Related papers: Dark soliton detection using persistent homology
Astronomical images are often plagued by unwanted artifacts that arise from a number of sources including imperfect optics, faulty image sensors, cosmic ray hits, and even airplanes and artificial satellites. Spurious reflections (known as…
Robust topological information commonly comes in the form of a set of persistence diagrams, finite measures that are in nature uneasy to affix to generic machine learning frameworks. We introduce a fast, learnt, unsupervised vectorization…
While deep learning has seen many recent applications to drug discovery, most have focused on predicting activity or toxicity directly from chemical structure. Phenotypic changes exhibited in cellular images are also indications of the…
The gesture recognition using motion capture data and depth sensors has recently drawn more attention in vision recognition. Currently most systems only classify dataset with a couple of dozens different actions. Moreover, feature…
Despite significant advances in clustering methods in recent years, the outcome of clustering of a natural image dataset is still unsatisfactory due to two important drawbacks. Firstly, clustering of images needs a good feature…
Identifying molecular signatures from complex disease patients with underlying symptomatic similarities is a significant challenge in the analysis of high dimensional multi-omics data. Topological data analysis (TDA) provides a way of…
Artificial neural networks can learn complex, salient data features to achieve a given task. On the opposite end of the spectrum, mathematically grounded methods such as topological data analysis allow users to design analysis pipelines…
We outline a detection method for adversarial inputs to deep neural networks. By viewing neural network computations as graphs upon which information flows from input space to out- put distribution, we compare the differences in graphs…
Visually similar characters, or homoglyphs, can be used to perform social engineering attacks or to evade spam and plagiarism detectors. It is thus important to understand the capabilities of an attacker to identify homoglyphs --…
Topological data analysis (TDA) uncovers crucial properties of objects in medical imaging. Methods based on persistent homology have demonstrated their advantages in capturing topological features that traditional deep learning methods…
Topological methods for data analysis present opportunities for enforcing certain invariances of broad interest in computer vision, including view-point in activity analysis, articulation in shape analysis, and measurement invariance in…
In this work, we introduce persistent homology for the analysis of cryo-electron microscopy (cryo-EM) density maps. We identify the topological fingerprint or topological signature of noise, which is widespread in cryo-EM data. For low…
Persistent Homology (PH) has been successfully used to train networks to detect curvilinear structures and to improve the topological quality of their results. However, existing methods are very global and ignore the location of topological…
Generation of dark solitons from large initial excitations and their evolution in a quasi-one-dimensional Bose-Einstein condensate trapped by a harmonic potential is studied analytically and numerically. In the case of a single deep soliton…
Understanding and predicting thermal transport in disordered materials remains a significant challenge due to the absence of periodicity and the complex nature of medium-range structural motifs. In this work, we investigate amorphous…
One of the paramount challenges in neuroscience is to understand the dynamics of individual neurons and how they give rise to network dynamics when interconnected. Historically, researchers have resorted to graph theory, statistics, and…
Contrastive learning (CL) has become a powerful approach for learning representations from unlabeled images. However, existing CL methods focus predominantly on visual appearance features while neglecting topological characteristics (e.g.,…
Topological correctness is critical for segmentation of tubular structures, which pervade in biomedical images. Existing topological segmentation loss functions are primarily based on the persistent homology of the image. They match the…
Topological data analysis (TDA) aims to extract noise-robust features from a data set by examining the number and persistence of holes in its topology. We show that a computational problem closely related to a core task in TDA --…
Persistent homology captures the evolution of topological features of a model as a parameter changes. The most commonly used summary statistics of persistent homology are the barcode and the persistence diagram. Another summary statistic,…