相关论文: Topological Residual Asymmetry for Bivariate Causa…

Time-delay embedding is a fundamental technique in Topological Data Analysis (TDA) for reconstructing the phase space dynamics of time-series data. Persistent homology effectively identifies global topological features, such as loops…

Tiny Recursive Models (TRM) were proposed as a parameter-efficient alternative to large language models for solving Abstraction and Reasoning Corpus (ARC) style tasks. The original work reports strong performance and suggests that recursive…

We propose a neural network-based approach to topology optimization that aims to reduce the use of support structures in additive manufacturing. Our approach uses a network architecture that allows the simultaneous determination of an…

We introduce a framework for analyzing topological tipping in time-evolutionary point clouds by extending the recently proposed Topological Optimal Transport (TpOT) distance. While TpOT unifies geometric, homological, and higher-order…

Topological Data Analysis (TDA) is a novel, and relatively new approach to analysing high-dimensional data sets. It does this by focussing on global properties like the shape and connectivity of the data giving it a significant advantage…

The problem of gridless direction of arrival (DOA) estimation is addressed in the non-uniform array (NUA) case. Traditionally, gridless DOA estimation and root-MUSIC are only applicable for measurements from a uniform linear array (ULA).…

We present new exact solutions for two-dimensional geometries generated by continuous distributions of topological defects within a conformal metric framework. By reformulating Einstein's equations in two dimensions as a Poisson equation…

We consider the problem of direction of arrival (DOA) estimation using a newly proposed structure of non-uniform linear arrays, referred to as co-prime arrays, in this paper. By exploiting the second order statistical information of the…

In this paper, we explore how to use topological tools to compare dimension reduction methods. We first make a brief overview of some of the methods often used dimension reduction such as Isometric Feature Mapping, Laplacian Eigenmaps, Fast…

Adaptive Resonance Theory (ART) is considered as an effective approach for realizing continual learning thanks to its ability to handle the plasticity-stability dilemma. In general, however, the clustering performance of ART-based…

Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology or the Euler Transform give a single complex description…

Bayesian doubly robust (DR) causal inference faces a fundamental dilemma: joint modeling of outcome and propensity score suffers from the feedback problem where outcome information contaminates propensity score estimation, while two-step…

In recent years a lot of research has been conducted within the area of causal inference and causal learning. Many methods have been developed to identify the cause-effect pairs in models and have been successfully applied to observational…

It is argued that topological disorder in amorphous solids can be described by local strains related to local reference crystals and local rotations. An intuitive localization criterion is formulated from this point of view. The Inverse…

Dimensionality reduction (DR) techniques are often characterized by whether they preserve global, high-level structures in the data or local, neighborhood structures. This distinction matters in visualization: global methods can obscure…

We consider data consisting of photon counts of diffracted x-ray radiation as a function of the angle of diffraction. The problem is to determine the positions, powers and shapes of the relevant peaks. An additional difficulty is that the…

Current state-of-the-art multi-class unsupervised anomaly detection (MUAD) methods rely on training encoder-decoder models to reconstruct anomaly-free features. We first show these approaches have an inherent fidelity-stability dilemma in…

The quasi-coherent effects in two-dimensional incompressible turbulence are analyzed starting from the test particle trajectories. They can acquire coherent aspects when the stochastic potential has slow time variation and the motion is not…

We propose robust sparse reduced rank regression for analyzing large and complex high-dimensional data with heavy-tailed random noise. The proposed method is based on a convex relaxation of a rank- and sparsity-constrained non-convex…

Directional media, such as nematic liquid crystals and ferromagnets, are characterized by their topologically stabilized defects in directional order. In nematics, boundary conditions and surface-treated inclusions often create complex…