Related papers: Implementation of the Habegger--Lin decision algor…
We compute the behaviour of Hodge data by tensor product with a unitary rank-one local system and middle convolution by a Kummer unitary rank-one local system for an irreducible variation of polarized complex Hodge structure on a punctured…
We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The…
We compare the following three families of geometric objects: Schubert varieties in flag manifolds, matrix Schubert varieties, and Borel orbits of 2-nilpotent matrices. The first family is governed by permutations, the second by partial…
Examples of non-trivial higher string topology operations have been regrettably rare in the literature. In this paper, working in the context of string topology of classifying spaces, we provide explicit calculations of a wealth of…
In this paper we announce the existence of a family of new $2$-variable polynomial invariants for oriented classical links defined via a Markov trace on the Yokonuma-Hecke algebra of type $A$. Yokonuma-Hecke algebras are generalizations of…
This thesis splits into two major parts. The connection between the two parts is the notion of "categorification" which we shortly explain/recall in the introduction. In the first part of this thesis we extend Bar-Natan's cobordism based…
We give an algorithm that decides whether a single equation in a group that is virtually a class $2$ nilpotent group with a virtually cyclic commutator subgroup, such as the Heisenberg group, admits a solution. This generalises the work of…
We propose a new family of regression models for analyzing categorical responses, called multinomial link models. It consists of four classes, namely, mixed-link models that generalize existing multinomial logistic models and their…
Edge-homotopy and vertex-homotopy are equivalence relations on spatial graphs which are generalizations of Milnor's link-homotopy. We introduce some edge (resp. vertex)-homotopy invariants of spatial graphs by applying the Sato-Levine…
Given a spin rational homology sphere $Y$ equipped with a $\mathbb{Z}/m$-action preserving the spin structure, we use the Seiberg--Witten equations to define equivariant refinements of the invariant $\kappa(Y)$ from \cite{Man14}, which take…
Computing polynomial invariants for knots and links using braid representations relies heavily on finding the trace of Hecke algebra elements. There is no easy method known for computing the trace and hence it becomes difficult to compute…
Hierarchical block diagrams (HBDs) are at the heart of embedded system design tools, including Simulink. Numerous translations exist from HBDs into languages with formal semantics, amenable to formal verification. However, none of these…
Link prediction infers potential links from observed networks, and is one of the essential problems in network analyses. In contrast to traditional graph representation modeling which only predicts two-way pairwise relations, we propose a…
This paper continues the study of decompositions of a smooth 4-manifold into two handlebodies with handles of index $\leq2$. Part I gave existence results in terms of spines and chain complexes over the fundamental group of the ambient…
Mutually connected components (MCCs) play an important role as a measure of resilience in the study of interdependent networks. Despite their importance, an efficient algorithm to obtain the statistics of all MCCs during the removal of…
Classification of datasets into two or more distinct classes is an important machine learning task. Many methods are able to classify binary classification tasks with a very high accuracy on test data, but cannot provide any easily…
Lattice Hamiltonian systems underpin models across condensed matter, nonlinear optics, and biophysics, yet learning their dynamics from data is obstructed by two unknowns: the interaction topology and whether node dynamics are homogeneous.…
Link prediction is an important learning task for graph-structured data. In this paper, we propose a novel topological approach to characterize interactions between two nodes. Our topological feature, based on the extended persistent…
This paper considers a network formation model when links are potentially misclassified. We focus on a game-theoretical model of strategic network formation with incomplete information, in which the linking decisions depend on agents'…
We study the skein relation that governs the HOMFLYPT invariant of links colored by one-column Young diagrams. Our main result is a categorification of this colored skein relation. This takes the form of a homotopy equivalence between two…