Related papers: Theta functions and optimal lattices for a grid ce…
We consider the hard-core model on finite triangular lattices with Metropolis dynamics. Under suitable conditions on the triangular lattice dimensions, this interacting particle system has three maximum-occupancy configurations and we…
This paper investigates the conformal isometry hypothesis as a potential explanation for the hexagonal periodic patterns in grid cell response maps. We posit that grid cell activities form a high-dimensional vector in neural space, encoding…
The theoretical minimum emittance cells are the optimal configurations for achieving the absolute minimum emittance, if specific optics constraints are satisfied at the middle of the cell's dipole. Linear lattice design options based on an…
We discuss an effective field theory of a triangular-lattice three-spin interaction model defined by the ${\mathbb Z}_p$ variables. Based on the symmetry properties and the ideal-state graph concept, we show that the vector dual sine-Gordon…
Encoding information about continuous variables using noisy computational units is a challenge; nonetheless, asymptotic theory shows that combining multiple periodic scales for coding can be highly precise despite the corrupting influence…
Grid cells in the entorhinal cortex, together with head direction, place, speed and border cells, are major contributors to the organization of spatial representations in the brain. In this work we introduce a novel theoretical and…
In statistical mechanics, the Potts model is a model for interacting spins with more than two discrete states. Neural networks which exhibit features of learning and associative memory can also be modeled by a system of Potts spins. A…
The relation between three-dimensional lattice structure and magnetism in correlated electron systems is explored for face centered cubic (FCC), body centered cubic (BCC), and simple cubic (SC) lattices. In particular, we question which…
We analyze high-temperature series expansions of the two-point and four-point correlation-functions in the three-dimensional euclidean lattice scalar field theory with quartic self-coupling, which have been recently extended through…
Given a family ${\mathcal F}$ of shapes in the plane, we study what is the lowest possible density of a point set $P$ that pierces (``intersects'', ``hits'') all translates of each shape in ${\mathcal F}$. For instance, if ${\mathcal F}$…
This paper introduces and analyses the new grid-based tensor approach for approximate solution of the eigenvalue problem for linearized Hartree-Fock equation applied to the 3D lattice-structured and periodic systems. The set of localized…
A lattice gauge theory framework for simulations on graphic processing units (GPUs) using NVIDIA's CUDA is presented. The code comprises template classes that take care of an optimal data pattern to ensure coalesced reading from device…
A crucial step in the early development of multicellular organisms involves the establishment of spatial patterns of gene expression which later direct proliferating cells to take on different cell fates. These patterns enable the cells to…
The accuracy of a large eddy simulation (LES) is determined by the accuracy of the model used to describe the effect of unresolved scales, the numerical errors of the resolved scales, and the optimality of the length scale that separates…
We present a lattice formulation of an interaction ${\phi\over\Lambda} F\tilde F$ between an axion and some $U(1)$ gauge sector with the following properties: it reproduces the continuum theory up to $\mathcal{O}(dx_\mu^2)$ corrections, it…
First principle study of QCD at finite temperature $T$ and chemical potential $\mu$ is essential for understanding a wide range of phenomena from heavy-ion collisions to cosmology and neutron stars. However, in the presence of finite…
Brain-computer interfaces surged extraordinary developments in recent years, and a significant discrepancy now exists between the abundance of available data and the limited headway made in achieving a unified theoretical framework. This…
We prove that if an activation function satisfies some mild conditions and number of neurons in a two-layered fully connected neural network with this activation function is beyond a certain threshold, then gradient descent on quadratic…
Spike train signals recorded from a large population of neurons often exhibit low-dimensional spatio-temporal structure and modeled as conditional Poisson observations. The low-dimensional signals that capture internal brain states are…
We discuss the local analysis of Gaussian potential energy of modular lattices. We present examples of $2$-modular lattices -- such as the $16$-dimensional Barnes-Wall lattice -- and $3$-modular lattices -- such as the $12$-dimensional…