arXiv research

Infinite rank surface cluster algebras extend traditional concepts to surfaces with accumulation points.

PANDA predicts protein binding affinity changes from sequences, outperforming existing methods.

MutaGAN predicts mutations of evolving protein populations using GANs.

The paper defines matrices related to cluster transformations and proves certain quivers have no maximal sequences.

DeepSequence model predicts mutation effects better than existing methods.

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.

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.

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.

Deep neural network improves cancer mutation calls with confidence.

Researchers propose improved multivariate prediction models for HIV drug resistance.

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.

Framework uses machine learning to distinguish major COVID-19 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.

Active learning speeds up antibody affinity prediction.

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.

New knot polynomials reveal patterns and mutations.

We propose a new description of 3d $\mathcal{N}=2$ theories which do not admit conventional Lagrangians. Given a quiver $Q$ and a mutation sequence $m$ on it, we define a 3d $\mathcal{N}=2$ theory $\mathcal{T}[(Q,m)]$ in such a way that the $S^3_b$ 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.

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.

Improved genetic programming by optimizing mutation operators for continuous program search.

Study links curve singularities to quiver mutations.

Mutation Validation method assesses model fit using mutated training labels without validation sets.

New invariants from framed instanton homology for knot concordance.

Let $\mathcal{L}$ be a knot with a fixed positive crossing and $\mathcal{L}_n$ the link obtained by replacing this crossing with $n$ positive twists. We prove that the knot Floer homology $\widehat{\text{HFK}}(\mathcal{L}_n)$ `stabilizes' as $n$ goes to infinity. This categorifies a similar stabilization phenomenon of …

Mathematician summarizes protein geometry and mutation effects.

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.

Mutation graph of support τ-tilting modules over skew-gentle algebras is connected.

Khovanov homology invariant under Conway mutation.

New invariant measures loop iterations in algebraic structures.

The paper studies alternating links in thickened surfaces using flow lattices and disc mutations.

New RL approach builds short ancestral recombination graphs.

Paper tackles gene mutation prediction for HCC using multi-instance multi-label learning.

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.

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.

EDAs with matrix transpose improve Bayesian structure learning performance.

Machine learning clusters mutations in cancer exomes, improving diagnostic speed and cost.