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The junction-tree representation provides an attractive structural property for organizing a decomposable graph. In this study, we present two novel stochastic algorithms, which we call the junction-tree expander and junction-tree collapser…
Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree…
A complex system comprises multiple interacting entities whose interdependencies form a unified whole, exhibiting emergent behaviours not present in individual components. Examples include the human brain, living cells, soft matter, Earth's…
We present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. As their primary applications, these decompositions allow us to achieve…
It is well known that a compact two dimensional surface is homeomorphic to a polygon with the edges identified in pairs. This paper not only presents a new proof of this statement but also generalizes it for any connected n-dimensional…
Dynamic programming on tree decompositions is a frequently used approach to solve otherwise intractable problems on instances of small treewidth. In recent work by Bodlaender et al., it was shown that for many connectivity problems, there…
It is a high-quality algorithm for hierarchical clustering of large software source code. This effectively allows to break the complexity of tens of millions lines of source code, so that a human software engineer can comprehend a software…
We present Spanning Tree Autoregressive (STAR) modeling, which can incorporate prior knowledge of images, such as center bias and locality, to maintain sampling performance while also providing sufficiently flexible sequence orders to…
Retinex theory is developed mainly to decompose an image into the illumination and reflectance components by analyzing local image derivatives. In this theory, larger derivatives are attributed to the changes in reflectance, while smaller…
We aim to investigate the connections existing between the density profiles of the stellar populations used to define a gravitationally bound stellar system and their star formation history: we do this by developing a general framework…
Large spatial datasets often represent a number of spatial point processes generated by distinct entities or classes of events. When crossed with covariates, such as discrete time buckets, this can quickly result in a data set with millions…
The SPQR-tree is a data structure that compactly represents all planar embeddings of a biconnected planar graph. It plays a key role in constrained planarity testing. We develop a similar data structure, called the UP-tree, that compactly…
Young massive star clusters spanning $\sim 10^4 - 10^8 M_\odot$ in mass have been observed to have similar surface brightness profiles. Recent hydrodynamical simulations of star cluster formation have also produced star clusters with this…
Matrices and more generally multidimensional arrays, form the backbone of computational studies. In this paper we demonstrate increases in computational efficiency by performing partial-tracing/tensor-contractions on sparse-arrays. It was…
The shapelets method for image analysis is based upon the decomposition of localised objects into a series of orthogonal components with convenient mathematical properties. We extend the "Cartesian shapelet" formalism from earlier work, and…
Stellar shells are low surface brightness features, created during nearly head-on galaxy mergers from the debris of the tidally disrupted satellite. Here, we investigate the formation and evolution mechanism of shells in six dimensions (3d…
This paper presents deformable templates as a tool for segmentation and localization of biological structures in medical images. Structures are represented by a prototype template, combined with a parametric warp mapping used to deform the…
Elliptically contoured distributions can be considered to be the distributions for which the contours of the density functions are proportional ellipsoids. Kamiya, Takemura and Kuriki (2006) generalized the elliptically contoured…
Subspace clustering is an unsupervised clustering technique designed to cluster data that is supported on a union of linear subspaces, with each subspace defining a cluster with dimension lower than the ambient space. Many existing…
The volume of data generated by modern astronomical telescopes is extremely large and rapidly growing. However, current high-performance data processing architectures/frameworks are not well suited for astronomers because of their…