Related papers: Poset Matrix Structure Via Partial Composition Ope…
We propose a matrix approach for generating naturally labeled posets by representing each poset $P$ on the set $[n]$ as a Boolean poset matrix $A$. This algebraic representation enables a systematic handling of partial orderings through…
In this paper, we propose a new type of matroids, namely covering matroids, and investigate the connections with the second type of covering-based rough sets and some existing special matroids. Firstly, as an extension of partitions,…
A frame in an $n$-dimensional Hilbert space $H_n$ is a possibly redundant collection of vectors $\{f_i\}_{i\in I}$ that span the space. A tight frame is a generalization of an orthonormal basis. A frame $\{f_i\}_{i\in I}$ is said to be…
We describe four natural operad structures on the vector space generated by isomorphism classes of finite posets. The three last ones are set-theoretical and can be seen as a simplified version of the first, the same way the NAP operad…
Pulling back sets of functions in involution by Poisson mappings and adding Casimir functions during the process allows to construct completely integrable systems. Some examples are investigated in detail.
In the present paper we introduce a lattice-ordered partial monoid structure on a suitable set of multilayer networks. We first study a kind of mappings that preserve the partial order and describe the order structure. After that we define…
Human pose is typically represented by a coordinate vector of body joints or their heatmap embeddings. While easy for data processing, unrealistic pose estimates are admitted due to the lack of dependency modeling between the body joints.…
Open dynamical systems are mathematical models of machines that take input, change their internal state, and produce output. For example, one may model anything from neurons to robots in this way. Several open dynamical systems can be…
We study the so-called closed and splitting subsemimodules and submodules of a given semimodule or module, respectively. We describe lattices of subsemimodules and of closed subsemimodules and posets of splitting subsemimodules and…
Algebraic structures with multiple copies of a given type of operations interrelated by various compatibility conditions have long being studied in mathematics and mathematical physics. They are broadly referred as linearly compatible,…
We provide elementary proofs of several results concerning the possible outcomes arising from a fixed profile within the class of positional voting systems. Our arguments enable a simple and explicit construction of paradoxical profiles,…
This work reports a new methodology aimed at describing characteristics of protein structural shapes, and suggests a framework in which to resolve or classify automatically such structures into known families. This new approach to protein…
In a multi-modeling based approach, the system under development is described by several models that represent various perspectives and concerns. Obviously, these partial representations are less complex than the global model, but they need…
Realignment operation has a significant role in detecting bound as well as free entanglement. Just like partial transposition, it is also based on permutations of the matrix elements. However, the physical implementation of realignment…
The contribution of this paper is threefold: first, it defines a framework for modelling component-based systems, as well as a formalization of integration rules to combine their behavior. This is based on finite state machines (FSM).…
New families of fourth-order composition methods for the numerical integration of initial value problems defined by ordinary differential equations are proposed. They are designed when the problem can be separated into three parts in such a…
The class of poset metrics is very large and contains some interesting families of metrics. A family of metrics, based on posets which are formed from disjoint chains which have the same size, is examined. A necessary and sufficient…
We define a new structure on a space endowed with convexities, and call it a fractoconvex structure (or, a space with fractoconvexity). We introduce two operations on a set of fractoconvexities and in a special case we show that they…
We introduce two partially ordered sets, $P^A_n$ and $P^B_n$, of the same cardinalities as the type-A and type-B noncrossing partition lattices. The ground sets of $P^A_n$ and $P^B_n$ are subsets of the symmetric and the hyperoctahedral…
In this paper, using group actions, we introduce a new method for constructing partial geometric designs (sometimes referred to as $1\frac{1}{2}$-designs). Using this new method, we construct several infinite families of partial geometric…