High Temperature Asymptotics of Orthogonal Mean-Field Spin Glasses

We evaluate the high temperature limit of the free energy of spin glasses on the hypercube with Hamiltonian $H_N(\sigma) = \sigma^T J \sigma$, where the coupling matrix $J$ is drawn from certain symmetric orthogonally invariant ensembles. Our derivation relates the annealed free energy of these models to a spherical integral, and expresses the limit of the free energy in terms of the limiting spectral measure of the coupling matrix $J$. As an application, we derive the limiting free energy of the Random Orthogonal Model (ROM) at high temperatures, which confirms non-rigorous calculations of Marinari et al. (1994). Our methods also apply to other well-known models of disordered systems, including the SK and Gaussian Hopfield models.Comment: 15 pages, 1 figur

Phase transitions of extremal cuts for the configuration model

The $k$-section width and the Max-Cut for the configuration model are shown to exhibit phase transitions according to the values of certain parameters of the asymptotic degree distribution. These transitions mirror those observed on Erd\H{o}s-R\'enyi random graphs, established by Luczak and McDiarmid (2001), and Coppersmith et al. (2004), respectively

A Comparative Analysis on Metaheuristic Algorithms Based Vision Transformer Model for Early Detection of Alzheimer's Disease

A number of life threatening neuro-degenerative disorders had degraded the quality of life for the older generation in particular. Dementia is one such symptom which may lead to a severe condition called Alzheimer's disease if not detected at an early stage. It has been reported that the progression of such disease from a normal stage is due to the change in several parameters inside the human brain. In this paper, an innovative metaheuristic algorithms based ViT model has been proposed for the identification of dementia at different stage. A sizeable number of test data have been utilized for the validation of the proposed scheme. It has also been demonstrated that our model exhibits superior performance in terms of accuracy, precision, recall as well as F1-score.Comment: 2023 IEEE 15th International Conference on Computational Intelligence and Communication Networks (CICN). arXiv admin note: text overlap with arXiv:2309.1679