Topological crystalline superconductors are known to have possible higher-order topology, which results in Majorana modes on $d-2$ or lower dimensional boundaries. Given the rich possibilities of boundary signatures, it is desirable to have topologic
al invariants that can predict the type of Majorana modes from band structures. Although symmetry indicators, a type of invariants that depends only on the band data at high-symmetry points, have been proposed for certain crystalline superconductors, there exist symmetry classes in which symmetry indicators fail to distinguish superconductors with different Majorana boundaries. Here, we systematically obtain topological invariants for an example of this kind, the two-dimensional time-reversal symmetric superconductors with two-fold rotational symmetry $C_2$. First, we show that the non-trivial topology is independent of band data on the high-symmetry points by conducting a momentum-space classification study. Then from the resulting K groups, we derive calculable expressions for four $mathbb{Z}_2$ invariants defined on the high-symmetry lines or general points in the Brillouin zone. Finally, together with a real-space classification study, we establish the bulk-boundary correspondence and show that the four $mathbb{Z}_2$ invariants can predict Majorana boundary types from band structures. Our proposed invariants can fuel practical material searches for $C_2$-symmetric topological superconductors featuring Majorana edge and corner modes.
Correlated data are ubiquitous in todays data-driven society. A fundamental task in analyzing these data is to understand, characterize and utilize the correlations in them in order to conduct valid inference. Yet explicit regression analysis of corr
elations has been so far limited to longitudinal data, a special form of correlated data, while implicit analysis via mixed-effects models lacks generality as a full inferential tool. This paper proposes a novel regression approach for modelling the correlation structure, leveraging a new generalized z-transformation. This transformation maps correlation matrices that are constrained to be positive definite to vectors with un-restricted support, and is order-invariant. Building on these two properties, we develop a regression model to relate the transformed parameters to any covariates. We show that coupled with a mean and a variance regression model, the use of maximum likelihood leads to asymptotically normal parameter estimates, and crucially enables statistical inference for all the parameters. The performance of our framework is demonstrated in extensive simulation. More importantly, we illustrate the use of our model with the analysis of the classroom data, a highly unbalanced multilevel clustered data with within-class and within-school correlations, and the analysis of the malaria immune response data in Benin, a longitudinal data with time-dependent covariates in addition to time. Our analyses reveal new insights not previously known.
Reproducible benchmarks are crucial in driving progress of machine translation research. However, existing machine translation benchmarks have been mostly limited to high-resource or well-represented languages. Despite an increasing interest in low-r
esource machine translation, there are no standardized reproducible benchmarks for many African languages, many of which are used by millions of speakers but have less digitized textual data. To tackle these challenges, we propose AfroMT, a standardized, clean, and reproducible machine translation benchmark for eight widely spoken African languages. We also develop a suite of analysis tools for system diagnosis taking into account the unique properties of these languages. Furthermore, we explore the newly considered case of low-resource focused pretraining and develop two novel data augmentation-based strategies, leveraging word-level alignment information and pseudo-monolingual data for pretraining multilingual sequence-to-sequence models. We demonstrate significant improvements when pretraining on 11 languages, with gains of up to 2 BLEU points over strong baselines. We also show gains of up to 12 BLEU points over cross-lingual transfer baselines in data-constrained scenarios. All code and pretrained models will be released as further steps towards larger reproducible benchmarks for African languages.
Recently, face recognition in the wild has achieved remarkable success and one key engine is the increasing size of training data. For example, the largest face dataset, WebFace42M contains about 2 million identities and 42 million faces. However, a
massive number of faces raise the constraints in training time, computing resources, and memory cost. The current research on this problem mainly focuses on designing an efficient Fully-connected layer (FC) to reduce GPU memory consumption caused by a large number of identities. In this work, we relax these constraints by resolving the redundancy problem of the up-to-date face datasets caused by the greedily collecting operation (i.e. the core-set selection perspective). As the first attempt in this perspective on the face recognition problem, we find that existing methods are limited in both performance and efficiency. For superior cost-efficiency, we contribute a novel filtering strategy dubbed Face-NMS. Face-NMS works on feature space and simultaneously considers the local and global sparsity in generating core sets. In practice, Face-NMS is analogous to Non-Maximum Suppression (NMS) in the object detection community. It ranks the faces by their potential contribution to the overall sparsity and filters out the superfluous face in the pairs with high similarity for local sparsity. With respect to the efficiency aspect, Face-NMS accelerates the whole pipeline by applying a smaller but sufficient proxy dataset in training the proxy model. As a result, with Face-NMS, we successfully scale down the WebFace42M dataset to 60% while retaining its performance on the main benchmarks, offering a 40% resource-saving and 1.64 times acceleration. The code is publicly available for reference at https://github.com/HuangJunJie2017/Face-NMS.
Signed networks are such social networks having both positive and negative links. A lot of theories and algorithms have been developed to model such networks (e.g., balance theory). However, previous work mainly focuses on the unipartite signed netwo
rks where the nodes have the same type. Signed bipartite networks are different from classical signed networks, which contain two different node sets and signed links between two node sets. Signed bipartite networks can be commonly found in many fields including business, politics, and academics, but have been less studied. In this work, we firstly define the signed relationship of the same set of nodes and provide a new perspective for analyzing signed bipartite networks. Then we do some comprehensive analysis of balance theory from two perspectives on several real-world datasets. Specifically, in the peer review dataset, we find that the ratio of balanced isomorphism in signed bipartite networks increased after rebuttal phases. Guided by these two perspectives, we propose a novel Signed Bipartite Graph Neural Networks (SBGNNs) to learn node embeddings for signed bipartite networks. SBGNNs follow most GNNs message-passing scheme, but we design new message functions, aggregation functions, and update functions for signed bipartite networks. We validate the effectiveness of our model on four real-world datasets on Link Sign Prediction task, which is the main machine learning task for signed networks. Experimental results show that our SBGNN model achieves significant improvement compared with strong baseline methods, including feature-based methods and network embedding methods.
Relations between entities can be represented by different instances, e.g., a sentence containing both entities or a fact in a Knowledge Graph (KG). However, these instances may not well capture the general relations between entities, may be difficul
t to understand by humans, even may not be found due to the incompleteness of the knowledge source. In this paper, we introduce the Open Relation Modeling task - given two entities, generate a coherent sentence describing the relation between them. To solve this task, we propose to teach machines to generate definition-like relation descriptions by letting them learn from definitions of entities. Specifically, we fine-tune Pre-trained Language Models (PLMs) to produce definitions conditioned on extracted entity pairs. To help PLMs reason between entities and provide additional relational knowledge to PLMs for open relation modeling, we incorporate reasoning paths in KGs and include a reasoning path selection mechanism. We show that PLMs can select interpretable and informative reasoning paths by confidence estimation, and the selected path can guide PLMs to generate better relation descriptions. Experimental results show that our model can generate concise but informative relation descriptions that capture the representative characteristics of entities and relations.
Terahertz (THz) communication is now being considered as one of possible technologies for the sixth generation (6G) wireless communication systems. In this paper, a novel three-dimensional (3D) space-time-frequency non-stationary theoretical channel
model is first proposed for 6G THz wireless communication systems employing ultra-massive multiple-input multiple-output (MIMO) technologies with long traveling paths. Considering frequency-dependent diffuse scattering, which is a special property of THz channels different from millimeter wave (mmWave) channels, the relative angles and delays of rays within one cluster will evolve in the frequency domain. Then, a corresponding simulation model is proposed with discrete angles calculated using the method of equal area (MEA). The statistical properties of the proposed theoretical and simulation models are derived and compared, showing good agreements. The accuracy and flexibility of the proposed simulation model are demonstrated by comparing the simulation results of the relative angle spread and root mean square (RMS) delay spread with corresponding measurements.
We study the cross-sectional returns of the firms connected by news articles. A conservative algorithm is proposed to tackle the type-I error in identifying firm tickers and the well-defined directed news networks of S&P500 stocks are formed based on
a modest assumption. After controlling for many other effects, we find strong evidence for the comovement effect between news-linked firms stock returns and reversal effect from lead stock return on 1-day ahead follower stock return, however, returns of lead stocks provide only marginal predictability on follower stock returns. Furthermore, both econometric and portfolio test reveals that network degree provides robust and significant cross-sectional predictability on monthly stock returns, and the type of linkages also matters for portfolio construction.
Warm ionized and cold neutral outflows with velocities exceeding $100,{rm km,s}^{-1}$ are commonly observed in galaxies and clusters. Theoretical studies however indicate that ram pressure from a hot wind, driven either by the central active galactic
nucleus (AGN) or a starburst, cannot accelerate existing cold gas to such high speeds without destroying it. In this work we explore a different scenario, where cold gas forms in a fast, radiatively cooling outflow with temperature $Tlesssim 10^7,{rm K}$. Using 3D hydrodynamic simulations, we demonstrate that cold gas continuously fragments out of the cooling outflow, forming elongated filamentary structures extending tens of kiloparsecs. For a range of physically relevant temperature and velocity configurations, a ring of cold gas perpendicular to the direction of motion forms in the outflow. This naturally explains the formation of transverse cold gas filaments such as the blue loop and the horseshoe filament in the Perseus cluster. Based on our results, we estimate that the AGN outburst responsible for the formation of these two features drove bipolar outflows with velocity $>2,000,{rm km,s}^{-1}$ and total kinetic energy $>8times10^{57},{rm erg}$ about $sim10$ Myr ago. We also examine the continuous cooling in the mixing layer between hot and cold gas, and find that radiative cooling only accounts for $sim10%$ of the total mass cooling rate, indicating that observations of soft X-ray and FUV emission may significantly underestimate the growth of cold gas in the cooling flow of galaxy clusters.
In this paper, we consider a distributed learning problem in a subnetwork zero-sum game, where agents are competing in different subnetworks. These agents are connected through time-varying graphs where each agent has its own cost function and can re
ceive information from its neighbors. We propose a distributed mirror descent algorithm for computing a Nash equilibrium and establish a sublinear regret bound on the sequence of iterates when the graphs are uniformly strongly connected and the cost functions are convex-concave. Moreover, we prove its convergence with suitably selected diminishing stepsizes for a strictly convex-concave cost function. We also consider a constant step-size variant of the algorithm and establish an asymptotic error bound between the cost function values of running average actions and a Nash equilibrium. In addition, we apply the algorithm to compute a mixed-strategy Nash equilibrium in subnetwork zero-sum finite-strategy games, which have merely convex-concave (to be specific, multilinear) cost functions, and obtain a final-iteration convergence result and an ergodic convergence result, respectively, under different assumptions.
