Related papers: Lattice induced threshold functions and Boolean fu…
Measure and integral are two closely related, but distinct objects of study. Nonetheless, they are both real-valued lattice valuations: order preserving real-valued functions $\phi$ on a lattice $L$ which are modular, i.e.,…
This work proposes an alternative approach to the so-called lattice of embedded subsets, which is included in the product of the subset and partition lattices of a finite set, and whose elements are pairs consisting of a subset and a…
Inspired by the work of Izakhian and Rhodes, a theory of representation of hereditary collections by boolean matrices is developed. This corresponds to representation by finite $\vee$-generated lattices. The lattice of flats, defined for…
Four point correlation functions for many electrons at finite temperature in periodic lattice are analyzed by the perturbation theory with respect to the coupling constant. The correlation functions are characterized as a limit of finite…
The main aim of this paper is to study aggregation functions on lattices via clone theory approach. Observing that the aggregation functions on lattices just correspond to $0,1$-monotone clones, as the main result we show that for any…
We are interested in representations and characterizations of lattice polynomial functions f:L^n -> L, where L is a given bounded distributive lattice. In companion papers [arXiv 0901.4888, arXiv 0808.2619], we investigated certain…
Lattices induced by coverings arise naturally in matroid theory and combinatorial optimization, providing a structured framework for analyzing relationships between independent sets and closures. In this paper, we explore the structural…
In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…
The lower moments of the unpolarized and polarized deep-inelastic structure functions of the nucleon are calculated on the lattice. The calculation is done with Wilson fermions and for three values of the hopping parameter $\kappa$, so that…
Recent lattice calculations of hadron structure functions are described.
We use a path integral approach to calculate the superfluid density of a Bose lattice gas in the limit where the number of atoms per site is large. Our analytical expressions agree with numerical results on small systems for low…
We propose a representation of boolean bent functions by bent rectangles, that is, by special matrices with restrictions on rows and columns. Using this representation, we exhibit new classes of bent functions, give an algorithm to…
Correlation functions and correlation lengths are frequently used to describe phase transitions in quantum systems, but they require an explicit choice of observables. The recently introduced information lattice instead provides an…
It is shown that, given a lattice H in a totally disconnected, locally compact group G, the contraction subgroups in G and the values of the scale function on G are determined by their restrictions to H. Group theoretic properties intrinsic…
This is a survey of some recent applications of Boolean valued models of set theory to order bounded operators in vector lattices.
We review a few results concerning interpolation of monotone functions on infinite lattices, emphasizing the role of set-theoretic considerations. We also discuss a few open problems.
The Galois lattice is a graphic method of representing knowledge structures. The first basic purpose in this paper is to introduce a new class of Galois lattices, called graded Galois lattices. As a direct result, one can obtain the notion…
This paper introduces control barrier functions for discrete-time systems, which can be shown to be necessary and sufficient for controlled invariance of a given set. Moreover, we propose nonlinear discrete-time control barrier functions…
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…
Our main goal is to develop a representation for finite distributive nearlattices through certain ordered structures. This representation generalizes the well-known representation given by Birkhoff for finite distributive lattices through…