arXiv research

This paper uses ML and EVT to analyze tree ring data, improving accuracy of predictions.

Study evaluates Tree-Ring Watermarking in rectified flow-based models, revealing detection and separability limitations.

We calculate the intersection ring of three-dimensional graph manifolds with rational coefficients and give an algebraic characterization of these rings when the manifold's underlying graph is a tree. We are able to use this characterization to show that the intersection ring obstructs arbitrary three-manifolds from be…

We calculate the integer cohomology ring and stable tangent bundle of a family of compact, 3-Sasakian 7-manifolds constructed by Boyer, Galicki, Mann, and Rees. Previously only the rational cohomology ring was known. The most important part of the cohomology ring is a torsion group that we describe explicitly and whose…

We prove that the Farrell-Jones isomorphism conjecture for non-connective algebraic K-theory for a discrete group G and a coefficient ring R holds true if G belongs to the class of groups acting on trees, under certain conditions on G (see theorem 0.5 below) and if the coefficient ring R is either regular or hereditary…

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 …

We focus on the commonly used synchronous Gradient Descent paradigm for large-scale distributed learning, for which there has been a growing interest to develop efficient and robust gradient aggregation strategies that overcome two key system bottlenecks: communication bandwidth and stragglers' delays. In particular, R…

We describe spaces of essential finite height (measured) laminations in a surface $S$ using a parameter space we call $\mathbb S$, an ordered semi-ring. We show that for every finite height essential lamination $L$ in $S$, there is an action of $π_1(S)$ on an $\mathbb S$-tree dual to the lift of $L$ to the universal co…

Both scientists and children make important structural discoveries, yet their computational underpinnings are not well understood. Structure discovery has previously been formalized as probabilistic inference about the right structural form --- where form could be a tree, ring, chain, grid, etc. [Kemp & Tenenbaum (2008…

Constructs a new graded variety from algebraic data.

The K-theoretic Farrell-Jones isomorphism conjecture for a group ring $R[G]$ has been proved for several groups. The toolbox for proving the Farrell-Jones conjecture for a given group depends on some geometric properties of the group as it is the case of hyperbolic groups. The technique used to prove it for hyperbolic …

Differential K-theory gets a $λ$-ring structure.

Classifies cobounded hyperbolic actions of metabelian groups.

In their recent preprint, Baldwin, Ozsváth and Szabó defined a twisted version (with coefficients in a Novikov ring) of a spectral sequence, previously defined by Ozsváth and Szabó, from Khovanov homology to Heegaard-Floer homology of the branched double cover along a link. In their preprint, they give a combinatorial …

There is a general trend towards solving problems suited to deep learning with more complex deep learning architectures trained on larger training sets. This requires longer compute times and greater data parallelization or model parallelization. Both data and model parallelism have been historically faster in paramete…

A new neural network model for molecular graphs that learns efficiently and accurately.

We show that the knot lattice homology of a knot in an L-space is equivalent to the knot Floer homology of the same knot (viewed these invariants as filtered chain complexes over the polynomial ring Z/2Z [U]). Suppose that G is a negative definite plumbing tree which contains a vertex w such that G-w is a union of rati…

Bayesian model improves image completion accuracy by automatically learning low rank structure.

The space C of conservative vertex colorings (over a field F) of a countable, locally finite graph G is introduced. The subspace of based colorings is shown to be isomorphic to the bicycle space of the graph. For graphs G with a free Z^d-action by automorphisms, C is a finitely generated module over the polynomial ring…

Let $M$ be a symplectic manifold, equipped with a Hamiltonian action of a torus $T$. We give an explicit formula for the rational cohomology ring of the symplectic quotient $M//T$ in terms of the cohomology ring of $M$ and fixed point data. Under some restrictions, our formulas apply to integral cohomology. In certain …

New link colorings using quandle rings and idempotents are stronger than existing methods.

The study proves knots and certain links support taut foliations.

Bayesian Tensor Ring factorization improved for scalability and handling of discrete data.

The paper develops further the theory of quandle rings which was introduced by the authors in a recent work. Orderability of quandles is defined and many interesting examples of orderable quandles are given. It is proved that quandle rings of left or right orderable quandles which are semi-latin have no zero-divisors. …

Scalable and robust TR decomposition for large-scale data with missing entries and outliers.

Lie-Rinehart algebras over $C^\infty$-rings defined and studied.

Nowadays, mobile telephony interruptions in our daily life activities are common because of the inappropriate ringing notifications of incoming phone calls in different contexts. Such interruptions may impact on the work attention not only for the mobile phone owners but also the surrounding people. Decision tree is th…

A new invariant of Poisson manifolds, a Poisson K-ring, is introduced. Hypothetically, this invariant is more tractable than such invariants as Poisson (co)homology. A version of this invariant is also defined for arbitrary algebroids. Basic properties of the Poisson K-ring are proved and the Poisson K-rings are calcul…

Investigates differential smoothness of 3D skew polynomial rings.

We define a notion of stability for chiral ring of four dimensional N=1 theory by introducing test chiral rings and generalized a maximization. We conjecture that a chiral ring is the chiral ring of a superconformal field theory if and only if it is stable. We then study N=1 field theory derived from D3 branes probing …

A classical theorem due to Quillen (1969) identifies the unitary bordism ring with the Lazard ring, which classifies the universal one-dimensional commutative formal group law. We prove an equivariant generalization of this result by identifying the homotopy theoretic $\mathbb{Z}/2$-equivariant unitary bordism ring, in…

The paper examines differential smoothness in skew PBW extensions over polynomial rings.

Criteria for smoothness of ambiskew polynomial rings.

This paper calculates the skein algebra of the Borromean rings complement.

The paper explores idempotents in quandle rings and their connections to quandle coverings.

Defines vector fields and differential forms on local C-infinity-ringed spaces.

Researchers found only one hyperbolic structure for Borromean rings.

One way to obtain invariants of some Legendrian submanifolds in 1-jet spaces $J^1M$, equipped with the standard contact structure, is through the Morse theoretic technique of generating families. This paper extends the invariant of generating family cohomology by giving it a product $μ_2$. To define the product, moduli…

New argument for 3-manifold cohomology with $\mathbb{F}_2$ coefficients.

Paper computes hyperbolic structure of Borromean rings complement.

New hyperbolic manifolds found with same trace ring.

Homological algebra used to study local equivalence of complex rings.

In this paper we compute a presentation for the group of ring motions of the split union of a Hopf link with Euclidean components and a Euclidean circle. A key part of this work is the study of a short exact sequence of groups of ring motions of general ring links in $\mathbb{R}^3$. This sequence allowed us to build th…

We show that solutions of Thurston equation on triangulated 3-manifolds in a commutative ring carry topological information. We also introduce a homogeneous Thurston equation and a commutative ring associated to triangulated 3-manifolds.

We build extensions of the arc rings, relate their centers to the cohomology rings of the Springer varieties, and categorify all level two representations of quantum sl(N).

Study Coxeter groups over fusion rings and their geometric realisations.

Division algorithm for surface group rings yields standard complexes and cohomological dimensions.

New Frobenius manifold structures found on Dicyclic group orbits.