Related papers: Multi-granular Perspectives on Covering
In this paper, I outline several conceptual and methodological issues related to modeling individual and group processes embedded in clustered/hierarchical data structures. We position multilevel modeling techniques within a broader set of…
We generalize the notion of a crossed module of groups to that of a crossed module of racks. We investigate the relation to categorified racks, namely strict 2-racks, and trunk-like objects in the category of racks, generalizing the…
We present the advantages of a multiscale modelling strategy for the understanding of systems with charged interfaces. On the one hand, one can simulate a complex system at different levels, depending on the relevant length and time scales…
In this paper, we are interested in study subgroups of topologized fundamental groups and their influences on generalized covering maps. More precisely, we find some relationships between generalized covering subgroups and the other famous…
Microstructural materials design is one of the most important applications of inverse modeling in materials science. Generally speaking, there are two broad modeling paradigms in scientific applications: forward and inverse. While the…
A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems is…
A planar set $P$ is said to be cover-decomposable if there is a constant $k=k(P)$ such that every $k$-fold covering of the plane with translates of $P$ can be decomposed into two coverings. It is known that open convex polygons are…
Data sites selected from modeling high-dimensional problems often appear scattered in non-paternalistic ways. Except for sporadic clustering at some spots, they become relatively far apart as the dimension of the ambient space grows. These…
In this paper, we mainly construct three types of $L$-fuzzy $\beta$-covering-based rough set models and study the axiom sets, matrix representations and interdependency of these three pairs of $L$-fuzzy $\beta$-covering-based rough…
It is important to classify covering subgroups of the fundamental group of a topological space using their topological properties in the topologized fundamental group. In this paper, we introduce and study some topologies on the fundamental…
Computing modular coincidences can show whether a given substitution system, which is supported on a point lattice in R^d, consists of model sets or not. We prove the computatibility of this problem and determine an upper bound for the…
The modeling of complex systems such as ecological or socio-economic systems can be very challenging. Although various modeling approaches exist, they are generally not compatible and mutually consistent, and empirical data often do not…
Recent innovations from machine learning allow for data unfolding, without binning and including correlations across many dimensions. We describe a set of known, upgraded, and new methods for ML-based unfolding. The performance of these…
Networks are a powerful tool to model complex systems, and the definition of many Graph Neural Networks (GNN), Deep Learning algorithms that can handle networks, has opened a new way to approach many real-world problems that would be hardly…
Machine learning models of vastly different modalities and architectures are being trained to predict the behavior of molecules, materials, and proteins. However, it remains unclear whether they learn similar internal representations of…
There have been some major advances in the theory of optimal designs for interference models. However, the majority of them focus on one-dimensional layout of the block and the study for two-dimensional interference model is quite limited…
We present a new multi-layer peeling technique to cluster points in a metric space. A well-known non-parametric objective is to embed the metric space into a simpler structured metric space such as a line (i.e., Linear Arrangement) or a…
We study bilinear embedding models for the task of multi-relational link prediction and knowledge graph completion. Bilinear models belong to the most basic models for this task, they are comparably efficient to train and use, and they can…
In multiscale modelling, multiple models are used simultaneously to describe scale-dependent phenomena in a system of interest. Here we introduce a machine learning (ML)-based multiscale modelling framework for modelling hierarchical…
Quadrilateral layouts on surfaces are valuable in texture mapping, and essential in generation of quadrilateral meshes and in fitting splines. Previous work has characterized such layouts as a special metric on a surface or as a meromorphic…