Related papers: Counting Lattice Animals in High Dimensions
The two-dimensional cage model for polymer motion is discussed with an emphasis on the effect of sideways motions, which cross the barriers imposed by the lattice. Using the Density Matrix Method as a solver of the Master Equation, the…
Monocular imaging of animals inherently reduces 3D structures to 2D projections. Detection algorithms lead to 2D bounding boxes that lack information about animal's orientation relative to the camera. To build 3D detection methods for RGB…
We describe a new algebraic technique for enumerating self-avoiding walks on the rectangular lattice. The computational complexity of enumerating walks of $N$ steps is of order $3^{N/4}$ times a polynomial in $N$, and so the approach is…
Let $\mathcal{T}$ be a collection of 3-element subsets $S$ of $\{1, \ldots,n\}$ with the property that if $i<j<k$ and $a<b<c$ are two 3-element subsets in $S$, then there exists an integer sequence $x_1 < x_2 < \cdots < x_n$ such that $x_i,…
In this paper, we revisit the enumeration of directed animals using gas models. We show that there exists a natural construction of random directed animals on any directed graph together with a particle system that explains at the level of…
For large ranks, there is no good algorithm that decides whether a given lattice has an orthonormal basis. But when the lattice is given with enough symmetry, we can construct a provably deterministic polynomial-time algorithm to accomplish…
Enumerating polygons on regular lattices is a classic problem in rigorous statistical mechanics. The goal of enumerating polygons on the square lattice via fermionic path integration was achieved using a free-fermion quadratic action in the…
In this paper we give a detailed analysis of deterministic and randomized algorithms that enumerate any number of irreducible polynomials of degree $n$ over a finite field and their roots in the extension field in quasilinear where $N=n^2$…
We consider the problem of finding the closest lattice point to a vector in n-dimensional Euclidean space when each component of the vector is available at a distinct node in a network. Our objectives are (i) minimize the communication cost…
We perform a high statistics calculation of the equation of state for non-compact QED on large lattices. The calculation extends to fermionic correlation lengths of $\approx 8$, and it is combined with a finite size scaling analysis of the…
Given a primitive collection of vectors in the integer lattice, we count the number of ways it can be extended to a basis by vectors with sup-norm bounded by $T$, producing an asymptotic estimate as $T \to \infty$. This problem can be…
We improve the error terms of some estimates related to counting lattices from recent work of L. Fukshansky, P. Guerzhoy and F. Luca (2017). This improvement is based on some analytic techniques, in particular on bounds of exponential sums…
New lattice quantizers with lower normalized second moments than previously reported are constructed in 13 and 14 dimensions and conjectured to be optimal. Our construction combines an initial numerical optimization with a subsequent…
Lattices are a popular field of study in mathematical research, but also in more practical areas like cryptology or multiple-input/multiple-output (MIMO) transmission. In mathematical theory, most often lattices over real numbers are…
Surrogate-assisted evolutionary algorithms have been widely developed to solve complex and computationally expensive multi-objective optimization problems in recent years. However, when dealing with high-dimensional optimization problems,…
In quantum gas microscopy experiments, reconstructing the site-resolved lattice occupation with high fidelity is essential for the accurate extraction of physical observables. For short interatomic separations and limited signal-to-noise…
This article deals with the enumeration of directed lattice walks on the integers with any finite set of steps, starting at a given altitude $j$ and ending at a given altitude $k$, with additional constraints such as, for example, to never…
We consider random energy landscapes constructed from d-dimensional lattices or trees. The distribution of the number of local minima in such landscapes follows a large deviation principle and we derive the associated law exactly for…
We give a quantum algorithm for solving the Bounded Distance Decoding (BDD) problem with a subexponential approximation factor on a class of integer lattices. The quantum algorithm uses a well-known but challenging-to-use quantum state on…
We investigate the algorithms for dynamical overlap fermions aiming at improving the performance for large-scale simulations. We look for the best combination of Hybrid Monte Carlo options and iterative quark solvers with respect to the…