Related papers: Factorizing Lattices by Interval Relations
Formal Concept Analysis (FCA) allows to analyze binary data by deriving concepts and ordering them in lattices. One of the main goals of FCA is to enable humans to comprehend the information that is encapsulated in the data; however, the…
In this paper, we consider the solution of ill-conditioned systems of linear algebraic equations that can be determined imprecisely. To improve the stability of the solution process, we "immerse" the original imprecise linear system in an…
We construct the universal realized limit sketch associated to a given limit sketch. The construction uses factorization systems to organize the classical argument of [2], yielding a streamlined and conceptually unified formulation of the…
Quadratic form reduction and lattice reduction are fundamental tools in computational number theory and in computer science, especially in cryptography. The celebrated Lenstra-Lenstra-Lov\'asz reduction algorithm (so-called LLL) has been…
High order calculation at semi-hard scale is very important, but a satisfactory calculation framework is still missing. We propose a systematic method to regularize rapidity divergences in the CGC factorization, which makes higher order…
The problem of causal inference is to determine if a given probability distribution on observed variables is compatible with some causal structure. The difficult case is when the causal structure includes latent variables. We here introduce…
We study lattices acting on $\mathrm{CAT}(0)$ spaces via their commensurated subgroups. To do this we introduce the notions of a graph of lattices and a complex of lattices giving graph and complex of group splittings of $\mathrm{CAT}(0)$…
In a previous paper I showed how the ideal SLAC derivative and second-derivative operators for an infinite lattice can be obtained in simple closed form in position space, and implemented very efficiently in a stochastic fashion for…
Given a formal context, an ordinal factor is a subset of its incidence relation that forms a chain in the concept lattice, i.e., a part of the dataset that corresponds to a linear order. To visualize the data in a formal context, Ganter and…
Strict inequalities in mixed-integer linear optimization can cause difficulties in guaranteeing convergence and exactness. Utilizing that optimal vertex solutions follow a lattice structure we propose a rounding rule for strict inequalities…
Motivated by lattice mixture identification and grain boundary detection, we present a framework for lattice pattern representation and comparison, and propose an efficient algorithm for lattice separation. We define new scale and shape…
The main objective of this thesis is a classification project for integral lattices. Using Kneser's neighbour method we have developed the computer program tn to classify complete genera of integral lattices. Main results are detailed…
We introduce and characterize various gluing constructions for residuated lattices that intersect on a common subreduct, and which are subalgebras, or appropriate subreducts, of the resulting structure. Starting from the 1-sum construction…
By a 1941 result of Ph. M. Whitman, the free lattice FL(3) on three generators includes a sublattice $S$ that is isomorphic to the lattice FL($\omega$)=FL($\aleph_0$) generated freely by denumerably many elements. The first author has…
We study different extended formulations for the set $X = \{x\in\mathbb{Z}^n \mid Ax = Ax^0\}$ in order to tackle the feasibility problem for the set $X_+=X \cap \mathbb{Z}^n_+$. Here the goal is not to find an improved polyhedral…
Divisible residuated lattices are algebraic structures corresponding to a more comprehensive logic than Hajek's basic logic with an important significance in the study of fuzzy logic. The purpose of this paper is to investigate commutative…
In this paper, firstly, we determine the number of sublogics of variable inclusion of an arbitrary finitary logic L with partition function. Then, we investigate their position into the lattice of consequence relations over the language of…
I review recent approaches to constructing supersymmetric lattice theories focusing in particular on the concept of topological twisting. The latter technique is shown to expose a nilpotent, scalar supersymmetry which can be implemented…
This paper presents a novel set-based computing method, called interval superposition arithmetic, for enclosing the image set of multivariate factorable functions on a given domain. In order to construct such enclosures, the proposed…
In typical non-idempotent intersection type systems, proof normalization is not confluent. In this paper we introduce a confluent non-idempotent intersection type system for the lambda-calculus. Typing derivations are presented using proof…