“…We carry out a deep mutational scanning to present the blueprint of such mAbs using algebraic topology and artificial intelligence (AI). To reduce the risk of clinical trial-related failure, we select five mAbs either with FDA EUA or in clinical trials as our starting point. …”
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“…We demonstrate how methods from computational algebraic geometry, differential algebra, Bayesian statistics and computational algebraic topology can inform the model reduction, identification and parameter inference of MEK variants, respectively. …”
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“…The author gives substantial application without requisites needed for algebraic topology and homological algebra. A sprinkling of additional exercises and a new section (13.8) involving commutative algebra, have been added. …”
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“…Using a computational algorithm based on recently developed tools from Persistent Homology theory in the field of algebraic topology, we find that the patterns of neuronal co-firing can, in fact, convey topological information about the environment in a biologically realistic length of time. …”
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“…We extend the standard network-based approach using the filtration method from algebraic topology which does not rely on the threshold selection problem. …”
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“…Furthermore, we characterize the emergent structures by metrics of graph theory and algebraic topology of graphs, and 4-point test for the intrinsic hyperbolicity of the networks. …”
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“…A central problem of algebraic topology is to understand the homotopy groups[Formula: see text] of a topological space X. …”
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“…Using genotyping, sequence-alignment, time-evolution, k-means clustering, protein-folding stability, algebraic topology, and network theory, we reveal that the US SARS-CoV-2 has four substrains and five top US SARS-CoV-2 mutations were first detected in China (2 cases), Singapore (2 cases), and the United Kingdom (1 case). …”
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“…By integrating genetics, biophysics, deep learning, and algebraic topology, we reveal that most of the 462 mutations on the receptor-binding domain (RBD) will weaken the binding of S protein and antibodies and disrupt the efficacy and reliability of antibody therapies and vaccines. …”
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“…The proposed kNN-PL is a new algebraic topology technique which addresses the many limitations of the traditional persistent homology. …”
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“…We have taken spatial learning as our starting point, computationally modeling the activity of place cells using methods derived from algebraic topology, especially persistent homology. We previously showed that ensembles of hundreds of place cells could accurately encode topological information about different environments (“learn” the space) within certain values of place cell firing rate, place field size, and cell population; we called this parameter space the learning region. …”
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“…However, rigorous determination of SARS-CoV-2 infectivity is very difficult owing to its continuous evolution with over 10,000 single nucleotide polymorphisms (SNP) variants in many subtypes. We employ an algebraic topology-based machine learning model to quantitatively evaluate the binding free energy changes of SARS-CoV-2 spike glycoprotein (S protein) and host angiotensin-converting enzyme 2 receptor following mutations. …”
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“…The altered network organisation of the human brain characteristic of many neuropsychiatric and neurodegenerative disorders can be detected using persistent homology network (PHN) analysis and algebraic topology. We used (18)F-fluorodeoxyglucose positron emission tomography ((18)F-FDG PET) imaging data to construct dopaminergic and cholinergic metabolism networks, and used PHN analysis to track the evolution of these networks in patients with different stages of dementia. …”
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“…In this work, we introduce an algebraic topology-based method, called atom-specific persistent homology (ASPH), as a unique representation of crystal structures. …”
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“…We construct a novel algebraic topology-based deep learning model trained with tens of thousands of mutational and deep mutational data to systematically evaluate BA.2’s and BA.3’s infectivity, vaccine breakthrough capability, and antibody resistance. …”
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“…We construct a novel algebraic topology-based deep learning model trained with tens of thousands of mutational and deep mutational data to systematically evaluate BA.2’s and BA.3’s infectivity, vaccine breakthrough capability, and antibody resistance. …”
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“…Hodge theory reveals the deep intrinsic relations of differential forms and provides a bridge between differential geometry, algebraic topology, and functional analysis. Here we use Hodge Laplacian and Hodge decomposition models to analyze biomolecular structures. …”
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“…These structures include topological algebras, Lie algebras, topological groups, and Lie groups. The book is divided into three parts. …”
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“…They arise in a natural way by completing a *-algebra under a locally convex *-algebra topology, with respect to which the multiplication is separately continuous. …”
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“…Introductory chapters are provided on algebra, topology and manifold theory together with a chapter on the basic ideas of space-time manifolds and Einstein's theory. …”
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