arXiv research

New bounds on diameters and generators for specific lattices and graphs.

Paper constructs new identities linking quantum invariants and modular forms.

We consider the cohomology group $H^1(Γ, ρ)$ of a discrete subgroup $Γ\subset G=SU(n, 1)$ and the symmetric tensor representation $ρ$ on $S^m(\mathbb C^{n+1})$. We give an elementary proof of the Eichler-Shimura isomorphism that harmonic forms $H^1(Γ\backslash G/K, ρ)$ are $(0, 1)$-forms for the automorphic holomorphic…

We study the SU(2) Witten--Reshetikhin--Turaev invariant for the Seifert fibered homology spheres with M-exceptional fibers. We show that the WRT invariant can be written in terms of (differential of) the Eichler integrals of modular forms with weight 1/2 and 3/2. By use of nearly modular property of the Eichler integr…

Quantum modularity proved for SU(2) TQFT signature on genus 2 surfaces.

Study on TQFT signatures converging to modular form.

We reveal an intimate connection between the quantum knot invariant for torus knot T(s,t) and the character of the minimal model M(s,t), where s and t are relatively prime integers. We show that Kashaev's invariant, i.e., the N-colored Jones polynomial at the N-th root of unity, coincides with the Eichler integral of t…

We consider an asymptotic expansion of Kashaev's invariant or the colored Jones function for the torus link T(2,2m). We shall give q-series identity related to these invariants, and show that the invariant is regarded as a limit of q being N-th root of unity of the Eichler integral of the modular form of weight 3/2.

Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that fivebrane compactifications provide a universal description of various old and new homological invariants of 3-manifolds. In terms of 3d/3d correspondence, such invariants are given by the Q-c…

Proves HNN extensions of nilpotent groups are left-orderable, constructs non-left-orderable examples.

The paper characterizes L-space 3-manifolds using quandle orderability.

In order-driven markets, limit-order book (LOB) resiliency is an important microscopic indicator of market quality when the order book is hit by a liquidity shock and plays an essential role in the design of optimal submission strategies of large orders. However, the evolutionary behavior of LOB resilience around liqui…

Optimal stock trading strategy with market orders and limit orders in a risky market.

Algorithm confirms non-order-preserving braids, proving infinite family not order-preserving.

Study analyzes order transitions in high, medium, and low market cap stocks using Markov chains.

The paper explores orderability in link quandles and provides various results.

We study the analytical properties of a one-side order book model in which the flows of limit and market orders are Poisson processes and the distribution of lifetimes of cancelled orders is exponential. Although simplistic, the model provides an analytical tractability that should not be overlooked. Using basic result…

Map quandle orders to actions, characterize isolated orders, and prove no isolated right orders.

The paper defines circular orderability for quandles and explores their properties.

Bi-orderable groups from left-orderable ones, showing non-profinite properties.

In financial markets, the order flow, defined as the process assuming value one for buy market orders and minus one for sell market orders, displays a very slowly decaying autocorrelation function. Since orders impact prices, reconciling the persistence of the order flow with market efficiency is a subtle issue. A poss…

It is well known that a countable group admits a left-invariant total order if and only if it acts faithfully on R by orientation preserving homeomorphisms. Such group actions are special cases of group actions on simply connected 1-manifolds, or equivalently, actions on oriented order trees. We characterize a class of…

New conditions for circular orderability of direct products, linking to left-orderability of groups.

New criterion for bi-ordering free groups under automorphisms.

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…

We identify and analyze statistical regularities and irregularities in the recent order flow of different NASDAQ stocks, focusing on the positions where orders are placed in the orderbook. This includes limit orders being placed outside of the spread, inside the spread and (effective) market orders. We find that limit …

A framework models order book dynamics using point processes and mass transport.

We investigate the probability distribution of order imbalance calculated from the order flow data of 43 Chinese stocks traded on the Shenzhen Stock Exchange. Two definitions of order imbalance are considered based on the order number and the order size. We find that the order imbalance distributions of individual stoc…

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…

The paper explores circular orderability in 3-manifold groups, related to the L-space conjecture.

We extend the Heegaard Floer homological definition of spectral order for closed contact 3-manifolds due to Kutluhan, Matić, Van Horn-Morris, and Wand to contact 3-manifolds with convex boundary. We show that the order of a codimension zero contact submanifold bounds the order of the ambient manifold from above. As the…

Improved stock price prediction model using generalized order flow imbalance.

Two price regimes identified in limit order books: close and far from quotes.

A key feature of inductive logic programming (ILP) is its ability to learn first-order programs, which are intrinsically more expressive than propositional programs. In this paper, we introduce techniques to learn higher-order programs. Specifically, we extend meta-interpretive learning (MIL) to support learning higher…

MIC improves VAR order selection accuracy.

In this paper we define $n$th order Hessian structures on manifolds and study them. In particular, when $n = 3$, we make a detailed study and establish a one-to-one correspondence between {\it third-order Hessian structures} and a {\it certain class of connections} on the second-order tangent bundle of a manifold. Furt…

Motivated by recent activity in low-dimensional topology, we provide a new criterion for left-orderability of a group under the assumption that the group is circularly-orderable: A group $G$ is left-orderable if and only if $G \times \mathbb{Z}/n\mathbb{Z}$ is circularly-orderable for all $n > 1$. This implies that eve…

We develop a second-order model for limit order books in a single scaling regime.

Study proposes a new GAN for realistic discrete financial orders.

To execute a trade, participants in electronic equity markets may choose to submit limit orders or market orders across various exchanges where a stock is traded. This decision is influenced by the characteristics of the order flow and queue sizes in each limit order book, as well as the structure of transaction fees a…

Order submission and cancellation are two constituent actions of stock trading behaviors in order-driven markets. Order submission dynamics has been extensively studied for different markets, while order cancellation dynamics is less understood. There are two positions associated with a cancellation, that is, the price…

New invariants show stronger virtual knot sets.

Let $Y$ be a sublattice of a vector lattice $X$. We consider the problem of identifying the smallest order closed sublattice of $X$ containing $Y$. It is known that the analogy with topological closure fails. Let $\overline{Y}^o$ be the order closure of $Y$ consisting of all order limits of nets of elements from $Y$. T…

The concordance orders of many algebraic order two knots of ten or fewer crossings have been heretofore unknown. We use Casson-Gordon invariants and twisted Alexander polynomials to find that, in all but one case, these knots do not have concordance order two. We also find that a certain family of algebraic order two t…

Study non-standard bi-orders on punctured torus bundles, matching standard ones in key subgroups.

We propose a parametric model for the simulation of limit order books. We assume that limit orders, market orders and cancellations are submitted according to point processes with state-dependent intensities. We propose new functional forms for these intensities, as well as new models for the placement of limit orders …

We observe that the iterated tangent group of a Lie group may be realized as a double cross product of the 2nd order tangent group, with the Lie algebra of the base Lie group. Based on this observation, we derive the 2nd order Euler-Lagrange equations on the 2nd order tangent group from the 1st order Euler-Lagrange equ…

Optimizes trade execution with reinforcement learning for limit orders.