A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Improved genetic programming by optimizing mutation operators for continuous program search.
EDAs with matrix transpose improve Bayesian structure learning performance.
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 …
An evolutionary algorithm separates mixed DNA profiles in forensic genetics.
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…
VEGN uses graph neural networks to predict disease-causing mutations from genetic variants.
A cluster variety of Fock and Goncharov is a scheme constructed by gluing split algebraic tori, called seed tori, via birational gluing maps called mutations. In quantum theory, the ring of functions on seed tori are deformed to non-commutative rings, represented as operators on Hilbert spaces. Mutations are quantized …
A cluster variety of Fock and Goncharov is a scheme constructed from the data related to the cluster algebras of Fomin and Zelevinsky. A seed is a combinatorial data which can be encoded as an matrix with integer entries, or as a quiver in special cases, together with formal variables. A mutation is a c…
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 …
Modeling correlated mutations in cancer for personalized treatment.
We illustrate from the viewpoint of braiding operations on WZNW conformal blocks how colored HOMFLY polynomials with multiplicity structure can detect mutations. As an example, we explicitly evaluate the (2,1)-colored HOMFLY polynomials that distinguish a famous mutant pair, Kinoshita-Terasaka and Conway knot.
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…
We try to give a cluster algebraic interpretation of complex volume of knots. We construct the R-operator from the cluster mutations, and we show that it is regarded as a hyperbolic octahedron. The cluster variables are interpreted as edge parameters used by Zickert in computing complex volume.
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…
Genetic algorithms have been widely used in many practical optimization problems. Inspired by natural selection, operators, including mutation, crossover and selection, provide effective heuristics for search and black-box optimization. However, they have not been shown useful for deep reinforcement learning, possibly …
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…
Khovanov homology invariant under Conway mutation.
Mutation graph of support τ-tilting modules over skew-gentle algebras is connected.
The paper studies alternating links in thickened surfaces using flow lattices and disc mutations.
Paper tackles gene mutation prediction for HCC using multi-instance multi-label learning.
We introduce a property of mutation loops, called the sign stability, with a focus on an asymptotic behavior of the iteration of the tropical -transformation. A sign-stable mutation loop has a numerical invariant which we call the cluster stretch factor, in analogy with that of a pseudo-Anosov mapping clas…
We show that instanton knot homology is mutation-invariant, as a consequence of earlier work of the third author.
We introduce an exploratory study on Mutation Validation (MV), a model validation method using mutated training labels for supervised learning. MV mutates training data labels, retrains the model against the mutated data, then uses the metamorphic relation that captures the consequent training performance changes to as…
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…
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.
Analysis of somatic mutation profiles from cancer patients is essential in the development of cancer research. However, the low frequency of most mutations and the varying rates of mutations across patients makes the data extremely challenging to statistically analyze as well as difficult to use in classification probl…
The study explores properties and mutations in oriented matroids, proving new results on Euclidean and non-Euclidean structures.
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.
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.
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…
We describe and investigate a connection between the topology of isolated singularities of plane curves and the mutation equivalence, in the sense of cluster algebra theory, of the quivers associated with their morsifications.
Motivation: HIV is difficult to treat because its virus mutates at a high rate and mutated viruses easily develop resistance to existing drugs. If the relationships between mutations and drug resistances can be determined from historical data, patients can be provided personalized treatment according to their own mutat…
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.
MutaGAN predicts mutations of evolving protein populations using GANs.
Determining the primary site of origin for metastatic tumors is one of the open problems in cancer care because the efficacy of treatment often depends on the cancer tissue of origin. Classification methods that can leverage tumor genomic data and predict the site of origin are therefore of great value. Because tumor D…
PANDA predicts protein binding affinity changes from sequences, outperforming existing methods.
New flows represent Thurston norm ball faces, differing by veering mutations.
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…
This paper establishes that sutured annular Khovanov homology is not invariant for braid closures under axis-preserving mutations. This follows from an explicit relationship between sutured annular Khovanov homology and the classical Burau representation for braid closures.
OpEvo automates tensor operator optimization for better efficiency.
In this paper, we prove that the Reidemeister torsion twisted by the adjoint representation, which is considered as a 1-form, on the SU(2)-character variety of a knot exterior is invariant under mutation along a Conway sphere.
For any quiver mutation sequence, we define a pair of matrices that describe a fixed point equation of a cluster transformation determined from the mutation sequence. We give an explicit relationship between this pair of matrices and the Jacobian matrix of the cluster transformation. Furthermore, we show that this rela…
We construct a family of hyperbolic link complements by gluing tangles along totally geodesic four-punctured spheres, then investigate the commensurability relation among its members. Those with different volume are incommensurable, distinguished by their scissors congruence classes. Mutation produces arbitrarily large…
Extending theorems of J. E. Greene [Invent. Math. 192 (2013), 717-750] and A. S. Lipson [Enseign. Math. (2) 36 (1990), 93-114], we prove that the equivalence class of a classical link L under mutation is determined by Goeritz matrices associated to diagrams of L.
Deep generative model for healthcare data identifies coherent substructures and mutational clusters.