Related papers: A lattice-ordered monoid on multilayer networks
Signed networks appear naturally in contexts where conflict or animosity is apparent. In this book chapter we review some of the literature on signed networks, especially in the context of partitioning. Most of the work is founded in what…
We consider partially ordered sets of combinatorial structures under consecutive orders, meaning that two structures are related when one embeds in the other such that `consecutive' elements remain consecutive in the image. Given such a…
In this paper, we introduce a partial order on neighborhood equivalence classes of maximally spread essential multibranched surfaces embedded in a 3-manifold. We show that if a maximally spread essential multibranched surface is atoroidal…
This paper presents a unified framework for determining the congruences on a number of monoids and categories of transformations, diagrams, matrices and braids, and on all their ideals. The key theoretical advances present an iterative…
We suggest that a certain one-to-one parametrization of completely positive maps on the matrix algebra might be useful in the study of quantum channels. This is illustrated in the case of binary quantum channels. While the algorithm is…
This paper introduces the concept of metric ideals in AL-monoids. We also examine the structure of AL-monoids and describe some of the properties of homomorphism and fundamentalisomorphism theorems.Additionaly we introduce and examine a…
In order theory, partially ordered sets are only equipped with one relation which decides the entire structure/Hasse diagram of the set. In this paper, we have presented how partially ordered sets can be studied under simultaneous partially…
Learning monotonic models with respect to a subset of the inputs is a desirable feature to effectively address the fairness, interpretability, and generalization issues in practice. Existing methods for learning monotonic neural networks…
We introduce a two layer network model for social coordination incorporating two relevant ingredients: a) different networks of interaction to learn and to obtain a payoff , and b) decision making processes based both on social and…
In this paper, we consider the monoid $\mathcal{PIO}_{n}$, of all partial order-preserving transformations on a chain with $n$ elements whose domains and ranges are intervals, along with its submonoid $\mathcal{PIO}_{n}^-$ of…
Two fundamental constructions operating on residuated lattices and partially ordered monoids (pomonoids) are so-called nuclear images and conuclear images. Nuclear images allow us to construct many of the ordered algebras which arise in…
Recent developments in complex systems have witnessed that many real-world scenarios, successfully represented as networks are not always restricted to binary interactions but often include higher-order interactions among the nodes. These…
In most natural and engineered systems, a set of entities interact with each other in complicated patterns that can encompass multiple types of relationships, change in time, and include other types of complications. Such systems include…
We study the signalling structure of higher order quantum maps from an order-theoretic perspective, building on the combinatorial characterization of higher order types by Bisio and Perinotti. We have shown in a previous work…
We study the properties of metrics aimed at the characterization of grid-like ordering in complex networks. These metrics are based on the global and local behavior of cycles of order four, which are the minimal structures able to identify…
We introduce two topological non-$\Sigma$ operad structures on planar line arrangements subject to a certain geometric order condition, ensuring a well-defined notion of particle ordering on a distinguished line. This is interpreted in…
Inferring network topology from smooth signals is a significant problem in data science and engineering. A common challenge in real-world scenarios is the availability of only partially observed nodes. While some studies have considered…
We define several sorts of mappings on a poset like monotone, strictly monotone, upper cone preserving and variants of these. Our aim is to characterize posets in which some of these mappings coincide. We define special mappings determined…
A lattice is a set of all the integer linear combinations of certain linearly independent vectors. One of the most important concepts on lattice is the successive minima which is of vital importance from both theoretical and practical…
There is a long tradition of the axiomatic study of consensus methods in phylogenetics that satisfy certain desirable properties. One recently-introduced property is associative stability, which is desirable because it confers a…