Related papers: Fast Khovanov Homology Computations
The paper provides a combinatorial method to decide when the space of local systems with non vanishing first cohomology on the complement to an arrangement of lines in a complex projective plane has as an irreducible component a subgroup of…
We study the `local entanglement' remaining after filtering operations corresponding to imperfect measurements performed by one or both parties, such that the parties can only determine whether or not the system is located in some region of…
Generalized singular values (GSVs) play an essential role in the comparative analysis. In the real world data for comparative analysis, both data matrices are usually numerically low-rank. This paper proposes a randomized algorithm to first…
We construct a simple translationally invariant, nearest-neighbor Hamiltonian on a chain of 10-dimensional qudits that makes it possible to realize universal quantum computing without any external control during the computational process.…
We give an algorithm for reducing the number of generators of the Khovanov chain complex of the torus braid $ft^k_n = (\sigma_1\sigma_2\cdots \sigma_{n-1})^k$ on $n$ strands by applying Bar-Natan Gaussian elimination along a distinguished…
The motivation of this work is to define cohomology classes in the space of knots that are both easy to find and to evaluate, by reducing the problem to simple linear algebra. We achieve this goal by defining a combinatorial graded cochain…
Khovanov homology and singular instanton Floer homology are both functorial with respect to link cobordisms. Although the two homology groups are related by a spectral sequence, direct correspondence between the cobordism maps has not been…
Using derived categories of equivariant coherent sheaves, we construct a categorification of the tangle calculus associated to sl(2) and its standard representation. Our construction is related to that of Seidel-Smith by homological mirror…
We partially solve the conjecture by A.Shumakovitch about torsion in the Khovanov homology of prime, non-split links in S^3. We give a size restriction on the Khovanov homology of almost alternating links. We relate the Khovanov homology of…
This paper proposes fast randomized algorithms for computing the Kronecker Tensor Decomposition (KTD). The proposed algorithms can decompose a given tensor into the KTD format much faster than the existing state-of-the-art algorithms. Our…
The Classic Howard's algorithm, a technique of resolution for discrete Hamilton-Jacobi equations, is of large use in applications for its high efficiency and good performances. A special beneficial characteristic of the method is the…
Most representation learning algorithms for language and image processing are local, in that they identify features for a data point based on surrounding points. Yet in language processing, the correct meaning of a word often depends on its…
We study homology groups of posets with functor coefficients and apply our results to give a novel approach to study Khovanov homology of knots and related homology theories.
We extend the persistence algorithm, viewed as an algorithm computing the homology of a complex of free persistence or graded modules, to complexes of modules that are not free. We replace persistence modules by their presentations and…
We introduce a new embarrassingly parallel parameter learning algorithm for Markov random fields with untied parameters which is efficient for a large class of practical models. Our algorithm parallelizes naturally over cliques and, for…
We present a systematic hierarchy of approximations for {\it local} exact-decoupling of four-component quantum chemical Hamiltonians based on the Dirac equation. Our ansatz reaches beyond the trivial local approximation that is based on a…
Best rank-one approximation is one of the most fundamental tasks in tensor computation. In order to fully exploit modern multi-core parallel computers, it is necessary to develop decoupling algorithms for computing the best rank-one…
Introducing a way to modify knots using $n$-trivial rational tangles, we show that knots with given values of Vassiliev invariants of bounded degree can have arbitrary unknotting number (extending a recent result of Ohyama, Taniyama and…
Topological simplification is the process of reducing complexity of a function while maintaining its essential features. Its goal is to find a new filter function, which reorders cells of the input complex in a way which eliminates some…
We present a parallelizable algorithm for computing the persistent homology of a filtered chain complex. Our approach differs from the commonly used reduction algorithm by first computing persistence pairs within local chunks, then…