Related papers: Templates, Arrays, and Overlays
We use elementary methods to establish three key recurrence relations: one for derangement numbers, a second for harmonic numbers, and a third for degenerate harmonic numbers. Our results not only contribute to the understanding of the…
Real world arrays often contain underlying structure, such as sparsity, runs of repeated values, or symmetry. Specializing for structure yields significant speedups. But automatically generating efficient code for structured data is…
The paper proposes a novel technique for representing templates and instances of concept classes. A template representation refers to the generic representation that captures the characteristics of an entire class. The proposed technique…
The visual world around us can be described as a structured set of objects and their associated relations. An image of a room may be conjured given only the description of the underlying objects and their associated relations. While there…
Data processing systems impose multiple views on data as it is processed by the system. These views include spreadsheets, databases, matrices, and graphs. Associative arrays unify and simplify these different approaches into a common…
We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types…
We present a second-order language that can be used to succinctly specify ontologies in a consistent and transparent manner. This language is based on ontology templates (OTTR), a framework for capturing recurring patterns of axioms in…
Several real-world and abstract structures and systems are characterized by marked hierarchy to the point of being expressed as trees. Because the study of these entities often involves sampling (or discovering) the tree nodes in a specific…
Graph construction, a fundamental operation in a data processing pipeline, is typically done by multiplying the incidence array representations of a graph, $\mathbf{E}_\mathrm{in}$ and $\mathbf{E}_\mathrm{out}$, to produce an adjacency…
We describe how the reversion of a series is related to convolutional recurrence relations for the series, and we place this relationship in the context of Riordan arrays. As an example of the approach, we give new recurrence relations for…
We study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to given properties…
Graphs are commonly used in mathematics to represent some relationships between items. However, as simple objects, they sometimes fail to capture all relevant aspects of real-world data. To address this problem, we generalize them and model…
We propose some new method of constructing configurations, which consists in consecutive inscribing copies of one underlying configuration. A uniform characterization of the obtained class and the one introduced in our paper untitled…
We use the persistent homology method of topological data analysis and dimensional analysis techniques to study data of syntactic structures of world languages. We analyze relations between syntactic parameters in terms of dimensionality,…
Template matching is a basic method in image analysis to extract useful information from images. In this paper, we suggest a new method for pattern matching. Our method transform the template image from two dimensional image into one…
Binary multirelations generalise binary relations by associating elements of a set to its subsets. We study the structure and algebra of multirelations under the operations of union, intersection, sequential and parallel composition, as…
We develop a learning framework for building deformable templates, which play a fundamental role in many image analysis and computational anatomy tasks. Conventional methods for template creation and image alignment to the template have…
The goal of this paper is to show that generalizing the notion of frequent patterns can be useful in extending association analysis to more complex higher order patterns. To that end, we describe a general framework for modeling a complex…
Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to…
This note is a survey on the topology of hyperplane arrangements. We mainly focus on the relationship between topology and the real structure, such as adjacent relations of chambers and stratifications related to real structures.