Related papers: Latin Hypercubes and Space-filling Designs
The study of topological information of spatial objects has for a long time been a focus of research in disciplines like computational geometry, spatial reasoning, cognitive science, and robotics. While the majority of these researches…
This paper defends an augmented cognitively oriented "generic-design hypothesis": There are both significant similarities between the design activities implemented in different situations and crucial differences between these and other…
Efficiently computing spatio-textual queries has become increasingly important in various applications that need to quickly retrieve geolocated entities associated with textual information, such as in location-based services and social…
Computer simulators are nowadays widely used to understand complex physical systems in many areas such as aerospace, renewable energy, climate modeling, and manufacturing. One fundamental issue in the study of computer simulators is known…
Given a finite collection of two-dimensional tile types, the field of study concerned with covering the plane with tiles of these types exclusively has a long history, having enjoyed great prominence in the last six to seven decades. Much…
We present filling as a new type of spatial subdivision problem that is related to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most…
A subspace arrangement in a vector space is a finite collection of vector subspaces. Similarly, a configuration of linear spaces in a projective space is a finite collection of linear subspaces. In this paper we study the degree 2 part of…
We explore the complex design space of behaviour planning for autonomous driving. Design choices that successfully address one aspect of behaviour planning can critically constrain others. To aid the design process, in this work we…
Over the last decade, the term spatial computing has grown to have two different, though not entirely unrelated, definitions. The first definition of spatial computing stems from industry, where it refers primarily to new kinds of…
Sequential design is a highly active field of research in active learning which provides a general framework for designing computer experiments with limited computational budgets. It aims to create efficient surrogate models to replace…
A rectangular layout is a partition of a rectangle into a finite set of interior-disjoint rectangles. Rectangular layouts appear in various applications: as rectangular cartograms in cartography, as floorplans in building architecture and…
A new type of experiment with joint considerations of quantitative and sequence factors is recently drawing much attention in medical science, bio-engineering, and many other disciplines. The input spaces of such experiments are…
This paper provides an overview of selected results and open problems in the theory of hyperplane arrangements, with an emphasis on computations and examples. We give an introduction to many of the essential tools used in the area, such as…
A partial cube is a graph having an isometric embedding in a hypercube. Partial cubes are characterized by a natural equivalence relation on the edges, whose classes are called zones. The number of zones determines the minimal dimension of…
Neuroscience models commonly have a high number of degrees of freedom and only specific regions within the parameter space are able to produce dynamics of interest. This makes the development of tools and strategies to efficiently find…
Various non-trivial spaces are becoming popular for embedding structured data such as graphs, texts, or images. Following spherical and hyperbolic spaces, more general product spaces have been proposed. However, searching for the best…
In our era of rapid technological advancement, the research landscape for writing assistants has become increasingly fragmented across various research communities. We seek to address this challenge by proposing a design space as a…
We apply polynomial techniques (linear programming) to obtain lower and upper bounds on the covering radius of spherical designs as function of their dimension, strength, and cardinality. In terms of inner products we improve the lower…
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points and concepts are represented by regions in a (potentially) high-dimensional space. Based on our…
A Latin hypercuboid of order $n$ is a $d$-dimensional matrix of dimensions $n\times n\times\cdots\times n\times k$, with symbols from a set of cardinality $n$ such that each symbol occurs at most once in each axis-parallel line. If $k=n$…