Related papers: Hyperorthogonal well-folded Hilbert curves
Accurately modeling protein 3D structure is essential for the design of functional proteins. An important sub-task of structure modeling is protein side-chain packing: predicting the conformation of side-chains (rotamers) given the…
Point clouds of 3D objects exhibit an inherent compositional nature where simple parts can be assembled into progressively more complex shapes to form whole objects. Explicitly capturing such part-whole hierarchy is a long-sought objective…
We obtain a new bound on the number of two-rich points spanned by an arrangement of low degree algebraic curves in $\mathbb{R}^4$. Specifically, we show that an arrangement of $n$ algebraic curves determines at most $C_\epsilon…
State-of-the-art techniques proposed for 6D object pose recovery depend on occlusion-free point clouds to accurately register objects in 3D space. To reduce this dependency, we introduce a novel architecture called Iterative Hough Forest…
This paper tackles the problem of finding optimal variable-height transport packaging. The goal is to reduce the empty space left in a box when shipping goods to customers, thereby saving on filler and reducing waste. We cast this problem…
We give an algorithm to explicitly compute the largest subtree, in the local Bruhat-Tits tree for PSL_2(k), whose vertices correspond to orders containing a given suborder H, in terms of a set of generators for H. The shape of this subtree…
We propose a general data structure CORoBTS for storing B-tree-like search trees dynamically in a cache-oblivious way combining the van Emde Boas memory layout with packed memory array. In the use of the vEB layout mostly search complexity…
Object Oriented Data Analysis is a new area in statistics that studies populations of general data objects. In this article we consider populations of tree-structured objects as our focus of interest. We develop improved analysis tools for…
Treemaps are a popular technique to visualize hierarchical data. The input is a weighted tree $\tree$ where the weight of each node is the sum of the weights of its children. A treemap for $\tree$ is a hierarchical partition of a rectangle…
This article is motivated by the objective of providing a new analytically tractable and fully frequentist framework to characterize and implement regression trees while also allowing a multivariate (potentially high dimensional) response.…
Fiber-orientation tensors describe the relevant features of the fiber-orientation distribution compactly and are thus ubiquitous in injection-molding simulations and subsequent mechanical analyses. In engineering applications to date, the…
We deepen the link between two classic areas of combinatorial optimization: augmentation and packing arborescences. We consider the following type of questions: What is the minimum number of arcs to be added to a digraph so that in the…
Persistence diagrams (PDs) are now routinely used to summarize the underlying topology of complex data. Despite several appealing properties, incorporating PDs in learning pipelines can be challenging because their natural geometry is not…
The efficiency of modern computer graphics allows us to explore collections of space curves simultaneously with "drag-to-rotate" interfaces. This inspires us to replace "scatterplots of points" with "scatterplots of curves" to…
We focus on the distribution regression problem: regressing to vector-valued outputs from probability measures. Many important machine learning and statistical tasks fit into this framework, including multi-instance learning and point…
Motivated by the growing interest in representation learning approaches that uncover the latent structure of high-dimensional data, this work proposes new algorithms for reconstruction-based manifold learning within Reproducing-Kernel…
We consider spaces of smooth immersed plane curves (modulo translations and/or rotations), equipped with reparameterization invariant weak Riemannian metrics involving second derivatives. This includes the full $H^2$-metric without zero…
A cut tree (or Gomory-Hu tree) of an undirected weighted graph G=(V,E) encodes a minimum s-t-cut for each vertex pair {s,t} \subseteq V and can be iteratively constructed by n-1 maximum flow computations. They solve the multiterminal…
A hypertree is a connected hypergraph without cycles. Further a hypertree is called an $r$-tree if, additionally, it is $r$-uniform. Note that 2-trees are just ordinary trees. A classical result states that for any 2-tree $T$ with…
The Hilbert scheme X^{[a]} of points on a complex manifold X is a compactification of the configuration space of a-element subsets of X. The integral cohomology of X^{[a]} is more subtle than the rational cohomology. In this paper, we…