arXiv research

Paper assesses how pandemic data impacts mortality models.

Neural network model improves longevity risk assessment.

Characterizes slopes for Markov ordering on prime pairs.

Calabi-Yau theorem extended to Vaisman manifolds.

We prove that a compact lcK manifold with holomorphic Lee vector field is Vaisman provided that either the Lee field has constant norm or the metric is Gauduchon (i.e., the Lee field is divergence-free). We also give examples of compact lcK manifolds with holomorphic Lee vector field which are not Vaisman.

The study examines Lee metrics on groups and their properties.

We give a complete description of all locally conformally Kähler structures with holomorphic Lee vector field on a compact complex manifold of Vaisman type. This provides in particular examples of such structures whose Lee vector field is not homothetic to the Lee vector field of a Vaisman structure. More generally, dr…

New theorem on Lee classes for LCK manifolds with potential.

Synthetic proof of Gannon-Lee theorem for spacetimes.

Paper uses neural networks to calibrate Lee-Carter models for multiple populations.

Proves Gannon-Lee theorem for $C^1$ spacetimes.

Holomorphic tensors on Vaisman manifolds are invariant under the Lee field.

Lobb observed in [arXiv:1103.1412] that each equivariant sl(N) Khovanov-Rozansky homology over C[a] admits a standard decomposition of a simple form. In the present paper, we derive a formula for the corresponding Lee-Gornik spectral sequence in terms of this decomposition. Based on this formula, we give a simple alter…

Study on Lee classes of complex surfaces, proving connectedness and bounds.

This note is devoted to partial study of recurrent equation $dω=β\wedge ω$, based on linear algebra of exterior forms. Such equation was considered by Lee, for non-degenerate 2-form. In this note we approach general case, when $ω$ is arbitrary. Particularly, we extend results obtained by Lee, on odd-forms.

Study examines Weyl structures on Riemannian manifolds with vanishing Lee form.

We discuss a remarkable formula discovered by Jerison and Lee to classify constant scalar curvature pseudohermitian structures on the sphere. We show that the formula is valid in the wider context of Einstein pseudohermitian manifolds. As an application we prove a uniqueness result that generalizes the theorem of Jeris…

In this paper, we extend the classical Ho-Lee binomial term structure model to the case of time-dependent parameters and, as a result, resolve a drawback associated with the model. This is achieved with the introduction of a more flexible no-arbitrage condition in contrast to the one assumed in the Ho-Lee model.

The Lee-Gauduchon cone is a convex cone of cohomology classes for complex manifolds.

We show that the page at which the Lee spectral sequence collapses gives a bound on the unknotting number, u(K). In particular, for knots with u(K)<3, we show that the Lee spectral sequence must collapse at the E_2 page. An immediate corollary is that the Knight Move Conjecture is true when u(K)<3.

Calculates knot $X$-torsion order using spectral sequences.

We give a simple proof of Lee's result from [Adv. Math. 179 (2005) 554-586; arXiv:math.GT/0210213], that the dimension of the Lee variant of the Khovanov homology of a c-component link is 2^c, regardless of the number of crossings. Our method of proof is entirely local and hence we can state a Lee-type theorem for tang…

New link homology theories for $\mathbb{RP}^3$ yield distinct invariants.

Developed a new homology theory for graph chromatic polynomials.

In this paper a multi-factor generalization of Ho-Lee model is proposed. In sharp contrast to the classical Ho-Lee, this generalization allows for those movements other than parallel shifts, while it still is described by a recombining tree, and is stationary to be compatible with principal component analysis. Based on…

Study shows torsion order bounds band-unlinking number for knot cobordisms.

The exterior derivative $d θ$ of the Lee form $θ$ of almost Hermitian manifolds is studied. If $ω$ is the Kähler two-form, it is proved that the $\mathbb{R}ω$-component of $dθ$ is always zero. expressions for the other components, in $[λ_0^{1,1}]$ and in $[[ λ^{2,0} ]]$, of $dθ$ are also obtained. They are given in ter…

MULTIFIT tests independence between two random vectors using multiscale Fisher's test.

Characterizes braid types and estimates twist coefficients.

Paper proves uniqueness of Einstein metrics on balls.

Researchers determine quantum filtration structure of torus links.

We study two kinds of transformation groups of a compact locally conformally Kahler (l.c.K.) manifold. First we study compact l.c.K. manifolds with parallel Lee form by means of the existence of a holomorphic l.c.K. flow. Next, we introduce the Lee-Cauchy-Riemann (LCR) transformations as a class of diffeomorphisms pres…

This article applies a long short-term memory recurrent neural network to mortality rate forecasting. The model can be trained jointly on the mortality rate history of different countries, ages, and sexes. The RNN-based method seems to outperform the popular Lee-Carter model.

New invariants from divisibility of Lee classes for slice-torus.

We construct new examples of self-similar solutions and translating solitons for Lagrangian mean curvature flow by extending the method of Joyce, Lee and Tsui. Those examples include examples in which the Lagrangian angle is arbitrarily small as the examples of Joyce, Lee and Tsui.

In their seminal work Carr and Lee (2008) show how to robustly price and replicate a variety of claims written on the quadratic variation of a risky asset under the assumption that the asset's volatility process is independent of the Brownian motion that drives the asset's price. Additionally, they propose a correlatio…

Butscher, D. Lee, Y. Lee, and Joyce constructed a special Lagrangian submanifold by gluing a Lawlor neck into a transverse intersection point of two special Lagrangian submanifolds. We prove a uniqueness theorem for the gluing of flat special Lagrangian tori of real dimension 3 in a flat complex torus of complex dimens…

Study negative band numbers in braids and links.

We establish a Hard Lefschetz Theorem for the de Rham cohomology of compact Vaisman manifolds. A similar result is proved for the basic cohomology with respect to the Lee vector field. Motivated by these results, we introduce the notions of a Lefschetz and of a basic Lefschetz locally conformal symplectic (l.c.s.) mani…

A graph is called intrinsically knotted if every embedding of the graph contains a knotted cycle. Johnson, Kidwell and Michael, and, independently, Mattman showed that intrinsically knotted graphs have at least 21 edges. Recently Lee, Kim, Lee and Oh, and, independently, Barsotti and Mattman, showed that $K_7$ and the …

The Lee Carter modelling framework is widely used because of its simplicity and robustness despite its inability to model specific cohort effects. A large number of extensions have been proposed that model cohort effects but there is no consensus. It is difficult to simultaneously account for cohort effects and age-adj…

New invariant distinguishes non-orientable surfaces.

There are recent cryptographic protocols that are based on Multiple Simultaneous Conjugacy Problems in braid groups. We improve an algorithm, due to Sang Jin Lee and Eonkyung Lee, to solve these problems, by applying a method developed by the author and Nuno Franco, originally intended to solve the Conjugacy Search Pro…

The paper classifies solutions to a specific elliptic equation in the Heisenberg group.

Integrable LCK manifolds characterized as Kähler Lie algebras.

Based on the results of the second author, we define an equivariant version of Lee and Bar-Natan homology for periodic links and show that there exists an equivariant spectral sequence from the equivariant Khovanov homology to equivariant Lee homology. As a result we obtain new obstructions for a link to be periodic. T…

Lee homology (a variant of Khovanov homology) over $\mathbb{Q}$ possesses the "canonical generators" as its basis. The generators (Lee's classes) $[α(D, o)]$ are constructed combinatorially from an oriented link diagram $D$, one for each alternative orientation $o$ on $D$. Let $R$ be an integral domain. There exists a …

Article finds a geometric connection between structures on manifolds.