arXiv research

Study shows stability of locally conformally balanced condition under modifications but not under small deformations.

In this paper, we consider a proper modification $f : \tilde M \to M$ between complex manifolds, and study when a generalized $p-$Kähler property goes back from $M$ to $\tilde M$. When $f$ is the blow-up at a point, every generalized $p-$Kähler property is conserved, while when $f$ is the blow-up along a submanifold, t…

In this paper we extend recent breakthrough of Chen-Cheng \cite{CC1, CC2, CC3} on existence of constant scalar Kähler metric on a compact Kähler manifold to Calabi's extremal metric. Our argument follows \cite{CC3} and there are no new a prior estimates needed, but rather there are necessary modifications adapted to th…

In this paper a novel modification of the multilevel Monte Carlo approach, allowing for further significant complexity reduction, is proposed. The idea of the modification is to use the method of control variates to reduce variance at level zero. We show that, under a proper choice of control variates, one can reduce t…

In this article we prove two formulas for the topological entropy of an F-optical Hamiltonian flow induced by a C^{\infty} Hamiltonian, where F is a Lagrangian distribution. In these formulas, we calculate the topological entropy as the exponential growth rate of the average of the determinant of the differential of th…

Well-known conjectures of Tian predict that existence of canonical Kahler metrics should be equivalent to various notions of properness of Mabuchi's K-energy functional. In some instances this has been verified, especially under restrictive assumptions on the automorphism group. We provide counterexamples to the origin…

In this paper, we study strongly Gauduchon metrics on compact complex manifolds. We study the cohomology cones SG in the de Rham cohomology groups generated by all strongly Gauduchon metrics and its direct images under proper modifications. We also study the moduli of strongly Gauduchon manifolds. We prove an existence…

Abstract: Generalizes stability theories over toric varieties and Novikov type rings.

Paper refines InfoNCE for accurate mutual information estimation.

The proper Euclidean geometry is considered to be metric space and described in terms of only metric and finite metric subspaces (sigma-immanent description). Constructing the geometry, one does not use topology and topological properties. For instance, the straight, passing through points A and B, is defined as a set …

This paper is motivated by questions about averages of stochastic processes which originate in mathematical finance, originally in connection with valuing the so-called Asian options. Starting with research of Yor's in 1992, these questions about exponential functionals of Brownian motion have been studied in terms of …

New concept of Lorentzian-Euclidean black holes and metric transitions explored.

Paper corrects GIRP algorithm to ensure isotonic models.

The last few years have seen a staggering number of empirical studies of the robustness of neural networks in a model of adversarial perturbations of their inputs. Most rely on an adversary which carries out local modifications within prescribed balls. None however has so far questioned the broader picture: how to fram…

This work improves testing of machine learning model modifications using novel statistical methods.

Our monograph presents the foundations of the theory of groups and semigroups acting isometrically on Gromov hyperbolic metric spaces. Our work unifies and extends a long list of results by many authors. We make it a point to avoid any assumption of properness/compactness, keeping in mind the motivating example of $\ma…

Regularized LAEs learn principal components efficiently.

We extend the existing framework of semi-implicit variational inference (SIVI) and introduce doubly semi-implicit variational inference (DSIVI), a way to perform variational inference and learning when both the approximate posterior and the prior distribution are semi-implicit. In other words, DSIVI performs inference …

In his book Mickelsson notices that the infinite-dimensional Grassmannian manifold of Segal and Wilson admits a Spin^c structure and after this he naturally considers the problem of defining a Dirac operator on it. Mickelsson gives a possible candidate for such an operator but unfortunately it proves out to be badly di…

New method detects RNA modifications without prior training, revealing novel sites.

Compressed Sensing using $\ell_1$ regularization is among the most powerful and popular sparsification technique in many applications, but why has it not been used to obtain sparse deep learning model such as convolutional neural network (CNN)? This paper is aimed to provide an answer to this question and to show how t…

We study (transverse) scalar curvature type equation on compact Sasaki manifolds, in view of recent breakthrough of Chen-Cheng \cite{CC1, CC2, CC3} on existence of Kähler metrics with constant scalar curvature (csck) on compact Kähler manifolds. Following their strategy, we prove that given a Sasaki structure (with Ree…

We define an operation on homology ${B}^4$ which we call an $n$-twist annulus modification. We give a new construction of smoothly slice knots and exotically slice knots via $n$-twist annulus modifications. As an application, we present a new example of a smoothly slice knot with non-slice derivatives. Such examples we…

Due to recent technical and scientific advances, we have a wealth of information hidden in unstructured text data such as offline/online narratives, research articles, and clinical reports. To mine these data properly, attributable to their innate ambiguity, a Word Sense Disambiguation (WSD) algorithm can avoid numbers…

Few-shot learning benchmarks can be solved without using support set labels at test-time.

Let $M^{n+1}$ ($n \ge 2$) be a simply-connected space form of sectional curvature $-κ^2$ for some $κ\geq 0$, and $I$ an interval not containing $[-κ,κ]$ in its interior. It is known that the domain of a closed immersed hypersurface of $M$ whose principal curvatures lie in $I$ must be diffeomorphic to th…

New concept of proper-calibeating extends classic calibrated forecasts to proper scoring rules.

A modification of the confidence screening mechanism based on adaptive weighing of every training instance at each cascade level of the Deep Forest is proposed. The idea underlying the modification is very simple and stems from the confidence screening mechanism idea proposed by Pang et al. to simplify the Deep Forest …

Proposes simplified SHAP for faster black-box model explanations.

Behavior modification improves prediction accuracy by nudging user behavior.

New method for simplifying knots with specific properties.

Study of unimodular Sasaki and Vaisman Lie groups, determining all modifications explicitly.

Paper proposes adversarial modifications for link prediction models to improve robustness and interpretability.

We study large-scale classification problems in changing environments where a small part of the dataset is modified, and the effect of the data modification must be quickly incorporated into the classifier. When the entire dataset is large, even if the amount of the data modification is fairly small, the computational …

Computational methods that predict differential gene expression from histone modification signals are highly desirable for understanding how histone modifications control the functional heterogeneity of cells through influencing differential gene regulation. Recent studies either failed to capture combinatorial effects…

The paper explores proper actions and their relation to representation theory, with new quantitative methods.

Method explains anomaly detection by generating normal modifications.

Classifies $π_1$-injective maps between non-compact surfaces.

We study Khovanov homology classes which have state cycle representatives, and examine how they interact with Jacobsson homomorphisms and Lee's map $Φ$. As an application, we describe a general procedure, quasipositive modification, for constructing H-thick knots in rational Khovanov homology. Moreover, we show that sp…

We show that immersed minimal surfaces of $\mathbb{R}^{3}$ with bounded curvature and proper self intersections are proper. We also show that the restriction of the immersing map to a wide component is always proper. When the immersing map is injective the whole surface is a wide component. Prior to these results it wa…

Paper develops proper, lower-bounded losses for weakly supervised classification.

Preserves hyperbolicity in link complements with two moves.

Non-proper surface group action on product of trees found.

Analytic linearization and holomorphic extensions for proper groupoids.

Classifies non-linear Fredholm maps linking to stable homotopy groups of spheres.

A novel framework quantifies uncertainty using proper scores for various tasks.

A study of proper affine vector fields in plane symmetric static space-times by using the rank of the Rieman matrix and holonomy. Studying proper affine vector fields in each case, It is shown that the special class of the above space-times admit proper affine vector fields.

First example of open manifold with positive Ricci curvature and non-proper Busemann function.