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Many materials, processes, and structures in science and engineering have important features at multiple scales of time and/or space; examples include biological tissues, active matter, oceans, networks, and images. Explicitly extracting,…
We propose to compose dynamic tree structures that place the objects in an image into a visual context, helping visual reasoning tasks such as scene graph generation and visual Q&A. Our visual context tree model, dubbed VCTree, has two key…
To most mathematicians and computer scientists the word ``tree'' conjures up, in addition to the usual image, the image of a connected graph with no circuits. In the last few years various types of trees have been the subject of much…
We consider the analysis of high dimensional data given in the form of a matrix with columns consisting of observations and rows consisting of features. Often the data is such that the observations do not reside on a regular grid, and the…
In order to speed-up classification models when facing a large number of categories, one usual approach consists in organizing the categories in a particular structure, this structure being then used as a way to speed-up the prediction…
Since they became observable, neuron morphologies have been informally compared with biological trees but they are studied by distinct communities, neuroscientists, and ecologists. The apparent structural similarity suggests there may be…
The paper surveys recent extensions of the Long-Short Term Memory networks to handle tree structures from the perspective of learning non-trivial forms of isomorph structured transductions. It provides a discussion of modern TreeLSTM…
In this paper we introduce a variation on the multidimensional segment tree, formed by unifying different interpretations of the dimensionalities of the data structure. We give some new definitions to previously well-defined concepts that…
Modern highly-concurrent search data structures, such as search trees, obtain multi-core scalability and performance by having operations traverse the data structure without any synchronization. As a result, however, these algorithms are…
Clustering is one of the fundamental tasks in data analytics and machine learning. In many situations, different clusterings of the same data set become relevant. For example, different algorithms for the same clustering task may return…
This paper presents a detailed comparison of a recently proposed algorithm for optimizing decision trees, tree alternating optimization (TAO), with other popular, established algorithms. We compare their performance on a number of…
The matrices of spanning rooted forests are studied as a tool for analysing the structure of networks and measuring their properties. The problems of revealing the basic bicomponents, measuring vertex proximity, and ranking from preference…
In the theoretical study of distributed communication networks, "history trees" are a discrete structure that naturally models the concept that anonymous agents become distinguishable upon receiving different sets of messages from…
This review paper is intended to give a useful guide for those who want to apply discrete wavelets in their practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous…
The integration and transmission of information in the brain are dependent on the interplay between structural and dynamical properties. Implicit in any pursuit aimed at understanding neural dynamics from appropriate sets of mathematically…
Volumetric maps are widely used in robotics due to their desirable properties in applications such as path planning, exploration, and manipulation. Constant advances in mapping technologies are needed to keep up with the improvements in…
Transmission matrices, mapping the propagation of light from one end of the tissue to the other, form an important mathematical tool in the analysis of tissue scattering and the design of wavefront shaping systems. To understand the…
Datalog has become a popular implementation language for solving large-scale, real-world problems, including bug finders, network analysis tools, and disassemblers. These applications express complex behaviour with hundreds of relations and…
Merge trees are fundamental structures in topological data analysis. Interleaving distance is a widely accepted metric for comparing merge trees, with applications in visualization and scientific computing. While a greedy algorithm exists…
Much of the information about the multi-valley structure of disordered spin systems can be convened in a simple tree structure -- a barrier tree -- the leaves and internal nodes of which represent, respectively, the local minima and the…