Genus 2 mutation is the process of cutting a 3-manifold along an embedded closed genus 2 surface, twisting by the hyper-elliptic involution, and gluing back. This paper compares genus 2 mutation with the better-known Conway mutation in the context of knots in the 3-sphere. Despite the fact that any Conway mutation can …
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48 results for “genus one mutation”
Kearton observed that mutation can change the concordance class of a knot. A close examination of his example reveals that it is of 4-genus 1 and has a mutant of 4-genus 0. The first goal of this paper is to construct examples to show that for any pair of nonnegative integers m and n there is a knot of 4-genus m with a…
In this paper, we study the distribution of the genuses of cluster quivers of finite mutation type. First, we prove that in the exceptional cases, the distribution of genuses is or . Next, we consider the relationship between the genus of an oriented surface and that of cluster quivers from this surface. It…
Mutation is an operation on 3-manifolds containing an embedded surface of genus 2. It is defined by cutting along the surface and regluing using the `hyperelliptic' involution, and is known to preserve many 3-manifold invariants. I show that mutation of a homology 3-sphere preserves its (instanton) Floer homology, and …
New knot polynomials reveal patterns and mutations.
problem Understanding the structure and behavior of knot polynomials.
method Using a specific multivariable polynomial invariant derived from Nichols algebras.
result Emerging patterns in knot polynomials, including genus bounds and unexpected mutations.
We exhibit an infinite family of knots with isomorphic knot Heegaard Floer homology. Each knot in this infinite family admits a nontrivial genus two mutant which shares the same total dimension in both knot Floer homology and Khovanov homology. Each knot is distinguished from its genus two mutant by both knot Floer hom…
The paper studies Heegaard Floer homology for manifolds with torus boundaries and proves properties.
problem Analyzing Heegaard Floer homology for manifolds with torus boundaries.
method Using immersed curves in a punctured torus and geometric descriptions.
result Establishes genus one mutation invariance in Heegaard Floer homology for closed three-manifolds.
In an earlier paper, we introduced a collection of graded Abelian groups $\HFKa(Y,K)$ associated to knots in a three-manifold. The aim of the present paper is to investigate these groups for several specific families of knots, including the Kinoshita-Terasaka knots and their ``Conway mutants''. These results show that …
Modeling correlated mutations in cancer for personalized treatment.
problem Identifying mutations for personalized cancer therapy in heterogeneous profiles.
method Proposed correlated zero-inflated negative binomial process with mixed beta-Bernoulli and variational inference.
result Identified biologically relevant correlations between somatic mutations.
Improved genetic programming by optimizing mutation operators for continuous program search.
problem Small syntactic mutations in genetic programming can lead to unpredictable behavioral shifts.
method Learned a compact trading-strategy DSL, created a block-factorized embedding, and designed geometry-compiled mutation operators.
result Geometry-compiled mutation operators discover strong strategies using fewer evaluations and achieve higher Sharpe ratios.
Morsifications and mutationsmath.GT
Study links curve singularities to quiver mutations.
problem Understanding the relationship between curve singularities and quiver mutations.
method Investigates the connection between the topology of curve singularities and the mutation equivalence of quivers associated with their morsifications.
result Established a connection between the topology of isolated curve singularities and the mutation equivalence of quivers.
We define a link homology theory that is readily seen to be both isomorphic to reduced odd Khovanov homology and fully determined by data impervious to Conway mutation. This gives an elementary proof that odd Khovanov homology is mutation invariant, and therefore that mod 2 Khovanov homology is mutation invariant. We a…
Mutation Validation method assesses model fit using mutated training labels without validation sets.
problem Model selection and hyperparameter tuning accuracy in supervised learning.
method Mutation Validation (MV) method using mutated training labels to assess model fit.
result MV provides more accurate model selection and stable hyperparameter tuning results.
We give a new, elementary proof that Khovanov homology with --coefficients is invariant under Conway mutation. This proof also gives a strategy to prove Baldwin and Levine's conjecture that --graded knot Floer homology is mutation--invariant. Using the Clifford module structure on $\widetilde…
Mathematician summarizes protein geometry and mutation effects.
problem Understanding how proteins mutate and their structure-function relationship.
method Mathematical analysis of protein structures and functions, focusing on hydrogen bonds and secondary structure.
result Protein secondary structure regulates mutation by stabilizing or destabilizing regions.
We study the effect of mutation on link concordance and 3-manifolds. We show that the set of links concordant to sublinks of homology boundary links is not closed under positive mutation. We show that mutation does not preserve homology cobordism classes of 3-manifolds. A significant consequence is that there exist 3-m…
Paper tackles cancer mutation data challenges by creating useful low-dimensional representations.
problem Challenges in analyzing and using cancer mutation data for classification and clustering.
method Flatsomatic: variational autoencoders (VAEs) to create latent representations of somatic profiles.
result VAE embeddings perform better than PCA for clustering and equally well for classification.
Mutation graph of support τ-tilting modules over skew-gentle algebras is connected.
problem Understanding the structure of support τ-tilting modules over skew-gentle algebras.
method Introducing mutation of maximal rigid objects and using exchange triangles to define mutations of support τ-tilting modules.
result The mutation graph of support τ-tilting modules over a skew-gentle algebra is connected.
Khovanov homology invariant under Conway mutation.
problem Invariance of Khovanov homology under specific transformations.
method Strong geography restrictions and homological mirror symmetry.
result Classification of components of a Khovanov multicurve invariant.
New invariant measures loop iterations in algebraic structures.
problem Measuring the asymptotic behavior of loop iterations in algebraic structures.
method Introduced sign stability and cluster stretch factor to measure loops.
result Cluster algebraic entropies match cluster stretch factor.
New invariants from framed instanton homology for knot concordance.
problem Concordance of knots and their properties.
method Framed instanton homology to define invariants.
result Computations and bounds on knot concordance invariants.
The paper studies alternating links in thickened surfaces using flow lattices and disc mutations.
problem Understanding alternating links in thickened surfaces and their invariants.
method Using integer flows on Tait graphs and disc mutations, the paper proves invariants and compares link properties.
result Found alternating knots with isometric flow lattices but different linking forms.
Paper tackles gene mutation prediction for HCC using multi-instance multi-label learning.
problem Gene mutation prediction in hepatocellular carcinoma for personalized treatments.
method Multi-instance multi-label learning with oversampling for data imbalance.
result Proposed approach shows superiority in gene mutation prediction.
Link equivalence determined by Goeritz matrices.
problem Determining link equivalence through Goeritz matrices.
method Extending Greene and Lipson's theorems, proving equivalence class determination.
result Link equivalence determined by Goeritz matrices.
We show that instanton knot homology is mutation-invariant, as a consequence of earlier work of the third author.
Study shows Conway mutation preserves a specific link invariant.
problem Investigating symmetry properties of peculiar modules.
method Analysis of Heegaard Floer invariants of 4-ended tangles.
result Conway mutation preserves the hat flavor of relatively δ-graded Heegaard Floer theory of links.
We construct finite volume hyperbolic manifolds with large symmetry groups. The construction makes use of the presentations of finite Coxeter groups provided by Barot and Marsh and involves mutations of quivers and diagrams defined in the theory of cluster algebras. We generalize our construction by assigning to every …
Researchers propose improved multivariate prediction models for HIV drug resistance.
problem Predicting drug resistances of HIV from mutation information.
method Revised stacking algorithms to borrow information among multiple prediction tasks.
result Proposed methods outperform other multivariate prediction methods.
We prove that generalized mutation preserves several geometric invariants such as the volume and Goncharov invariant of Q-rank 1 locally symmetric spaces.
The study explores properties and mutations in oriented matroids, proving new results on Euclidean and non-Euclidean structures.
problem Investigating the Euclidean and non-Euclidean properties of oriented matroids.
method Analyzing the minimum number of mutations, using lexicographic extensions, and mutation-flips to prove properties.
result For rank 4 uniform oriented matroids, the minimum number of mutations adjacent to an element is at most 3.
EDAs with matrix transpose improve Bayesian structure learning performance.
problem Improving Bayesian structure learning performance.
method Introducing a matrix transpose mutation operator for EDAs in Bayesian structure learning.
result EDAs with transpose mutation give markedly better performance than conventional EDAs.
Machine learning clusters mutations in cancer exomes, improving diagnostic speed and cost.
problem Extracting stable mutation structures from cancer exome data for early diagnostics.
method Statistically deterministic machine learning algorithm *K-means applied to exome samples.
result Majority of cancer types exhibit stable mutation clustering, while NMF methods are unstable.
We show that the reduced sl(n) homology defined by Khovanov and Rozansky is invariant under component-preserving positive mutation when n is odd.
We prove that Khovanov homology and Lee homology with coefficients in are invariant under component-preserving link mutations.
Khovanov-Floer theories are shown to be invariant under mutation.
problem Invariance of Khovanov-Floer theories under Conway mutation.
method Spectral sequences from Khovanov homology and proofs of conjectures.
result Strong Khovanov-Floer theories are mutation-invariant.
We give a short topological proof for Rubermans Theorem about mutation and volume, using the Maskit combination theorem and the homology of the linear group.
Deep learning improves tumor type classification accuracy.
problem Classifying cancer types based on DNA mutations is challenging.
method Deep transfer learning and fine-tuning of gene expression data.
result Significantly improved tumor type classification accuracy (78.3%) using DNA point mutations.
In this paper, we explicitly construct large classes of incommensurable hyperbolic knot complements with the same volume and the same initial (complex) length spectrum. Furthermore, we show that these knot complements are the only knot complements in their respective commensurabiltiy classes by analyzing their cusp sha…
For the alternating knots or links, mutations do not change the arc index. In the case of nonalternating knots, some semi-alternating knots or links have this property. We mainly focus on the problem of mutation invariance of the arc index for nonalternating knots which are not semi-alternating. In this paper, we found…
Given a hyperbolic knot, we prove that the Reidemeister torsion of any lift of the holonomy to SL(2,C) is invariant under mutation along a Conway sphere.
EA improves clustering efficiency using crossover and mutation.
problem Efficiently clustering data using model-based methods.
method Developed an evolutionary algorithm with crossover and mutation for model-based clustering.
result EA outperforms EM algorithm and k-means in clustering performance.
MutaGAN predicts mutations of evolving protein populations using GANs.
problem Predicting mutations in evolving protein populations.
method Generative adversarial networks (GANs) with recurrent neural networks (RNNs).
result MutaGAN generates complete protein sequences with mutations.
Deep neural network improves cancer mutation calls with confidence.
problem Improving accuracy and confidence in somatic variant calls from cancer sequencing.
method Deep Bayesian Recurrent Neural Network (RNN) with flexible priors.
result Enhanced confidence in mutation calls without performance degradation.
Deep Learning identifies 20 critical proteins linked to FLT3-ITD mutation in leukemia.
problem Identifying critical proteins associated with FLT3-ITD mutation in leukemia.
method Hierarchical Deep Learning network using autoencoders for feature extraction.
result Deep Learning accurately correlates 20 critical proteins with FLT3-ITD mutation (97% accuracy).
PANDA: Predicting the change in proteins binding affinity upon mutations using sequence informationq-bio.BM
PANDA predicts protein binding affinity changes from sequences, outperforming existing methods.
problem Accurately predicting changes in protein binding affinity due to mutations.
method Sequence-based machine learning approach using protein sequence information.
result PANDA achieves higher Pearson correlation coefficients than existing methods.
Mutations and faces of the Thurston norm ball dynamically represented by multiple distinct flowsmath.GT
New flows represent Thurston norm ball faces, differing by veering mutations.
problem Dynamic representation of Thurston norm ball faces by distinct flows.
method Combining veering triangulations and mutations to represent faces by multiple flows.
result Non-fibered faces can be represented by two distinct flows differing by veering mutations.
DeepSequence model predicts mutation effects better than existing methods.
problem Quantifying complex interactions in biomolecules.
method Latent variable models with nonlinear dependencies.
result DeepSequence predicts mutation effects significantly better than site-independent or pairwise models.
It is conjectured that the Khovanov homology of a knot is invariant under mutation. In this paper, we review the spanning tree complex for Khovanov homology, and reformulate this conjecture using a matroid obtained from the Tait graph (checkerboard graph) G of a knot diagram K. The spanning trees of G provide a filtrat…