Related papers: Near-best adaptive approximation on conforming mes…
We introduce TreeMeshGPT, an autoregressive Transformer designed to generate high-quality artistic meshes aligned with input point clouds. Instead of the conventional next-token prediction in autoregressive Transformer, we propose a novel…
In this work, we present an adaptive unfitted finite element scheme that combines the aggregated finite element method with parallel adaptive mesh refinement. We introduce a novel scalable distributed-memory implementation of the resulting…
In this paper we show how to find nearly optimal embeddings of large trees in several natural classes of graphs. The size of the tree T can be as large as a constant fraction of the size of the graph G, and the maximum degree of T can be…
We examine the interaction of multigrid methods and shape optimization in appropriate shape spaces. Our aim is a scalable algorithm for application on supercomputers, which can only be achieved by mesh-independent convergence. The impact of…
Comparative analysis of scalar fields is an important problem with various applications including feature-directed visualization and feature tracking in time-varying data. Comparing topological structures that are abstract and succinct…
A drawing of a given (abstract) tree that is a minimum spanning tree of the vertex set is considered aesthetically pleasing. However, such a drawing can only exist if the tree has maximum degree at most 6. What can be said for trees of…
Conformance checking techniques let us find out to what degree a process model and real execution data correspond to each other. In recent years, alignments have proven extremely useful in calculating conformance statistics. Most techniques…
Many iterative and non-iterative methods have been developed for inverse problems associated with Ising models. Aiming to derive an accurate non-iterative method for the inverse problems, we employ the tree-reweighted approximation. Using…
Computational analysis with the finite element method requires geometrically accurate meshes. It is well known that high-order meshes can accurately capture curved surfaces with fewer degrees of freedom in comparison to low-order meshes.…
Deciding what to sense is a crucial task, made harder by dependencies and by a nonadditive utility function. We develop approximation algorithms for selecting an optimal set of measurements, under a dependency structure modeled by a…
Full binary trees naturally represent commutative non-associative products. There are many important examples of these products: finite-precision floating-point addition and NAND gates, among others. Balance in such a tree is highly…
We present a novel approach for designing complex approximate arithmetic circuits that trade correctness for power consumption and play important role in many energy-aware applications. Our approach integrates in a unique way formal methods…
Regression trees and their ensemble methods are popular methods for nonparametric regression: they combine strong predictive performance with interpretable estimators. To improve their utility for locally smooth response surfaces, we study…
We introduce a multiplicative neural network architecture in which multiplicative interactions constitute the fundamental representation, rather than appearing as auxiliary components within an additive model. We establish a universal…
A \emph{binary tanglegram} is a drawing of a pair of rooted binary trees whose leaf sets are in one-to-one correspondence; matching leaves are connected by inter-tree edges. For applications, for example, in phylogenetics, it is essential…
In this paper, we introduce a multiscale framework based on adaptive edge basis functions to solve second-order linear elliptic PDEs with rough coefficients. One of the main results is that we prove the proposed multiscale method achieves…
We consider the numerical taxonomy problem of fitting a positive distance function ${D:{S\choose 2}\rightarrow \mathbb R_{>0}}$ by a tree metric. We want a tree $T$ with positive edge weights and including $S$ among the vertices so that…
We study adaptive approximation algorithms for general multivariate linear problems where the sets of input functions are non-convex cones. While it is known that adaptive algorithms perform essentially no better than non-adaptive…
Meshes composed of well-centered simplices have nice orthogonal dual meshes (the dual Voronoi diagram). This is useful for certain numerical algorithms that prefer such primal-dual mesh pairs. We prove that well-centered meshes also have…
Spatial relations between objects in an image have proved useful for structural object recognition. Structural constraints can act as regularization in neural network training, improving generalization capability with small datasets.…