arXiv subjects

Zijian Shi

Publications and source records attributed to Zijian Shi.

11 recordsLinked to original sources

arXiv2026

Periodic orbits and gravitational waveforms of black holes in bumblebee gravity

In this paper, we investigate the dynamics of massive particles and the associated gravitational waveforms in the spacetime of a black hole within the framework of Einstein-Bumblebee gravity. Our analysis encompasses both charged and uncharged black hole configurations, with a particular focus on the spontaneous Lorentz symmetry breaking mechanism inherent to this model, which is governed by a dimensionless coupling parameter $l$. We analyze the geodesic equations and the effective potential to determine the allowed parameter space for bound orbits, demonstrating that in the charged case, both the Lorentz-violating parameter $l$ and the electric charge $Q$ significantly enhance the confinement capacity of the potential, thereby broadening the energy and angular momentum windows for bound states. A key focus is placed on the classification and properties of periodic orbits, characterized by rational frequency ratios using the whirl, zoom, and vertex taxonomy. We demonstrate that in the uncharged case ($Q=0$), the radial effective potential and standard innermost stable circular orbit (ISCO) properties are degenerate with those of a Schwarzschild black hole. However, despite this degeneracy in static potential properties, the structure of periodic orbits exhibits qualitative differences, providing a possible observational signature that can break this degeneracy. Finally, we compute the corresponding gravitational waveforms extracted from these periodic orbits using the quadrupole formula. The results reveal that $l$ and $Q$ introduce contrasting phase-shifting effects on the waveforms. This suggests that bumblebee gravity leaves measurable imprints on gravitational-wave signals that could be detected by future space-based gravitational-wave observatories.

gr-qc↗

arXiv2024

Higher-dimensional quantum Oppenheimer-Snyder model

The quantum Oppenheimer-Snyder model for higher-dimensional spacetimes is studied. The higher-dimensional quantum-corrected Schwarzschild black hole is obtained by the junction condition. It turns out that quantum bounces always occur in the collapse thus that the classical gravitational collapse singularities are avoided. The scalar perturbations upon the quantum-corrected black holes are also studied. It turns out that the quantum corrections enhance the oscillation frequency in lower dimensions and decrease it in higher dimensions. Moreover, the thermodynamic laws of the quantum-corrected black holes imply that the Hawking temperature of quantum-corrected black hole decreases as the mass decreases in contrast to the classical situation. The behaviour of heat capacity indicates that quantum corrections introduce an extra phase transition of the black holes.

gr-qc↗

arXiv2024

Coderivative-Based Newton Methods with Wolfe Linesearch for Nonsmooth Optimization

This paper introduces and develops novel coderivative-based Newton methods with Wolfe linesearch conditions to solve various classes of problems in nonsmooth optimization. We first propose a generalized regularized Newton method with Wolfe linesearch (GRNM-W) for unconstrained $C^{1,1}$ minimization problems (which are second-order nonsmooth) and establish global as well as local superlinear convergence of their iterates. To deal with convex composite minimization problems (which are first-order nonsmooth and can be constrained), we combine the proposed GRNM-W with two algorithmic frameworks: the forward-backward envelope and the augmented Lagrangian method resulting in the two new algorithms called CNFB and CNAL, respectively. Finally, we present numerical results to solve Lasso and support vector machine problems appearing in, e.g., machine learning and statistics, which demonstrate the efficiency of the proposed algorithms.

math.OC↗

arXiv2024

DGDNN: Decoupled Graph Diffusion Neural Network for Stock Movement Prediction

Forecasting future stock trends remains challenging for academia and industry due to stochastic inter-stock dynamics and hierarchical intra-stock dynamics influencing stock prices. In recent years, graph neural networks have achieved remarkable performance in this problem by formulating multiple stocks as graph-structured data. However, most of these approaches rely on artificially defined factors to construct static stock graphs, which fail to capture the intrinsic interdependencies between stocks that rapidly evolve. In addition, these methods often ignore the hierarchical features of the stocks and lose distinctive information within. In this work, we propose a novel graph learning approach implemented without expert knowledge to address these issues. First, our approach automatically constructs dynamic stock graphs by entropy-driven edge generation from a signal processing perspective. Then, we further learn task-optimal dependencies between stocks via a generalized graph diffusion process on constructed stock graphs. Last, a decoupled representation learning scheme is adopted to capture distinctive hierarchical intra-stock features. Experimental results demonstrate substantial improvements over state-of-the-art baselines on real-world datasets. Moreover, the ablation study and sensitivity study further illustrate the effectiveness of the proposed method in modeling the time-evolving inter-stock and intra-stock dynamics.

cs.LG↗

arXiv2023

Frequency-astigmatism asymmetric nonlinear conversion of structured light lasers

Nonlinear optics of structured light has recently delivered intriguing fundamental physical phenomena in light-matter interactions and advanced applications from classical imaging to quantum informatics. The mutual interaction between spin, orbital angular momentum (OAM) and wavelength is extensively studied in such cases. In this work, we go beyond only considering OAM and wavelength by taking the nonlinear frequency conversion and transverse mode astigmatism conversion as two building blocks and investigating how single modes and complicated multiplexed modes evolve after them. In particular, We found a generalized law of nonlinear conversion structured light from experiments and theories, that the converted modes are highly related to the sequence of these two blocks, obeying an inherent (non)commutative rule in which. This effect not only creates extended structured laser modes but serve as new rules in nonlinear structured light manipulation.

physics.optics↗

arXiv2023

Neural Stochastic Agent-Based Limit Order Book Simulation: A Hybrid Methodology

Modern financial exchanges use an electronic limit order book (LOB) to store bid and ask orders for a specific financial asset. As the most fine-grained information depicting the demand and supply of an asset, LOB data is essential in understanding market dynamics. Therefore, realistic LOB simulations offer a valuable methodology for explaining empirical properties of markets. Mainstream simulation models include agent-based models (ABMs) and stochastic models (SMs). However, ABMs tend not to be grounded on real historical data, while SMs tend not to enable dynamic agent-interaction. To overcome these limitations, we propose a novel hybrid LOB simulation paradigm characterised by: (1) representing the aggregation of market events' logic by a neural stochastic background trader that is pre-trained on historical LOB data through a neural point process model; and (2) embedding the background trader in a multi-agent simulation with other trading agents. We instantiate this hybrid NS-ABM model using the ABIDES platform. We first run the background trader in isolation and show that the simulated LOB can recreate a comprehensive list of stylised facts that demonstrate realistic market behaviour. We then introduce a population of `trend' and `value' trading agents, which interact with the background trader. We show that the stylised facts remain and we demonstrate order flow impact and financial herding behaviours that are in accordance with empirical observations of real markets.

q-fin.TR↗

arXiv2021

Divergence-degenerated spatial multiplexing towards ultrahigh capacity, low bit-error-rate optical communications

Spatial mode (de)multiplexing of orbital angular momentum (OAM) beams is a promising solution to address future bandwidth issues, but the rapidly increasing divergence with the mode order severely limits the practically addressable number of OAM modes. Here we present a set of multi-vortex geometric beams (MVGBs) as high-dimensional information carriers, by virtue of three independent degrees of freedom (DoFs) including central OAM, sub-beam OAM, and coherent-state phase. The novel modal basis set has high divergence degeneracy, and highly consistent propagation behaviors among all spatial modes, capable of increasing the addressable spatial channels by two orders of magnitude than OAM basis as predicted. We experimentally realize the tri-DoF MVGB mode (de)multiplexing and shift keying encoding/decoding by the conjugated modulation method, demonstrating ultra-low bit error rates (BERs) caused by center offset and coherent background noise. Our work provides a useful basis for next generation of large-scale dense data communication.

physics.optics↗

arXiv2021

Deep-learning-based recognition of multi-singularity structured light

Structured light with customized complex topological pattern inspires diverse classical and quantum investigations underpinned by accurate detection techniques. However, the current detection schemes are limited to vortex beam with simple phase singularity. The precise recognition of general structured light with multiple singularities remains elusive. Here, we report a deep learning (DL) framework that can unveil multi-singularity phase structures in an end-to-end manner after feeding only two intensity patterns upon beam propagation captured via a camera, thus unleashing intuitive information of twisted photons. The DL toolbox can also acquire phases of Laguerre-Gaussian (LG) modes with single singularity and other general phase objects likewise. Leveraging this DL platform, a phase-based optical secret sharing (OSS) protocol is proposed, which is based on a more general class of multi-singularity modes than conventional LG beams. The OSS protocol features strong security, wealthy state space and convenient intensity-based measurements. This study opens new avenues for vortex beam communications, laser mode analysis, microscopy, Bose-Einstein condensates characterization, etc.

physics.optics↗

arXiv2021

Applications And Potentials Of Intelligent Swarms For Magnetospheric Studies

Earth's magnetosphere is vital for today's technologically dependent society. To date, numerous design studies have been conducted and over a dozen science missions have own to study the magnetosphere. However, a majority of these solutions relied on large monolithic satellites, which limited the spatial resolution of these investigations, as did the technological limitations of the past. To counter these limitations, we propose the use of a satellite swarm carrying numerous and distributed payloads for magnetospheric measurements. Our mission is named APIS (Applications and Potentials of Intelligent Swarms), which aims to characterize fundamental plasma processes in the Earth's magnetosphere and measure the effect of the solar wind on our magnetosphere. We propose a swarm of 40 CubeSats in two highly-elliptical orbits around the Earth, which perform radio tomography in the magnetotail at 8-12 Earth Radii (RE) downstream, and the subsolar magnetosphere at 8-12RE upstream. In addition, in-situ measurements of the magnetic and electric fields, plasma density will be performed by on-board instruments. In this article, we present an outline of previous missions and designs for magnetospheric studies, along with the science drivers and motivation for the APIS mission. Furthermore, preliminary design results are included to show the feasibility of such a mission. The science requirements drive the APIS mission design, the mission operation and the system requirements. In addition to the various science payloads, critical subsystems of the satellites are investigated e.g., navigation, communication, processing and power systems. We summarize our findings, along with the potential next steps to strengthen our design study.

astro-ph.IM↗

arXiv2021

The Limit Order Book Recreation Model (LOBRM): An Extended Analysis

The limit order book (LOB) depicts the fine-grained demand and supply relationship for financial assets and is widely used in market microstructure studies. Nevertheless, the availability and high cost of LOB data restrict its wider application. The LOB recreation model (LOBRM) was recently proposed to bridge this gap by synthesizing the LOB from trades and quotes (TAQ) data. However, in the original LOBRM study, there were two limitations: (1) experiments were conducted on a relatively small dataset containing only one day of LOB data; and (2) the training and testing were performed in a non-chronological fashion, which essentially re-frames the task as interpolation and potentially introduces lookahead bias. In this study, we extend the research on LOBRM and further validate its use in real-world application scenarios. We first advance the workflow of LOBRM by (1) adding a time-weighted z-score standardization for the LOB and (2) substituting the ordinary differential equation kernel with an exponential decay kernel to lower computation complexity. Experiments are conducted on the extended LOBSTER dataset in a chronological fashion, as it would be used in a real-world application. We find that (1) LOBRM with decay kernel is superior to traditional non-linear models, and module ensembling is effective; (2) prediction accuracy is negatively related to the volatility of order volumes resting in the LOB; (3) the proposed sparse encoding method for TAQ exhibits good generalization ability and can facilitate manifold tasks; and (4) the influence of stochastic drift on prediction accuracy can be alleviated by increasing historical samples.

q-fin.TR↗

arXiv2021

The LOB Recreation Model: Predicting the Limit Order Book from TAQ History Using an Ordinary Differential Equation Recurrent Neural Network

In an order-driven financial market, the price of a financial asset is discovered through the interaction of orders - requests to buy or sell at a particular price - that are posted to the public limit order book (LOB). Therefore, LOB data is extremely valuable for modelling market dynamics. However, LOB data is not freely accessible, which poses a challenge to market participants and researchers wishing to exploit this information. Fortunately, trades and quotes (TAQ) data - orders arriving at the top of the LOB, and trades executing in the market - are more readily available. In this paper, we present the LOB recreation model, a first attempt from a deep learning perspective to recreate the top five price levels of the LOB for small-tick stocks using only TAQ data. Volumes of orders sitting deep in the LOB are predicted by combining outputs from: (1) a history compiler that uses a Gated Recurrent Unit (GRU) module to selectively compile prediction relevant quote history; (2) a market events simulator, which uses an Ordinary Differential Equation Recurrent Neural Network (ODE-RNN) to simulate the accumulation of net order arrivals; and (3) a weighting scheme to adaptively combine the predictions generated by (1) and (2). By the paradigm of transfer learning, the source model trained on one stock can be fine-tuned to enable application to other financial assets of the same class with much lower demand on additional data. Comprehensive experiments conducted on two real world intraday LOB datasets demonstrate that the proposed model can efficiently recreate the LOB with high accuracy using only TAQ data as input.

q-fin.TR↗