A5035196580- Topological and Geometric Data Analysis
- Single-cell and spatial transcriptomics
- Cell Image Analysis Techniques
- Homotopy and Cohomology in Algebraic Topology
- Neuroinflammation and Neurodegeneration Mechanisms
- Digital Image Processing Techniques
- Memory and Neural Mechanisms
- Artificial Intelligence in Games
- Neuroscience and Neuropharmacology Research
- Constraint Satisfaction and Optimization
- RNA and protein synthesis mechanisms
- RNA modifications and cancer
- Advanced Neuroimaging Techniques and Applications
- Color Science and Applications
- Genome Rearrangement Algorithms
- Immune cells in cancer
- Clusterin in disease pathology
- Hydrocarbon exploration and reservoir analysis
- Bioinformatics and Genomic Networks
- Neural dynamics and brain function
- RNA Research and Splicing
Wesleyan University
2024
University of Oxford
2023-2024
Georgia Institute of Technology
2019
Abstract Extracellular matrix (ECM) organization influences cancer development and progression. It modulates the invasion of cells can hinder access immune to cells. Effective quantification ECM architecture its relationship position different cell types is, therefore, important when investigating role in development. Using topological data analysis (TDA), particularly persistent homology Dowker homology, we develop a novel pipeline for quantifying architecture, spatial patterns positions,...
Abstract A central challenge in topological data analysis is the interpretation of barcodes. The classical algebraic-topological approach to interpreting homology classes build maps spaces whose carries semantics we understand and then appeal functoriality. However, often lack such real data; instead, must rely on a cross-dissimilarity measure between our observations system reference. In this paper, develop pair computational homological algebra approaches for relating persistent barcodes:...
Topological data analysis (TDA) is an active field of mathematics for quantifying shape in complex data. Standard methods TDA such as persistent homology (PH) are typically focused on the consisting a single entity (e.g., cells or molecular species). However, state-of-the-art collection techniques now generate exquisitely detailed multispecies data, prompting need that can examine and quantify relations among them. Such heterogeneous types arise many contexts, ranging from biomedical...
A method is presented for the distributed computation of persistent homology, based on an extension generalized Mayer-Vietoris principle to filtered spaces. Cellular cosheaves and spectral sequences are used compute global homology local computations indexed by a scalar field. These techniques permit localized not merely geography, but other features data points, such as density. As example latter, construction in multi-scale analysis point clouds detect varying sizes that overlooked...
SummaryThis paper introduces a new matrix tool for the sowing game Tchoukaillon, which establishes relationship between board vectors and move that does not depend on actually playing game. This allows simpler proofs than currently appear in literature two key theorems, as well method constructing vectors.We also explore extensions to Mancala, popular two-player
The intent of this paper is to explore Dowker duality from a combinatorial, topological, and categorical perspective. presents three short, new proofs using various poset fiber lemmas. We introduce modifications joins products simplicial complexes called relational join product complexes. These can be constructed whenever there relation between complexes, which includes the context covers In more general setting, we show that homologies fit together in long exact sequence. Similar results...
Neural manifolds summarize the intrinsic structure of information encoded by a population neurons. Advances in experimental techniques have made simultaneous recordings from multiple brain regions increasingly commonplace, raising possibility studying how these relate across populations. However, when are nonlinear and possibly code for unknown variables, it is challenging to extract robust falsifiable about their relationships. We introduce framework, called method analogous cycles,...
The complex and dynamic crosstalk between tumour immune cells results in tumours that can exhibit distinct qualitative behaviours - elimination, equilibrium, escape intricate spatial patterns, yet share similar cell configurations the early stages. We offer a topological approach to analyse time series of data locations (including macrophages) order predict malignant behaviour. propose four vectorisations specialised such data: persistence images Vietoris-Rips radial filtrations at static...
A central challenge in topological data analysis is the interpretation of barcodes. The classical algebraic-topological approach to interpreting homology classes build maps spaces whose carries semantics we understand and then appeal functoriality. However, often lack such real data; instead, must rely on a cross-dissimilarity measure between our observations system reference. In this paper, develop pair computational homological algebra approaches for relating persistent barcodes:...
Abstract A riboswitch is a type of RNA molecule that regulates important biological functions by changing structure, typically under ligand-binding. We assess the extent these ligand-bound structural alternatives are present in Boltzmann sample, standard secondary structure prediction method, for three test cases. use cluster analysis tool RNAStructProfiling to characterize different modalities among suboptimal structures sampled. compare putative base pairing models obtained from...
Scientific data has been growing in both size and complexity across the modern physical, engineering, life social sciences. Spatial structure, for example, is a hallmark of many most important real-world complex systems, but its analysis fraught with statistical challenges. Topological can provide powerful computational window on systems. Here we present framework to extend interpret persistent homology summaries analyse spatial multiple scales. We introduce hyperTDA, topological pipeline...