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Decomposition puzzles are pencil-and-paper logic puzzles that involve partitioning a rectangular grid into several regions to satisfy certain rules. In this paper, we construct a generic card-based protocol called printing protocol, which…

This note shows the equivalence of two projection operators which both can be used in cylindrical algebraic decomposition (CAD) . One is known as Brown's Projection (C. W. Brown (2001)); the other was proposed by Lu Yang in his earlier work…

Lifting is an efficient technique to scale up graphical models generalized to relational domains by exploiting the underlying symmetries. Concurrently, neural models are continuously expanding from grid-like tensor data into structured…

Many high-dimensional uncertainty quantification problems are solved by polynomial dimensional decomposition (PDD), which represents Fourier-like series expansion in terms of random orthonormal polynomials with increasing dimensions. This…

When folding a 3D object from a 2D material like paper, typically only an approximation of the original surface geometry is needed. Such an approximation can effectively be created by a (progressive) mesh simplification approach, e.g. using…

We provide a natural smooth projective compactification of the space of algebraic maps from the projective line to the projective space of dimension n by adding a divisor with simple normal crossings.

Connecting cosmological simulations to real-world observational programs is often complicated by a mismatch in geometry: while surveys often cover highly irregular cosmological volumes, simulations are customarily performed in a periodic…

Direct manipulation has been established as the main interaction paradigm for Computer-Aided Design (CAD) for decades. It provides fast, incremental, and reversible actions that allow for an iterative process on a visual representation of…

The cylindrical algebraic covering method was originally proposed to decide the satisfiability of a set of non-linear real arithmetic constraints. We reformulate and extend the cylindrical algebraic covering method to allow for checking the…

Three-dimensional (3D) printing is a powerful development tool both in industry, as well as in biomedical research. Additive-lathe 3D printing is an emerging sub-class of 3D printing whereby material is layered outward from the surface of a…

We present Real2Code, a novel approach to reconstructing articulated objects via code generation. Given visual observations of an object, we first reconstruct its part geometry using an image segmentation model and a shape completion model.…

Parametric Computer-aided design (CAD) enables the creation of reusable models by integrating variables into geometric properties, facilitating customization without a complete redesign. However, creating parametric designs in…

Logic-based Benders decomposition (LBBD) is a substantial generalization of classical Benders decomposition that, in principle, allows the subproblem to be any optimization problem rather than specifically a linear or nonlinear programming…

Creating CAD digital twins from the physical world is crucial for manufacturing, design, and simulation. However, current methods typically rely on costly 3D scanning with labor-intensive post-processing. To provide a user-friendly design…

We present in this paper a framework which leverages the underlying topology of a data set, in order to produce appropriate coordinate representations. In particular, we show how to construct maps to real and complex projective spaces,…

We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is here approximated from its random sketch, which is a set of…

This paper documents a computational implementation of a {\em projection and rescaling algorithm} for finding most interior solutions to the pair of feasibility problems \[ \text{find} \; x\in L\cap\mathbb{R}^n_{+} \;\;\;\; \text{ and } \;…

In this paper we present algorithms for an efficient implementation of the Localized Orthogonal Decomposition method (LOD). The LOD is a multiscale method for the numerical simulation of partial differential equations with a continuum of…

This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…

We propose a machine learning based approach for automatic regularization and polygonization of building segmentation masks. Taking an image as input, we first predict building segmentation maps exploiting generic fully convolutional…