Existence and Stability of Standing Pulses in Neural Networks: II Stability

We analyze the stability of standing pulse solutions of a neural network integro-differential equation. The network consists of a coarse-grained layer of neurons synaptically connected by lateral inhibition with a non-saturating nonlinear gain function. When two standing single-pulse solutions coexist, the small pulse is unstable, and the large pulse is stable. The large single-pulse is bistable with the ``all-off'' state. This bistable localized activity may have strong implications for the mechanism underlying working memory. We show that dimple pulses have similar stability properties to large pulses but double pulses are unstable.Comment: 31 pages, 16 figures, submitted to SIAM Journal on Applied Dynamical System

Cooper pairing and tripling in one-dimensional spinless fermions with attractive two- and three-body forces

We theoretically investigate in-medium three-body correlations in one-dimensional spinless fermions with antisymmetrized two- and three-body attractive interactions. By investigating the variational problem of three-body states above the Fermi sea, we illuminate the fate of the in-medium three-body cluster states both in the special case with pure attractive three-body interaction as well as in the case with the coexistence of two- and three-body interactions. Our results testify that the fermion-dimer repulsion is canceled by including the three-body interactions, and stable three-body clusters can be formed. We further feature a phase diagram consisting of the $p$-wave Cooper pairing and Cooper tripling phases in a plane of $p$-wave two- and three-body coupling strengths.Comment: 11 pages, 5 figure

A Study of the Symbolic Meaning and Period Value of Pearl in The Scarlet Letter

Pearl is a distinctive artistic figure created by Nathaniel Hawthorne in his novel The Scarlet Letter. She is highly symbolic in her identity, name, appearance and character. Her existence not only drives the development of the main characters’ thoughts and behavioral changes, but also carries the author’s praise of truth, goodness and beauty, his communication of ideals and hopes, and the profound understanding of the awakening of women’s consciousness. This kind of praise, communication and understanding has wide contemporary value in today’s society