arXiv research

Paper finds infinitely many 3-spheres without nice orderings.

Method produces Einstein metrics on Lie groups.

Programs compute Heegaard Floer invariants from open books.

The study classifies nilpotent Lie algebras up to dimension 9.

Study on nilpotent Lie algebras with specific metrics.

The paper studies nice bases for Lie algebras and their properties.

The study shows manifolds with special generic maps also have nice multisections.

The paper connects higher order risk measures and stochastic dominance, showing their equivalence and integrating them with optimization.

NICE model estimates causal effects for image treatments.

A-NICE-MC trains flexible MCMC kernels to efficiently sample from complex distributions.

The paper explores density of stable mappings and their properties.

The paper studies the structure of endpoint maps near nice singular curves in sub-Riemannian structures.

NICE learns a representation to avoid bad controls in causal inference.

In some sense, the world is composed of shapes and words, of continuous things and discrete things. The recognition and study of continuous objects in the form of shapes occupies a significant part of the effort of unraveling many geometric questions. Shapes can be rep- resented with great generality by objects called …

Let $G$ be a real reductive Lie group and $τ:G \longrightarrow GL(V)$ be a real reductive representation of $G$ with (restricted) moment map $m_{\ggo}: V-{0} \longrightarrow \ggo$. In this work, we introduce the notion of "nice space" of a real reductive representation to study the problem of how to determine if a $G$-…

Although neural networks are routinely and successfully trained in practice using simple gradient-based methods, most existing theoretical results are negative, showing that learning such networks is difficult, in a worst-case sense over all data distributions. In this paper, we take a more nuanced view, and consider w…

NICE framework explains CNN predictions and compresses images.

Study on surfaces in product space with curvature inequality.

We introduce a method for creating a special type of tree, called a tree position, from a weighted graph. Leaves of the tree correspond to vertices of the original graph, and the tree edges contain information which can be used to partition these vertices. By repeatedly applying reducing operations to the tree position…

Analyzing historical data of price indices we find an extraordinary growth phenomenon in several examples of hyper-inflation in which price changes are approximated nicely by double-exponential functions of time. In order to explain such behavior we introduce the general coarse-graining technique in physics, the Monte …

We have analyzed the statistical probabilities of limit-order book (LOB) shape through building the book using the ultra-high-frequency data from 23 liquid stocks traded on the Shenzhen Stock Exchange in 2003. We find that the averaged LOB shape has a maximum away from the same best price for both buy and sell LOBs. Th…

Deep learning improves causal effect estimation from complex observational data.

Improved CR Sobolev inequalities on CR sphere established.

Generalizes moment-angle manifolds to arbitrary nice manifolds with corners.

Constructs real algebraic functions with both compact and non-compact preimages.

Given a monotone convex function on the space of essentially bounded random variables with the Lebesgue property (order continuity), we consider its extension preserving the Lebesgue property to as big solid vector space of random variables as possible. We show that there exists a maximum such extension, with explicit …

This is an elementary geometrical proof of Birkhoff theorem. It is hardly important, but the pictures behind are quite nice.

As a generalization of Davis-Januszkiewicz theory, there is an essential link between locally standard $(\Z_2)^n$-actions (or $T^n$-actions) actions and nice manifolds with corners, so that a class of nicely behaved equivariant cut-and-paste operations on locally standard actions can be carried out in step on nice mani…

We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which is a provably convergent, second order incremental algorithm for solving large-scale partially separable optimization problems. The algorithm is based on a local quadratic approximation, and hence, allows incorporating curvature information to sp…

Introduces new spaces for configurations of points with specific monodromies.

The tame flows are ``nice'' flows on ``nice'' spaces. The nice (tame) sets are the pfaffian sets introduced by Khovanski, and a flow $Φ: \mathbb{R}\times X\to X$ on pfaffian set $X$ is tame if the graph of $Φ$ is a pfaffian subset of $\mathbb{R}\times X\times X$. Any compact tame set admits plenty tame flows. We prove …

Scalable spaces are simply connected manifolds with nice cohomology properties.

New method constructs Ricci-flat metrics on Lie groups.

There are various results that frame left-orderability of a group as a geometric property. Indeed, the fundamental group of a 3-manifold is left-orderable whenever the first Betti number is positive; in the case that the first Betti number is zero this property is closely tied to the existence of certain nice foliation…

The study restricts manifolds with certain explicit SGL maps and constructs them.

We prove that the Casimir operator acting on sections of a homogeneous vector bundle over a generalized flag manifold naturally extends to an invariant differential operator on arbitrary parabolic geometries. We study some properties of the resulting invariant operators and compute their action on various special types…

In some scientific fields, a scaling is able to modify the topology of an observed object. Our goal in the present work is to introduce a new formalism adapted to the mathematical representation of this kind of phenomenon. To this end, we introduce a new metric structure - the galactic spaces - which depends on an orde…

In this paper, we investigate the properties of the full colored HOMFLYPT invariants in the full skein of the annulus $\mathcal{C}$. We show that the full colored HOMFLYPT invariant has a nice structure when $q\rightarrow 1$. The composite invariant is a combination of the full colored HOMFLYPT invariants. In order to …

We provide an intergral lift of the combinatorial definition of Heegaard Floer homology for nice diagrams, and show that the proof of independence using convenient diagrams adapts to this setting.

Extends classical jets theory to algebraic ideals of smooth functions.

Study of geodesics on circle using Moebius transformations.

A limaçon-like curve, allowing 2π-transition with monotone curvature between concentric curvature elements, is presented. The curve is 4th degree algebraic, 4th degree rational, and shares other common features with Pascal's limaçon.

We define a `nice representation' of a finitely presented group G as being a non-degenerate essentially surjective simplicial map f from a `nice' space X into a 3-complex associated to a presentation of G, with a strong control over the singularities of f, and such that X is WGSC (weakly geometrically simply connected)…

Paper describes links of mixed polynomials with specific properties.

The study introduces new foliations and structures on complex manifolds.

Six quaternionic lines with optimal angles found in 2D quaternion space.

HessFormer enables distributed Hessian computation for large models.

In L^3, cuspidal edges can have bounded mean curvature under specific conditions.