Related papers: Factorizing Lattices by Interval Relations
The general deterministic recombination equation in continuous time is analysed for various lattices, with special emphasis on the lattice of interval (or ordered) partitions. Based on the recently constructed general solution for the…
We construct a simple multicomponent lattice gas model in one dimension in which each site can either be empty or occupied by at most one particle of any one of $D$ species. Particles interact with a nearest neighbor interaction which…
We study maximal sublattices of finite semidistributive lattices via their complements. We focus on the conjecture that such complements are always intervals, which is known to be true for bounded lattices. Since the class of…
Modern data science applications often involve complex relational data with dynamic structures. An abrupt change in such dynamic relational data is typically observed in systems that undergo regime changes due to interventions. In such a…
Each finite algebra $\mathbf A$ induces a lattice~$\mathbf L_{\mathbf A}$ via the quasi-order~$\to$ on the finite members of the variety generated by~$\mathbf A$, where $\mathbf B \to \mathbf C$ if there exists a homomorphism from $\mathbf…
This article is part of my upcoming masters thesis which investigates the following open problem from the book, Free Lattices, by R.Freese, J.Jezek, and J.B. Nation published in 1995: "Which lattices (and in particular which countable…
We propose a new approach to temporal inference, inspired by the Pearlian causal inference paradigm - though quite different from Pearl's approach formally. Rather than using directed acyclic graphs, we make use of factored sets, which are…
In this paper, using compute-and-forward as an example, we provide an overview of constructions of lattices from codes that possess the right algebraic structures for harnessing interference. This includes Construction A, Construction D,…
This article is the second part of an essay dedicated to lattices freely generated by posets within a variety. The first part dealt with four easy varieties while this part is concerned with finitely generated varieties. Here we present a…
Cut vertices, a generalization of matrix elements of local operators, are revisited, and an expansion in terms of minimally subtracted cut vertices is formulated. An extension of the formalism to deal with semi-inclusive deep inelastic…
Lifted inference exploits symmetries in probabilistic graphical models by using a representative for indistinguishable objects, thereby speeding up query answering while maintaining exact answers. Even though lifting is a well-established…
In a recent paper we proposed the study of aggregation functions on lattices via clone theory approach. Observing that aggregation functions on lattices just correspond to $0,1$-monotone clones, we have shown that all aggregation functions…
Drawing inspiration from Emmy Noether'set-theoretic foundations for algebra and Charles Ehresmann's topology without points, we adopt a new order-theoretic approach to ideal theory. For this we emphasize the order of divisibility in…
Temporal relation classification is the task of determining the temporal relation between pairs of temporal entities in a text. Despite recent advancements in natural language processing, temporal relation classification remains a…
Let $\mathbf{F}=\left\langle F,R\right\rangle $ be a finite Kripke frame. A congruence of $\mathbf{F}$ is a bisimulation of $\mathbf{F}$ that is also an equivalence relation on F. The set of all congruences of $\mathbf{F}$ is a lattice…
We introduce the concept of a quasiresiduated lattice and prove that every lattice effect algebra can be organized into a commutative quasiresiduated lattice with divisibility. Also conversely, every such a lattice can be converted into a…
This note addresses the input and output of intervals in the sense of interval arithmetic and interval constraints. The most obvious, and so far most widely used notation, for intervals has drawbacks that we remedy with a new notation that…
The natural join and the inner union combine in different ways tables of a relational database. Tropashko [18] observed that these two operations are the meet and join in a class of lattices-called the relational lattices- and proposed…
Properties of intervals in the lattice of antichains of subsets of a universe of finite size are investigated. New objects and quantities in this lattice are defined. Expressions and numerical values are deduced for the number of connected…
We characterize the finite intervals of the Muchnik lattice by proving that they are a certain proper subclass of the finite distributive lattices.