arXiv subjects

Xuan Tao

Publications and source records attributed to Xuan Tao.

5 recordsLinked to original sources

arXiv2026

Red noise and evolving signals: a complete frequentist approach to supermassive black hole binary searches with pulsar timing array

Searches for gravitational waves (GWs) from isolated supermassive black hole binaries (SMBHBs) in pulsar timing array (PTA) data require simultaneous estimation of signal and noise parameters, so the dimensionality of the fit scales with the number of observed pulsars. This computational difficulty is exacerbated when source evolution from GW emission is included, since retaining both Earth and pulsar terms introduces the unknown pulsar distances. Existing frequentist methods such as the $\mathcal{F}$-statistic, restricted so far to non-evolving sources, effectively, imply a circular analysis, which may lead to biased estimators. We present a Generalized Likelihood Ratio Test (GLRT) and the associated $\mathcal{T}$-statistic that overcomes the aforementioned limitations. The formulation of the GLRT extends earlier work in which the dimensionality of the fitting problem was drastically reduced by semi-analytical maximization of the likelihood over the pulsar phase parameters, followed by efficient global optimization over the remaining parameters using Particle Swarm Optimization. Our simulations demonstrate that for an evolving SMBHB signal with chirp mass $\mathcal{M}=10^{9.2}\,M_\odot$ and signal-to-noise ratio $20$, this detection statistic achieves a $100\%$ detection probability at a false-alarm probability of $0.06$ in a 30-pulsar timing array, which is characterized by a $100~\mathrm{ns}$ root-mean-square white noise residual and pulsar-specific red noise.

gr-qc↗

arXiv2026

One Currency, Two Forward Prices: The Onshore-Offshore Renminbi Puzzle

Partially convertible economies face a market-design problem: trade integration, cross-border investment, and domestic balance-sheet exposure increase the demand for currency hedging before full financial integration is complete. China adopted a distinctive architecture for this problem by fostering a deliverable offshore Renminbi market (CNH) alongside the segmented onshore market (CNY), rather than relying only on non-deliverable forwards. This creates two venues for closely related claims on the same currency. Spot prices are tightly linked, yet CNY and CNH forwards display a persistent and economically large discrepancy. We study that discrepancy in a joint equilibrium model for spot and forward trading with transaction costs and segmented supply. In the benchmark case with common constant supply and deterministic costs, spot parity implies a forward differential with the wrong sign relative to the data. Random offshore stress, modeled as a jump in trading costs, overturns this benchmark while preserving tight spot parity. The model yields a semi-explicit representation in the CNY/CNH application and a calibration of the observed forward discrepancy in terms of the market-implied likelihood and severity of offshore liquidity stress.

q-fin.MF↗

arXiv2025

Periodic limit for non-autonomous Lagrangian systems and applications to a Kuramoto type model

This paper explores the asymptotic properties of non-autonomous Lagrangian systems, assuming that the associated Tonelli Lagrangian converges to a time-periodic function. Specifically, given a continuous initial condition, we provide a suitable construction of a Lax-Oleinik semigroup such that it converges toward a periodic solution of the equation. Moreover, the graph of its gradient converges as time tends to infinity to the graph of the gradient of the periodic limit function with respect to the Hausdorff distance. Finally, we apply this result to a Kuramoto-type model, proving the existence of an invariant torus given by the graph of the gradient of the limiting periodic solution of the Hamilton-Jacobi equation.

math.OC↗

arXiv2024

Detection and parameter estimation of supermassive black hole ringdown signals using a pulsar timing array

Gravitational wave (GW) searches using pulsar timing arrays (PTAs) are commonly assumed to be limited to a GW frequency of $\lesssim 4\times 10^{-7}$Hz given by the Nyquist rate associated with the average observational cadence of $2$ weeks for a single pulsar. However, by taking advantage of asynchronous observations of multiple pulsars, a PTA can detect GW signals at higher frequencies. This allows a sufficiently large PTA to detect and characterize the ringdown signals emitted following the merger of supermassive binary black holes (SMBBHs), leading to stringent tests of the no-hair theorem in the mass range of such systems. Such large-scale PTAs are imminent with the advent of the FAST telescope and the upcoming era of the Square Kilometer Array (SKA). To scope out the data analysis challenges involved in such a search, we propose a likelihood-based method coupled with Particle Swarm Optimization and apply it to a simulated large-scale PTA comprised of $100$ pulsars, each having a timing residual noise standard deviation of $100$~nsec, with randomized observation times. Focusing on the dominant $(2,2)$ mode of the ringdown signal, we show that it is possible to achieve a $99\%$ detection probability with a false alarm probability below $0.2\%$ for an optimal signal-to-noise ratio (SNR) $>10$. This corresponds, for example, to an equal-mass non-spinning SMBBH with an observer frame chirp mass $M_c = 9.52\times10^{9}M_{\odot}$ at a luminosity distance of $D_L = 420$ Mpc.

astro-ph.HE↗

arXiv2020

On Detecting Spoofing Strategies in High Frequency Trading

Spoofing is an illegal act of artificially modifying the supply to drive temporarily prices in a given direction for profit. In practice, detection of such an act is challenging due to the complexity of modern electronic platforms and the high frequency at which orders are channeled. We present a micro-structural study of spoofing in a simple static setting. A multilevel imbalance which influences the resulting price movement is introduced upon which we describe the optimization strategy of a potential spoofer. We provide conditions under which a market is more likely to admit spoofing behavior as a function of the characteristics of the market. We describe the optimal spoofing strategy after optimization which allows us to quantify the resulting impact on the imbalance after spoofing. Based on these results we calibrate the model to real Level 2 datasets from TMX, and provide some monitoring procedures based on the Wasserstein distance to detect spoofing strategies in real time.

q-fin.TR↗