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Tabular data is one of the most common data sources in machine learning. Although a wide range of classical methods demonstrate practical utilities in this field, deep learning methods on tabular data are becoming promising alternatives due to their flexibility and ability to capture complex interactions within the data. Considering that deep tabular methods have diverse design philosophies, including the ways they handle features, design learning objectives, and construct model architectures, we introduce a versatile deep-learning toolbox called TALENT (Tabular Analytics and LEarNing Toolbox) to utilize, analyze, and compare tabular methods. TALENT encompasses an extensive collection of more than 20 deep tabular prediction methods, associated with various encoding and normalization modules, and provides a unified interface that is easily integrable with new methods as they emerge. In this paper, we present the design and functionality of the toolbox, illustrate its practical application through several case studies, and investigate the performance of various methods fairly based on our toolbox. Code is available at https://github.com/qile2000/LAMDA-TALENT.

Tabular data is prevalent across various domains in machine learning. Although Deep Neural Network (DNN)-based methods have shown promising performance comparable to tree-based ones, in-depth evaluation of these methods is challenging due to varying performance ranks across diverse datasets. In this paper, we propose a comprehensive benchmark comprising 300 tabular datasets, covering a wide range of task types, size distributions, and domains. We perform an extensive comparison between state-of-the-art deep tabular methods and tree-based methods, revealing the average rank of all methods and highlighting the key factors that influence the success of deep tabular methods. Next, we analyze deep tabular methods based on their training dynamics, including changes in validation metrics and other statistics. For each dataset-method pair, we learn a mapping from both the meta-features of datasets and the first part of the validation curve to the final validation set performance and even the evolution of validation curves. This mapping extracts essential meta-features that influence prediction accuracy, helping the analysis of tabular methods from novel aspects. Based on the performance of all methods on this large benchmark, we identify two subsets of 45 datasets each. The first subset contains datasets that favor either tree-based methods or DNN-based methods, serving as effective analysis tools to evaluate strategies (e.g., attribute encoding strategies) for improving deep tabular models. The second subset contains datasets where the ranks of methods are consistent with the overall benchmark, acting as a probe for tabular analysis. These ``tiny tabular benchmarks'' will facilitate further studies on tabular data.

To a simple polarized hyperplane arrangement (not necessarily cyclic) $\mathbb{V}$, one can associate a stopped Liouville manifold (equivalently, a Liouville sector) $\left(M(\mathbb{V}),\xi\right)$, where $M(\mathbb{V})$ is the complement of finitely many hyperplanes in $\mathbb{C}^d$, obtained as the complexifications of the real hyperplanes in $\mathbb{V}$. The Liouville structure on $M(\mathbb{V})$ comes from a very affine embedding, and the stop $\xi$ is determined by the polarization. In this article, we study the symplectic topology of $\left(M(\mathbb{V}),\xi\right)$. In particular, we prove that their partially wrapped Fukaya categories are generated by Lagrangian submanifolds associated to the bounded and feasible chambers of $\mathbb{V}$. A computation of the Fukaya $A_\infty$-algebra of these Lagrangians then enables us to identity these wrapped Fukaya categories with the $\mathbb{G}_m^d$-equivariant hypertoric convolution algebras $\widetilde{B}(\mathbb{V})$ associated to $\mathbb{V}$. This confirms a conjecture of Lauda-Licata-Manion (arXiv:2009.03981) and provides evidence for the general conjecture of Lekili-Segal (arXiv:2304.10969) on the equivariant Fukaya categories of symplectic manifolds with Hamiltonian torus actions., Comment: Fix graphical issues, add some references and expand some of the expositions in section 3. Comments welcome!

In this work, we investigate the semileptonic decays of $B_{c}$ meson to $\eta_{c}(1S,2S,3S)$, $\psi(1S,2S,3S)$ and $X(3872)$ within the framework of covariant light-front quark model (CLFQM). We combine the helicity amplitudes via the corresponding form factors to obtain the branching ratios of the semileptonic decays $B_{c}\to \eta_{c}(1S, 2S, 3S)\ell\nu_{\ell}$, $B_{c}\to \psi(1S, 2S, 3S))\ell\nu_{\ell}$ and $B_{c}\to X(3872)\ell\nu_{\ell}$ with $\ell=e,\mu,\tau$. In view of the $R_{J/\Psi}$ anomaly released by the LHCb collaboration, it is necessary to calculate the ratios $R_X$ with $X=\psi(1S,2S,3S),\eta_c(1S,2S,3S),X(3872)$ systematically, which are helpful to check the lepton flavor universality (LFU). Furthermore, we also take into account another two physical observables, one is the longitudinal polarization fraction $f_{L}$ and the other is the forward-backward asymmetry $A_{FB}$, which can provide new clues to understand the $R_{J /\Psi}$ anomaly. Such theoretical predictions are necessary and interesting, which can be tested in the future LHCb experiments., Comment: 23 pages, 4 figures

In this work we study the quasi-two-body decays $B_c \to \ K^{*} h \to K \pi h (h = D, D_s, K, \pi, \eta, \eta')$ in the perturbative QCD (PQCD) approach. The two-meson distribution amplitudes (DAs) $\Phi^{\text{P-wave}}_{K\pi}$ are introduced to describe the final state interactions of the K \pi pair, which involve the time-like form factors F_{K\pi}(s) parameterized by the relativistic Breit-Wigner function and the Gegenbauer polynomials. We calculate the branching ratios for these quasi-two-body decays, from which one can obtain the branching raios for the corresponding two-body decays under the narrow width approximation relation. We find that $B^+_c\to K^{*+}D^0$ and $B^+_c\to K^{*0}D^+$ have the largest branching ratios, which can reach up to $10^{-6}$, while the branching ratios for other two-body decays are very small and only about $10^{-8}\sim10^{-7}$. As we expected that the branching ratios of the pure annihilation decays are usually small, while in our considered such type of decays, the channel $B_c^+ \to \bar K^{*0}K^{+}$ has the largest branching ratio, which is near $10^{-6}$. These results are consistent with the previously PQCD calculations obtained in the two-body framework, which can be tested by the future LHCb experiments. For the decays $B_c^+ \to K^{*+} D^{0}\to K^{0}\pi^+D^{0} , B_c^+ \to K^{*0}D^{+}\to K^{+}\pi^-D^{+}$ and $B_c^+ \to \bar K^{*0}D_s^{+}\to K^{-}\pi^+D_s^{+}$, we calculate their direct CP violations and find that $A_{CP}(B_c^+ \to K^{*+}D^{0}\to K^{0}\pi^+D^{0})=(-14.6_{-1.12}^{+9.19})\%$ is the largest one, which is possible measured by the present LHCb experiments. For the pure annihilation type decays, there is no CP violations because only the tree operators are involved. Furthermore, we also give the differential distributions of the branching ratios and the direct CP violations for the decays $B_c\to K^* D_{(s)}\to K \pi D_{(s)}$., Comment: 15 pages, 3 figures, 2 tables

Reservoir computing (RC), a particular form of recurrent neural network, is under explosive development due to its exceptional efficacy and high performance in reconstruction or/and prediction of complex physical systems. However, the mechanism triggering such effective applications of RC is still unclear, awaiting deep and systematic exploration. Here, combining the delayed embedding theory with the generalized embedding theory, we rigorously prove that RC is essentially a high dimensional embedding of the original input nonlinear dynamical system. Thus, using this embedding property, we unify into a universal framework the standard RC and the time-delayed RC where we novelly introduce time delays only into the network's output layer, and we further find a trade-off relation between the time delays and the number of neurons in RC. Based on this finding, we significantly reduce the network size of RC for reconstructing and predicting some representative physical systems, and, more surprisingly, only using a single neuron reservoir with time delays is sometimes sufficient for achieving those tasks.

Data based detection and quantification of causation in complex, nonlinear dynamical systems is of paramount importance to science, engineering and beyond. Inspired by the widely used methodology in recent years, the cross-map-based techniques, we develop a general framework to advance towards a comprehensive understanding of dynamical causal mechanisms, which is consistent with the natural interpretation of causality. In particular, instead of measuring the smoothness of the cross map as conventionally implemented, we define causation through measuring the {\it scaling law} for the continuity of the investigated dynamical system directly. The uncovered scaling law enables accurate, reliable, and efficient detection of causation and assessment of its strength in general complex dynamical systems, outperforming those existing representative methods. The continuity scaling based framework is rigorously established and demonstrated using datasets from model complex systems and the real world., Comment: 7 figures; The article has been peer reviewed and accepted by RESEARCH

We consider the fidelity of the vector meson dominance (VMD) assumption as an instrument for relating the electromagnetic vector-meson production reaction $e + p \to e^\prime + V + p$ to the purely hadronic process $V + p \to V+p$. Analyses of the photon vacuum polarisation and the photon-quark vertex reveal that such a VMD Ansatz might be reasonable for light vector-mesons. However, when the vector-mesons are described by momentum-dependent bound-state amplitudes, VMD fails for heavy vector-mesons: it cannot be used reliably to estimate either a photon-to-vector-meson transition strength or the momentum dependence of those integrands that would arise in calculations of the different reaction amplitudes. Consequently, for processes involving heavy mesons, the veracity of both cross-section estimates and conclusions based on the VMD assumption should be reviewed, e.g., those relating to hidden-charm pentaquark production and the origin of the proton mass., Comment: 12 pages, 2 figures, 2 tables

We propose a scheme to directly measure the entangled W states with cross-Kerr nonlinearity mediums. This scheme can measure three-photon, four-photon, and even N-photon W states in one step. Only PBSs and cross-Kerr nonlinearity mediums are used in this scheme, which is feasible for experiments. We describe the three-photon W states measurement process and extend it to four-photon and N-photon W states., Comment: 8 pages, 3 figures

We studied the B meson decays $B\to J/\Psi K_1(1270,1400)$ in the pQCD approach beyond the leading order. With the vertex corrections and the NLO Wilson coefficients included, the branching ratios of the considered decays are $Br(B^+\to J/\Psi K_1(1270)^+)=1.76^{+0.65}_{-0.69}\times10^{-3}, Br(B^+\to J/\Psi K_1(1400)^+)=7.03^{+2.70}_{-2.52}\times10^{-4}$, and $Br(B^0\to J/\Psi K_1(1270)^0)=(1.63^{+0.60}_{-0.64})\times10^{-3}$ with the mixing angle $\theta_{K_1}=33^\circ$, which can agree well with the data or the present experimental upper limit within errors. So we support the opinion that $\theta_{K_1}\sim33^\circ$ is much more favored than $58^{\circ}$. Furthermore, we also give the predictions for the polarization fractions, direct CP violations from the different polarization components, the relative phase angles for the considered decays with the mixing angle $\theta_{K_1}=33^\circ$ and $58^\circ$, respectively. The direct CP violations of the two charged decays $B^+\to J/\Psi K_1(1270,1400)^+$ are very small $(10^{-4}\sim10^{-5})$, because there is no weak phase until up to $\mathcal{O}(\lambda^4)$ with the Wolfenstein parameter $\lambda=0.22537$. These results can be tested at the running LHCb and forthcoming Super-B experiments., Comment: 14 pages,3 figures,to appear in EPJC

Through analyzing the $B_{(s)}$ charmed decays $B^{0}\to \bar D_{0}f_0(980)$ and $B_{s}\to \bar D_{0}f_0(980)$ within the framework of the PQCD factorization approach and comparing with the current data, we find that there are two possible regions for the $f_0(980)-f_0(500)$ mixing angle $\theta$: one is centered at $34^\circ\sim38^\circ$ and the other is falls into $142^\circ\sim154^\circ$. The former can overlap mostly with one of allowed angle regions extracted from the decay $B^{0}\to \bar D_{0}f_0(500)$. The branching fractions of $B_s$ decay modes are less sensitive to the mixing angle compared with those of B decay modes. Especially, for the decay $B_{s}\to D^0 f_0(980)$, its branching fraction changes only slightly between $(1.2\sim1.8)\times10^{-7}$ when the mixing angle $\theta$ runs from $0^\circ$ to $180^\circ$. All of our results support the picture that the $f_0(980)$ is dominated by two quark component in the B decay dynamic mechanism. Furthermore, the $s\bar s$ component is more important than the $q\bar q=(u\bar u+d\bar d)/\sqrt{2}$ component. This point is different from $f_0(500)/\sigma$. Last but not least, our picture is not in conflict with the popular four-quark explanation., Comment: 15 pages, 4 figures

We propose a scheme to deterministically generate Greenberger-Horne-Zeilinger states of $N\geq 3$ atoms trapped in spatially separated cavities connected by optical fibers. The scheme is based on the technique of fractional stimulated Raman adiabatic passage which is one-step in the sense that one needs just wait for the desired entangled state to be generated in the stationary regime. The parametrized shapes of the Rabi frequencies of the classical fields that drive the two end atoms are chosen appropriately to realize the scheme. We also show numerically that the proposed scheme is insensitive to the fluctuations of the pulses' parameters and, at the same time, robust against decoherence caused by the dissipation due to fiber decay. Moreover, a relatively high fidelity can be obtained even in the presence of cavity decay and atomic spontaneous emission., Comment: Accepted by JOSA B