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In the context of Stirling polynomials, Gessel and Stanley introduced the definition of Stirling permutation, which has attracted extensive attention over the past decades. Recently, we introduced Stirling permutation code and provided numerous equidistribution results as applications. The purpose of the present work is to further analyse Stirling permutation code. First, we derive an expansion formula expressing the joint distribution of the types $A$ and $B$ descent statistics over the hyperoctahedral group, and we also find an interlacing property involving the zeros of its coefficient polynomials. Next, we prove a strong connection between signed permutations in the hyperoctahedral group and Stirling permutations. Furthermore, we investigate unified generalizations of the trivariate second-order Eulerian polynomials and ascent-plateau polynomials. Using Stirling permutation codes, we provide expansion formulas for eight-variable and seventeen-variable polynomials, which imply several $e$-positive expansions and clarify the connections among several statistics. Our results generalize the results of B\'ona, Chen-Fu, Dumont, Janson, Haglund-Visontai and Petersen., Comment: 19 pages

Floquet engineering is a powerful manipulation method in modern quantum technology. However, unwanted heating is the main challenge of Floquet engineering, therefore the Floquet thermalization has attracting considerable attentions recently. In this work, we investigate thermalization of periodically driven many-body systems through the lens of Krylov complexity, and find a topological origin of different thermalization behaviors. We demonstrate that If the topology of the Krylov chain is nontrivial, a periodically driven system will reach a state with finite temperature. When the Krylov chain is topologically trivial, the system will be heated to infinite temperature. We further show that the prethermalization can be understood as the tunnelling process of a quasi-edge mode through the local gap on Krylov chain. This picture provides a systematically method to obtain the effective prethermal Hamiltonian., Comment: 6 pages, 5 figures

The motivation of this paper is to investigate the joint distribution of succession and Eulerian statistics. We first investigate the enumerators for the joint distribution of descents, big ascents and successions over all permutations in the symmetric group. As an generalization a result of Diaconis-Evans-Graham (Adv. in Appl. Math., 61 (2014), 102-124), we show that two triple set-valued statistics of permutations are equidistributed on symmetric groups. We then introduce the definition of proper left-to-right minimum, and discover that the joint distribution of the succession and proper left-to-right minimum statistics over permutations is a symmetric distribution. In the final part, we discuss the relationship between the fix and cyc (p,q)-Eulerian polynomials and the joint distribution of succession and Eulerian-type statistics. In particular, we give a concise derivation of the generating function for a six-variable Eulerian polynomials., Comment: 21 pages. arXiv admin note: text overlap with arXiv:2002.06930

Underwater images normally suffer from degradation due to the transmission medium of water bodies. Both traditional prior-based approaches and deep learning-based methods have been used to address this problem. However, the inflexible assumption of the former often impairs their effectiveness in handling diverse underwater scenes, while the generalization of the latter to unseen images is usually weakened by insufficient data. In this study, we leverage both the physics-based Image Formation Model (IFM) and deep learning techniques for Underwater Image Enhancement (UIE). To this end, we propose a novel Physics-Aware Triple-Stream Underwater Image Enhancement Network, i.e., PATS-UIENet, which comprises a Direct Signal Transmission Estimation Steam (D-Stream), a Backscatter Signal Transmission Estimation Steam (B-Stream) and an Ambient Light Estimation Stream (A-Stream). This network fulfills the UIE task by explicitly estimating the degradation parameters of a revised IFM. We also adopt an IFM-inspired semi-supervised learning framework, which exploits both the labeled and unlabeled images, to address the issue of insufficient data. To our knowledge, such a physics-aware deep network and the IFM-inspired semi-supervised learning framework have not been used for the UIE task before. Our method performs better than, or at least comparably to, sixteen baselines across six testing sets in the degradation estimation and UIE tasks. These promising results should be due to the fact that the proposed method can not only model the degradation but also learn the characteristics of diverse underwater scenes., Comment: 13 pages, 10 figures

Recently synthetic gauge fields have been implemented on quantum simulators. Unlike the gauge fields in the real world, in synthetic gauge fields, the gauge charge can fluctuate and gauge invariance can be violated, which leading rich physics unexplored before. In this work, we propose the gauge violation spectroscopy as a useful experimentally accessible measurement in the synthetic gauge theories. We show that the gauge violation spectroscopy exhibits no dispersion. Using three models as examples, two of them can be exactly solved by bosonization, and one has been realized in experiment, we further demonstrate the gauge violation spectroscopy can be used to detect the confinement and deconfinement phases. In the confinement phase, it shows a delta function behavior, while in the deconfinement phase, it has a finite width., Comment: 12 pages, 6 figures

Charge-changing cross section ($\sigma_{\text{cc}}$) measurements via the transmission method have made important progress recently aiming to determine the charge radii of exotic nuclei. In this work, we report a new $\sigma_{\text{cc}}$ measurement of 304(9) MeV/nucleon $^{28}$Si on carbon at the second Radioactive Ion Beam Line in Lanzhou (RIBLL2) and describe the data analysis procedure in detail. This procedure is essential to evaluate the systematic uncertainty in the transmission method. The determined $\sigma_{\mathrm{cc}}$ of 1125(11) mb is found to be consistent with the existing data at similar energies. The present work will serve as a reference in the $\sigma_{\text{cc}}$ determinations at RIBLL2., Comment: 9 pages, 13 figures, to be published in Chinese Physics C

Motivated by the work of Visontai and Dey-Sivasubramanian on the gamma-positivity of some polynomials, we find the commutative property of a pair of Eulerian operators. As an application, we show the bi-gamma-positivity of the descent polynomials on permutations of the multiset $\{1^{a_1},2^{a_2},\ldots,n^{a_n}\}$, where $0\leqslant a_i\leqslant 2$. Therefore, these descent polynomials are all alternatingly increasing, and so they are unimodal with modes in the middle., Comment: 9 pages

The development of the theories of the second-order Eulerian polynomials began with the works of Buckholtz and Carlitz in their studies of an asymptotic expansion. Gessel-Stanley introduced Stirling permutations and presented combinatorial interpretations of the second-order Eulerian polynomials. Recently, there is a growing interest in the properties of Stirling permutations. The motivation of this paper is to develop a general method for finding equidistributed statistics on Stirling permutations. Firstly, we show that the up-down-pair statistic is equidistributed with ascent-plateau statistic, and that the exterior up-down-pair statistic is equidistributed with left ascent-plateau statistic. Secondly, we introduce the Stirling permutation codes. Several equidistribution results follow from simple applications. In particular, we find that six bivariable set-valued statistics are equidistributed on the set of Stirling permutations. As an application, we extend a classical result independently established by Dumont and Bona. Thirdly, we explore bijections among Stirling permutation codes, perfect matchings and trapezoidal words. We then show the e-positivity of the enumerators of Stirling permutations by left ascent-plateaux, exterior up-down-pairs and right plateau-descents. In the final part, the e-positivity of the multivariate k-th order Eulerian polynomials is established, which improves a result of Janson-Kuba-Panholzer and generalizes a recent result of Chen-Fu., Comment: 26 pages

Traditional online advertising systems for sponsored search follow a cascade paradigm with retrieval, pre-ranking,ranking, respectively. Constrained by strict requirements on online inference efficiency, it tend to be difficult to deploy useful but computationally intensive modules in the ranking stage. Moreover, ranking models currently used in the industry assume the user click only relies on the advertisements itself, which results in the ranking stage overlooking the impact of organic search results on the predicted advertisements (ads). In this work, we propose a novel framework PCDF(Parallel-Computing Distributed Framework), allowing to split the computation cost into three parts and to deploy them in the pre-module in parallel with the retrieval stage, the middle-module for ranking ads, and the post-module for re-ranking ads with external items. Our PCDF effectively reduces the overall inference latency compared with the classic framework. The whole module is end-to-end offline training and adapt for the online learning paradigm. To our knowledge, we are the first to propose an end-to-end solution for online training and deployment on complex CTR models from the system framework side.

Recently, Graph Convolutional Network (GCN) has become a novel state-of-art for Collaborative Filtering (CF) based Recommender Systems (RS). It is a common practice to learn informative user and item representations by performing embedding propagation on a user-item bipartite graph, and then provide the users with personalized item suggestions based on the representations. Despite effectiveness, existing algorithms neglect precious interactive features between user-item pairs in the embedding process. When predicting a user's preference for different items, they still aggregate the user tree in the same way, without emphasizing target-related information in the user neighborhood. Such a uniform aggregation scheme easily leads to suboptimal user and item representations, limiting the model expressiveness to some extent. In this work, we address this problem by building bilateral interactive guidance between each user-item pair and proposing a new model named IA-GCN (short for InterActive GCN). Specifically, when learning the user representation from its neighborhood, we assign higher attention weights to those neighbors similar to the target item. Correspondingly, when learning the item representation, we pay more attention to those neighbors resembling the target user. This leads to interactive and interpretable features, effectively distilling target-specific information through each graph convolutional operation. Our model is built on top of LightGCN, a state-of-the-art GCN model for CF, and can be combined with various GCN-based CF architectures in an end-to-end fashion. Extensive experiments on three benchmark datasets demonstrate the effectiveness and robustness of IA-GCN.

Gamma-positivity appears frequently in finite geometries, combinatorics and number theory. Motivated by the recent work of Sagan and Tirrell (Adv. Math., 374 (2020), 107387), we study the relationships between gamma-positivity and alternating gamma-positivity. As applications, we derive several alternatingly gamma-positive polynomials related to Narayana polynomials and Eulerian polynomials. In particular, we show the alternating gamma-positivity and Hurwitz stability of a combination of the modified Narayana polynomials of types A and B. By using colored $2\times n$ Young diagrams, we present a unified combinatorial interpretations of three identities involving Narayana numbers of type B. A general result of this paper is that every gamma-positive polynomial is also alternatingly semi-gamma-positive. At the end of this paper, we pose two conjectures, one concerns the Boros-Moll polynomials and the other concerns the enumerators of permutations by descents and excedances., Comment: 26 pages

A graph $G$ is $d$-degenerate if every non-null subgraph of $G$ has a vertex of degree at most $d$. We prove that every $n$-vertex planar graph has a $3$-degenerate induced subgraph of order at least $3n/4$., Comment: 28 pages, 12 figures

It has become widely known that when two flows of pedestrians cross stripes emerge spontaneously by which the pedestrians of the two walking directions manage to pass each other in an orderly manner. In this work, we report about the results of an experiment on crossing flows which has been carried out at a German school. These results include that previously reported high flow volumes on the crossing area can be confirmed. The empirical results are furthermore compared to the results of a simulation model which succesfully could be calibrated to catch the specific properties of the population of participants., Comment: contribution to proceedings of Traffic and Granular Flow 2013 held in J\"ulich, Germany

As is well known, a varying effective gravitational "constant" is one of the common features of most modified gravity theories. Of course, as a modified gravity theory, $f(T)$ theory is not an exception. Noting that the observational constraint on the varying gravitational "constant" is very tight, in the present work we try to constrain $f(T)$ theories with the varying gravitational "constant". We find that the allowed model parameter $n$ or $\beta$ has been significantly shrunk to a very narrow range around zero. In fact, the results improve the previous constraints by an order of magnitude., Comment: 10 pages, 2 tables, 2 figures, revtex4; v2: discussions added, Eur. Phys. J. C in press; v3: published version. arXiv admin note: text overlap with arXiv:1106.0102

In analogy to $f(R)$ theory, recently a new modified gravity theory, namely the so-called $f(T)$ theory, has been proposed to drive the current accelerated expansion without invoking dark energy. In the present work, by extending Bisabr's idea, we try to constrain $f(T)$ theories with the varying fine structure "constant", $\alpha\equiv e^2/\hbar c$. We find that the constraints on $f(T)$ theories from the observational $\Delta\alpha/\alpha$ data are very severe. In fact, they make $f(T)$ theories almost indistinguishable from $\Lambda$CDM model., Comment: 12 pages, 4 figures, 1 table, revtex4; v2: discussions added, Phys. Lett. B in press; v3: published version

We report a numerical study of van der Waals adsoprtion and capillary condensation effects on self-similar fractal surfaces. An assembly of uncoupled spherical pores with a power-law distributin of radii is used to model fractal surfaces with adjustable dimensions. We find that the commonly used fractal Frankel-Halsey-Hill equation systematically fails to give the correct dimension due to crossover effects, consistent with the findings of recent experiments. The effects of pore coupling and curvature dependent surface tension were also studied., Comment: 11 pages, 3 figures