arXiv subjects
Publications and source records attributed to Yao Ma.
In this paper, we mainly study structure of multiplicative simple Hom-Jordan algebras. We talk about equivalent conditions for multiplicative Hom-Jordan algebras being solvable, simple and semi-simple. As an application, we give a theorem about classification of multiplicative simple Hom-Jordan algebras. Moreover, some propositions about bimodules of multiplicative Hom-Jordan algebras are also displayed.
We give a pedagogical analysis on $K$ matrix models describing the $πN$ scattering amplitude, in $S_{11}$ channel at low energies. We show how the correct use of analyticity in the $s$ channel and crossing symmetry in $t$ and $u$ channels leads to a much improved analytic behavior in the negative $s$ region, in agreement with the prediction from chiral perturbation amplitudes in its validity region. The analysis leads again to the conclusion that a genuine $N^*(890)$ resonance exists.
In this paper, we give some construction about ternary Jordan algebras at first. Next we study relationships between generalized derivations, quasiderivations and centroids of ternary Jordan algebras. We show that for ternary Jordan algebras, generalized derivation algebras are the sum of quasiderivation algebras and centroids where centroids are ideals of generalized derivation algebras. We also prove that quasiderivations can be embedded into larger ternary Jordan algebras as derivations. In particular, we also determine dimensions of ternary Jordan algebras in the case of all linear transformations are quasiderivations. Some properties about centroids of ternary Jordan algebras are also displayed.
We present a phenomenological Green's function to characterize the superconducting and pseudogap phases of the cuprates based on a microscopic theory of doped Mott insulators. In this framework, the "Fermi arc" and "kink" phenomena observed by angle-resolved photoemission spectroscopy (ARPES) experiments in the pseudogap phase can be systematically explained as a function of doping, which is further connected to the two-gap feature in the superconducting phase with dichotomy between the nodal and antinodal physics. We demonstrate that a phase-string-induced fractionalization plays the key role in giving rise to such a peculiar Green's function with a unique two-component structure.
In recent years, Graph Neural Networks (GNNs), which can naturally integrate node information and topological structure, have been demonstrated to be powerful in learning on graph data. These advantages of GNNs provide great potential to advance social recommendation since data in social recommender systems can be represented as user-user social graph and user-item graph; and learning latent factors of users and items is the key. However, building social recommender systems based on GNNs faces challenges. For example, the user-item graph encodes both interactions and their associated opinions; social relations have heterogeneous strengths; users involve in two graphs (e.g., the user-user social graph and the user-item graph). To address the three aforementioned challenges simultaneously, in this paper, we present a novel graph neural network framework (GraphRec) for social recommendations. In particular, we provide a principled approach to jointly capture interactions and opinions in the user-item graph and propose the framework GraphRec, which coherently models two graphs and heterogeneous strengths. Extensive experiments on two real-world datasets demonstrate the effectiveness of the proposed framework GraphRec. Our code is available at \url{https://github.com/wenqifan03/GraphRec-WWW19}
For any hard QCD amplitude with massless partons, infrared (IR) singularities arise from pinches in the complex planes of loop momenta, called pinch surfaces. To organize and study their leading behaviors in the neighborhoods of these surfaces, we can construct approximation operators for collinear and soft singularities. A BPHZ-like forest formula can be developed to subtract them systematically. In this paper, we utilize the position-space analysis of Erdogan and Sterman for Green functions, and develop the formalism for momentum space. A related analysis has been carried out by Collins for the Sudakov form factors, and is generalized here to any wide-angle kinematics with an arbitrary number of external momenta. We will first see that the approximations yield much richer IR structures than those of an original amplitude, then construct the forest formula and prove that all the singularities appearing in its subtraction terms cancel pairwise. With the help of the forest formula, the full amplitude can also be reorganized into a factorized expression, which helps to generalize the Sudakov form factor result to arbitrary numbers of external momenta. All our analysis will be on the amplitude level.
Deep neural networks (DNN) have achieved unprecedented success in numerous machine learning tasks in various domains. However, the existence of adversarial examples has raised concerns about applying deep learning to safety-critical applications. As a result, we have witnessed increasing interests in studying attack and defense mechanisms for DNN models on different data types, such as images, graphs and text. Thus, it is necessary to provide a systematic and comprehensive overview of the main threats of attacks and the success of corresponding countermeasures. In this survey, we review the state of the art algorithms for generating adversarial examples and the countermeasures against adversarial examples, for the three popular data types, i.e., images, graphs and text.
Graph Neural Networks (GNNs) have boosted the performance of many graph related tasks such as node classification and graph classification. Recent researches show that graph neural networks are vulnerable to adversarial attacks, which deliberately add carefully created unnoticeable perturbation to the graph structure. The perturbation is usually created by adding/deleting a few edges, which might be noticeable even when the number of edges modified is small. In this paper, we propose a graph rewiring operation which affects the graph in a less noticeable way compared to adding/deleting edges. We then use reinforcement learning to learn the attack strategy based on the proposed rewiring operation. Experiments on real world graphs demonstrate the effectiveness of the proposed framework. To understand the proposed framework, we further analyze how its generated perturbation to the graph structure affects the output of the target model.
Recommender systems are crucial to alleviate the information overload problem in online worlds. Most of the modern recommender systems capture users' preference towards items via their interactions based on collaborative filtering techniques. In addition to the user-item interactions, social networks can also provide useful information to understand users' preference as suggested by the social theories such as homophily and influence. Recently, deep neural networks have been utilized for social recommendations, which facilitate both the user-item interactions and the social network information. However, most of these models cannot take full advantage of the social network information. They only use information from direct neighbors, but distant neighbors can also provide helpful information. Meanwhile, most of these models treat neighbors' information equally without considering the specific recommendations. However, for a specific recommendation case, the information relevant to the specific item would be helpful. Besides, most of these models do not explicitly capture the neighbor's opinions to items for social recommendations, while different opinions could affect the user differently. In this paper, to address the aforementioned challenges, we propose DSCF, a Deep Social Collaborative Filtering framework, which can exploit the social relations with various aspects for recommender systems. Comprehensive experiments on two-real world datasets show the effectiveness of the proposed framework.
Recurrent Neural Networks have long been the dominating choice for sequence modeling. However, it severely suffers from two issues: impotent in capturing very long-term dependencies and unable to parallelize the sequential computation procedure. Therefore, many non-recurrent sequence models that are built on convolution and attention operations have been proposed recently. Notably, models with multi-head attention such as Transformer have demonstrated extreme effectiveness in capturing long-term dependencies in a variety of sequence modeling tasks. Despite their success, however, these models lack necessary components to model local structures in sequences and heavily rely on position embeddings that have limited effects and require a considerable amount of design efforts. In this paper, we propose the R-Transformer which enjoys the advantages of both RNNs and the multi-head attention mechanism while avoids their respective drawbacks. The proposed model can effectively capture both local structures and global long-term dependencies in sequences without any use of position embeddings. We evaluate R-Transformer through extensive experiments with data from a wide range of domains and the empirical results show that R-Transformer outperforms the state-of-the-art methods by a large margin in most of the tasks. We have made the code publicly available at \url{https://github.com/DSE-MSU/R-transformer}.
Recent years have witnessed rapid developments on social recommendation techniques for improving the performance of recommender systems due to the growing influence of social networks to our daily life. The majority of existing social recommendation methods unify user representation for the user-item interactions (item domain) and user-user connections (social domain). However, it may restrain user representation learning in each respective domain, since users behave and interact differently in the two domains, which makes their representations to be heterogeneous. In addition, most of traditional recommender systems can not efficiently optimize these objectives, since they utilize negative sampling technique which is unable to provide enough informative guidance towards the training during the optimization process. In this paper, to address the aforementioned challenges, we propose a novel deep adversarial social recommendation framework DASO. It adopts a bidirectional mapping method to transfer users' information between social domain and item domain using adversarial learning. Comprehensive experiments on two real-world datasets show the effectiveness of the proposed framework.
In this paper, we mainly study a class of biderivations and triple homomorphisms on perfect Jordan algebras. Let $J$ be a Jordan algebra and $δ:J \times J \rightarrow J$ a symmetric biderivation satisfying $δ(w , u \circ v) = w \cdot δ(u , v), \forall u,v,w \in J$. If $J$ is perfect and satisfies $Z(J) = \{0\}$, then $δ$ is of the form $δ(x , y) = γ(x \circ y)$ for all $x , y \in J$, where $γ\in Cent(J)$ satisfying $z \cdot γ(x \circ y) = x \cdot γ(y \circ z) + y \cdot γ(x \circ z), \forall x , y , z \in J$. This is the special case of our main theorem which concerns biderivations having their range in a $J$-module. What's more, we give an algorithm which can be applied to find biderivations satisfying $δ(w , u \circ v) = w \cdot δ(u , v), \forall u,v,w \in J$ on any Jordan algebra. We also show that for a triple homomorphism between perfect Jordan algebras, $f(x^{2}) = (f(x))^{2}$ or $f(x^{2}) = -(f(x))^{2}$. As an application, such $f$ is a homomorphism if and only if $f(x^{2}) = (f(x))^{2}$. Moreover, we give an algorithm which can be applied to any Jordan algebra.
In this paper, we give some properties of generalized derivation algebras of Hom-Jordan algebras. In particular, we show that $GDer(V) = QDer(V) + QC(V)$, the sum of the quasiderivation algebra and the quasicentroid. We also prove that $QDer(V)$ can be embedded as derivations into a larger Hom-Jordan algebra. General results on centroids of Hom-Jordan algebras are also developed in this paper.
In this paper, we mainly study the derivation algebras of semi-simple Jordan algebras over a field of characteristic $0$ and give sufficient and necessary conditions that the derivation algebras of them are simple. As an application, we prove that for a semi-simple Jordan algebra $J$, $TDer(Der(J)) = Der(Der(J)) = ad(Der(J))$ under some assumptions. Moreover, we also show that for a semi-simple Jordan algebra $J$ which has a finite basis over a field of characteristic $0$, $TDer(J) = Der(J) = Inn(J)$. This is a corollary about our theorem which concerns Jordan algebras with unit.
Graph neural networks, which generalize deep neural network models to graph structured data, have attracted increasing attention in recent years. They usually learn node representations by transforming, propagating and aggregating node features and have been proven to improve the performance of many graph related tasks such as node classification and link prediction. To apply graph neural networks for the graph classification task, approaches to generate the \textit{graph representation} from node representations are demanded. A common way is to globally combine the node representations. However, rich structural information is overlooked. Thus a hierarchical pooling procedure is desired to preserve the graph structure during the graph representation learning. There are some recent works on hierarchically learning graph representation analogous to the pooling step in conventional convolutional neural (CNN) networks. However, the local structural information is still largely neglected during the pooling process. In this paper, we introduce a pooling operator $\pooling$ based on graph Fourier transform, which can utilize the node features and local structures during the pooling process. We then design pooling layers based on the pooling operator, which are further combined with traditional GCN convolutional layers to form a graph neural network framework $\m$ for graph classification. Theoretical analysis is provided to understand $\pooling$ from both local and global perspectives. Experimental results of the graph classification task on $6$ commonly used benchmarks demonstrate the effectiveness of the proposed framework.
Quantum-enhanced parameter estimation has widespread applications in many fields. An important issue is to protect the estimation precision against the noise-induced decoherence. Here we develop a general theoretical framework for improving the precision for estimating an arbitrary parameter by monitoring the noise-induced quantum trajectorie (MQT) and establish its connections to the purification-based approach to quantum parameter estimation. MQT can be achieved in two ways: (i) Any quantum trajectories can be monitored by directly monitoring the environment, which is experimentally challenging for realistic noises; (ii) Certain quantum trajectories can also be monitored by frequently measuring the quantum probe alone via ancilla-assisted encoding and error detection. This establishes an interesting connection between MQT and the full quantum error correction protocol. Application of MQT to estimate the level splitting and decoherence rate of a spin-1/2 under typical decoherence channels demonstrate that it can avoid the long-time exponential loss of the estimation precision and, in special cases, recover the Heisenberg scaling.
The concept of derivation for Lie-Yamaguti algebras is generalized in this paper. A quasi-derivation of an LY-algebra is embedded as derivation in a larger LY-algebra. The relationship between quasi-derivations and robustness of Lie-Yamaguti algebras has been studied.
Graphs are essential representations of many real-world data such as social networks. Recent years have witnessed the increasing efforts made to extend the neural network models to graph-structured data. These methods, which are usually known as the graph neural networks, have been applied to advance many graphs related tasks such as reasoning dynamics of the physical system, graph classification, and node classification. Most of the existing graph neural network models have been designed for static graphs, while many real-world graphs are inherently dynamic. For example, social networks are naturally evolving as new users joining and new relations being created. Current graph neural network models cannot utilize the dynamic information in dynamic graphs. However, the dynamic information has been proven to enhance the performance of many graph analytic tasks such as community detection and link prediction. Hence, it is necessary to design dedicated graph neural networks for dynamic graphs. In this paper, we propose DGNN, a new {\bf D}ynamic {\bf G}raph {\bf N}eural {\bf N}etwork model, which can model the dynamic information as the graph evolving. In particular, the proposed framework can keep updating node information by capturing the sequential information of edges (interactions), the time intervals between edges and information propagation coherently. Experimental results on various dynamic graphs demonstrate the effectiveness of the proposed framework.