Related papers: Isomorphism of Hierarchical Structures
We consider tiling dynamical systems and topological conjugacies between them. We prove that the criterion of being finite type is invariant under topological conjugacy. For substitution tiling systems under rather general conditions,…
Abstract algebra provides a large hierarchy of properties that a collection of objects can satisfy, such as forming an abelian group or a semiring. These classifications can arranged into a broad and typically acyclic directed graph. This…
We combine several folklore observations to provide a working framework for iterating constructions which contradict the axiom of choice. We use this to define a model in which any kind of structural failure must fail with a proper class of…
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…
To improve the perception of hierarchical structures in data sets, several color map generation algorithms have been proposed to take this structure into account. But the design of hierarchical color maps elicits different requirements to…
Inspired by the modelization of 2D materials systems, we characterize arrangements of identical nonflat squares in 3D. We prove that the fine geometry of such arrangements is completely characterized in terms of patterns of mutual…
Rhombus Penrose tilings are tilings of the plane by two decorated rhombi such that the decoration match at the junction between two tiles (like in a jigsaw puzzle). In dynamical terms, they form a tiling space of finite type. If we remove…
One property of networks that has received comparatively little attention is hierarchy, i.e., the property of having vertices that cluster together in groups, which then join to form groups of groups, and so forth, up through all levels of…
We present a concept of uniform encodability of theories and develop tools related to this concept. As an application we obtain general undecidability results which are uniform for large families of structures. In the way, we define…
The poset of copies of a relational structure ${\mathbb X}$ is the partial order $\langle {\mathbb P} ({\mathbb X}) ,\subset \rangle$, where ${\mathbb P} ({\mathbb X})=\{ Y\subset X: {\mathbb Y} \cong {\mathbb X}\}$. Investigating the…
This paper introduces a class of objects called decision rules that map infinite sequences of alternatives to a decision space. These objects can be used to model situations where a decision maker encounters alternatives in a sequence such…
An equivalence structure is a set with a single binary relation, satisfying sentences stating that the relation is an equivalence relation. A computable structure A is said to be $\Delta^0_\alpha$ categorical if for any computable structure…
In this paper, we study the structure of the set of tilings produced by any given tile-set. For better understanding this structure, we address the set of finite patterns that each tiling contains. This set of patterns can be analyzed in…
We study tilings of the plane composed of two repeating tiles of different assigned areas relative to an arbitrary periodic lattice. We classify isoperimetric configurations (i.e., configurations with minimal length of the interfaces) both…
In classification problems, especially those that categorize data into a large number of classes, the classes often naturally follow a hierarchical structure. That is, some classes are likely to share similar structures and features. Those…
Two type structures are hierarchy-equivalent if they induce the same set of hierarchies of beliefs. This note shows that the behavioral implications of "cautious rationality and common cautious belief in cautious rationality" (Catonini and…
Morphisms are homomorphisms under the concatenation operation of the set of words over a finite set. Changing the elements of the finite set does not essentially change the morphism. We propose a way to select a unique representing member…
Let P be an object such as tiling, Delone set and weighted Dirac comb. There corresponds a dynamical system to P, called the corresponding dynamical system. Such dynamical systems are geometric analogues of symbolic dynamics. It is…
We associate a tower with an infinitesimal algebraic skeleton to the (2+1)-dimensional (compact and noncompact) Heisenberg spin model. In particular, we construct the absolute parallelism defining the tower and the corresponding extension…
We investigate combinations of structures by families of structures relative to families of unary predicates and equivalence relations. Conditions preserving $\omega$-categoricity and Ehrenfeuchtness under these combinations are…