Pathology of the rhinencephalon has been a subject of interest in the fields of neurodegenerative diseases, trauma, epilepsy and other neurological conditions. Most of what is known about the human rhinencephalon comes from comparative anatomy studies in other mammals and histological studies in primates. Functional imaging studies can provide new and important insight into the function of the rhinencephalon in humans but have limited spatial resolution, limiting its contribution to the study of the anatomy of the human rhinencephalon. In this study we aim to provide a brief and objective review of the anatomy of this important and often overlooked area of the nervous system.
We study resurgence in the context of the partition function of 2-dimensional SU(N) and U(N) Yang-Mills theory on a surface of genus h. After discussing the properties of the transseries in the undeformed theory, we add a term to the action to deform the theory. The partition function can still be calculated exactly, and the deformation has the effect of analytically continuing the effective genus parameter in the exact answer to be non-integer. In the deformed theory we find new saddle solutions and study their properties. In this context each saddle contributes an asymptotic series to the transseries which can be analysed using Borel-Ècalle resummation. For specific values of the deformation parameter we find Cheshire cat points where the asymptotic series in the transseries truncate to a few terms. We also find new partial differential equations satisfied by the partition function, and a number of applications of these are explained, including low-order/low-order resurgence.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.