Related papers: Counting Lattice Animals in High Dimensions
We provide combinatorial arguments based on a two-dimensional extension of a locally-free semigroup allowing us to compute the growth rate, $\Lambda$, of the partition function $Z_N=N^{\theta}\Lambda^N$ of the $N$-particle directed animals…
We present general algorithms (fully implemented in Maple) for calculations of various quantities related to constrained directed walks for a general set of steps on the square lattice in two dimensions. As a special case, we rederive…
In this paper we investigate the scaling limit of the range (the set of visited vertices) for a class of critical lattice models, starting from a single initial particle at the origin. We give conditions on the random sets and an associated…
We study a class of rearrangement problems under a novel pick-n-swap prehensile manipulation model, in which a robotic manipulator, capable of carrying an item and making item swaps, is tasked to sort items stored in lattices of variable…
Many algorithms have been developed for enumerating various combinatorial objects in time exponentially less than the number of objects. Two common classes of algorithms are dynamic programming and the transfer matrix method. This paper…
In practical applications, lattice quantizers leverage discrete lattice points to approximate arbitrary points in the lattice. An effective lattice quantizer significantly enhances both the accuracy and efficiency of these approximations.…
We discuss the lattice formulation of gauge theories with fermions in arbitrary representations of the color group, and present in detail the implementation of the HMC/RHMC algorithm for simulating dynamical fermions. We discuss the…
The lattice size of a lattice polytope is a geometric invariant which was formally introduced in the context of simplification of the defining equation of an algebraic curve, but appeared implicitly earlier in geometric combinatorics.…
Lattice sieving in two or more dimensions has proven to be an indispensable practical aid in integer factorization and discrete log computations involving the number field sieve. The main contribution of this article is to show that a…
Animals move in three dimensions (3D). Thus, 3D measurement is necessary to report the true kinematics of animal movement. Existing 3D measurement techniques draw on specialized hardware, such as motion capture or depth cameras, as well as…
The reconstruction of high-dimensional sparse signals is a challenging task in a wide range of applications. In order to deal with high-dimensional problems, efficient sparse fast Fourier transform algorithms are essential tools. The second…
Enumeration of various types of lattice polygons and in particular polyominoes is of primary importance in many machine learning, pattern recognition, and geometric analysis problems. In this work, we develop a large deviation principle for…
We study regularized estimation in high-dimensional longitudinal classification problems, using the lasso and fused lasso regularizers. The constructed coefficient estimates are piecewise constant across the time dimension in the…
We describe algorithms which address two classical problems in lattice geometry: the lattice covering and the simultaneous lattice packing-covering problem. Theoretically our algorithms solve the two problems in any fixed dimension d in the…
Following Richardson and using results of Kesten on First-passage percolation, we obtain an upper bound on the expected perimeter in an Eden Growth Process. Using results of the author from a problem in Statistical Mechanics, we show that…
We examine the percolation model on $\mathbb{Z}^d$ by an approach involving lattice animals and their surface-area-to-volume ratio. For $\beta \in [0,2(d-1))$, let $f(\beta)$ be the asymptotic exponential rate in the number of edges of the…
In this short note we give incremental algorithms for the following lattice problems: finding a basis of a lattice, computing the successive minima, and determining the orthogonal decomposition. We prove an upper bound for the number of…
This article introduces a new, simple solvable lattice for directed animals: the directed king's lattice, or square lattice with next nearest neighbor bonds and preferred directions {W, NW, N, NE, E}. We show that the directed animals in…
Hyperparameter optimization is a crucial problem in Evolutionary Computation. In fact, the values of the hyperparameters directly impact the trajectory taken by the optimization process, and their choice requires extensive reasoning by…
The site percolation problem is studied on d-dimensional generalisations of the Kagome' lattice. These lattices are isotropic and have the same coordination number q as the hyper-cubic lattices in d dimensions, namely q=2d. The site…