Related papers: Sequential parametrized topological complexity and…
Automated feature engineering (AFE) enables AI systems to autonomously construct high-utility representations from raw tabular data. However, existing AFE methods rely on statistical heuristics, yielding brittle features that fail under…
We show that the symmetry topological field theory (SymTFT) construction, also known as the topological holography, provides a natural and intuitive framework for the entropic order parameter characterising phases with (partially) broken…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part we discus the main structures…
Temporal graphs provide a useful model for many real-world networks. Unfortunately the majority of algorithmic problems we might consider on such graphs are intractable. There has been recent progress in defining structural parameters which…
Robot motion planning is central to real-world autonomous applications, such as self-driving cars, persistence surveillance, and robotic arm manipulation. One challenge in motion planning is generating control signals for nonlinear systems…
This paper studies the unification problem with associative, commutative, and associative-commutative functions mainly from a viewpoint of the parameterized complexity on the number of variables. It is shown that both associative and…
As robots play an increasingly important role in the industrial, the expectations about their applications for everyday living tasks are getting higher. Robots need to perform long-horizon tasks that consist of several sub-tasks that need…
We introduce an harmonic analysis for iterated function systems (IFS) (X, mu) which is based on a Markov process on certain paths. The probabilities are determined by a weight function W on X. From W we define a transition operator R_W…
A fundamental advantage of Petri net models is the possibility to automatically compute useful system invariants from the syntax of the net. Classical techniques used for this are place invariants, P-components, siphons or traps. Recently,…
We study computationally-hard fundamental motion planning problems where the goal is to translate $k$ axis-aligned rectangular robots from their initial positions to their final positions without collision, and with the minimum number of…
In this paper, we begin constructing a new finite-dimensional topological quantum field theory (TQFT) for three-manifolds, based on group PSL(2,C) and its action on a complex variable by fractional-linear transformations, by providing its…
We construct a state-sum type invariant of smooth closed oriented $4$-manifolds out of a $G$-crossed braided spherical fusion category ($G$-BSFC) for $G$ a finite group. The construction can be extended to obtain a $(3+1)$-dimensional…
The conditional particle filter (CPF) is a promising algorithm for general hidden Markov model smoothing. Empirical evidence suggests that the variant of CPF with backward sampling (CBPF) performs well even with long time series. Previous…
Fine-grained visual classification (FGVC) remains highly sensitive to geometric variability, where objects appear under arbitrary orientations, scales, and perspective distortions. While equivariant architectures address this issue, they…
Based on a recent development in the area of error control coding, we introduce the notion of convolutional factor graphs (CFGs) as a new class of probabilistic graphical models. In this context, the conventional factor graphs are referred…
An equivariant topological field theory is defined on a cobordism category of manifolds with principal fiber bundles for a fixed (finite) structure group. We provide a geometric construction which for any given morphism $G \to H$ of finite…
Learning to plan for multi-step, multi-manipulator tasks is notoriously difficult because of the large search space and the complex constraint satisfaction problems. We present Generative Factor Chaining~(GFC), a composable generative model…
We present a machine learning approach that leverages persistent homology to classify bacterial flagellar motors into two functional states: rotated and stalled. By embedding protein structural data into a topological framework, we extract…
Designing a multi-layer optical system with designated optical characteristics is an inverse design problem in which the resulting design is determined by several discrete and continuous parameters. In particular, we consider three design…
In this paper, we deal with the robot motion planning problem in multi-valued function theory. We first enrich the multi-homotopy studies by introducing a multi-homotopy lifting property and a multi-fibration. Then we compute both a…