arXiv research

This is the third part of the work on the exact triangles. We construct chain homomorphisms and show exactness of the resulting sequence.

Study on compact manifolds for exact G$_{2}$-Structures without additional constraints.

Defines band maps in unoriented link Floer homology forming a skein exact triangle.

Non-exact Poisson structures found on toric varieties.

Exact selective inference with randomization for Gaussian regression models.

Exact discrete mechanics for nonholonomic systems defined.

For a Legendrian $(2,n)$ torus knot or link with maximal Thurston-Bennequin number, Ekholm, Honda, and Kálmán constructed $C_n$ exact Lagrangian fillings, where $C_n$ is the $n$-th Catalan number. We show that these exact Lagrangian fillings are pairwise non-isotopic through exact Lagrangian isotopy. To do that, we com…

Between the category of exact metric spaces with bounded geometry (about which much is known) and the larger category of arbitrary exact metric spaces (about which little is known) lies the intermediate category of asymptotically exact metric spaces. We show that the coarse Baum-Connes assembly map is naturally split s…

Study on Lie groups with exact G2 structures and closed eigenforms.

Exact optimality achieved in distributed mean estimation with shared randomness.

New skein exact triangles for link Floer homology.

Study exact surgery formula in involutive Heegaard Floer homology.

The paper studies splitting maps in link Floer homology using skein exact sequences.

We show that if a contact open book $(Σ,h)$ on a $(2n+1)$-manifold $M$ ($n\geq1$) is induced by a Lefschetz fibration $π:W \to D^2$, then there is a one-to-one correspondence between positive stabilizations of $(Σ,h)$ and \emph{positive stabilizations} of $π$. More precisely, any positive stabilization of $(Σ,h)$ is in…

Paper explores exact recovery of communities in weighted graphs using Gaussian and exponential distributions.

Exact Bayesian inference for discrete models using probability generating functions.

In this note we show that given an exact QS-manifold (a natural generalisation of an exact Poisson manifold) one can associate a family of odd Jacobi structures on the same underlying supermanifold.

Proves a new skein exact triangle for real monopole Floer homology.

No exact G₂-structures on compact Lie group quotients.

We introduce constructions of exact Lagrangian cobordisms with cylindrical Legendrian ends and study their invariants which arise from Symplectic Field Theory. A pair $(X,L)$ consisting of an exact symplectic manifold $X$ and an exact Lagrangian cobordism $L\subset X$ which agrees with cylinders over Legendrian links $…

New surgery exact triangles in Heegaard Floer homology for rational slopes.

Paper explores limits of exact inference in structured prediction models.

We provide in this note two relevant examples of Lagrangian cobordisms. The first one gives an example of two exact Lagrangian submanifolds which cannot be composed in an exact fashion. The second one is an example of an exact Lagrangian cobordism on which all primitive of the Liouville form is not constant on the nega…

We prove an existence result for exact lagrangian cobordisms between closed legendrians.

We provide an explicit section for a mapping class group sequence.

Exact second-order optimization for deep learning reduces computational cost and improves performance.

In this paper we introduce the notion of exact links, which constitute a broad class of high dimensional links.

Paper presents new cobordism sequences for singular maps.

We find various exact solutions for a new stochastic volatility (SV) model: the transition probability density, European-style option values, and (when it exists) the martingale defect. This may represent the first example of an SV model combining exact solutions, GBM-type volatility noise, and a stationary volatility …

This paper answers a basic question about the Birman exact sequence in the theory of mapping class groups. We prove that the Birman exact sequence does not admit a section over any subgroup $Γ$ contained in the Torelli group with finite index. A fortiori this proves that there is no section of the Birman exact sequence…

Exact minibatch MH method improves scalability for large datasets.

Corrects earlier work on surface orbifold pure braid groups.

In this paper, we will give a rigorous construction of the exact discrete Lagrangian formulation associated to a continuous Lagrangian problem. Moreover, we work in the setting of Lie groupoids and Lie algebroids which is enough general to simultaneously cover several cases of interest in discrete and continuous descri…

To a Legendrian knot, one can associate an $\mathcal{A}_{\infty}$ category, the augmentation category. An exact Lagrangian cobordism between two Legendrian knots gives a functor of the augmentation categories of the two knots. We study the functor and establish a long exact sequence relating the corresponding cohomolog…

New conditions ensure Dantzig-Wolfe relaxation matches rank-constrained optimization problems.

We determine the information-theoretic cutoff value on separation of cluster centers for exact recovery of cluster labels in a $K$-component Gaussian mixture model with equal cluster sizes. Moreover, we show that a semidefinite programming (SDP) relaxation of the $K$-means clustering method achieves such sharp threshol…

We study graph matching with correlated Gaussian features and find thresholds for exact recovery.

Exact learning improves naive Bayes classifier performance for small samples.

The exact nonnegative matrix factorization (exact NMF) problem is the following: given an $m$-by-$n$ nonnegative matrix $X$ and a factorization rank $r$, find, if possible, an $m$-by-$r$ nonnegative matrix $W$ and an $r$-by-$n$ nonnegative matrix $H$ such that $X = WH$. In this paper, we propose two heuristics for exac…

PhD dissertation on Finsler geometry and gravity, focusing on Berwald spaces and exact solutions.

We study some properties of decomposable exact Lagrangian cobordisms between Legendrian links in $\mathbb{R}^3$ with the standard contact structure. In particular, for any decomposable exact Lagrangian filling $L$ of a Legendrian link $K$, we may obtain a normal ruling of $K$ associated with $L$. We prove that the asso…

We study the obstruction to the exactness of the variational complex for a field theory on an affine bundle.

Study exact Lie bialgebras from flat Lie groups, classifying them.

The article provides obstructions for exact submanifolds in symplectic applications.

Sharp threshold for exact recovery in non-uniform hypergraph stochastic block model.

New exact sequence links cohomology, automorphisms, and extensions of symmetric quandles.

Study of Legendrian links using Floer theory and cluster varieties.

We develop an analogue of the Birman exact sequence for the Torelli subgroup of Aut(F_n). This builds on earlier work of the authors who studied an analogue of the Birman exact sequence for the entire group Aut(F_n). These results play an important role in the authors' recent work on the second homology group of the To…