arXiv research

We empirically analyze the price and liquidity responses to trade signs, traded volumes and signed traded volumes. Utilizing the singular value decomposition, we explore the interconnections of price responses and of liquidity responses across the whole market. The statistical characteristics of their singular vectors …

Uniform linear bounds on volume changes in 3D hyperbolic spaces.

Effective drilling and filling bounds for hyperbolic 3-manifolds.

Given a hyperbolic 3-manifold M containing an embedded closed geodesic, we estimate the volume of a complete hyperbolic metric on the complement of the geodesic in terms of the geometry of M. As a corollary, we show that the smallest volume orientable hyperbolic 3-manifold has volume >.32 .

The behavior under conformal change of the renormalized volume coefficients associated to a pseudo-Riemannian metric is investigated. It is shown that they define second order fully nonlinear operators in the conformal factor whose algebraic structure is elucidated via the introduction of "extended obstruction tensors"…

Defines circumcenter of mass for polytopes without triangulation.

In finance, one usually deals not with prices but with growth rates $R$, defined as the difference in logarithm between two consecutive prices. Here we consider not the trading volume, but rather the volume growth rate $\tilde R$, the difference in logarithm between two consecutive values of trading volume. To this end…

New properties are derived of renormalized volume functionals, which arise as coefficients in the asymptotic expansion of the volume of an asymptotically hyperbolic Einstein (AHE) manifold. A formula is given for the renormalized volume of an even-dimensional AHE manifold in terms of an arbitrary totally geodesic compa…

Study proves a new flow method for mean curvature with volume change analysis.

Given a hyperbolic 3-manifold with torus boundary, we bound the change in volume under a Dehn filling where all slopes have length at least 2π. This result is applied to give explicit diagrammatic bounds on the volumes of many knots and links, as well as their Dehn fillings and branched covers. Finally, we use this res…

Model predicts trade volume changes from financial filings.

Study of volume dynamics at market spread in Bitcoin/USD.

Proposes methods to accurately learn manifolds and their distributions.

We study the price impact of order book events - limit orders, market orders and cancelations - using the NYSE TAQ data for 50 U.S. stocks. We show that, over short time intervals, price changes are mainly driven by the order flow imbalance, defined as the imbalance between supply and demand at the best bid and ask pri…

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…

Let $G$ be the group of complex points of a real semi-simple Lie group whose fundamental rank is equal to 1, e.g. $G= \SL_2 (\C) \times \SL_2 (\C)$ or $\SL_3 (\C)$. Then the fundamental rank of $G$ is $2,$ and according to the conjecture made in \cite{BV}, lattices in $G$ should have 'little' --- in the very weak sense…

We derive a new renormalized volume formula for conformally compact asymptotically hyperbolic manifolds in dimension four. The formula generalizes the ones given by Anderson, Albin, and Chang-Qing-Yang for the case of Poincare-Einstein manifolds. We also derive variational formulas for the renormalized seen as a functi…

Analyzing real data on international trade covering the time interval 1950-2000, we show that in each year over the analyzed period the network is a typical representative of the ensemble of maximally random weighted networks, whose directed connections (bilateral trade volumes) are only characterized by the product of…

We prove two-sided inequalities for the $L^p$-norm of a pushforward or pullback (with respect to an orientation-preserving diffeomorphism) on oriented volume and Riemannian manifolds. For a function or density on a volume manifold, these bounds depend only on the Jacobian determinant, which arises through the change of…

In many large-scale machine learning applications, data are accumulated with time, and thus, an appropriate model should be able to update in an online paradigm. Moreover, as the whole data volume is unknown when constructing the model, it is desired to scan each data item only once with a storage independent with the …

How large can be the width of Riemannian three-spheres of the same volume in the same conformal class? If a maximum value is attained, how does a maximising metric look like? What happens as the conformal class changes? In this paper, we investigate these and other related questions, focusing on the context of Simon-Sm…

Study shows cryptocurrency investor base affects volatility.

Volatility, fitting with first order Landau expansion, stationarity, and causality of the Taiwan stock market (TAIEX) are investigated based on daily records. Instead of consensuses that consider stock market index change as a random time series we propose the market change as a dual time series consists of the index a…

In Thurston's notes, he gives two different definitions of the Gromov norm (also called simplicial volume) of a manifold and states that they are equal but does not prove it. Gromov proves it in the special case of hyperbolic manifolds as a consequence of his proof that simplicial volume is proportional to volume. We g…

Study finds critical points of volume functionals on Sasaki manifolds.

New framework uses trading volume instead of volatility for stock pricing.

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…

Proves existence of multi-phase flows from arbitrary initial data.

In this study we examine the evolution of price, volume, and the bid-ask spread after extreme 15 minute intraday price changes on the NYSE and the NASDAQ. We find that due to strong behavioral trading there is an overreaction. Furthermore we find that volatility which increases sharply at the event decays according to …

DVAO predicts volumetric ambient occlusion for real-time volume rendering.

Method predicts disease outbreaks using search logs, overcoming instability.

According to a recent investigation, an estimated 33-50% of the world's coral reefs have undergone degradation, believed to be as a result of climate change. A strong driver of climate change and the subsequent environmental impact are greenhouse gases such as methane. However, the exact relation climate change has to …

The observation of power laws in the time to extrema of volatility, volume and intertrade times, from milliseconds to years, are shown to result straightforwardly from the selection of biased statistical subsets of realizations in otherwise featureless processes such as random walks. The bias stems from the selection o…

Efficiently simulates Langevin dynamics on manifold using diffusion maps and finite volume schemes.

New model explains price, volume, and waiting times in financial markets.

Normalizing flows optimize Jacobian determinant for unique likelihood objective.

Employing a recent technique which allows the representation of nonstationary data by means of a juxtaposition of locally stationary patches of different length, we introduce a comprehensive analysis of the key observables in a financial market: the trading volume and the price fluctuations. From the segmentation proce…

Study shows systole behavior changes significantly for large genus hyperbolic surfaces.

We investigate the rigidity of hyperbolic cone metrics on $3$-manifolds which are isometric gluing of ideal and hyper-ideal tetrahedra in hyperbolic spaces. These metrics will be called ideal and hyper-ideal hyperbolic polyhedral metrics. It is shown that a hyper-ideal hyperbolic polyhedral metric is determined up to i…

Given a polyhedral surface, assume that it is prohibited to change the shape and size of any face but it is permissible to change the dihedral angles between the faces. A polyhedral surface is said to be flexible if it is possible to change its shape under the above restrictions. We prove that flexible polyhedral surfa…

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 report on the occurrence of an anomaly in the price impacts of small transaction volumes following a change in the fee structure of an electronic market. We first review evidence for the existence of a master curve for price impact on the Johannesburg Stock Exchange (JSE). On attempting to re-estimate a master curve…

The stationary points of the total scalar curvature functional on the space of unit volume metrics on a given closed manifold are known to be precisely the Einstein metrics. One may consider the modified problem of finding stationary points for the volume functional on the space of metrics whose scalar curvature is equ…

We study the solutions $u\in C^\infty(R^{2m})$ of the problem $(-Δ)^m u= Qe^{2mu}$, where $Q=\pm (2m-1)!$, and $V :=\int_{R^{2m}}e^{2mu}dx <\infty$, particularly when $m>1$. This corresponds to finding conformal metrics $g_u:=e^{2u}|dx|^2$ on $R^{2m}$ with constant Q-curvature $Q$ and finite volume $V$. Extending previ…

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…

In this paper we derive a second order approximation for an infinite dimensional limit order book model, in which the dynamics of the incoming order flow is allowed to depend on the current market price as well as on a volume indicator (e.g.~the volume standing at the top of the book). We study the fluctuations of the …

A new approach to obtaining market--directional information, based on a non-stationary solution to the dynamic equation "future price tends to the value that maximizes the number of shares traded per unit time" [1] is presented. In our previous work[2], we established that it is the share execution flow ($I=dV/dt$) and…

Paper proves no nontrivial solutions to certain elliptic equations on graphs.