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We investigate the upper bound of charge diffusion constant in holography. For this purpose, we apply the conjectured upper bound proposal related to the equilibration scales ($\omega_{\text{eq}}, k_{\text{eq}}$) to the Einstein-Maxwell-Axion model. ($\omega_{\text{eq}}, k_{\text{eq}}$) is defined as the collision point between the diffusive hydrodynamic mode and the first non-hydrodynamic mode, giving rise to the upper bound of the diffusion constant $D$ at low temperature $T$ as $D = \omega_{\text{eq}}/k_{\text{eq}}^2$. We show that the upper bound proposal also works for the charge diffusion and ($\omega_{\text{eq}}, k_{\text{eq}}$), at low $T$, is determined by $D$ and the scaling dimension $\Delta(0)$ of an infra-red operator as $(\omega_{\text{eq}}, \, k_{\text{eq}}^2) \,=\, (2 \pi T \Delta(0) \,, \omega_{\text{eq}}/D)$, as for other diffusion constants. However, for the charge diffusion, we find that the collision occurs at real $k_{\text{eq}}$, while it is complex for other diffusions. In order to examine the universality of the conjectured upper bound, we also introduce a higher derivative coupling to the Einstein-Maxwell-Axion model. This coupling is particularly interesting since it leads to the violation of the \textit{lower} bound of the charge diffusion constant so the correction may also have effects on the \textit{upper} bound of the charge diffusion. We find that the higher derivative coupling does not affect the upper bound so that the conjectured upper bound would not be easily violated., Comment: v1: 23 pages, 10 figures; v2: minor edits, references added

We present effective field theories for the weakly coupled Weyl-$\mathrm{Z}_2$ semimetal, as well as the holographic realization for the strongly coupled case. In both cases, the anomalous systems have both the chiral anomaly and the $\mathrm{Z}_2$ anomaly and possess topological quantum phase transitions from the Weyl-$\mathrm{Z}_2$ semimetal phases to partly or fully topological trivial phases. We find that the topological phase transition is characterized by the anomalous transport parameters, i.e. the anomalous Hall conductivity and the $\mathrm{Z}_2$ anomalous Hall conductivity. These two parameters are nonzero at the Weyl-$\mathrm{Z}_2$ semimetal phase and vanish at the topologically trivial phases. In the holographic case, the different behavior between the two anomalous transport coefficients is discussed. Our work reveals the novel phase structure of strongly interacting Weyl-$\mathrm{Z}_2$ semimetal with two pairs of nodes., Comment: v2: 45 pages,12 figures. References and comments added, typos corrected. Final version to appear in JHEP

Link prediction for knowledge graphs aims to predict missing connections between entities. Prevailing methods are limited to a transductive setting and hard to process unseen entities. The recent proposed subgraph-based models provided alternatives to predict links from the subgraph structure surrounding a candidate triplet. However, these methods require abundant known facts of training triplets and perform poorly on relationships that only have a few triplets. In this paper, we propose Meta-iKG, a novel subgraph-based meta-learner for few-shot inductive relation reasoning. Meta-iKG utilizes local subgraphs to transfer subgraph-specific information and learn transferable patterns faster via meta gradients. In this way, we find the model can quickly adapt to few-shot relationships using only a handful of known facts with inductive settings. Moreover, we introduce a large-shot relation update procedure to traditional meta-learning to ensure that our model can generalize well both on few-shot and large-shot relations. We evaluate Meta-iKG on inductive benchmarks sampled from NELL and Freebase, and the results show that Meta-iKG outperforms the current state-of-the-art methods both in few-shot scenarios and standard inductive settings., Comment: under review

We investigate the Page curve for a non-standard black hole which is asymptotically non-flat/AdS/dS. For this purpose, we apply the island prescription to the charged linear dilaton black holes and analyze, in detail, the entanglement entropy of Hawking radiation for both the non-extremal case and the extremal case. In the non-extremal case, we find the Page curve consistent with the unitarity principle: at early times the entanglement entropy grows linearly in time without the island and at late times it is saturated double of the Bekenstein-Hawking entropy in the presence of the island. We observe the Page time is universal for all different models studied by our method: $t_{\text{Page}}=\frac{3}{ \pi c}\frac{S_{\text{BH}}}{T_H}.$ For the extremal case, the island prescription provides the well defined entanglement entropy only with the island, which can not be obtained from the continuous limit of the non-extremal case. This implies that the Page curve may not be reproduced for the extremal case and further investigation is needed., Comment: v1: 20 pages, 4 figures; v2: minor edits, references added

We investigate the breakdown of magneto-hydrodynamics at low temperature ($T$) with black holes whose extremal geometry is AdS$_2\times$R$^2$. The breakdown is identified by the equilibration scales ($\omega_{\text{eq}}, k_{\text{eq}}$) defined as the collision point between the diffusive hydrodynamic mode and the longest-lived non-hydrodynamic mode. We show ($\omega_{\text{eq}}, k_{\text{eq}}$) at low $T$ is determined by the diffusion constant $D$ and the scaling dimension $\Delta(0)$ of an infra-red operator: $\omega_{\text{eq}} = 2\pi T \Delta(0), \, k_{\text{eq}}^2 = \omega_{\text{eq}}/D$, where $\Delta(0)=1$ in the presence of magnetic fields. For the purpose of comparison, we have analytically shown $\Delta(0)=2$ for the axion model independent of the translational symmetry breaking pattern (explicit or spontaneous), which is complementary to previous numerical results. Our results support the conjectured universal upper bound of the energy diffusion $D \,\le\, \omega_{\text{eq}}/k_{\text{eq}}^2 \,:=\, v_{\text{eq}}^2 \, \tau_{\text{eq}}$ where $v_{\text{eq}}:= \omega_{\text{eq}}/k_{\text{eq}}$ and $\tau_{\text{eq}}:=\omega_{\text{eq}}^{-1}$ are the velocity and the timescale associated to equilibration, implying that the breakdown of hydrodynamics sets the upper bound of the diffusion constant $D$ at low $T$., Comment: v1:26 pages, 17 figures. arXiv admin note: text overlap with arXiv:2104.13084; v2: minor edits, references added

We investigate the properties of pole-skipping of the sound channel in which the translational symmetry is broken explicitly or spontaneously. For this purpose, we analyze, in detail, not only the holographic axion model, but also the magnetically charged black holes with two methods: the near-horizon analysis and quasi-normal mode computations. We find that the pole-skipping points are related with the chaotic properties, Lyapunov exponent ($\lambda_L$) and butterfly velocity ($v_B$), independently of the symmetry breaking patterns. We show that the diffusion constant ($D$) is bounded by $D \,\geqslant\, v_{B}^2/\lambda_{L}$, where $D$ is the energy diffusion (crystal diffusion) bound for explicit (spontaneous) symmetry breaking. We confirm that the lower bound is obtained by the pole-skipping analysis in the low temperature limit., Comment: v1: 34 pages, 23 figures; v2: 35 pages, minor edits, references added

We study topological modes in relativistic hydrodynamics by weakly breaking the conservation of energy momentum tensor. Several systems have been found to have topologically nontrivial crossing nodes in the spectrum of hydrodynamic modes and some of them are only topologically nontrivial with the protection of reflection symmetries in two directions. The nontrivial topology for all these systems is further confirmed from a calculation of the topological invariant. Associated transport properties and second order effects have also been studied for these systems. The non-conservation terms of the energy momentum tensor could come from an external effective symmetric tensor matter field or a gravitational field which could be generated by a specific non-inertial reference frame transformation from the original inertial reference frame. Finally we introduce a possible holographic realization of one of these systems. We propose a new method to calculate the holographic Ward identities for the energy momentum tensor without calculating out all components of the Green functions and match the Ward identities of both sides., Comment: 53 pages, 19 figures; v3: matches the published version

We show that gapless modes in relativistic hydrodynamics could become topologically nontrivial by weakly breaking the conservation of energy momentum tensor in a specific way. This system has topological semimetal-like crossing nodes in the spectrum of hydrodynamic modes that require the protection of a special combination of translational and boost symmetries in two spatial directions. We confirm the nontrivial topology from the existence of an undetermined Berry phase. These energy momentum non-conservation terms could naturally be produced by an external gravitational field that comes from a reference frame change from the original inertial frame, i.e. by fictitious forces in a non-inertial reference frame. This non-inertial frame is the rest frame of an accelerating observer moving along a trajectory of a helix. This suggests that topologically trivial modes could become nontrivial by being observed in a special non-inertial reference frame, and this fact could be verified in laboratories, in principle. Finally, we propose a holographic realization of this system., Comment: 8 pages, 2 figures; v2: published version

The holographic duality allows to construct and study models of strongly coupled quantum matter via dual gravitational theories. In general such models are characterized by the absence of quasiparticles, hydrodynamic behavior and Planckian dissipation times. One particular interesting class of quantum materials are ungapped topological semimetals which have many interesting properties from Hall transport to topologically protected edge states. We review the application of the holographic duality to this type of quantum matter including the construction of holographic Weyl semimetals, nodal line semimetals, quantum phase transition to trivial states (ungapped and gapped), the holographic dual of Fermi arcs and how new unexpected transport properties, such as Hall viscosities arise. The holographic models promise to lead to new insights into the properties of this type of quantum matter., Comment: Review, 53 pages, 20 figures

Due to the enormous requirement in public security and intelligent transportation system, searching an identical vehicle has become more and more important. Current studies usually treat vehicle as an integral object and then train a distance metric to measure the similarity among vehicles. However, these raw images may be exactly similar to ones with different identification and include some pixels in background that may disturb the distance metric learning. In this paper, we propose a novel and useful method to segment an original vehicle image into several discriminative foreground parts, and these parts consist of some fine grained regions that are named discriminative patches. After that, these parts combined with the raw image are fed into the proposed deep learning network. We can easily measure the similarity of two vehicle images by computing the Euclidean distance of the features from FC layer. Two main contributions of this paper are as follows. Firstly, a method is proposed to estimate if a patch in a raw vehicle image is discriminative or not. Secondly, a new Part-based Multi-Stream Model (PMSM) is designed and optimized for vehicle retrieval and re-identification tasks. We evaluate the proposed method on the VehicleID dataset, and the experimental results show that our method can outperform the baseline., Comment: Published in International Conference on Pattern Recognition 2018