arXiv research

Order positions are key variables in algorithmic trading. This paper studies the limiting behavior of order positions and related queues in a limit order book. In addition to the fluid and diffusion limits for the processes, fluctuations of order positions and related queues around their fluid limits are analyzed. As a…

Study k-positive surface group representations and their degenerations.

Study shows limits of metrics with positive scalar curvature on spheres.

Study on positive scalar curvature and its impact on Ricci limit spaces.

Study of conformal limits for special opers in Lie groups.

We prove a central limit theorem for the components of the largest eigenvectors of the adjacency matrix of a finite-dimensional random dot product graph whose true latent positions are unknown. In particular, we follow the methodology outlined in \citet{sussman2012universally} to construct consistent estimates for the …

Solves asset allocation for investors with utility functions and limits.

Approximations to utility indifference prices are provided for a contingent claim in the large position size limit. Results are valid for general utility functions on the real line and semi-martingale models. It is shown that as the position size approaches infinity, the utility function's decay rate for large negative…

Parreau compactified the Hitchin component of a closed surface $S$ of negative Euler characteristic in such a way that a boundary point corresponds to the projectivized length spectrum of an action of $π_1(S)$ on an $\mathbb R$-Euclidean building. In this paper, we use the positivity properties of Hitchin representatio…

Classifies Zariski closures of positive representations in Lie groups.

New examples of manifolds with positive scalar curvature and infinitely many poles.

Optimal diameter estimates for 3D spaces with non-negative Ricci curvature.

Study shows mass distribution of random holomorphic sections follows a central limit theorem.

The paper proves that Kähler manifolds with positive holomorphic sectional curvature have a limited diameter.

In [5] Herzlich proved a new positive mass theorem for Riemannian 3-manifolds $(N, g)$ whose mean curvature of the boundary allows some positivity. In this paper we study what happens to the limit case of the theorem when, at a point of the boundary, the smallest positive eigenvalue of the Dirac operator of the boundar…

We confirm a conjecture of Hamilton: On compact manifolds the normalized Ricci flow evolves metrics with positive curvature operators to limit metrics with constant curvature.

The study examines exceptional sets for radial limits of superharmonic functions on curved manifolds.

The study of random positive 3-strand braids reveals patterns in the roots of their Alexander polynomials.

Geometrically infinite Kleinain groups have nonconical limit sets with the cardinality of the continuum. In this paper, we construct a geometrically infinite Fuchsian group such that the Hausdorff dimension of the nonconical limit set equals zero. For finitely generated, geometrically infinite Kleinian groups, we prove…

We develop two new methods of constructing sequences of manifolds with positive scalar curvature that converge in the Gromov-Hausdorff and Intrinsic Flat sense to limit spaces with "pulled regions". The examples created rigorously within using these methods were announced by us a few years ago and have influenced the s…

The Chow-Mumford (CM) line bundle is a functorial line bundle on the base of any family of klt Fano varieties. It is conjectured that it yields a polarization on the moduli space of K-poly-stable klt Fano varieties. Proving ampleness of the CM line bundle boils down to showing semi-positivity/positivity statements abou…

Combines machine learning and convex limiting for accurate subgrid flux modeling in shallow-water equations.

We analyze the limit of the p-form Laplacian under a collapse, with bounded sectional curvature and bounded diameter, to a smooth limit space. As an application, we characterize when the p-form Laplacian has small positive eigenvalues in a collapsing sequence.

Two types of nonidentifiability in latent position graphs identified and characterized.

Solves Lempert's question on Nakano semi-positivity preservation.

Whether you trade futures for yourself or a hedge fund, your strategy is counted. Long and short position limits make the number of unique strategies finite. Formulas of the numbers of strategies, transactions, do nothing actions are derived. A discrete distribution of actions, corresponding probability mass, cumulativ…

Survey of nonnegative scalar curvature sequences and their limits.

New examples of manifolds in tangent cones of non-collapsed Ricci limit spaces.

Taxonomies are semantic hierarchies of concepts. One limitation of current taxonomy learning systems is that they define concepts as single words. This position paper argues that contextualized word representations, which recently achieved state-of-the-art results on many competitive NLP tasks, are a promising method t…

New method learns from either positive or negative feedback alone.

We use the notion of intrinsic flat distance to address the almost rigidity of the positive mass theorem for asymptotically hyperbolic manifolds. In particular, we prove that a sequence of spherically symmetric asymptotically hyperbolic manifolds satisfying the conditions of the positive mass theorem converges to hyper…

The paper examines compactness of scalar curvature sequences on conformal manifolds.

In the bordered Floer theory, gluing thickened torus of positive meridional Dehn twist to the boundary of a knot complement result in the knot complement of increased framing. For a fixed knot K, we construct a direct system of positively framed knot complements and study the direct limit. We also study the morphism sp…

New method for Transformer models to encode position information without sequential bias.

Ancient Ricci flows with bounded girth found in 3D and higher.

We show that the limiting unicolored $\mathfrak{sl}(N)$ Khovanov-Rozansky chain complex of any infinite positive braid categorifies a highest-weight projector. This result extends an earlier result of Cautis categorifying highest-weight projectors using the limiting complex of infinite torus braids. Additionally, we sh…

New flow expands hypersurfaces in hyperbolic space, showing round limiting shape for certain powers.

New manifolds with negative curvature limit to one with negative curvature.

We show that the limiting Khovanov chain complex of any infinite positive braid categorifies the Jones-Wenzl projector. This result extends Lev Rozansky's categorification of the Jones-Wenzl projectors using the limiting complex of infinite torus braids. We also show a similar result for the limiting Lipshitz-Sarkar-Kh…

Modified Perceptron handles strategic agents with limited position changes.

In this work, we consider the task of classifying binary positive-unlabeled (PU) data. The existing discriminative learning based PU models attempt to seek an optimal reweighting strategy for U data, so that a decent decision boundary can be found. However, given limited P data, the conventional PU models tend to suffe…

I study Gromov-Hausdorff limits of complex curves endowed with singular flat metrics of constant diameter. I formulate a criterion that the limit is collapsed in terms of a certain piecewise affine weight function on the dual intersection complex of a semi-stable model of the degeneration introduced by Kontsevich and S…

In this paper we consider Riemannian manifolds $(M^n,g)$ of dimension $n \geq 5$, with semi-positive $Q$-curvature and non-negative scalar curvature. Under these assumptions we prove $(i)$ the Paneitz operator satisfies a strong maximum principle; $(ii)$ the Paneitz operator is a positive operator; and $(iii)$ its Gree…

New metrics found for 6k-dimensional manifolds with positive Ricci curvature.

The paper classifies and proves properties of ALE manifolds and orbifolds.

In this paper we produce a sequence of Riemannian manifolds $M_j^m$, $m \ge 2$, which converge in the intrinsic flat sense to the unit $m$-sphere with the restricted Euclidean distance. This limit space has no geodesics achieving the distances between points, exhibiting previously unknown behavior of intrinsic flat lim…

We propose an approach to reduce both computational complexity and data storage requirements for the online positioning stage of a fingerprinting-based indoor positioning system (FIPS) by introducing segmentation of the region of interest (RoI) into sub-regions, sub-region selection using a modified Jaccard index, and …

In this paper, we study a nonlocal elliptic problem with the fractional Laplacian on $R^n$. We show that the problem has infinite positive solutions in $C^τ(R^n)\bigcap H^α_{loc}(R^n)$. Moreover each of these solutions tends to some positive constant limit at infinity. We extend Lin's result to the nonlocal problem on …