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Motivated by recent work on mixtures of classical and free probabilities, we introduce and study the notion of $\epsilon$-noncrossing partitions. It is shown that the set of such partitions forms a lattice, which interpolates as a poset…
Recent interest in point and line node semimetals has led to the proposal and discovery of these phenomena in numerous systems. Frequently, though, these nodal systems are described in terms of individual properties reliant on specific…
Network embedding aims to learn the low-dimensional representations of vertexes in a network, while structure and inherent properties of the network is preserved. Existing network embedding works primarily focus on preserving the…
A notion of general manifolds is introduced. It covers all usual manifolds in mathematics. Essentially, it is a way how to get a bigger 'fibration' over a site which locally coincides with a given one. An enrichment with generalized…
We study the homotopy theory of diagrams of chain complexes over a field indexed by a finite poset, and show that it can be completely described in terms of appropriate diagrams of graded vector spaces.
Partially ordered sets (posets) play a universal role as an abstract structure in many areas of mathematics. For finite posets, an explicit enumeration of distinct partial orders on a set of unlabelled elements is known only up to a…
Category-level object pose estimation aims to predict the pose and size of arbitrary objects in specific categories. Existing methods struggle with the inherent incompleteness of observed point clouds, which limits their ability to capture…
In this paper, we use a unified framework introduced in [3] to study two classes of nonconforming immersed finite element (IFE) spaces with integral value degrees of freedom. The shape functions on interface elements are piecewise…
We introduce a notion of strong proximity join-semilattice, a predicative notion of continuous lattice which arises as the Karoubi envelop of the category of algebraic lattices. Strong proximity join-semilattices can be characterised by the…
Alternating sign matrices (ASMs) are square matrices with entries 0, 1, or -1 whose rows and columns sum to 1 and whose nonzero entries alternate in sign. We put ASMs into a larger context by studying the order ideals of subposets of a…
We prove that for any distributive join-semilattice S, there are a meet-semilattice P with zero and a map f:PxP-->S such that f(x,z)<=f(x,y)vf(y,z) and x<=y implies that f(x,y)=0, for all x,y,z in P, together with the following conditions:…
The symmetries of paths in a manifold $M$ are classified with respect to a given pointwise proper action of a Lie group $G$ on $M$. Here, paths are embeddings of a compact interval into $M$. There are at least two types of symmetries:…
A topological mating is a map defined by gluing together the filled Julia sets of two quadratic polynomials. The identifications are visualized and understood by pinching ray-equivalence classes of the formal mating. For postcritically…
This work investigates minimal parametric networks in hyperspaces of closed subsets of metric spaces endowed with the Hausdorff distance. It is shown that the problems of finding such networks are nontrivial only within finiteness classes,…
We explore a pointfree approach to spaces which extends the category of $T_0$ spaces. Our pointfree objects are Raney extensions, pairs $(L,C)$ where $C$ is a coframe, $L\subseteq C$ is a frame which meet-generates it, and the inclusion…
Using tools from topology and functional analysis, we provide a framework where artificial neural networks, and their architectures, can be formally described. We define the notion of machine in a general topological context and show how…
Matrix factorizations of a hypersurface yield a description of the asymptotic structure of minimal free resolutions over the hypersurface. We introduce a new concept of matrix factorizations for complete intersections that allows us to…
In matching theory, barrier sets (also known as Tutte sets) have been studied extensively due to its connection to maximum matchings in a graph. In this paper, we first define $\theta$-barrier sets. Our definition of a $\theta$-barrier set…
The topological classification of a system depends on the discrete symmetries of its Hamiltonian. In Floquet photonic waveguide arrays, the abstract symmetries of the Altland--Zirnbauer (AZ) scheme -- chiral, particle-hole, and…
A new algorithm, termed subspace evolution and transfer (SET), is proposed for solving the consistent matrix completion problem. In this setting, one is given a subset of the entries of a low-rank matrix, and asked to find one low-rank…