Infinite rank surface cluster algebras extend traditional concepts to surfaces with accumulation points.
problem Extending surface cluster algebras to infinite surfaces with accumulation points.
method Consider infinite mutation sequences and hyperbolic structures to define cluster variables as lambda lengths of arcs.
result Established transitivity of infinite mutation sequences on triangulations of infinite surfaces and provided expansion formulas for cluster variables.
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.
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.
The paper defines matrices related to cluster transformations and proves certain quivers have no maximal sequences.
problem Proving quivers associated with once-punctured surfaces do not have maximal green or reddening sequences.
method Defining matrices related to cluster transformations and showing their relationships to the Jacobian and C-matrix.
result Quivers associated with once-punctured surfaces do not have maximal green or reddening sequences.
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.
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…
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.
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…
Study shows mutation invariance of arc index for some Montesinos knots.
problem Investigate mutation invariance of arc index for nonalternating knots.
method Analyzed families of Montesinos knots, found mutant pairs/triples with same arc index.
result Found infinitely many mutant pairs/triples of Montesinos knots with the same arc index.
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 …
New proof of Khovanov homology invariance via Conway mutation.
problem Invariance of Khovanov homology under Conway mutation.
method Elementary proof using Clifford module structure and rational closures.
result Mutation invariance of δ-graded knot Floer homology for a large class of tangles.
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.
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 provide a framework for studying the interplay between concordance and positive mutation and identify some of the basic structures relating the two. The fundamental result in understanding knot concordance is the structure theorem proved by Levine: for n>1 there is an isomorphism phi from the concordance group C_n o…
Bayesian optimization of antibodies learns from immune system evolution.
problem Efficiently optimizing antibody sequences in a large space of possibilities.
method Bayesian optimization guided by a generative model of evolving antibody sequences.
result CloneBO optimizes antibodies more efficiently than previous methods.
Framework uses machine learning to distinguish major COVID-19 variants.
problem Discriminate and visualize associations between major COVID-19 variants based on genome sequences.
method Unsupervised machine learning methods, including k-mer analysis, PCA, t-SNE, UMAP, and agglomerative hierarchical clustering.
result Framework effectively distinguishes between major variants and identifies emerging variants.
Tumors often contain multiple subpopulations of cancerous cells defined by distinct somatic mutations. We describe a new method, PhyloWGS, that can be applied to WGS data from one or more tumor samples to reconstruct complete genotypes of these subpopulations based on variant allele frequencies (VAFs) of point mutation…
The paper constructs unbounded symplectic embeddings of rational homology balls into surfaces.
problem Bounding symplectic embeddings of rational homology balls into surfaces.
method Using Mori's theory of flips and mutations of polygons.
result Unbounded sequences of symplectically embedded rational homology balls into surfaces.
Active learning speeds up antibody affinity prediction.
problem Challenging to identify mutations enhancing antibody affinity.
method Iterative proposal of promising sequences for simulation.
result Accelerates search for improved binders.
Anstee, Przyticki and Rolfsen introduced the idea of rotants, pairs of links related by a generalised form of link mutation. We exhibit infinitely many pairs of rotants which can be distinguished by Khovanov homology, but not by the Jones polynomial.
Deep Learning predicts prognosis of AML cases using cytogenetics, age, and mutations.
problem Predicting prognosis of acute myeloid leukemia (AML) cases.
method Hierarchical Deep Learning model using autoencoders, trained on TCGA database.
result Achieved 83% accuracy in predicting prognosis of AML cases.
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 propose a new description of 3d N=2 theories which do not admit conventional Lagrangians. Given a quiver Q and a mutation sequence m on it, we define a 3d N=2 theory T[(Q,m)] in such a way that the Sb3 partition function of the theory coincides with the cluster partition f…
The paper proves there are many Lagrangian fillings for Legendrian links of affine type.
problem Proving the existence of many Lagrangian fillings for Legendrian links of affine type.
method Using cluster structures and Coxeter mutation to prove the existence of fillings.
result There are at least as many exact embedded Lagrangian fillings as seeds for Legendrian links of affine type.
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…
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.
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.
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.
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.
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.
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.
New RL approach builds short ancestral recombination graphs.
problem Building short ancestral recombination graphs (ARGs).
method Reinforcement Learning applied to genetic sequences.
result RL can build ARGs as short as heuristic algorithms.
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.
Studied knot Floer homology stabilization and prime mutant knots.
problem Studied knot Floer homology and its stabilization.
method Analyzed links with varying positive twists and used knot Floer homology.
result Stabilization of knot Floer homology as the number of twists increases.
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 …
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.