Holographic complexity of the disk subregion in (2+1)-dimensional gapped systems

Using the volume of the space enclosed by the Ryu-Takayanagi (RT) surface, we study the complexity of the disk-shape subregion (with radius R) in various (2+1)-dimensional gapped systems with gravity dual. These systems include a class of toy models with singular IR and the bottom-up models for quantum chromodynamics and fractional quantum Hall effects. Two main results are: i) in the large-R expansion of the complexity, the R-linear term is always absent, similar to the absence of topological entanglement entropy; ii) when the entanglement entropy exhibits the classic `swallowtail' phase transition, the complexity is sensitive but reacts differently.Comment: 30 pages, 7 figures, revised version accepted for publication in PR

Minimal Gated Unit for Recurrent Neural Networks

Recently recurrent neural networks (RNN) has been very successful in handling sequence data. However, understanding RNN and finding the best practices for RNN is a difficult task, partly because there are many competing and complex hidden units (such as LSTM and GRU). We propose a gated unit for RNN, named as Minimal Gated Unit (MGU), since it only contains one gate, which is a minimal design among all gated hidden units. The design of MGU benefits from evaluation results on LSTM and GRU in the literature. Experiments on various sequence data show that MGU has comparable accuracy with GRU, but has a simpler structure, fewer parameters, and faster training. Hence, MGU is suitable in RNN's applications. Its simple architecture also means that it is easier to evaluate and tune, and in principle it is easier to study MGU's properties theoretically and empirically

A Memory-Network Based Solution for Multivariate Time-Series Forecasting

Multivariate time series forecasting is extensively studied throughout the years with ubiquitous applications in areas such as finance, traffic, environment, etc. Still, concerns have been raised on traditional methods for incapable of modeling complex patterns or dependencies lying in real word data. To address such concerns, various deep learning models, mainly Recurrent Neural Network (RNN) based methods, are proposed. Nevertheless, capturing extremely long-term patterns while effectively incorporating information from other variables remains a challenge for time-series forecasting. Furthermore, lack-of-explainability remains one serious drawback for deep neural network models. Inspired by Memory Network proposed for solving the question-answering task, we propose a deep learning based model named Memory Time-series network (MTNet) for time series forecasting. MTNet consists of a large memory component, three separate encoders, and an autoregressive component to train jointly. Additionally, the attention mechanism designed enable MTNet to be highly interpretable. We can easily tell which part of the historic data is referenced the most.Comment: 8 pages, 4 figures, submitted to AAAI 2019. arXiv admin note: text overlap with arXiv:1703.07015 by other author

A Regulation Enforcement Solution for Multi-agent Reinforcement Learning

Human behaviors are regularized by a variety of norms or regulations, either to maintain orders or to enhance social welfare. If artificially intelligent (AI) agents make decisions on behalf of human beings, we would hope they can also follow established regulations while interacting with humans or other AI agents. However, it is possible that an AI agent can opt to disobey the regulations (being defective) for self-interests. In this paper, we aim to answer the following question: Consider a multi-agent decentralized environment. Agents make decisions in complete isolation of other agents. Each agent knows the state of its own MDP and its own actions but it does not know the states and the actions taken by other players. There is a set of regulations for all agents to follow. Although most agents are benign and will comply to regulations but not all agents are compliant at first, can we develop a framework such that it is in the self-interest of non-compliant agents to comply after all?. We first introduce the problem as Regulation Enforcement and formulate it using reinforcement learning and game theory under the scenario where agents make decisions in complete isolation of other agents. We then propose a solution based on the key idea that although we could not alter how defective agents choose to behave, we can, however, leverage the aggregated power of compliant agents to boycott the defective ones. We conducted simulated experiments on two scenarios: Replenishing Resource Management Dilemma and Diminishing Reward Shaping Enforcement, using deep multi-agent reinforcement learning algorithms. We further use empirical game-theoretic analysis to show that the method alters the resulting empirical payoff matrices in a way that promotes compliance (making mutual compliant a Nash Equilibrium)

Dual Gabriel Theorem with applications

We introduce the quiver of a bicomodule over a cosemisimple coalgebra. Applying this to the coradical $C_0$ of an arbitrary coalgebra $C$, we give an alternative definition of the Gabriel quiver of $C$, and then show that it coincides with the known $\operatorname {Ext}$ quiver of $C$ and the link quiver of $C$. The dual Gabriel theorem for a coalgebra with separable coradical is obtained, which generalizes the corresponding result for a pointed coalgebra. We also give a new description of $C_1$ of any coalgebra $C$, which can be regarded as a generalization of the first part of the well-known Taft-Wilson Theorem for pointed coalgebras. As applications, we give a characterization of locally finite coalgebras via their Gabriel quivers, and a property of the Gabriel quiver of a quasi-coFrobenius coalgebra.Comment: 23 page

Geometric, magnetic and electronic properties of folded graphene nanoribbons

Geometric and electronic properties of folded graphene nanoribbons (FGNRs) are investigated by first-principles calculations. These properties are mainly dominated by the competition or cooperation among stacking, curvature and edge effects. For the zigzag FGNRs, the more stable structures are revealed to be AB stackings, while for the armchair types, AA" stackings are more stable. The interlayer interactions and hybridization of four orbitals lead to smaller energy gaps, anti-crossing bands, and more band-edge states. Specifically, the broken mirror symmetry in the odd-AB stacked zigzag FGNRs is responsible for the spin-up and spin-down splitting subbands. All FGNRs are direct-gap semiconductors except that the edge-edge interactions cause the even-AA stacked zigzag FGNRs to exhibit a pair of metallic linear bands. The width-dependent energy gaps in the armchair FGNRs can be classified into six groups. Furthermore, there exist rich features in density of states, including the form, number, intensity and energy of the special structures

The Domination Number of Generalized Petersen Graphs with a Faulty Vertex

In this paper, we investigate the domination number of generalized Petersen graphs P(n, 2) when there is a faulty vertex. Denote by $\gamma(P(n,2))$ the domination number of P(n,2) and $\gamma(P_f(n,2))$ the domination number of P(n,2) with a faulty vertex $u_f$. We show that $\gamma(P_f(n,2))=\gamma(P(n,2))-1$ when $n=5k+1$ or $5k+2$ and $\gamma(P_f(n,2))=\gamma(P(n,2))$ for the other cases.Comment: 14 pages,9 figure

Nematic Metal and Antiferromagnetic Insulator on Hexagonal Kagome Lattice

Hexagonal Kagome lattice is a multiband system with a quadratic band crossing point, in contrast with honeycomb lattice with linear band crossing point, which has exotic correlated effect and can produce various novel quantum states. Here we investigate the phase diagram of the fermions on the hexagonal Kagome lattice as a function of interaction, temperature and lattice anisotropy, by combining the cellular dynamical mean-field theory with the continuous time quantum Monte Carlo method. For weak interaction, the quadratic band-crossing point is broken to linear band crossing point and the system is the semi-metal. With the increasing of the interaction, the system goes a first order transition to antiferromagnetic Mott insulator at low temperature. Below a critical temperature, due to the charge nematic fluctuation, a nematic metal forms between the weak coupling semi-metal and strong correlated Mott insulator. When the lattice anisotropy increases, the region of the nematic metal is enlarged. Furthermore, we discuss how to detect these phases in real experiments

Unsupervised Object Discovery and Co-Localization by Deep Descriptor Transforming

Reusable model design becomes desirable with the rapid expansion of computer vision and machine learning applications. In this paper, we focus on the reusability of pre-trained deep convolutional models. Specifically, different from treating pre-trained models as feature extractors, we reveal more treasures beneath convolutional layers, i.e., the convolutional activations could act as a detector for the common object in the image co-localization problem. We propose a simple yet effective method, termed Deep Descriptor Transforming (DDT), for evaluating the correlations of descriptors and then obtaining the category-consistent regions, which can accurately locate the common object in a set of unlabeled images, i.e., unsupervised object discovery. Empirical studies validate the effectiveness of the proposed DDT method. On benchmark image co-localization datasets, DDT consistently outperforms existing state-of-the-art methods by a large margin. Moreover, DDT also demonstrates good generalization ability for unseen categories and robustness for dealing with noisy data. Beyond those, DDT can be also employed for harvesting web images into valid external data sources for improving performance of both image recognition and object detection.Comment: This paper is extended based on our preliminary work published in IJCAI 2017 [arXiv:1705.02758

ANS: Adaptive Network Scaling for Deep Rectifier Reinforcement Learning Models

This work provides a thorough study on how reward scaling can affect performance of deep reinforcement learning agents. In particular, we would like to answer the question that how does reward scaling affect non-saturating ReLU networks in RL? This question matters because ReLU is one of the most effective activation functions for deep learning models. We also propose an Adaptive Network Scaling framework to find a suitable scale of the rewards during learning for better performance. We conducted empirical studies to justify the solution