arXiv subjects

Xincheng Zhang

Publications and source records attributed to Xincheng Zhang.

7 recordsLinked to original sources

arXiv2025

TASEP in half-space

In this work, we present the multi-point probability distribution of the totally asymmetric simple exclusion process (TASEP) in a half-space, starting from a general deterministic initial condition. More precisely, let $h(t,x)$ denote the height function of TASEP at position $x$ and time $t$; we provide an explicit formula for \begin{equation*} \mathbb{P}(h(t,y_1)\leq s_1, \ldots, h(t,y_m)\leq s_m). \end{equation*} The formula presented is well-suited for the scaling limit analysis. By applying a 1:2:3 scaling, we derive the probability distribution for the half-space KPZ fixed point, which is conjectured to be the universal process for the limit of the KPZ universality models restricted to a half-space.

math.PR↗

arXiv2024

COIG-CQIA: Quality is All You Need for Chinese Instruction Fine-tuning

Remarkable progress on English instruction tuning has facilitated the efficacy and reliability of large language models (LLMs). However, there remains a noticeable gap in instruction tuning for Chinese, where the complex linguistic features pose significant challenges. Existing datasets, generally distilled from English-centric LLMs, are not well-aligned with Chinese users' interaction patterns. To bridge this gap, we introduce COIG-CQIA, a new Chinese instruction tuning dataset derived from various real-world resources and undergoing rigorous human verification. We conduct extensive experiments on COIG-CQIA, and compare them with strong baseline models and datasets. The experimental results show that models trained on COIG-CQIA achieve highly competitive performance in diverse benchmarks. Additionally, our findings offer several insights for designing effective Chinese instruction-tuning datasets and data-mixing strategies. Our dataset are available at https://huggingface.co/datasets/m-a-p/COIG-CQIA.

cs.CL↗

arXiv2024

t^{1/3} fluctuation around the shock of TASEP with random initial condition

The totally asymmetric exclusion process (TASEP) is one of the solvable models in the KPZ universality class. When TASEP starts with the product Bernoulli measure with a smaller density on the left of the origin, it presents shocks in the evolution. For a long time, it has been known that fluctuations are the product of Gaussians on the scale t^{1/2} due to initial randomness. In this paper, we will describe how to see the t^{1/3} fluctuations for these initial conditions.

math.PR↗

arXiv2024

Ptychographic non-line-of-sight imaging for depth-resolved visualization of hidden objects

Non-line-of-sight (NLOS) imaging enables the visualization of objects hidden from direct view, with applications in surveillance, remote sensing, and light detection and ranging. Here, we introduce a NLOS imaging technique termed ptychographic NLOS (pNLOS), which leverages coded ptychography for depth-resolved imaging of obscured objects. Our approach involves scanning a laser spot on a wall to illuminate the hidden objects in an obscured region. The reflected wavefields from these objects then travel back to the wall, get modulated by the wall's complex-valued profile, and the resulting diffraction patterns are captured by a camera. By modulating the object wavefields, the wall surface serves the role of the coded layer as in coded ptychography. As we scan the laser spot to different positions, the reflected object wavefields on the wall translate accordingly, with the shifts varying for objects at different depths. This translational diversity enables the acquisition of a set of modulated diffraction patterns referred to as a ptychogram. By processing the ptychogram, we recover both the objects at different depths and the modulation profile of the wall surface. Experimental results demonstrate high-resolution, high-fidelity imaging of hidden objects, showcasing the potential of pNLOS for depth-aware vision beyond the direct line of sight.

eess.IV↗

arXiv2023

Spatially-coded Fourier ptychography: flexible and detachable coded thin films for quantitative phase imaging with uniform phase transfer characteristics

Fourier ptychography (FP) is an enabling imaging technique that produces high-resolution complex-valued images with extended field coverages. However, when FP images a phase object with any specific spatial frequency, the captured images contain only constant values, rendering the recovery of the corresponding linear phase ramp impossible. This challenge is not unique to FP but also affects other common microscopy techniques -- a rather counterintuitive outcome given their widespread use in phase imaging. The underlying issue originates from the non-uniform phase transfer characteristic inherent in microscope systems, which impedes the conversion of object wavefields into discernible intensity variations. To address this challenge, we present spatially-coded Fourier ptychography (scFP), a new method that synergizes FP with spatial-domain coded detection for true quantitative phase imaging. In scFP, a flexible and detachable coded thin film is attached atop the image sensor in a regular FP setup. The spatial modulation of this thin film ensures a uniform phase response across the entire synthetic bandwidth. It improves reconstruction quality and corrects refractive index underestimation issues prevalent in conventional FP and related tomographic implementations. The inclusion of the coded thin film further adds a new dimension of measurement diversity in the spatial domain. The development of scFP is expected to catalyse new research directions and applications for phase imaging, emphasizing the need for true quantitative accuracy with uniform frequency response.

physics.optics↗

arXiv2020

A System of PDEs for the Baik-Rains Distribution

It has been discovered that the Kadomtsev-Petviashvili(KP) equation governs the distribution of the fluctuation of many random growth models, in particular, the Tracy-Widom distributions appear as special self-similar solutions of the KP equation. We prove that the anti-derivative of Baik-Rains distribution, which governs the fluctuation of the models in the KPZ universality class starting with stationary initial data, satisfies the KP equation. We start from a determinantal formula of the generating function of the KPZ equation, which satisfies the KP. Then we observe that the equation still holds in the large time limit.

math.PR↗

arXiv2014

Steady-state one-way Einstein-Podolsky-Rosen steering in optomechanical interfaces

Einstein-Podolsky-Rosen (EPR) steering is a form of quantum correlations and its intrinsic asymmetry makes it distinct from entanglement and Bell nonlocality. We propose here a scheme for realizing one-way Gaussian steering of two electromagnetic fields mediated by a mechanical oscillator. We reveal that the steady-state one-way steering of the intracavity and output fields is obtainable with different cavity losses or strong mechanical damping. The conditions for achieving this asymmetric steering are found, and it shows that the steering is robust against thermal mechanical fluctuations. The present scheme can realize hybrid microwave-optical asymmetric steering by optoelectromechanics. In addition, our results are generic and can also be applied to other three-mode parametrically-coupled bosonic systems.

quant-ph↗