into the topology of a 4-manifold, such that the 4-manifold is homeomorphic to a certain other 4-manifold if and only if the corresponding Turing machine halts on the associated input. Physical implications are briefly discussed.Comment: Submitted to Class. Quant. Gra

Coping Methods that Predict Reduced Symptoms of Posttraumatic Stress Disorder (PTSD)

Objective: Most individuals experience a stressful event at some point in their lives. A third to half of those individuals will meet criteria for Posttraumatic Stress Disorder (PTSD) during their lifetime. Individuals that do not develop PTSD likely have better coping skills regarding trauma. Targeting specific coping strategies that reduce PTSD symptoms helps mental health professionals and providers create interventions and prevention skills. Method: Eighty-four participants from a university took an online survey. Demographic information were gathered. Questionnaires were given to determine if the participant had experienced one or more traumatic events. Next, a questionnaire that measured the extent that participants endorsed symptoms of PTSD. Finally, participants completed coping questionnaires looking at different types of coping. Results: Results found an increase in all coping methods, both positive and negative, when there was an increase in PTSD symptomology. Results also showed higher PTSD symptomology, coping, and higher levels of both positive and negative religious coping for those who provided trauma anecdotes when compared to those who did not. Women endorsed more positive coping, religious coping and positive religious coping than men. About half of the variance in traumatic experiences was accounted for by TLEQ, ACE, and Negative Coping. Conclusions: Individuals are more likely to engage in all types of coping when experiencing PTSD symptomology. Individuals who provided anecdotal information about trauma tended to show more distress and coping efforts compared to those who do not. Finally, women were more prone to report increased use of coping methods