arXiv subjects

Tiange Li

Publications and source records attributed to Tiange Li.

4 recordsLinked to original sources

arXiv2026

On the average-case complexity landscape for Tensor-Isomorphism-complete problems over finite fields

In Grochow and Qiao (SIAM J. Comput., 2021), the complexity class Tensor Isomorphism (TI) was introduced and isomorphism problems for groups, algebras, and polynomials were shown to be TI-complete. In this paper, we study average-case algorithms for several TI-complete problems over finite fields, including algebra isomorphism, matrix code conjugacy, and $4$-tensor isomorphism. Our main results are as follows. Over the finite field of order $q$, we devise (1) average-case polynomial-time algorithms for algebra isomorphism and matrix code conjugacy that succeed in a $1/Θ(q)$ fraction of inputs and (2) an average-case polynomial-time algorithm for the $4$-tensor isomorphism that succeeds in a $1/q^{Θ(1)}$ fraction of inputs. Prior to our work, algorithms for algebra isomorphism with rigorous average-case analyses ran in exponential time, albeit succeeding on a larger fraction of inputs (Li--Qiao, FOCS'17; Brooksbank--Li--Qiao--Wilson, ESA'20; Grochow--Qiao--Tang, STACS'21). These results reveal a finer landscape of the average-case complexities of TI-complete problems, providing guidance for cryptographic systems based on isomorphism problems. Our main technical contribution is to introduce the spectral properties of random matrices into algorithms for TI-complete problems. This leads to not only new algorithms but also new questions in random matrix theory over finite fields. To settle these questions, we need to extend both the generating function approach as in Neumann and Praeger (J. London Math. Soc., 1998) and the characteristic sum method of Gorodetsky and Rodgers (Trans. Amer. Math. Soc., 2021).

cs.CC↗

arXiv2026

A Telescope System for Charge and Position Measurement of High Energy Nuclei

A high-granularity telescope system with a large sensitive area and low material budget has been developed for high-energy heavy ion beam tests. The telescope consists of nine layers of silicon microstrip detectors (SSDs), whose performance was validated through a heavy ion beam test at the CERN SPS. A hybrid machine learning algorithm is proposed to address the challenges of nuclear charge measurement with SSDs. The system achieves a spatial resolution of $\mathcal{O}(1) \,$\SI{}{\micro\metre} and a charge resolution better than 0.16 charge units for nuclei from $Z = 1$ to $Z = 29$, with a sensitive area of $8 \times 8 \, \mathrm{cm}^2$. To the best of our knowledge, this represents the most precise charge and spatial resolution simultaneously achieved by a silicon telescope to date.

physics.ins-det↗

arXiv2026

Beam Test Characterization of Silicon Microstrip Detector Flight-Model Ladders for the AMS-02 Upgrade

The AMS-02 experiment plans to install a new silicon microstrip tracker layer (Layer-0) on top of the existing detector, increasing the cosmic-ray acceptance by a factor of 3. Layer-0 employs a design in which multiple silicon microstrip detectors (SSDs) are connected in series to form long detector ladders. We present a detailed performance study of the flight-model ladders using a 350~GeV mixed hadron beam at the CERN SPS. The study focuses on the following aspects: (i) the performance of ladders with different numbers of SSDs, for which the intrinsic spatial resolution at normal incidence varies from $9.5~μ\mathrm{m}$ to $11.4~μ\mathrm{m}$ for ladders composed of 8 to 12 SSDs; (ii) the response consistency for particles impacting on the \emph{Head} and \emph{Tail} regions of the ladder; and (iii) the dependence of the detector performance on the particle incidence angle.

physics.ins-det↗

arXiv2022

A Screening Strategy for Structured Optimization Involving Nonconvex $\ell_{q,p}$ Regularization

In this paper, we develop a simple yet effective screening rule strategy to improve the computational efficiency in solving structured optimization involving nonconvex $\ell_{q,p}$ regularization. Based on an iteratively reweighted $\ell_1$ (IRL1) framework, the proposed screening rule works like a preprocessing module that potentially removes the inactive groups before starting the subproblem solver, thereby reducing the computational time in total. This is mainly achieved by heuristically exploiting the dual subproblem information during each iteration.Moreover, we prove that our screening rule can remove all inactive variables in a finite number of iterations of the IRL1 method. Numerical experiments illustrate the efficiency of our screening rule strategy compared with several state-of-the-art algorithms.

cs.LG↗