arXiv research

New partition designs reduce star discrepancy in high-dimensional sampling.

The paper studies volumes of direct images for high tensor powers of ample bundles.

Study predicts intraday stock trading volume using ML models.

Paper uses Transformers to predict intraday volume ratio with high accuracy.

In this paper we study the high frequency dynamic of financial volumes of traded stocks by using a semi-Markov approach. More precisely we assume that the intraday logarithmic change of volume is described by a weighted-indexed semi-Markov chain model. Based on this assumptions we show that this model is able to reprod…

This manuscript reports a stochastic dynamical scenario whose associated stationary probability density function is exactly a previously proposed one to adjust high-frequency traded volume distributions. This dynamical conjecture, physically connected to superstatiscs, which is intimately related with the current nonex…

Study on hyperbolic surfaces' volumes, proving asymptotic expansion for high genus.

Using high-frequency time series of stock prices and share volumes sizes from January 2002-May 2009, this paper investigates whether the effects of the onset of high-frequency trading, most prominent since 2005, are apparent in the dynamics of the dollar traded volume. Indeed it is found in almost all of 14 heavily tra…

We develop an efficient algorithm to find confidence ellipsoids with volume guarantees in high dimensions.

For each natural number n >= 4, we determine the unique lowest volume hyperbolic 3-orbifold whose torsion orders are bounded below by n. This lowest volume orbifold has base space the 3-sphere and singular locus the figure-8 knot, marked n. We apply this result to give sharp lower bounds on the volume of a hyperbolic m…

The Gibbs algorithm's generalization error is bounded, improving with prior volume in low temperatures.

Study finds option volume imbalance predicts equity market returns.

The paper introduces a new price model based on entropy that better fits high-frequency market data.

We prove that the space of complete, finite volume, pinched negatively curved Riemannian metrics on a smooth high-dimensional manifold is either empty or it is highly non-connected, provided their behavior at infinity is similar.

Non-vanishing steady Euler flows and Beltrami fields found in high dimensions.

Defines cross product for m vectors in n-dimensional spaces.

Deep learning reveals ubiquitous predictability in high-frequency returns.

Algorithm finds small confidence sets for arbitrary distributions.

A new policy minimizes loss in high-volume, short-lived multi-armed bandit problems.

New proof of a unique 3-part partition in 8D space.

Econophysics and econometrics agree that there is a correlation between volume and volatility in a time series. Using empirical data and their distributions, we further investigate this correlation and discover new ways that volatility and volume interact, particularly when the levels of both are high. We find that the…

Study shows spheres in high dimensions have maximum volume if they are smooth and have a specific reach.

New constructions in group homology allow us to manufacture high-dimensional manifolds with controlled simplicial volume. We prove that for every dimension bigger than 3 the set of simplicial volumes of orientable closed connected manifolds is dense in $\mathbb{R}_{\geq 0}$. In dimension 4 we prove that every non-negat…

In this short note, exploits of constructions of $\mathcal{F}$-structures coupled with technology developed by Cheeger-Gromov and Paternain-Petean are seen to yield a procedure to compute minimal entropy, minimal volume, Yamabe invariant and to study collapsing with bounded sectional curvature on inequivalent smooth st…

We study the relationship between price spread, volatility and trading volume. We find that spread forms as a result of interplay between order liquidity and order impact. When trading volume is small adding more liquidity helps improve price accuracy and reduce spread, but after some point additional liquidity begins …

New examples show some manifolds can't be decomposed.

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…

High-fee pools attract more liquidity but execute less volume; low-fee pools have more stable LPs.

Paper introduces PHI to identify structurally distinct payment patterns in UK municipal procurement.

This paper poses a few fundamental questions regarding the attributes of the volume profile of a Limit Order Books stochastic structure by taking into consideration aspects of intraday and interday statistical features, the impact of different exchange features and the impact of market participants in different asset s…

We study the volume distribution of nodal domains of random band-limited functions on generic manifolds, and find that in the high energy limit a typical instance obeys a deterministic universal law, independent of the manifold. Some of the basic qualitative properties of this law, such as its support, monotonicity and…

In this article we analyse linear correlation and non-linear dependence of traded volume, $v$, of the 30 constituents of Dow Jones Industrial Average at different value scales. Specifically, we have raised $v$ to some real value $α$ or $β$, which introduces a bias for small ($α, β<0$) or large ($α, β>1$) values. Our r…

We introduce a new model in order to describe the fluctuation of tick-by-tick financial time series. Our model, based on marked point process, allows us to incorporate in a unique process the duration of the transaction and the corresponding volume of orders. The model is motivated by the fact that the "excitation" of …

Motivated by a zero-intelligence approach, the aim of this paper is to connect the microscopic (discrete price and volume), mesoscopic (discrete price and continuous volume) and macroscopic (continuous price and volume) frameworks for the modelling of limit order books, with a view to providing a natural probabilistic …

Bray's football theorem (\cite{bray2009penrose}) is a weakening of Bishop theorem in dimension 3. It gives a sharp volume upper bound for a three dimensional manifold with scalar curvature larger than $n(n-1)$ and Ricci curvature larger than $\varepsilon$. This paper extends Bray's football theorem in high dimensions, …

The paper finds singular isoperimetric regions in high-dimensional spaces.

Proposes methods to accurately learn manifolds and their distributions.

DiffVolume generates realistic volume snapshots for LOBs.

Generic smooth boundaries for isoperimetric regions in 8D manifolds.

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…

Measures neural network decision boundary volume to predict model performance.

Study on simplicial volume and Euler characteristic of aspherical manifolds.

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…

Study on renormalized volume of minimal submanifolds in Poincare-Einstein manifolds.

This paper presents a quantitative analysis of the relationship between the stock market returns and corresponding trading volumes using high- frequency data from the Polish stock market. First, for stocks that were traded for suffciently long period of time, we study the return and volume distributions and identify th…

Study reveals optimal price prediction through volume imbalance analysis.

Study shows flash crashes in finance are self-organized criticality events.

One-step diffusion samplers reduce sampling time and computational costs.