Related papers: Sequential parametrized topological complexity and…
The identification and classification of transitions in topological and microstructural regimes in pattern-forming processes are critical for understanding and fabricating microstructurally precise novel materials in many application…
A neural network with fixed topology can be regarded as a parametrization of functions, which decides on the correlations between functional variations when parameters are adapted. We propose an analysis, based on a differential geometry…
The embedding problem is to decide, given an ordered pair of structures, whether or not there is an injective homomorphism from the first structure to the second. We study this problem using an established perspective in parameterized…
Let $X$ be a two-cell complex with attaching map $\alpha\colon S^q\to S^p$, and let $C_X$ be the cofiber of the diagonal inclusion $X\to X\times X$. It is shown that the topological complexity (${\rm TC}$) of $X$ agrees with the…
Many mechanical systems have configuration spaces that admit symmetries. Mathematically, such symmetries are modelled by the action of a group on a topological space. Several variations of topological complexity have emerged that take…
In this paper we study the classifying theory of principal bundles in the parametrized setting, motivated by recent interest in higher gauge theory. Using simplicial techniques, we construct a product-preserving classifying space functor…
Control-flow graphs (CFGs) of structured programs are well known to exhibit strong sparsity properties. Traditionally, this sparsity has been modeled using graph parameters such as treewidth and pathwidth, enabling the development of faster…
The performance of multi-task learning in Convolutional Neural Networks (CNNs) hinges on the design of feature sharing between tasks within the architecture. The number of possible sharing patterns are combinatorial in the depth of the…
In this paper, we investigate structural properties of finite groups that are detected by certain group invariants arising from Dijkgraaf--Witten theory, a topological quantum field theory, in one space and one time dimension. In this…
Industrial control applications require high performance under strict constraints. Control barrier functions (CBFs) provide principled safety mechanisms, but constructing CBF-based safety filters for large-scale systems is challenging. We…
The versatility of self-attention mechanism earned transformers great success in almost all data modalities, with limitations on the quadratic complexity and difficulty of training. To apply transformers across different data modalities,…
We address the problem of planning robot motions in constrained configuration spaces where the constraints change throughout the motion. The problem is formulated as a fixed sequence of intersecting manifolds, which the robot needs to…
To enumerate 3-manifold triangulations with a given property, one typically begins with a set of potential face pairing graphs (also known as dual 1-skeletons), and then attempts to flesh each graph out into full triangulations using an…
We propose a new approach to image segmentation, which exploits the advantages of both conditional random fields (CRFs) and decision trees. In the literature, the potential functions of CRFs are mostly defined as a linear combination of…
We give simple upper bounds for rational sectional category and use them to compute invariants of the type of Farber's topological complexity of rational spaces. In particular we show that the sectional category of formal morphisms reaches…
In various web applications like targeted advertising and recommender systems, the available categorical features (e.g., product type) are often of great importance but sparse. As a widely adopted solution, models based on Factorization…
In this paper we combine a survey of the most important topological properties of kinematic maps that appear in robotics, with the exposition of some basic results regarding the topological complexity of a map. In particular, we discuss…
We investigate the parameterized complexity of Binary CSP parameterized by the vertex cover number and the treedepth of the constraint graph, as well as by a selection of related modulator-based parameters. The main findings are as follows:…
We show that topological phases include disordered materials if the underlying invariant is interpreted as originating from coarse geometry. This coarse geometric framework, grounded in physical principles, offers a natural setting for the…
We set the foundations for a new approach to Topological Data Analysis (TDA) based on homotopical methods at chain complexes level. We present the category of tame parametrised chain complexes as a comprehensive environment that includes…