Traumatic memories: bridging the gap between functional neuroimaging and psychotherapy

Objective: Neuroimaging studies have highlighted important issues related to structural and functional brain changes found in sufferers of psychological trauma that may influence their ability to synthesize, categorize, and integrate traumatic memories. Methods: Literature review and critical analysis and synthesis. Results: Traumatic memories are diagnostic symptoms of post-traumatic stress disorder (PTSD), and the dual representation theory posits separate memory systems subserving vivid re-experiencing (non-hippocampally dependent) versus declarative autobiographical memories of trauma (hippocampally dependent). But the psychopathological signs of trauma are not static over time, nor is the expression of traumatic memories. Multiple memory systems are activated simultaneously and in parallel on various occasions. Neural circuitry interaction is a crucial aspect in the development of a psychotherapeutic approach that may favour an integrative translation of the sensory fragments of the traumatic memory into a declarative memory system. Conclusion: The relationship between neuroimaging findings and psychological approaches is discussed for greater efficacy in the treatment of psychologically traumatized patients.

The analytic torsion of a disc

In this article, we study the Reidemeister torsion and the analytic torsion of the m dimensional disc, with the Ray and Singer homology basis (Adv Math 7:145-210, 1971). We prove that the Reidemeister torsion coincides with a power of the volume of the disc. We study the additional terms arising in the analytic torsion due to the boundary, using generalizations of the Cheeger-Muller theorem. We use a formula proved by Bruning and Ma (GAFA 16:767-873, 2006) that predicts a new anomaly boundary term beside the known term proportional to the Euler characteristic of the boundary (Luck, J Diff Geom 37:263-322, 1993). Some of our results extend to the case of the cone over a sphere, in particular we evaluate directly the analytic torsion for a cone over the circle and over the two sphere. We compare the results obtained in the low dimensional cases. We also consider a different formula for the boundary term given by Dai and Fang (Asian J Math 4:695-714, 2000), and we compare the results. The results of these work were announced in the study of Hartmann et al. (BUMI 2:529-533, 2009).