Homology (biology)
View article: Genome-Wide Identification and Expression Pattern Analysis of CrLBD Family Reveal Their Involvement in Floral Development in Chionanthus retusus
Genome-Wide Identification and Expression Pattern Analysis of CrLBD Family Reveal Their Involvement in Floral Development in Chionanthus retusus Open
The growth and development of plants are modulated by multiple genes, among which the LBD (Lateral Organ Boundaries Domain) family—a group of plant-specific transcription factors—plays pivotal roles. In this study, we utilized the latest r…
View article: Genome-wide analysis of the CrRLK1L gene family in Puccinellia tenuiflora and functional study of PutFER1 in Arabidopsis underpinning salt tolerance
Genome-wide analysis of the CrRLK1L gene family in Puccinellia tenuiflora and functional study of PutFER1 in Arabidopsis underpinning salt tolerance Open
CrRLK1L receptor-like kinases have attracted significant interest in plant biology owing to their pivotal roles in development, stress response, and signal transduction. However, our understanding of their importance in the extreme saline-…
View article: Persistent Homology of River Networks: Characterizing Hierarchical Geomorphic Organization
Persistent Homology of River Networks: Characterizing Hierarchical Geomorphic Organization Open
River networks are fundamental components of the Earth's surface, critical for water resource management, ecological studies, and understanding geomorphological processes. Their intricate branching patterns and hierarchical organization pr…
View article: Persistent Homology of Inter-American Socioeconomic Divergence
Persistent Homology of Inter-American Socioeconomic Divergence Open
This paper explores the application of Persistent Homology (PH), a foundational tool in Topological Data Analysis (TDA), to investigate socioeconomic divergence across the Inter-American region. Traditional econometric methods often strugg…
View article: Simplex polynomial in complex networks and its applications to compute the Euler characteristic
Simplex polynomial in complex networks and its applications to compute the Euler characteristic Open
In algebraic topology, a k -dimensional simplex is defined as a convex polytope consisting of k + 1 vertices. If spatial dimensionality is not considered, it corresponds to the complete graph with k + 1 vertices in graph theory. The altern…
View article: Fray functors and equivalence of colored HOMFLYPT homologies
Fray functors and equivalence of colored HOMFLYPT homologies Open
We construct several families of functors on the homotopy category of singular Soergel bimodules that mimic cabling and insertion of column-colored projectors. We use these functors to identify the intrinsically-colored homology of Webster…
View article: The hemagglutinin-like proteins of basal vertebrate influenza-like viruses exhibit sialic-acid receptor binding disparity and their structural bases
The hemagglutinin-like proteins of basal vertebrate influenza-like viruses exhibit sialic-acid receptor binding disparity and their structural bases Open
In 2018, two novel influenza-like virus genomes were first identified in basal vertebrates: the Asiatic toads ( Bufo gargarizans ) and spiny eels ( Mastacembelus aculeatus ). Their hemagglutinin (HA) proteins exhibit remarkably low amino a…
View article: Persistent Homology of River Networks: Characterizing Hierarchical Geomorphic Organization
Persistent Homology of River Networks: Characterizing Hierarchical Geomorphic Organization Open
River networks are fundamental components of the Earth's surface, critical for water resource management, ecological studies, and understanding geomorphological processes. Their intricate branching patterns and hierarchical organization pr…
View article: Topological Invariants of Functional Regions
Topological Invariants of Functional Regions Open
This paper explores the utility of topological invariants for characterizing and understanding functional regions across diverse scientific domains. Functional regions, defined by coherent activity or specific properties within a larger sy…
View article: Topological Invariants of Functional Regions
Topological Invariants of Functional Regions Open
This paper explores the utility of topological invariants for characterizing and understanding functional regions across diverse scientific domains. Functional regions, defined by coherent activity or specific properties within a larger sy…
View article: Persistent Homology of Inter-American Socioeconomic Divergence
Persistent Homology of Inter-American Socioeconomic Divergence Open
This paper explores the application of Persistent Homology (PH), a foundational tool in Topological Data Analysis (TDA), to investigate socioeconomic divergence across the Inter-American region. Traditional econometric methods often strugg…
View article: $δ$-core subsampling, strong collapses and TDA
$δ$-core subsampling, strong collapses and TDA Open
We introduce a subsampling method for topological data analysis based on strong collapses of simplicial complexes. Given a point cloud and a scale parameter $δ$, we construct a subsampling that preserves both global and local topological f…
View article: Equivariant homology of the symplectic affine Grassmannian and dual affine Schur $P$-functions
Equivariant homology of the symplectic affine Grassmannian and dual affine Schur $P$-functions Open
We study the torus-equivariant homology $H_*^T(\mathrm{Gr}_G)$ of the affine Grassmannian $\mathrm{Gr}_G$, where $G=\mathrm{Sp}_{2n}(\mathbb{C})$ is the symplectic group. This homology admits a natural ring structure and a Schubert basis, …
View article: The K-theoretic Classification of Smooth Structures on Topological Manifolds
The K-theoretic Classification of Smooth Structures on Topological Manifolds Open
The classification of smooth structures on topological manifolds stands as one of the most profound and challenging problems in differential topology. While topological manifolds are relatively well-understood through surgery theory, the r…
View article: A Comprehensive Profiling of the Rice LATERAL ORGAN BOUNDARIES DOMAIN (LBD) Gene Family: Structure, Evolution, and Expressional Dynamics
A Comprehensive Profiling of the Rice LATERAL ORGAN BOUNDARIES DOMAIN (LBD) Gene Family: Structure, Evolution, and Expressional Dynamics Open
The LATERAL ORGAN BOUNDARIES DOMAIN (LBD) gene family encodes plant-specific transcription factors that play vital roles in plant growth, development, and stress responses. Rice (Oryza sativa L.), a staple food for more than half of the wo…
View article: Resolving Exotic Spheres Through Lagrangian Floer Homology
Resolving Exotic Spheres Through Lagrangian Floer Homology Open
Exotic spheres represent one of the most profound discoveries in differential topology, revealing that higher-dimensional spheres can possess multiple distinct smooth structures, despite being homeomorphic to the standard sphere. These obj…
View article: Resolving Exotic Spheres Through Lagrangian Floer Homology
Resolving Exotic Spheres Through Lagrangian Floer Homology Open
Exotic spheres represent one of the most profound discoveries in differential topology, revealing that higher-dimensional spheres can possess multiple distinct smooth structures, despite being homeomorphic to the standard sphere. These obj…
View article: An Isolate of <i>Xanthomonas hortorum</i> pv. <i>vitians</i> for the Study of Asteraceae Immune Responses
An Isolate of <i>Xanthomonas hortorum</i> pv. <i>vitians</i> for the Study of Asteraceae Immune Responses Open
The AvrRps4 effector family is characterized by homology with the bipartite bacterial effector AvrRps4. The known members of this family (HopK1, XopO, and AvrRps4) are processed into two moieties within the plant cell. Previous research ha…
View article: Iterated h-Cobordism Surgery and Exotic Spheres
Iterated h-Cobordism Surgery and Exotic Spheres Open
This paper explores the intricate relationship between iterated h-cobordism surgery and the construction and classification of exotic spheres. Exotic spheres are differentiable manifolds that are homeomorphic but not diffeomorphic to the s…
View article: Krull Dimension, Homological Depth, and the Noncommutative Auslander-Buchsbaum Theorem
Krull Dimension, Homological Depth, and the Noncommutative Auslander-Buchsbaum Theorem Open
The classical Auslander-Buchsbaum theorem establishes a fundamental relationship between the projective dimension of a finitely generated module and the homological depth of the module over a commutative Noetherian local ring, specifically…
View article: Krull Dimension, Homological Depth, and the Noncommutative Auslander-Buchsbaum Theorem
Krull Dimension, Homological Depth, and the Noncommutative Auslander-Buchsbaum Theorem Open
The classical Auslander-Buchsbaum theorem establishes a fundamental relationship between the projective dimension of a finitely generated module and the homological depth of the module over a commutative Noetherian local ring, specifically…
View article: Stable Homotopy of Persistence Modules
Stable Homotopy of Persistence Modules Open
Persistent homology, a cornerstone of Topological Data Analysis (TDA), provides a robust framework for quantifying the shape of data across multiple scales. Its fundamental algebraic objects, persistence modules, encode the evolution of to…
View article: Hyperbolic Geometrization of L-Space Surgeries on Knots
Hyperbolic Geometrization of L-Space Surgeries on Knots Open
This paper explores the intricate relationship between L-space surgeries on knots and the resulting three-manifolds' hyperbolic geometry. L-spaces, defined by their minimal Heegaard Floer homology, represent a topologically 'simple' class …
View article: Stable Homotopy of Persistence Modules
Stable Homotopy of Persistence Modules Open
Persistent homology, a cornerstone of Topological Data Analysis (TDA), provides a robust framework for quantifying the shape of data across multiple scales. Its fundamental algebraic objects, persistence modules, encode the evolution of to…
View article: Hyperbolic Geometrization of L-Space Surgeries on Knots
Hyperbolic Geometrization of L-Space Surgeries on Knots Open
This paper explores the intricate relationship between L-space surgeries on knots and the resulting three-manifolds' hyperbolic geometry. L-spaces, defined by their minimal Heegaard Floer homology, represent a topologically 'simple' class …
View article: Six Exceptional Properties of the "Perez Hourglass": Perspectives toward New Types of Artificial Intelligence and Quantum Computers
Six Exceptional Properties of the "Perez Hourglass": Perspectives toward New Types of Artificial Intelligence and Quantum Computers Open
AbstractMore than thirty-five years after the first intuitions linking self-organization, neuronal networks and the golden ratio (Perez, 19…
View article: The Geometrization of L-Space Knot Surgeries
The Geometrization of L-Space Knot Surgeries Open
This paper explores the intricate relationship between L-space knots, Dehn surgeries, and the geometrization of 3-manifolds. L-space knots, characterized by their minimal Heegaard Floer homology, play a crucial role in distinguishing manif…
View article: Topological Structure of the Cyclonic-Anticyclonic Interactions
Topological Structure of the Cyclonic-Anticyclonic Interactions Open
We investigate the large-scale structure and temporal evolution of cyclonic and anticyclonic systems in the North Atlantic using persistent homology applied to daily sea-level pressure anomalies from the ERA5 reanalysis (1950-2022). By int…
View article: Topological Structure of the Cyclonic-Anticyclonic Interactions
Topological Structure of the Cyclonic-Anticyclonic Interactions Open
We investigate the large-scale structure and temporal evolution of cyclonic and anticyclonic systems in the North Atlantic using persistent homology applied to daily sea-level pressure anomalies from the ERA5 reanalysis (1950-2022). By int…
View article: A Faithful Discretization of Verbose Directional Transforms
A Faithful Discretization of Verbose Directional Transforms Open
The persistent homology transform, Betti function transform, and Euler characteristic transform represent a shape with a multiset of persistence diagrams, Betti functions, or Euler characteristic functions, respectively, parameterized by t…