Principal component analysis (PCA) is a dimensionality reduction method that is known for
being simple and easy to interpret. Principal components are often interpreted as low …

Many recent models study the downstream projection from grid cells to place cells, while
recent data have pointed out the importance of the feedback projection. We thus asked how …

The bulk-boundary correspondence relates topologically protected edge modes to bulk
topological invariants and is well understood for short-range free-fermion chains. Although …

The paper presents higher-order asymptotic formulas for the eigenvalues of large Hermitian
Toeplitz matrices with moderately smooth symbols which trace out a simple loop on the real …

Navigation requires integration of external and internal inputs to form a representation of
location. Part of this integration is considered to be carried out by the grid cells network in …

Abstract Analysis of the asymptotic behaviour of the spectral characteristics of Toeplitz
matrices as the dimension of the matrix tends to infinity has a history of over 100 years. For …

In this paper we consider a family of tetradiagonal (= four non-zero diagonals) Toeplitz
matrices with a limiting set consisting in one analytic arc only and obtain individual …

The present work is devoted to the eigenvalue asymptotic expansion of the Toeplitz matrix,
whose generating function is complex-valued and has a power singularity at one point. As a …

The present work is devoted to the construction of an asymptotic expansion for the
eigenvalues of a Toeplitz matrix T n (a) T _n (a) as nn goes to infinity, with a continuous and …

Trapped-ion quantum simulators have demonstrated a long history of studying the physics of
interacting spin-lattice systems using globally addressed entangling operations. Yet despite …