arXiv research

In this paper, we prove that the zero-locus of any global holomorphic log-one-form on a projective log-smooth pair $\left(X,D\right)$ of log-general type must be non-empty. Applying this result, we give an answer to the algebraic hyperbolicity part of Shafarevich's conjecture, with the generic fiber being Kawamata-log-…

Proves log-concavity of cluster algebra coefficients for type $A_n$.

In this article we construct a canonical Kähler-Einstein current on a LC (log canonical) pairs of log general type as the limit of a sequence of canonical Kähler-Einstein currents on KLT(Kawamata log terminal) pairs of log general type. We call the volume form associated with the canonical Kähler-Einstein current the c…

Paper proves integrability and entropy compactness for Kähler potentials with uniform log-log threshold.

Log-periodic oscillations have been used to predict price trends and crashes on financial markets. So far two types of log-periodic oscillations have been associated with the real markets. The first type are oscillations which accompany a rising market and which ends in a crash. The second type oscillations, called "an…

The cyclic block coordinate descent-type (CBCD-type) methods, which performs iterative updates for a few coordinates (a block) simultaneously throughout the procedure, have shown remarkable computational performance for solving strongly convex minimization problems. Typical applications include many popular statistical…

Study detects signals in spiked Wigner models using log likelihood ratio.

The paper proves properties of manifolds with negative holomorphic sectional curvature.

Log-Sobolev inequality proven for submanifolds in specific types of manifolds.

On a complete Riemannian manifold M with Ricci curvature satisfying $\textrm{Ric}(\nabla r,\nabla r) \geq -Ar^2(\log r)^2(\log(\log r))^2...(\log^{k}r)^2$ for $r\gg 1$, where A>0 is a constant, and r is the distance from an arbitrarily fixed point in M. we prove some Liouville-type theorems for a C^2 function $f:M\ri…

The study improves Poincaré and log-Sobolev inequalities on hyperbolic spaces.

We consider a log-Riemann surface $\mathcal{S}$ with a finite number of ramification points and finitely generated fundamental group. The log-Riemann surface is equipped with a local holomorphic difffeomorphism $π: \mathcal{S} \to \C$. We prove that $\mathcal{S}$ is biholomorphic to a compact Riemann surface with finit…

Ancient Ricci flows are identified without curvature sign condition.

Upper bounds on map degrees for various manifold types.

Flow-based generative models (Dinh et al., 2014) are conceptually attractive due to tractability of the exact log-likelihood, tractability of exact latent-variable inference, and parallelizability of both training and synthesis. In this paper we propose Glow, a simple type of generative flow using an invertible 1x1 con…

Generalizes complex manifolds to manifolds with corners and generalized corners.

In this paper, we study the gradient estimates of Li-Yau-Hamilton type for positive solutions to both drifting heat equation and the simple nonlinear heat equation problem $u_t-Δu=au\log u, \ \ u>0$ on the compact Riemannian manifold $(M,g)$ of dimension $n$ and with non-negative (Bakry-Emery)-Ricci curvature. Here…

The paper derives inequalities and formulas for generalized Ricci flow.

Motivated by the study of Fano type varieties we define a new class of log pairs that we call asymptotically log Fano varieties and strongly asymptotically log Fano varieties. We study their properties in dimension two under an additional assumption of log smoothness, and give a complete classification of two dimension…

Holomorphic torsion invariant for log-Enriques surfaces derived from Borcherds products.

Let $(X,ω)$ be a compact Kähler manifold. We prove the existence and uniqueness of solutions to complex Monge-Ampère equations with prescribed singularity type. Compared to previous work, the assumption of small unbounded locus is dropped, and we work with general model type singularities. We state and prove our theore…

Corrects pseudo log-likelihood method issues in various applications.

Holomorphic families yield metrics with explicit curvature formulas.

Paper proves generalized Talagrand inequality for Sinkhorn distance.

The study proves a key inequality for specific types of three-dimensional spaces.

Study the relationship between type problem and first eigenvalues on Riemannian manifolds.

LogAnMeta detects anomalies from log events using meta learning.

Given a probability measure $μ$ supported on a convex subset $Ω$ of Euclidean space $(\mathbb{R}^d,g_0)$, we are interested in obtaining Poincaré and log-Sobolev type inequalities on $(Ω,g_0,μ)$. To this end, we change the metric $g_0$ to a more general Riemannian one $g$, adapted in a certain sense to $μ$, and perform…

The Links-Gould polynomial of alternating knots is shown to be log-concave and positive.

Burq-Gérard-Tzvetkov and Hu established $L^p$ estimates ($2\le p\le \infty$) for the restriction of eigenfunctions to submanifolds. The estimates are sharp, except for the log loss at the endpoint $L^2$ estimates for submanifolds of codimension 2. It has long been believed that the log loss at the endpoint can be remov…

We show the vanishing of the log-term in the Fefferman expansion of the Bergman kernel of the disk bundle over a compact simply-connected homogeneous Kaehler--Einstein manifold of classical type.

Noise-Contrastive Estimation improves efficiency for estimating log-likelihood of complex point processes.

Paper proposes robust estimators for heavy-tailed data with infinite variance.

The Milnor fiber conjecture is proven for splice type singularities.

After establishing suitable notions of stability and Chern classes for singular pairs, we use Kähler-Einstein metrics with conical and cuspidal singularities to prove the slope semistability of orbifold tangent sheaves of minimal log-canonical pairs of log general type. We then proceed to prove the Miyaoka-Yau inequali…

Large deviation principles for multivariate stochastic volatility models.

In this note, we study the integral of the 1-form $\log x\frac{dy}{y}-\log y\frac{dx}{x}$ over certain plane curves defined by A-polynomials of knots. It is quite surprising that a Chern-Simons type invariant of 3-manifolds, which can be geometrically computed, may be used to get the exact values of those integrals. Th…

The purpose of this paper is to study gradient estimate of Hamilton - Souplet - Zhang type for the general heat equation $u_t=Δ_V u + au\log u+bu$ on noncompact Riemannian manifolds. As its application, we show a Harnak inequality for the heat solution and a Liouville type theorem for a nonlinear elliptic equation.…

Fixed points found in cluster modular groups under specific conditions.

New inequality shows energy growth and decay in geometric problems.

McDiarmid's inequality under dependence via approximate tensorization of entropy

Proposes categorification of Z-invariants for specific 3-manifolds.

The paper explores obstructions for symplectic Lie algebroids on surfaces.

New weighted surface area measures for convex bodies with applications.

Study shows curvature rigidity of specific metric types.

The study proves a theorem about subword complexity for free group automorphisms.

Paper approximates Kähler metrics with cone singularities near a hypersurface.

The paper defines and analyzes Kähler metrics near a compact manifold, showing their deviation from Poincaré-type metrics.