Related papers: Sweeping Orders for Simplicial Complex Reconstruct…
In a previous paper, an implementable algorithm was introduced to compute discrete solutions of sweeping processes (i.e. specific first order differential inclusions). The convergence of this numerical scheme was proved thanks to…
Reconstructing a complete object from its parts is a fundamental problem in many scientific domains. The purpose of this article is to provide a systematic survey on this topic. The reassembly problem requires understanding the attributes…
Graph reconstruction can efficiently detect the underlying topology of massive networks such as the Internet. Given a query oracle and a set of nodes, the goal is to obtain the edge set by performing as few queries as possible. An algorithm…
Building upon the foundational work of Thomas and Williams on the modular sweep map, Garsia and Xin have developed a straightforward algorithm for the inversion of the sweep map on rational $(m,n)$-Dyck paths, where $(m,n)$ represents…
Sweeping is a commonly used procedure to explicitly solve the discrete ordinates equation, which itself is a common approximation of the neutron transport equation. To sweep through the computational domain, an ordering of the spatial cells…
We introduce and analyze parallelizable algorithms to compress and accurately reconstruct finite simplicial complexes that have non-trivial automorphisms. The compressed data -- called a complex of groups -- amounts to a functor from (the…
We study faster algorithms for producing the minimum degree ordering used to speed up Gaussian elimination. This ordering is based on viewing the non-zero elements of a symmetric positive definite matrix as edges of an undirected graph, and…
Given a convex region in the plane, and a sweep-line as a tool, what is best way to reduce the region to a single point by a sequence of sweeps? The problem of sweeping points by orthogonal sweeps was first studied in [2]. Here we consider…
We propose a hybrid image-space/object-space solution to the classical hidden surface removal problem: Given n disjoint triangles in Real^3 and p sample points (``pixels'') in the xy-plane, determine the first triangle directly behind each…
Surface reconstruction with preservation of geometric features is a challenging computer vision task. Despite significant progress in implicit shape reconstruction, state-of-the-art mesh extraction methods often produce aliased,…
An extended range of energy stable flux reconstruction schemes, developed using a summation-by-parts approach, is presented on quadrilateral elements for various sets of polynomial bases. For the maximal order bases, a new set of correction…
The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this…
The aim of this paper is to study a whole class of first order differential inclusions, which fit into the framework of perturbed sweeping process by uniformly prox-regular sets. After obtaining well-posedness results, we propose a…
In this paper, we study the fundamental open question of finding the optimal high-order algorithm for solving smooth convex minimization problems. Arjevani et al. (2019) established the lower bound $\Omega\left(\epsilon^{-2/(3p+1)}\right)$…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
Simplicial arrangements are classical objects in discrete geometry. Their classification remains an open problem but there is a list conjectured to be complete at least for rank three. A further important class in the theory of hyperplane…
We study the optimization of (strongly) quasar-convex functions, a class that arises naturally in many machine learning and data science applications due to its favorable properties. The fundamental properties of this class are first…
We develop algorithms for the optimization of convex objectives that have H\"older continuous $q$-th derivatives by using a $q$-th order oracle, for any $q \geq 1$. Our algorithms work for general norms under mild conditions, including the…
We propose an image processing scheme based on reordering of its patches. For a given corrupted image, we extract all patches with overlaps, refer to these as coordinates in high-dimensional space, and order them such that they are chained…
We consider the problem of positioning a cloud of points in the Euclidean space $\mathbb{R}^d$, using noisy measurements of a subset of pairwise distances. This task has applications in various areas, such as sensor network localization and…