arXiv research

We prove that there are finite area flat surfaces whose Veech group is an infinite cyclic group consisting of hyperbolic elements

A new learning rule consistently reduces error over data samples.

We consider convex SGD updates with a block-cyclic structure, i.e. where each cycle consists of a small number of blocks, each with many samples from a possibly different, block-specific, distribution. This situation arises, e.g., in Federated Learning where the mobile devices available for updates at different times d…

Develops a new framework for causal models on cyclic graphs, solving unique solvability issues.

Identifies root causes of outliers in unknown cyclic graphs.

Improved neural network surrogates for ICF using manifold and cycle consistency.

Recent techniques built on Generative Adversarial Networks (GANs), such as Cycle-Consistent GANs, are able to learn mappings among different domains built from unpaired datasets, through min-max optimization games between generators and discriminators. However, it remains challenging to stabilize the training process a…

MissNODAG learns cyclic causal graphs from incomplete data.

New framework for cyclic quantum causal models with graph separation property.

CycleGAN (Zhu et al. 2017) is one recent successful approach to learn a transformation between two image distributions. In a series of experiments, we demonstrate an intriguing property of the model: CycleGAN learns to "hide" information about a source image into the images it generates in a nearly imperceptible, high-…

We construct a variant $\mathcal{K}_n$ of the Hopf algebra $\mathcal{H}_n$, which acts directly on the noncommutative model for the generic space of leaves rather than on its frame bundle. We prove that the Hopf cyclic cohomology of $\mathcal{K}_n$ is isomorphic to that of the pair $(\mathcal{H}_n, {\mathop{\rm GL}_n})…

We let $\varphi$ be an ageometric fully irreducible outer automorphism so that its Handel-Mosher axis bundle consists of a single unique axis. We show that the centralizer $Cen(\langle\varphi\rangle)$ of the cyclic subgroup generated by $\varphi$ equals the stabilizer $\text{Stab}(Λ^+_\varphi)$ of the attracting lamina…

Variational autoencoders (VAEs) with an auto-regressive decoder have been applied for many natural language processing (NLP) tasks. The VAE objective consists of two terms, (i) reconstruction and (ii) KL regularization, balanced by a weighting hyper-parameter β. One notorious training difficulty is that the KL term ten…

In this paper we define and study the "ghost loop orbifold" of an orbifold $X$ consisting of those loops that remain constant in the coarse moduli space of $X$. We construct a configuration space model for the ghost loop orbifold using an idea of G. Segal. From this we exhibit the relation between the Hochschild and cy…

We show that for groups acting acylindrically on simplicial trees the $K$- and $L$-theoretic Farrell-Jones Conjecture relative to the family of subgroups consisting of virtually cyclic subgroups and all subconjugates of vertex stabilisers holds. As an application, for amalgamated free products acting acylindrically on …

RECLAIM discovers causal graphs in cyclic, noisy systems.

Study cyclic group actions on spin 4-manifolds with boundary using Seiberg-Witten theory.

The study connects monopole chains to Higgs bundles and classifies symmetric chains.

DCCD-CONF discovers causal graphs with unmeasured confounders.

This paper introduces 'General Cyclical Training' for neural networks.

This paper studies connectivity of cyclic-Schottky strata in Schottky space.

Consider the moduli space $\mathcal{M}_{g}$ of Riemann surfaces of genus $g\geq 2$ and its Deligne-Munford compactification $\bar{\mathcal{M}_{g}}$. We are interested in the branch locus ${\mathcal{B}_{g}}$ for $g>2$, i.e., the subset of $\mathcal{M}_{g}$ consisting of surfaces with automorphisms. It is well-known that…

The paper generalizes cyclic metrics in homogeneous Finsler geometry.

In this paper we study the connections between cyclic presentations of groups and branched cyclic coverings of (1,1)-knots. In particular, we prove that every n-fold strongly-cyclic branched covering of a (1,1)-knot admits a cyclic presentation for the fundamental group encoded by a Heegaard diagram of genus n.

Characterizes non-degenerate cyclic metric Lie algebras.

The aim of this paper is to define a chain level refinement of the Batalin-Vilkovisky (BV) algebra structure on the homology of the free loop space of a closed, oriented $C^\infty$-manifold. For this purpose, we define a (nonsymmetric) cyclic dg operad which consists of "de Rham chains" of free loops with marked points…

The study classifies and explores $SU(2)$-cyclic and $SU(2)$-abelian 3-manifolds.

Proves almost profinite rigidity for certain free-by-cyclic groups.

A new method learns DAGs from Gaussian data without verifying acyclicity.

We study the connections among the mapping class group of the twice punctured torus, the cyclic branched coverings of (1,1)-knots and the cyclic presentations of groups. We give the necessary and sufficient conditions for the existence and uniqueness of the n-fold strongly-cyclic branched coverings of (1,1)-knots, thro…

New cyclicity measures defined in weighted Besov spaces, with stability and geometric analysis.

We refine the cyclic cohomological apparatus for computing the Hopf cyclic cohomology of the Hopf algebras associated to infinite primitive Cartan-Lie pseudogroups, and for the transfer of their characteristic classes to foliations. The main novel feature is the precise identification as a Hopf cyclic complex of the im…

In this paper, we study quandles of cyclic type, which form a particular subclass of finite quandles. The main result of this paper describes the set of isomorphism classes of quandles of cyclic type in terms of certain cyclic permutations. By using our description, we give a direct classification of quandles of cyclic…

Cyclical learning rates improve DRL performance without manual tuning.

The paper investigates cyclic arbitrage opportunities in decentralized exchanges.

Unified rigidity theorem for cyclic and alternating surfaces.

In spin geometry, traceless cyclic homogeneous Riemannian manifolds equipped with a homogeneous spin structure can be viewed as the simplest manifolds after Riemannian symmetric spin spaces. In this paper, we give some characterizations and properties of cyclic and traceless cyclic homogeneous Riemannian manifolds and …

The abstract introduces a new cyclic structure for surfaces.

Study integrable discretizations of cyclic systems with circular coordinate lines.

We give a construction of cyclic cocycles representing the equivariant characteristic classes of equivariant bundles. Our formulas generalize Connes' Godbillon-Vey cyclic cocycle. An essential tool of our construction is Connes-Moscovici's theory of cyclic cohomology of Hopf algebras.

A surgery on a knot in 3-sphere is called SU(2)-cyclic if it gives a manifold whose fundamental group has no non-cyclic SU(2) representations. Using holonomy perturbations on the Chern-Simons functional, we prove that the distance of two SU(2)-cyclic surgery coefficients is bounded by the sum of the absolute values of …

New definite 4-manifolds found with non-cyclic groups.

Cyclic projections in Hadamard spaces can be irregular, unlike in Hilbert spaces.

Cyclic covers of knots uniquely determine the original knot.

New Heegaard Floer homology for orbifolds with cyclic singularities.

A central result here is the computation of the entire cyclic homology of canonical smooth subalgebras of stable continuous trace C*-algebras having smooth manifolds M as their spectrum. More precisely, the entire cyclic homology is shown to be canonically isomorphic to the continuous periodic cyclic homology for these…

Let $M$ be an irreducible, compact, connected, orientable 3-manifold whose boundary is a torus. We show that if $M$ is hyperbolic, then it admits at most six finite/cyclic fillings of maximal distance 5. Further, the distance of a finite/cyclic filling to a cyclic filling is at most 2. If $M$ has a non-boundary-paralle…

We discuss 3-manifolds which are cyclic coverings of the 3-sphere, branched over 2-bridge knots and links. Different descriptions of these manifolds are presented: polyhedral, Heegaard diagram, Dehn surgery and coloured graph constructions. Using these descriptions, we give presentations for their fundamental groups, w…