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Xiang Fan

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Published work

7 published item(s)

preprint2026arXiv

A deep learning approach for predicting multiple observables in Au+Au collisions at RHIC

We develop a neural network model, based on the processes of high-energy heavy-ion collisions, to study and predict several experimental observables in Au+Au collisions. We present a data-driven deep learning framework for predicting multiple bulk observables in Au+Au collisions at RHIC energies. A single neural network is trained exclusively on experimental measurements of charged-particle pseudorapidity density distributions, transverse-momentum spectra and elliptic flow coefficients over a broad range of collision energies and centralities. The network architecture is inspired by the stages of a heavy-ion collision, from the quark-gluon plasma to chemical and kinetic freeze-out, and employs locally connected hidden layers and a structured input design that encodes basic geometric and kinematic features of the system. We demonstrate that these physics-motivated choices significantly improve test performance compared to purely fully connected baselines. The trained model is then used to predict the above observables at collision energies not yet explored experimentally at RHIC, and the results are validated using the energy dependence of the total charged-particle multiplicity per participant pair as well as comparisons to a CLVisc hydrodynamic calculation with TRENTo initial conditions. Our findings indicate that such physics-guided neural networks can serve as efficient surrogates to fill critical data gaps at RHIC and to support further phenomenological studies of QGP properties.

preprint2026arXiv

RefDecoder: Enhancing Visual Generation with Conditional Video Decoding

Video generation powers a vast array of downstream applications. However, while the de facto standard, i.e., latent diffusion models, typically employ heavily conditioned denoising networks, their decoders often remain unconditional. We observe that this architectural asymmetry leads to significant loss of detail and inconsistency relative to the input image. To address this, we argue that the decoder requires equal conditioning to preserve structural integrity. We introduce RefDecoder, a reference-conditioned video VAE decoder by injecting high-fidelity reference image signal directly into the decoding process via reference attention. Specifically, a lightweight image encoder maps the reference frame into the detail-rich high-dimensional tokens, which are co-processed with the denoised video latent tokens at each decoder up-sampling stage. We demonstrate consistent improvements across several distinct decoder backbones (e.g., Wan 2.1 and VideoVAE+), achieving up to +2.1dB PSNR over the unconditional baselines on the Inter4K, WebVid, and Large Motion reconstruction benchmarks. Notably, RefDecoder can be directly swapped into existing video generation systems without additional fine-tuning, and we report across-the-board improvements in subject consistency, background consistency, and overall quality scores on the VBench I2V benchmark. Beyond I2V, RefDecoder generalizes well to a wide range of visual generation tasks such as style transfer and video editing refinement.

preprint2019arXiv

Permutation polynomials of degree 8 over finite fields of characteristic 2

Up to linear transformations, we obtain a classification of permutation polynomials (PPs) of degree $8$ over $\mathbb{F}_{2^r}$ with $r>3$. By [J. Number Theory 176 (2017) 466-66], a polynomial $f$ of degree $8$ over $\mathbb{F}_{2^r}$ is exceptional if and only if $f-f(0)$ is a linearized PP. So it suffices to search for non-exceptional PPs of degree $8$ over $\mathbb{F}_{2^r}$, which exist only when $r\leqslant9$ by a previous result. This can be exhausted by the SageMath software running on a personal computer. To facilitate the computation, some requirements after linear transformations and explicit equations by Hermite's criterion are provided for the polynomial coefficients. The main result is that a non-exceptional PP $f$ of degree $8$ over $\mathbb{F}_{2^r}$ (with $r>3$) exists if and only if $r\in\{4,5,6\}$, and such $f$ is explicitly listed up to linear transformations.

preprint2019arXiv

Permutation polynomials of degree 8 over finite fields of odd characteristic

This paper provides an algorithmic generalization of Dickson's method of classifying permutation polynomials (PPs) of a given degree $d$ over finite fields. Dickson's idea is to formulate from Hermite's criterion several polynomial equations satisfied by the coefficients of an arbitrary PP of degree $d$. Previous classifications of PPs of degree at most $6$ were essentially deduced from manual analysis of these polynomial equations. However, these polynomials, needed for that purpose when $d>6$, are too complicated to solve. Our idea is to make them more solvable by calculating some radicals of ideals generated by them, implemented by a computer algebra system (CAS). Our algorithms running in SageMath 8.6 on a personal computer work very fast to determine all PPs of degree $8$ over an arbitrary finite field of odd order $q>8$. The main result is that for an odd prime power $q>8$, a PP $f$ of degree $8$ exists over the finite field of order $q$ if and only if $q\leqslant 31$ and $q\not\equiv 1\ (\mathrm{mod}\ 8)$, and $f$ is explicitly listed up to linear transformations.

preprint2019arXiv

Probing stops in the coannihilation region at the HL-LHC: a comparative study of different processes

In the minimal supersymmetric model, the coannihilation of the lighter stop $\tilde{t}_1$ and bino-like dark matter $χ$ provides a feasible way to accommodate the correct dark matter relic abundance. In this scenario, due to the compressed masses, $\tilde{t}_1$ merely appears as missing energy at the LHC and thus the pair production of $\tilde{t}_1$ can only be probed by requiring an associated energetic jet. Meanwhile, since $\tilde{t}_2$ and $\tilde{b}_1$ are correlated in mass and mixing with $\tilde{t}_1$, the production of $\tilde{t}_2\tilde{t}_2^*$ or $\tilde{b}_1\tilde{b}_1^*$, each of which dominantly decays into $\tilde{t}_1$ plus $Z$, $h$ or $W$ boson, may serve as a complementary probe. We examine all these processes at the HL-LHC and find that the $2σ$ sensitivity to $χ$ mass can be as large as about 570 GeV, 600 GeV and 1.1 TeV from the production process of $\tilde{t}_1\tilde{t}_1^*+{\rm jet}$, $\tilde{t}_2\tilde{t}_2^*$ and $\tilde{b}_1\tilde{b}_1^*$, respectively.

preprint2018arXiv

Linear complexity of Ding-Helleseth generalized cyclotomic sequences of order eight

During the last two decades, many kinds of periodic sequences with good pseudo-random properties have been constructed from classical and generalized cyclotomic classes, and used as keystreams for stream ciphers and secure communications. Among them are a family DH-GCS$_{d}$ of generalized cyclotomic sequences on the basis of Ding and Helleseth's generalized cyclotomy, of length $pq$ and order $d=\mathrm{gcd}(p-1,q-1)$ for distinct odd primes $p$ and $q$. The linear complexity (or linear span), as a valuable measure of unpredictability, is precisely determined for DH-GCS$_{8}$ in this paper. Our approach is based on Edemskiy and Antonova's computation method with the help of explicit expressions of Gaussian classical cyclotomic numbers of order $8$. Our result for $d=8$ is compatible with Yan's low bound $(pq-1)/2$ of the linear complexity for any order $d$, which means high enough to resist security attacks of the Berlekamp-Massey algorithm. Finally, we include SageMath codes to illustrate the validity of our result by examples.

preprint2016arXiv

Cascades and Spectra of a Turbulent Spinodal Decomposition in 2D Symmetric Binary Liquid Mixture

We study the fundamental physics of cascades and spectra in 2D Cahn-Hilliard-Navier-Stokes (CHNS) turbulence, and compare and contrast this system with 2D MagnetoHydroDynamic (MHD) turbulence. The important similarities include basic equations, ideal quadratic invariants, cascades and the role of linear elastic waves. Surface tension induces elasticity, and the balance between surface tension energy and turbulent kinetic energy determines a length scale (Hinze scale) of the system. The Hinze scale may be thought of as the scale of emergent critical balance between fluid straining and elastic restoring forces. The scales between the Hinze scale and dissipation scale constitute the elastic range of the 2D CHNS system. By direct numerical simulation, we find that in the elastic range, the mean square concentration spectrum $H^ψ_k$ of the 2D CHNS system exhibits the same power law ($-7/3$) as the mean square magnetic potential spectrum $H^A_k$ in the inverse cascade regime of 2D MHD. This power law is consistent with an inverse cascade of $H^ψ$, which is observed. The kinetic energy spectrum of the 2D CHNS system is $E^K_k\sim k^{-3}$ if forced at large scale, suggestive of the direct enstrophy cascade power law of 2D Navier-Stokes (NS) turbulence. The difference from the energy spectra of 2D MHD turbulence implies that the back reaction of the concentration field to fluid motion is limited. We suggest this is because the surface tension back reaction is significant only in the interfacial regions. The interfacial regions fill only a small portion of the 2D CHNS system, and their interface packing fraction is much smaller than that for 2D MHD.