Related papers: Too Many or Too Few? Sampling Bounds for Topologic…

Topological transforms are parametrized families of topological invariants, which, by analogy with transforms in signal processing, are much more discriminative than single measurements. The first two topological transforms to be defined…

Topological Data Analysis (TDA) is a recent and growing branch of statistics devoted to the study of the shape of the data. In this work we investigate the predictive power of TDA in the context of supervised learning. Since topological…

Understanding the macroscopic characteristics of biological complexes demands precision and specificity in statistical ensemble modeling. One of the primary challenges in this domain lies in sampling from particular subsets of the…

Phenomenological (P-type) bifurcations are qualitative changes in stochastic dynamical systems whereby the stationary probability density function (PDF) changes its topology. The current state of the art for detecting these bifurcations…

Graph convolutions have gained popularity due to their ability to efficiently operate on data with an irregular geometric structure. However, graph convolutions cause over-smoothing, which refers to representations becoming more similar…

Ensuring that analyses performed on a dataset are representative of the entire population is one of the central problems in statistics. Most classical techniques assume that the dataset is independent of the analyst's query and break down…

Dimensionality is one of the most important properties of complex physical systems. However, only recently this concept has been considered in the context of complex networks. In this paper we further develop the previously introduced…

Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…

We review some recently published methods to represent atomic neighbourhood environments, and analyse their relative merits in terms of their faithfulness and suitability for fitting potential energy surfaces. The crucial properties that…

Recently, the computer vision and machine learning community has been in favor of feature extraction pipelines that rely on a coding step followed by a linear classifier, due to their overall simplicity, well understood properties of linear…

Topological deep learning (TDL) is a rapidly growing field that seeks to leverage topological structure in data and facilitate learning from data supported on topological objects, ranging from molecules to 3D shapes. Most TDL architectures…

Evaluating the quality of reasoning traces from large language models remains understudied, labor-intensive, and unreliable: current practice relies on expert rubrics, manual annotation, and slow pairwise judgments. Automated efforts are…

This article presents an algebraic topology perspective on the problem of finding a complete coverage probability of a one dimensional domain $X$ by a random covering, and develops techniques applicable to the problem beyond the one…

Persistent Homology is a powerful tool in Topological Data Analysis (TDA) to capture topological properties of data succinctly at different spatial resolutions. For graphical data, shape, and structure of the neighborhood of individual data…

The classification of shapes is of great interest in diverse areas ranging from medical imaging to computer vision and beyond. While many statistical frameworks have been developed for the classification problem, most are strongly tied to…

Graph is powerful for representing various types of real-world data. The topology (edges' presence) and edges' features of a graph decides the message passing mechanism among vertices within the graph. While most existing approaches only…

Symbolic regression is the machine learning method for learning functions from data. After a brief overview of the symbolic regression landscape, I will describe the two main challenges that traditional algorithms face: they have an unknown…

Recent genomic and bioinformatic advances have motivated the development of numerous random network models purporting to describe graphs of biological, technological, and sociological origin. The success of a model has been evaluated by how…

Boolean formulae compactly encode huge, constrained search spaces. Thus, variability-intensive systems are often encoded with Boolean formulae. The search space of a variability-intensive system is usually too large to explore without…

We investigate topological descriptors for 3D surface analysis, i.e. the classification of surfaces according to their geometric fine structure. On a dataset of high-resolution 3D surface reconstructions we compute persistence diagrams for…