Related papers: Templates, Arrays, and Overlays
We introduce layer systems for proving generalizations of the modularity of confluence for first-order rewrite systems. Layer systems specify how terms can be divided into layers. We establish structural conditions on those systems that…
Patterns are fundamental to human cognition, enabling the recognition of structure and regularity across diverse domains. In this work, we focus on structural repeats, patterns that arise from the repetition of hierarchical relations within…
We define recurrence matrices and study a few properties (links with automatic sequences, branch groups etc.) of them.
Since the development of photography art, many so-called "templates" have been formed, namely visual styles summarized from a series of themed and stylized photography works. In this paper, we propose to analysize and and summarize these…
Starting from filters over the set of indices, we introduce structures in a product of sets where the coordinate sets have the given structures.
Our earlier paper "Patterns of Patterns" combined three techniques from training, futures studies, and design in a design pattern called PLACARD that helps groups of people work together effectively. We used that pattern in five hands-on…
{When visualizing data in a realistically rendered 3D virtual environment, it is often important to represent not only the 3D scene but also overlaid information about additional, abstract data. These overlays must be usefully visible, i.e.…
Hierarchical structure and repetition are prevalent in graphs originating from nature or engineering. These patterns can be represented by a class of parametric-structure graphs, which are defined by templates that generate structure by way…
Scenarios elicit possibilities that may be ignored otherwise, as well as causal relations between them. Even when too little information is available to assess reliable probabilities, the structure of linkages between evoked alternatives…
Two-dimensional patterns are used in many research areas in computer science, ranging from image processing to specification and verification of complex software systems (via scenarios). The contribution of this paper is twofold. First, we…
In this paper, we present a new algorithm for computing the linear recurrence relations of multi-dimensional sequences. Existing algorithms for computing these relations arise in computational algebra and include constructing structured…
Patterns describe proven solutions for recurring problems. Typically, patterns in a particular domain are interrelated and organized in pattern languages. As real-world problems often require patterns of multiple domains, different pattern…
We investigate circular planar nearrings constructed from finite fields as well the complex number field using a multiplicative subgroup of order $k$, and characterize the overlaps of the basic graphs which arise in the associated…
In this article one builds a class of recursive sets, one establishes properties of these sets, and one proposes applications.
Complex systems are characterized by many interacting units that give rise to emergent behavior. A particularly advantageous way to study these systems is through the analysis of the networks that encode the interactions among the system's…
We introduce a family of reconfiguration puzzles arising from ideas in geometry and topology. We present their construction from square-tiled shapes, discuss some of the underlying mathematics and describe how they are naturally associated…
We present a mathematical and algorithmic scheme for learning the principal geometric elements in an image or 3D object. We build on recent work that convexifies the basic problem of finding a combination of a small number shapes that…
In this paper, we present an Ontology Design Pattern for representing situations that recur at regular periods and share some invariant factors, which unify them conceptually: we refer to this set of recurring situations as recurrent…
This article presents a model which is capable of learning and abstracting new concepts based on comparing observations and finding the resemblance between the observations. In the model, the new observations are compared with the templates…
This article examines matrices whose entries are determined by recursive relations of the form $A_{i, j} = x A_{i, j-1} + y A_{i-1, j-1} + z A_{i-1, j}$, where $x, y, z$ are constants, and the initial conditions are defined along the first…