Related papers: A logifold structure on measure space
This work studies the limitations of uniquely identifying the structure (i.e., topology) of a networked linear system from partial measurements of its nodal dynamics. In general, many networks can be consistent with these measurements; this…
It is now well accepted that the galaxies are distributed in filaments, sheets and clusters all of which form an interconnected network known as the Cosmic Web. It is a big challenge to quantify the shapes of the interconnected structural…
We study mathematical and computational models for computing the deformation of fiber-reinforced cross-plied laminates due to external forces. This requires an understanding of both micro-structural effects and different sources of…
Image-level regression is an important task in Earth observation, where visual domain and label shifts are a core challenge hampering generalization. However, cross-domain regression within remote sensing data remains understudied due to…
Local clustering aims at extracting a local structure inside a graph without the necessity of knowing the entire graph structure. As the local structure is usually small in size compared to the entire graph, one can think of it as a…
Generalization to unseen data remains poorly understood for deep learning classification and foundation models, especially in the open set scenario. How can one assess the ability of networks to adapt to new or extended versions of their…
We introduce shift algebras as certain crossed product algebras based on general function spaces and study properties, as well as the classification, of a particular class of modules depending on a set of matrix parameters. It turns out…
With recent success of deep learning in 2D visual recognition, deep learning-based 3D point cloud analysis has received increasing attention from the community, especially due to the rapid development of autonomous driving technologies.…
Datasets of real-world applications are characterized by entities of different types, which are defined by multiple features and connected via varied types of relationships. A critical challenge for these datasets is developing models and…
Data living on manifolds commonly appear in many applications. Often this results from an inherently latent low-dimensional system being observed through higher dimensional measurements. We show that under certain conditions, it is possible…
Large datasets have become commonplace in NLP research. However, the increased emphasis on data quantity has made it challenging to assess the quality of data. We introduce Data Maps---a model-based tool to characterize and diagnose…
Dialectica categories are a very versatile categorical model of linear logic. These have been used to model many seemingly different things (e.g., Petri nets and Lambek's calculus). In this note, we expand our previous work on fuzzy petri…
We consider a simply supported plate with constant thickness, defined on an unknown multiply connected domain. We optimize its shape according to some given performance functional. Our method is of fixed domain type, easy to be implemented,…
Proximity measures on graphs have a variety of applications in network analysis, including community detection. Previously they have been mainly studied in the context of networks without attributes. If node attributes are taken into…
Key to structured prediction is exploiting the problem structure to simplify the learning process. A major challenge arises when data exhibit a local structure (e.g., are made by "parts") that can be leveraged to better approximate the…
We develop a kind of pregeometry consisting of a web of overlapping fuzzy lumps which interact with each other. The individual lumps are understood as certain closely entangled subgraphs (cliques) in a dynamically evolving network which, in…
A statistical, data-driven method is presented that quantifies influences between variables of a dynamical system. The method is based on finding a suitable representation of points by fuzzy affiliations with respect to landmark points…
Network percolation has recently been proposed as a method to characterize the global structure of an urban system form the bottom-up. This paper proposes to extend urban network percolation in a multi-dimensional way, to take into account…
Viewing neural network models in terms of their loss landscapes has a long history in the statistical mechanics approach to learning, and in recent years it has received attention within machine learning proper. Among other things, local…
We address the question of designing isotropic analysis functions on the sphere which are perfectly limited in the spectral domain and optimally localized in the spatial domain. This work is motivated by the need of localized analysis tools…