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Let $p$ be an odd prime and $x$ be an indeterminate. Recently, Z.-W. Sun proposed the following conjecture: $$\det\left[x+\left(\frac{j-i}{p}\right)\right]_{0\le i,j\le \frac{p-1}{2}}=\begin{cases} (\frac{2}{p})pb_px-a_p & \mbox{if}\ p\equiv 1\pmod4, 1 & \mbox{if}\ p\equiv 3\pmod4, \end{cases}$$ where $a_p$ and $b_p$ are rational numbers related to the fundamental unit and class number of the real quadratic field $\mathbb{Q}(\sqrt{p})$. In this paper, we confirm the above conjecture of Sun based on Vsemirnov's decomposition of Chapman's "evil determinant".

We investigate the thermoelectric effect, which describes the generation of an electric field induced by temperature and conserved charge chemical potential gradients, in the hot and dense hadronic matter created in heavy-ion collisions. Utilizing the Boltzmann kinetic theory within the repulsive mean-field hadron resonance gas model, we evaluate both the diffusion thermopower matrix and diffusion coefficient matrix for the baryon number ($B$), electric charge ($Q$), and strangeness ($S$). The Landau-Lifshitz choice for the rest frame of the fluid is enforced in the derivation. We find that the thermoelectric effect hinders the diffusion processes of multiple conserved charges, particularly reducing the coupling between electric charge and baryon number (strangeness) in baryon (strangeness) diffusion. Given that the repulsive mean-field interactions between hadrons have a significant effect on the diffusion thermopower matrix and diffusion coefficient matrix in the baryon-rich region, we extend the investigation to include the impact of magnetic fields, analyzing the magneto-thermoelectric effect on both the diffusion coefficient matrix and the Hall-like diffusion coefficient matrix. The sensitivities of the magnetic field-dependent diffusion thermopower matrix and magneto-thermoelectric modified diffusion coefficient matrix to the choices of various transverse conditions are also studied., Comment: 21 pages, 12 figures, Version accepted by Phys. Rev. D

We investigate the impact of the magnetic field generated by colliding nuclei on heavy quark-antiquark interactions and heavy quark dynamics in the quark-gluon plasma (QGP). By means of hard-thermal-loop resummation technique combined with dimension-two gluon condensates, the static heavy quark potential and heavy quark momentum diffusion coefficient, which incorporate both perturbative and non-perturbative interactions between heavy quarks and the QGP medium, are computed beyond the lowest Landau level approximation. We find that the imaginary part of the heavy quark potential in the magnetic field exhibits significant anisotropy. Specifically, the absolute value of the imaginary part is larger when the quark-antiquark separation is aligned perpendicular to the magnetic field direction, compared to when it is aligned parallel to the magnetic field direction. The heavy quark momentum diffusion coefficient in the magnetized QGP medium also becomes anisotropic. As the temperature rises, the influence of higher Landau levels becomes increasingly significant, resulting in a decrease in the anisotropy ratio of the heavy quark momentum diffusion coefficient to values even below 1. At sufficiently high temperatures, this ratio ultimately approaches 1. The non-perturbative interactions are indispensable for understanding heavy quark dynamics in the low-temperature region. We also study the response of viscous quark matter to the magnetic field and explore its implications for heavy quark potential, thermal decay widths of quarkonium states, as well as heavy quark momentum diffusion coefficient., Comment: 24 pages, 15 figures; Version published in Phys. Rev. D

Suppose that $p$ is an odd prime and $m$ is an integer not divisible by $p$. Sun and Tauraso [Adv. in Appl. Math., 45(2010), 125--148] gave $\sum_{k=0}^{n-1}\binom{2k}{k+d}/m^k$ and $\sum_{k=0}^{n-1}\binom{2k}{k+d}/(km^k)$ modulo $p$ for all $d=0,1, \ldots n$ and $n= p^a$, where $a$ is a positive integer. In this paper, we present some $q$-analogues of these congruences in the cases $m=2, 4$ for any positive integer $n$., Comment: 13 pages

Let $\Phi_{n}(q)$ denote the $n$-th cyclotomic polynomial in $q$. Recently, Guo and Schlosser [Constr. Approx. 53 (2021), 155--200] put forward the following conjecture: for an odd integer $n>1$, \begin{align*} &\sum_{k=0}^{n-1}[8k-1]\frac{(q^{-1};q^4)_k^6(q^2;q^2)_{2k}}{(q^4;q^4)_k^6(q^{-1};q^2)_{2k}}q^{8k}\notag\\ &\quad\equiv\begin{cases}0 \pmod{[n]\Phi_n(q)^2}, &\text{if }n\equiv 1\pmod{4},\\[5pt] 0 \pmod{[n]},&\text{if }n\equiv 3\pmod{4}. \end{cases} \end{align*} Applying the `creative microscoping' method and several summation and transformation formulas for basic hypergeometric series and the Chinese remainder theorem for coprime polynomials, we confirm the above conjecture, as well as another similar $q$-supercongruence conjectured by Guo and Schlosser., Comment: 15 pages

In this paper, we study certain determinants over finite fields. Let $\mathbb{F}_q$ be the finite field of $q$ elements and let $a_1,a_2,\cdots,a_{q-1}$ be all nonzero elements of $\mathbb{F}_q$. Let $T_q=\left[\frac{1}{a_i^2-a_ia_j+a_j^2}\right]_{1\le i,j\le q-1}$ be a matrix over $\mathbb{F}_q$. We obtain the explicit value of $\det T_q$. Also, as a consequence of our result, we confirm a conjecture posed by Zhi-Wei Sun.

Feature selection is an important part of building a machine learning model. By eliminating redundant or misleading features from data, the machine learning model can achieve better performance while reducing the demand on com-puting resources. Metaheuristic algorithms are mostly used to implement feature selection such as swarm intelligence algorithms and evolutionary algorithms. However, they suffer from the disadvantage of relative complexity and slowness. In this paper, a concise method is proposed for universal feature selection. The proposed method uses a fusion of the filter method and the wrapper method, rather than a combination of them. In the method, one-hoting encoding is used to preprocess the dataset, and random forest is utilized as the classifier. The proposed method uses normalized frequencies to assign a value to each feature, which will be used to find the optimal feature subset. Furthermore, we propose a novel approach to exploit the outputs of mutual information, which allows for a better starting point for the experiments. Two real-world dataset in the field of intrusion detection were used to evaluate the proposed method. The evaluation results show that the proposed method outperformed several state-of-the-art related works in terms of accuracy, precision, recall, F-score and AUC., Comment: 15 pages, 6 figures

With the two flavor Nambu-Jona-Lasinio (NJL) model we carry out a phenomenological study on the chiral phase structure, mesonic properties and transport properties in a momentum-space anisotropic quark matter. To calculate transport coefficients we have utilized the kinetic theory in the relaxation time approximation, where the momentum anisotropy is embedded in the estimation of both distribution function and the relaxation time. It is shown that an increase of the anisotropy parameter $\xi$ may results in a catalysis of chiral symmetry breaking. The critical endpoint (CEP) is shifted to smaller temperatures and larger quark chemical potentials as $\xi $ increases, the impact of momentum anisotropy on temperature of CEP is almost the same as that on the quark chemical potential of CEP. The meson masses and the associated decay widths also exhibit a significant $\xi$ dependence. It is observed that the temperature behavior of scaled shear viscosity $\eta/T^3$ and scaled electrical conductivity $\sigma_{el}/T$ exhibit a similar dip structure, with the minima of both $\eta/T^3$ and $\sigma_{el}/T$ shifting toward higher temperatures with increasing $\xi$. Furthermore, we demonstrate that the Seebeck coefficient $S$ decreases when temperature goes up and its sign is positive, indicating the dominant carriers for converting the temperature gradient to the electric field are up-quarks. The Seebeck coefficient $S$ is significantly enhanced with a large $\xi$ for the temperature below the critical temperature., Comment: 20 pages, 10figures