arXiv research

Optimizes large stock order execution with LSTM neural networks.

We study the isoperimetric structure of asymptotically flat Riemannian 3-manifolds (M,g) that are C^0-asymptotic to Schwarzschild of mass m>0. Refining an argument due to H. Bray we obtain an effective volume comparison theorem in Schwarzschild. We use it to show that isoperimetric regions exist in (M, g) for all suffi…

Infinite family of hyperbolic 3-manifolds with large volumes.

Equity auctions show linear price impact up to a large volume, then non-linear.

The paper proposes a new order slicing strategy to reduce market impact in large-volume trading.

Study Turaev-Viro invariants of Seifert fibered 3-manifolds, proving volume conjecture.

The paper calculates super Weil-Petersson volumes for large genus.

We describe a class of genus 2 closed hyperbolic 3-manifolds of arbitrarily large volume.

The study proves uniqueness of large isoperimetric sets in specific noncompact manifolds.

Acquisition cost is a crucial bottleneck for seismic workflows, and low-rank formulations for data interpolation allow practitioners to `fill in' data volumes from critically subsampled data acquired in the field. Tremendous size of seismic data volumes required for seismic processing remains a major challenge for thes…

We study the dynamics of order flows around large intraday price changes using ultra-high-frequency data from the Shenzhen Stock Exchange. We find a significant reversal of price for both intraday price decreases and increases with a permanent price impact. The volatility, the volume of different types of orders, the b…

The immense amount of daily generated and communicated data presents unique challenges in their processing. Clustering, the grouping of data without the presence of ground-truth labels, is an important tool for drawing inferences from data. Subspace clustering (SC) is a relatively recent method that is able to successf…

We study the statistical properties of the recurrence intervals $τ$ between successive trading volumes exceeding a certain threshold $q$. The recurrence interval analysis is carried out for the 20 liquid Chinese stocks covering a period from January 2000 to May 2009, and two Chinese indices from January 2003 to April 2…

Study shows volume and genus unrelated for hyperbolic fibred knots.

We construct an algorithm that lists all closed essential surfaces in the complement of a knot that lies on the fiber of a trefoil or figure eight knot. Such knots are Berge knots and hence admit lens space surgeries. Furthermore they may have arbitrarily large hyperbolic volume. Using this algorithm we concoct large v…

We prove that a reversible Berwaldian Finsler structure $\left(M,F\right)$ with base-independent non-negative radial flag curvature and large volume growth does not have any closed geodesics.

In this paper, we study the topology of complete noncompact Riemannian manifolds with asymptotically nonnegative Ricci curvature and large volume growth. We prove that they have finite topological types under some curvature decay and volume growth conditions. We also generize it to the manifolds with $k$-th asymptotica…

An important conjecture in knot theory relates the large-$N$, double scaling limit of the colored Jones polynomial $J_{K,N}(q)$ of a knot $K$ to the hyperbolic volume of the knot complement, $\text{Vol}(K)$. A less studied question is whether $\text{Vol}(K)$ can be recovered directly from the original Jones polynomial …

Study of limits of Einstein-Bogomol'nyi metrics on P^1 in two regimes.

By obtaining surgery descriptions of knots which lie on the genus one fiber of the trefoil or figure eight knot, we show that these include hyperbolic knots with arbitrarily large volume. These knots admit lens space surgeries and form two families of Berge knots. By way of tangle descriptions we also obtain surgery de…

In this paper we consider the problem of minimizing the relative perimeter under a volume constraint in the interior of a conically bounded convex set, i.e., an unbounded convex body admitting an \emph{exterior} asymptotic cone. Results concerning existence of isoperimetric regions, the behavior of the isoperimetric pr…

High volume of data, perceived as either challenge or opportunity. Deep learning architecture demands high volume of data to effectively back propagate and train the weights without bias. At the same time, large volume of data demands higher capacity of the machine where it could be executed seamlessly. Budding data sc…

Motivated by empirical data, we develop a statistical description of the queue dynamics for large tick assets based on a two-dimensional Fokker-Planck (diffusion) equation, that explicitly includes state dependence, i.e. the fact that the drift and diffusion depends on the volume present on both sides of the spread. "J…

Study on fibered knots in 3-manifolds, proving unrelated volume and genus.

The availability of data on digital traces is growing to unprecedented sizes, but inferring actionable knowledge from large-scale data is far from being trivial. This is especially important for computational finance, where digital traces of human behavior offer a great potential to drive trading strategies. We contrib…

With the increased need for multi-center magnetic resonance imaging studies, problems arise related to differences in hardware and software between centers. Namely, current algorithms for brain volume quantification are unreliable for the longitudinal assessment of volume changes in this type of setting. Currently most…

We study the average price impact of a single trade executed in the NYSE. After appropriate averaging and rescaling, the data for the 1000 most highly capitalized stocks collapse onto a single function, giving average price shift as a function of trade size. This function increases as a power that is the order of 1/2 f…

New metrics on 3D manifolds with large Steklov eigenvalues.

This paper proves that every oriented non-disk Seifert surface $F$ for a knot $K$ in $S^3$ is smoothly concordant to a Seifert surface $F^{\prime}$ for a hyperbolic knot $K^{\prime}$ of arbitrarily large volume. This gives a new and simpler proof of the result of Friedl and of Kawauchi that every knot is $S$-equivalent…

Upper bound for Laplacian eigenvalue via conformal volume.

Study Turaev-Viro invariants of 3-manifolds with toroidal boundary.

The scaling properties of the time series of asset prices and trading volumes of stock markets are analysed. It is shown that similarly to the asset prices, the trading volume data obey multi-scaling length-distribution of low-variability periods. In the case of asset prices, such scaling behaviour can be used for risk…

The paper calculates large genus limits for quadratic differential volumes and constants.

We obtain an estimate for the volume of neighbourhoods of sets of large curvature in three-dimensional Kähler-Einstein manifolds.

We consider the rate of volume growth of large Carnot-Carathéodory metric balls on a class of unbounded model hypersurfaces in $\mathbb{C}^2$. When the hypersurface has a uniform global structure, we show that a metric ball of radius $δ\gg 1$ either has volume on the order of $δ^3$ or $δ^4$. We also give necessary and …

We use a large census of hyperbolic 3-manifolds to experimentally investigate a conjecture of Neumann regarding the Bloch Group. We present an augmented census including, for feasible invariant trace fields, explicit manifolds (associated to that field) that appear to generate the Bloch group of that field. We also mak…

Study of large-$n$ asymptotics for Weil-Petersson volumes of hyperbolic surfaces with cusps.

We show that the renormalized volume of a quasifuchsian hyperbolic 3-manifold is equal, up to an additive constant, to the volume of its convex core. We also provide a precise upper bound on the renormalized volume in terms of the Weil-Petersson distance between the conformal structures at infinity. As a consequence we…

If (M^n, g) is a complete Riemannian manifold with filling radius at least R, then we prove that it contains a ball of radius R and volume at least c(n)R^n. If (M^n, hyp) is a closed hyperbolic manifold and if g is another metric on M with volume at most c(n)Volume(M,hyp), then we prove that the universal cover of (M,g…

Traffic speed prediction is a critically important component of intelligent transportation systems (ITS). Recently, with the rapid development of deep learning and transportation data science, a growing body of new traffic speed prediction models have been designed, which achieved high accuracy and large-scale predicti…

This research aims to identify how Bitcoin-related news publications and online discourse are expressed in Bitcoin exchange movements of price and volume. Being inherently digital, all Bitcoin-related fundamental data (from exchanges, as well as transactional data directly from the blockchain) is available online, some…

Let (M,g) be a complete 3-dimensional asymptotically flat manifold with everywhere positive scalar curvature. We prove that, given a compact subset K of M, all volume preserving stable constant mean curvature surfaces of sufficiently large area will avoid K. This complements the work of G. Huisken and S.-T. Yau and J. …

Minimal volume entropy vanishes or is positive under certain fiber growth conditions.

We respond to the issues discussed by Farmer and Lillo (FL) related to our proposed approach to understanding the origin of power-law distributions in stock price fluctuations. First, we extend our previous analysis to 1000 US stocks and perform a new estimation of market impact that accounts for splitting of large ord…

We prove a law of large numbers for the volumes of families of random hyperbolic mapping tori and Heegaard splittings providing a sharp answer to a conjecture of Dunfield and Thurston.

Intense volatility in financial markets affect humans worldwide. Therefore, relatively accurate prediction of volatility is critical. We suggest that massive data sources resulting from human interaction with the Internet may offer a new perspective on the behavior of market participants in periods of large market move…

To be effective, state of the art machine learning technology needs large amounts of annotated data. There are numerous compelling applications in healthcare that can benefit from high performance automated decision support systems provided by deep learning technology, but they lack the comprehensive data resources req…

Proves a conjecture about the maximum tet-volume of triangulations of a 2-sphere.