arXiv research

Algorithm decides if odd-dimensional maps can be immersed.

We demonstrate that the question whether or not a given postcritically finite topological ramified covering map of the 2-sphere is Thurston equivalent to a rational map is algorithmically decidable.

Algorithm decides if pseudo-Anosov flows have perfect fits.

Deciding 3-manifolds fibering over the circle is in NP

Paper tackles decidability of subgroup discreteness problem.

Decides undecidability of equations and first-order theory for Seifert 3-manifold groups.

We address the question of whether the property of being virtually special (in the sense of Haglund and Wise) is algorithmically decidable for finite, non-positively curved cube complexes. Our main theorem shows that it cannot be decided locally, i.e. by examining one hyperplane at a time. Specifically, we prove that t…

Authors show that genus defects of Hopf arborescent links are decidable.

We prove that for every $d\geq 2$, deciding if a pure, $d$-dimensional, simplicial complex is shellable is NP-hard, hence NP-complete. This resolves a question raised, e.g., by Danaraj and Klee in 1978. Our reduction also yields that for every $d \ge 2$ and $k \ge 0$, deciding if a pure, $d$-dimensional, simplicial com…

No algorithm exists to decide 4-manifold homeomorphism.

We find a constructive bound for the word length of a generating set for the centralizer of an element of the Mapping Class Group. As a consequence, we show that it is algorithmically decidable whether two postcritically finite branched coverings of the sphere are Thurston equivalent.

Algorithm decides homeomorphism of 4-manifolds.

Efficient algorithms decide algebraic constraints of causal graphs.

We show that the following algorithmic problem is decidable: given a $2$-dimensional simplicial complex, can it be embedded (topologically, or equivalently, piecewise linearly) in $\mathbf{R}^3$? By a known reduction, it suffices to decide the embeddability of a given triangulated 3-manifold $X$ into the 3-sphere $S^3$…

A new UU-test decides unimodality of datasets.

Algorithm decides if genus-two surfaces in 3-sphere are isotopic.

We present an algorithm which given a presentation of a group $G$ without 2-torsion, a solution to the word problem with respect to this presentation, and an acylindricity constant $κ$, outputs a collection of tracks in an appropriate presentation complex. We give two applications: the first is an algorithm which decid…

We give an algorithm to decide which elements of pi_2(S^2\times S^1#...#S^2\times S^1) can be represented by embedded spheres. Such spheres correspond to splittings of the free group on k generators. Equivalently our algorithm decides whether, for a handlebody N, an element in pi_2(N,\partial N) can be represented by a…

We propose and systematically evaluate three strategies for training dynamically-routed artificial neural networks: graphs of learned transformations through which different input signals may take different paths. Though some approaches have advantages over others, the resulting networks are often qualitatively similar…

We give a method of constructing maps between tubular groups inductively according to a set of strategies. This map will be a quasi-isometry exactly when the set of strategies is consistent. Conversely, if there exists a quasi-isometry between tubular groups, then there is a consistent set of strategies for them. There…

We prove that there is an algorithm to decide whehter two virtual links are equivalent or not

Algorithm decides if two hyperbolic 3-manifolds are homeomorphic.

New bounds for causal effect identification in time series graphs with latent confounders.

Classifies tilings of hyperbolic plane by regular polygons.

An algorithm is proposed that solves two decision problems for pseudo-Anosov elements in the mapping class group of a surface with at least one marked fixed point. The first problem is the root problem: decide if the element is a power and in this case compute the roots. The second problem is the symmetry problem: deci…

For a fixed marked surface $S$, we show that the problem of deciding whether or not a mapping class is reducible lies in $\textbf{NP}$. As usual this immediately gives an exponential time algorithm to decide whether or not a mapping class is reducible. To do this we use an (ideal) triangulation to obtain a coordinate s…

Generalizing empirical findings to new environments, settings, or populations is essential in most scientific explorations. This article treats a particular problem of generalizability, called "transportability", defined as a license to transfer information learned in experimental studies to a different population, on …

We apply Deep Q-network (DQN) with the consideration of safety during the task for deciding whether to conduct the maneuver. Furthermore, we design two similar Deep Q learning frameworks with quadratic approximator for deciding how to select a comfortable gap and just follow the preceding vehicle. Finally, a polynomial…

Agent decides when to measure latent states in RL to improve efficiency.

Whenever a social media user decides to share a story, she is typically pleased to receive likes, comments, shares, or, more generally, feedback from her followers. As a result, she may feel compelled to use the feedback she receives to (re-)estimate her followers' preferences and decides which stories to share next to…

We produce an algorithm that, given $φ\in Out(F_N)$, where $N\ge 2$, decides wether or not $φ$ is an iwip ("fully irreducible") automorphism.

This is a report on our long term project to find an algorithm to decide if a finitely presented group has a non-trivial action on a tree.

Algorithm finds minimal volume hyperbolic links in 3-manifolds.

Research on knots and their 4-manifold covers.

We prove that the homeomorphism problem for 2-manifolds can be decided in logspace. The proof relies on Reingold's logspace solution to the undirected $s,t$-connectivity problem in graphs.

Paper proposes efficient online estimation of causal effects by deciding which data sources to query.

A generalized Baumslag-Solitar group (GBS group) is a finitely generated group $G$ which acts on a tree with all edge and vertex stabilizers infinite cyclic. We show that Out(G) either contains non-abelian free groups or is virtually nilpotent of class at most 2. It has torsion only at finitely many primes. One may dec…

More and more processes governing our lives use in some part an automatic decision step, where -- based on a feature vector derived from an applicant -- an algorithm has the decision power over the final outcome. Here we present a simple idea which gives some of the power back to the applicant by providing her with alt…

We show that there are at most finitely many one cusped orientable hyperbolic 3-manifolds which have more than eight non-hyperbolic Dehn fillings. Moreover, we show that determining these finitely many manifolds is decidable.

We prove that the problem of deciding whether a 2- or 3-dimensional simplicial complex embeds into $\mathbb{R}^3$ is NP-hard. Our construction also shows that deciding whether a 3-manifold with boundary tori admits an $\mathbb{S}^{3}$ filling is NP-hard. The former stands in contrast with the lower dimensional cases wh…

Efficient algorithm for identifying causal effects in linear models.

We provide a machine learning solution that replaces the traditional methods for deciding the pesticide application time of Sunn Pest. We correlate climate data with phases of Sunn Pest in its life-cycle and decide whether the fields should be sprayed. Our solution includes two groups of prediction models. The first gr…

We give a more geometric approach to an algorithm for deciding whether two hyperbolic 3-manifolds are homeomorphic. We also give a more algebraic approach to the homeomorphism problem for geometric, but non-hyperbolic, 3-manifolds.

This work facilitates ensuring fairness of machine learning in the real world by decoupling fairness considerations in compound decisions. In particular, this work studies how fairness propagates through a compound decision-making processes, which we call a pipeline. Prior work in algorithmic fairness only focuses on f…

We show that there can be no algorithm to decide whether infinite recursively described acyclic aspherical 2-complexes are contractible. We construct such a complex that is contractible if and only if the Collatz conjecture holds.

We solve Dehn's isomorphism problem for virtually torsion-free relatively hyperbolic groups with nilpotent parabolic subgroups. We do so by reducing the isomorphism problem to three algorithmic problems in the parabolic subgroups, namely the isomorphism problem, separation of torsion (in their outer automorphism groups…

We propose some natural generalizations of Reidemeister moves that do not increase the number of crossings in the generated diagrams. Experimentations make us conjecture that this class of monotonic moves is complete for computing canonical forms and then deciding isotopy.

We describe a birational map between subvarieties in the character varieties of mutative 3-manifolds. By studying the birational map, one can decide in certain circumstances whether a mutation surface is detected by an ideal point of the character variety.