Related papers: Hierarchical Rectangle Packing Solved by Multi-Lev…
In this work, we propose a high-order multiscale method for an elliptic model problem with rough and possibly highly oscillatory coefficients. Convergence rates of higher order are obtained using the regularity of the right-hand side only.…
Hierarchical categorical variables often exhibit many levels (high granularity) and many classes within each level (high dimensionality). This may cause overfitting and estimation issues when including such covariates in a predictive model.…
Grid-based storage systems with uniformly shaped loads (e.g., containers, pallets, totes) are commonplace in logistics, industrial, and transportation domains. A key performance metric for such systems is the maximization of space…
We develop an optimization framework for identifying ideal Mixed Binary Linear Programs (MBLP) which is linear when using known input data and nonconvex quadratic over parametric input data. These techniques are applied to various…
We study the generalized multidimensional bin packing problem (GVBP) that generalizes both geometric packing and vector packing. Here, we are given $n$ rectangular items where the $i^{\textrm{th}}$ item has width $w(i)$, height $h(i)$, and…
Many problems in sequential decision making and stochastic control often have natural multiscale structure: sub-tasks are assembled together to accomplish complex goals. Systematically inferring and leveraging hierarchical structure,…
Establishing semantic correspondence across images when the objects in the images have undergone complex deformations remains a challenging task in the field of computer vision. In this paper, we propose a hierarchical method to tackle this…
This paper encompasses the mathematical derivations of the analytic and generalized formula and recurrence relations to find out the radii of n umber of circles inscribed or packed in the plane region bounded by circular arcs (including…
Disjointly constrained multilinear programming concerns the problem of maximizing a multilinear function on the product of finitely many disjoint polyhedra. While maximizing a linear function on a polytope (linear programming) is known to…
We investigate the problem of multiplex graph embedding, that is, graphs in which nodes interact through multiple types of relations (dimensions). In recent years, several methods have been developed to address this problem. However, the…
Kernel matrices are ubiquitous in computational mathematics, often arising from applications in machine learning and scientific computing. In two or three spatial or feature dimensions, such problems can be approximated efficiently by a…
We detail the application of bounding volume hierarchies to accelerate second-virial evaluations for arbitrary complex particles interacting through hard and soft finite-range potentials. This procedure, based on the construction of…
Hierarchical classification problems are commonly seen in practice. However, most existing methods do not fully utilize the hierarchical information among class labels. In this paper, a novel label embedding approach is proposed, which…
In this paper we present a fast scalable heuristic for bin packing that partitions the given problem into identical sub-problems of constant size and solves these constant size sub-problems by considering only a constant number of bin…
In this paper we propose and analyze a new Multiscale Method for solving semi-linear elliptic problems with heterogeneous and highly variable coefficient functions. For this purpose we construct a generalized finite element basis that spans…
Supply chain transportation operations often account for a large proportion of product total cost to market. Such operations can be optimized by solving the Logistics Service Network Design Problem (LSNDP), wherein a logistics service…
We describe an algorithm that allows one to find dense packing configurations of a number of congruent disks in arbitrary domains in two or more dimensions. We have applied it to a large class of two dimensional domains such as rectangles,…
Hyperdimensional Computing (HDC) is an emerging computational paradigm for representing compositional information as high-dimensional vectors, and has a promising potential in applications ranging from machine learning to neuromorphic…
The Multiscale Hierarchical Decomposition Method (MHDM) was introduced as an iterative method for total variation regularization, with the aim of recovering details at various scales from images corrupted by additive or multiplicative…
The structural properties of mechanical metamaterials are typically studied with two-scale methods based on computational homogenization. Because such materials have a complex microstructure, enriched schemes such as second-order…