Related papers: On the Stability of the Euler Characteristic Trans…
This paper introduces the Strain Elevation Tension Spring embedding (SETSe) algorithm, a graph embedding method that uses a physics model to create node and edge embeddings in undirected attribute networks. Using a low-dimensional…
Unitary transformations are an essential tool for the theoretical understanding of many systems by mapping them to simpler effective models. A systematically controlled variant to perform such a mapping is a perturbative continuous unitary…
The approximation of invariant measures for nonlinear ergodic stochastic differential equations (SDEs) is a central problem in scientific computing, with important applications in stochastic sampling, physics, and ecology. We first propose…
Euler diagrams are an intuitive and popular method to visualize set-based data. In a Euler diagram, each set is represented as a closed curve, and set intersections are shown by curve overlaps. However, Euler diagrams are not visually…
The space of two-dimensional geometric adeles of a surface is far from being a locally compact space and there is no translation countably additive invariant nontrivial measure on it. At the same time, certain subquotients of the adeles are…
Two well studied invariants of a complex projective variety are the unit Euclidean distance degree and the generic Euclidean distance degree. These numbers give a measure of the algebraic complexity for "nearest" point problems of the…
Mesh deformation plays a pivotal role in many 3D vision tasks including dynamic simulations, rendering, and reconstruction. However, defining an efficient discrepancy between predicted and target meshes remains an open problem. A prevalent…
Transformer-based models have achieved remarkable success, but their core components, Transformer layers, are largely heuristics-driven and engineered from the bottom up, calling for a prototypical model with high interpretability and…
While analytics of sleep electroencephalography (EEG) holds certain advantages over other methods in clinical applications, high variability across subjects poses a significant challenge when it comes to deploying machine learning models…
How can prior knowledge on the transformation invariances of a domain be incorporated into the architecture of a neural network? We propose Equivariant Transformers (ETs), a family of differentiable image-to-image mappings that improve the…
Persistence diagrams (PD)s play a central role in topological data analysis, and are used in an ever increasing variety of applications. The comparison of PD data requires computing comparison metrics among large sets of PDs, with metrics…
Creating comprehensible visualizations of highly overlapping set-typed data is a challenging task due to its complexity. To facilitate insights into set connectivity and to leverage semantic relations between intersections, we propose a…
Equation Discovery techniques have shown considerable success in regression tasks, where they are used to discover concise and interpretable models (\textit{Symbolic Regression}). In this paper, we propose a new ED-based binary…
Edit-distance-based string similarity search has many applications such as spell correction, data de-duplication, and sequence alignment. However, computing edit distance is known to have high complexity, which makes string similarity…
The Energy Mover's Distance (EMD) has seen use in collider physics as a metric between events and as a geometric method of defining infrared and collinear safe observables. Recently, the Spectral Energy Mover's Distance (SEMD) has been…
Feature selection is a dimensionality reduction technique that selects a subset of representative features from high dimensional data by eliminating irrelevant and redundant features. Recently, feature selection combined with sparse…
Let $F$ be a probability distribution on $\mathbb{R}^d$ which admits a bounded density. We investigate the Euler characteristic of the \v{C}ech complex on $n$ points sampled from $F$ i.i.d. as $n\to\infty$ in the thermodynamic limit regime.…
A central challenge in dynamic network analysis is to represent temporal evolution in a way that is both geometrically meaningful and statistically identifiable. One approach embeds a sequence of network snapshots as trajectories in a…
In this paper, a B-spline chained multiple random matrices representation is proposed to model geometric characteristics of an elongated deformable object. The hyper degrees of freedom structure of the elongated deformable object make its…
Learning graph representations via low-dimensional embeddings that preserve relevant network properties is an important class of problems in machine learning. We here present a novel method to embed directed acyclic graphs. Following prior…