Related papers: CAD Adjacency Computation Using Validated Numerics
Cylindrical Algebraic Decomposition (CAD) is a key proof technique for formal verification of cyber-physical systems. CAD is computationally expensive, with worst-case doubly-exponential complexity. Selecting an optimal variable ordering is…
Generation of realistic topologies plays an important role in determining the accuracy and validity of simulation studies. This study presents a discussion to justify why, and how often randomly generated adjacency matrices may not not…
Segmentation is often an essential intermediate step in image analysis. A volume segmentation characterizes the underlying volume image in terms of geometric information--segments, faces between segments, curves in which several faces…
Dynamic or temporal networks enable representation of time-varying edges between nodes. Conventional adjacency-based data structures used for storing networks such as adjacency lists were designed without incorporating time and can thus…
Cellular manufacturing (CM) is an approach that includes both flexibility of job shops and high production rate of flow lines. Although CM provides many benefits in reducing throughput times, setup times, work-in-process inventories but the…
Calibration refers to the estimation of unknown parameters which are present in computer experiments but not available in physical experiments. An accurate estimation of these parameters is important because it provides a scientific…
We solve the Matrix Completion (MC) problem based on manifold optimization by incorporating the side information under which the columns of the intended matrix are drawn from a union of low dimensional subspaces. It is proved that this side…
In colored graphs, node classes are often associated with either their neighbors class or with information not incorporated in the graph associated with each node. We here propose that node classes are also associated with topological…
Mesoscale simulations of woven composites using parameterized analytical geometries offer a way to connect constituent material properties and their geometric arrangement to effective composite properties and performance. However, the…
We present a novel area matching algorithm for merging two different 2D grid maps. There are many approaches to address this problem, nevertheless, most previous work is built on some assumptions, such as rigid transformation, or similar…
This paper presents a classification of Cellular Automata rules based on its properties at the nth iteration. Elaborate computer program has been designed to get the nth iteration for arbitrary 1-D or 2-D CA rules. Studies indicate that the…
Traditional attempts for loop closure detection typically use hand-crafted features, relying on geometric and visual information only, whereas more modern approaches tend to use semantic, appearance or geometric features extracted from deep…
A low-rank approximation of a parameter-dependent matrix $A(t)$ is an important task in the computational sciences appearing for example in dynamical systems and compression of a series of images. In this work, we introduce AdaCUR, an…
Skyline computation is an essential database operation that has many applications in multi-criteria decision making scenarios such as recommender systems. Existing algorithms have focused on checking point domination, which lack efficiency…
A matrix-compression algorithm is derived from a novel isogenic block decomposition for square matrices. The resulting compression and inflation operations possess strong functorial and spectral-permanence properties. The basic observation…
We propose an application-tailored data-driven fully automated method for functional approximation of combinational circuits. We demonstrate how an application-level error metric such as the classification accuracy can be translated to a…
When building a cylindrical algebraic decomposition (CAD) savings can be made in the presence of an equational constraint (EC): an equation logically implied by a formula. The present paper is concerned with how to use multiple ECs,…
While high-capacity AI models have advanced state-of-the-art performance, their practical deployment is often hindered by high inference costs, environmental impact, and a "one-size-fits-all" approach that ignores varying sample complexity.…
We solve some computational problems for triangulated closed three-dimensional manifolds using groups of simplicial homology and cohomology modulo 2. Two efficient algorithms for computing the intersection numbers of 1- and 2-dimensional…
The representation of graphs is commonly based on the adjacency matrix concept. This formulation is the foundation of most algebraic and computational approaches to graph processing. The advent of deep learning language models offers a wide…