相关论文: Barcodes distinguish morphology of neuronal tauopa…

Networks are important representations in computer science to communicate structural aspects of a given system of interacting components. The evolution of a network has several topological properties that can provide us information on the…

Bars are important drivers of galaxy evolution, influencing many physical processes and properties. Characterising bars is a difficult task, especially in large-scale surveys. In this work, we propose a novel morphological segmentation…

Information networks are becoming increasingly popular to capture complex relationships across various disciplines, such as social networks, citation networks, and biological networks. The primary challenge in this domain is measuring…

Decoding approaches are widely used in neuroscience and machine learning to compare stimulus representations across neural systems, such as different brain regions, organisms, and deep learning models. Popular methods include decoding…

Persistent homology is a topological data analysis tool that has been widely generalized, extending its scope beyond the field of topology. Among its extensions, steady and ranging persistence were developed to study a wide variety of graph…

We construct "barcodes" for the chain complexes over Novikov rings that arise in Novikov's Morse theory for closed one-forms and in Floer theory on not-necessarily-monotone symplectic manifolds. In the case of classical Morse theory these…

This paper develops the idea of homology for 1-parameter families of topological spaces. We express parametrized homology as a collection of real intervals with each corresponding to a homological feature supported over that interval or,…

A standard problem in applied topology is how to discover topological invariants of data from a noisy point cloud that approximates it. We consider the case where a sample is drawn from a properly embedded C1-submanifold without boundary in…

Fruit of the relationship of our research group with the team coordinated by the biologist Miguel Morales (http://spineup.es), we have applied different topo-geometric techniques for neuronal image processing. The images, captured with a…

This article discusses how the individual morphological properties of basic objects (e.g. neurons, molecules and aggregates), jointly with their particular spatial distribution, can determine the connectivity and dynamics of systems…

The general goal of this paper is to gather and review several methods from homotopy and combinatorial topology and formal concepts analysis (FCA) and analyze their connections. FCA appears naturally in the problem of combinatorial…

In this paper, we apply persistent entropy, a novel topological statistic, for characterization of images of epithelial tissues. We have found out that persistent entropy is able to summarize topological and geometric information encoded by…

For groups of a topological origin, such as braid groups and mapping class groups, an important source of interesting and highly non-trivial representations is given by their actions on the twisted homology of associated spaces; these are…

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…

The ability to reroute and control flow is vital to the function of venation networks across a wide range of organisms. By modifying individual edges in these networks, either by adjusting edge conductances or creating and destroying edges,…

In computer vision, keypoint detection is a fundamental task, with applications spanning from robotics to image retrieval; however, existing learning-based methods suffer from scale dependency and lack flexibility. This paper introduces a…

Seeking effective neural networks is a critical and practical field in deep learning. Besides designing the depth, type of convolution, normalization, and nonlinearities, the topological connectivity of neural networks is also important.…

We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher-dimensional topological…

Tumor shape plays a critical role in influencing both growth and metastasis. We introduce a novel topological radiomic feature derived from persistent homology to characterize tumor shape, focusing on its association with time-to-event…

Given the amino acid sequence of a protein, researchers often infer its structure and function by finding homologous, or evolutionarily-related, proteins of known structure and function. Since structure is typically more conserved than…