arXiv research

This paper proposes and evaluates the k-greedy equivalence search algorithm (KES) for learning Bayesian networks (BNs) from complete data. The main characteristic of KES is that it allows a trade-off between greediness and randomness, thus exploring different good local optima. When greediness is set at maximum, KES co…

In this paper we prove that generic small partial smoothings of Kahler-Einstein (KE) Del Pezzo orbifolds with only nodal singularities, and with no non-zero holomorphic vector fields, admit orbifold KE metrics which are close in the Gromov-Hausdorff sense to the original KE metric.

Paper presents a technique using Spearman's Rank Correlation Coefficient for KE in TDs.

In this paper, we study the Nakano-positivity and dual-Nakano-positivity of certain adjoint vector bundles associated to ample vector bundles. As applications, we get new vanishing theorems about ample vector bundles. For example, we prove that if $E$ is an ample vector bundle over a compact Kähler manifold $X$, $S^kE\…

Unique tangent cones found for Kahler-Einstein metrics on singular varieties.

In this paper, we study the boundary behavior of the negatively curved Kähler-Einstein metric attached to a log canonical pair $(X,D)$ such that $K_X+D$ is ample. In the case where $X$ is smooth and $D$ has simple normal crossings support (but possibly negative coefficients), we provide a very precise estimate on the p…

Paper proposes KE-GCN for better graph embedding.

We recall an extension of Kirby's Calculus on non-simply connected 3-manifolds given in [FR], and the surgery calculus of bridged links from [Ke], which involves only local moves. We give a short combinatorial proof that the two calculi are equivalent, and thus describe the same classes of 3-manifolds. This makes the p…

In this paper, we prove that Kähler-Ricci flow converges to a Kähler-Einstein metric (or a Kähler-Ricci soliton) in the sense of Cheeger-Gromov as long as an initial Kähler metric is very closed to $g_{KE}$ (or $g_{KS}$) if a compact Kähler manifold with $c_1(M)>0$ admits a Kähler Einstein metric $g_{KE}$ (or a Kähler-…

Typical existence result on Ricci-flat metrics is in manifolds of finite geometry, that is, on $F=\bar F-D$ where $\bar F$ is a compact Kähler manifold and $D$ is a smooth divisor. We view this existence problem from a different perspective. For a given complex manifold $X$, we take a suitable exhaustion $\{X_r\}_{r>0}…

This paper optimizes paths for generative models using kinetic energy.

Let (X,[ω]) be a compact Kaehler manifold with a fixed Kaehler class [ω]. Let K_ωbe the set of all Kaehler metrics on X whose Kaehler class equals [ω]. In this paper we investigate the critical points of the functional Q(g)= |v|_g T_0(X,g)^{1/2} for g \in K_ω, where v is a fixed nonzero vector of the determinant line λ…

Let X be a smooth closed oriented non-spin 4-manifold with even intersection form kE_8\oplus nH. In this article we show that n\geq |k| on X. Thus we confirm the 10/8-conjecture affirmatively. As an application, we also give an estimate of intersection forms of spin coverings of non-spin 4-manifolds with even intersect…

Uniform RC-positivity results for direct image bundles.

The Adomian decomposition method is shown to be equivalent to the Taylor series approach.

This paper provides an explicit formula for complex structures in embeddings of manifolds.

In this paper we perform a blow-up and quantization analysis of the following nonlocal Liouville-type equation \begin{equation}(-Δ)^\frac12 u= κe^u-1~\mbox{in $S^1$,} \end{equation} where $(-Δ)^\frac{1}{2}$ stands for the fractional Laplacian and $κ$ is a bounded function. We interpret the above equation as the prescri…

In this paper we perform a blow-up and quantization analysis of the fractional Liouville equation in dimension $1$. More precisely, given a sequence $u_k :\mathbb{R} \to \mathbb{R}$ of solutions to \begin{equation} (-Δ)^\frac{1}{2} u_k =K_ke^{u_k}\quad \text{in }\mathbb{R}, \end{equation} with $K_k$ bounded in $L^\inft…

Given a Kähler fiber space $p:X\to Y$ whose generic fiber is of general type, we prove that the fiberwise singular Kähler-Einstein metric induces a semipositively curved metric on the relative canonical bundle $K_{X/Y}$ of $p$. We also propose a conjectural generalization of this result for relative twisted Kähler-Eins…

We prove the K-moduli space of cubic threefolds is identical to their GIT moduli. More precisely, the K-(semi,poly)-stability of cubic threefolds coincide to the corresponding GIT stabilities, which could be explicitly calculated. In particular, this implies that all smooth cubic threefolds admit Kähler-Einstein metric…

Constructs a convex Finsler metric on vector bundles under specific conditions.

We introduce uniform K-stability and its relationship with the coercivity property of the K-energy functional, for general polarized manifolds. Since the automorphism groups are not necessarily finite, size of the norm measuring uniformity should be reduced with respect to the group action. About this point we explain …

In this paper, we study the behavior of Ricci flows on compact orbifolds with finite singularities. We show that Perelman's pseudolocality theorem also holds on orbifold Ricci flow. Using this property, we obtain a weak compactness theorem of Ricci flows on orbifolds under some natural technical conditions. This genera…

The paper proves conditions for vector bundles to be Kobayashi and Griffiths positive.

New flow for Yang-Mills-Higgs theory avoids singularities.

New method improves imitation learning from expert observations.

The paper shows convergence of Sasaki-Ricci flow on Sasakian 5-manifolds.

A new method estimates multi-dimensional value distributions using Hilbert space embeddings.

Transformer-based method improves causal discovery from observational data.

System classifies lung CT scans into normal or COVID-19 using machine learning.

Maps between circle bundles are studied, proving fiber-preserving and finiteness results for mapping degrees.

Study differential operators and their solutions on manifolds, proving upper bounds and curvature.