Frustrated quantum magnets are expected to host many exotic quantum spin states like quantum spin liquid (QSL), and have attracted numerous interest in modern condensed matter physics. The discovery of the triangular lattice spin liquid candidate YbMgGaO4 stimulated an increasing attention on the rare-earth-based frustrated magnets with strong spin-orbit coupling. Here we report the synthesis and characterization of a large family of rare-earth chalcogenides AReCh2 (A = alkali or monovalent ions, Re = rare earth, Ch = O, S, Se). The family compounds share the same structure (R3m) as YbMgGaO4, and antiferromagnetically coupled rare-earth ions form perfect triangular layers that are well separated along the c-axis. Specific heat and magnetic susceptibility measurements on NaYbO2, NaYbS2 and NaYbSe2 single crystals and polycrystals, reveal no structural or magnetic transition down to 50mK. The family, having the simplest structure and chemical formula among the known QSL candidates, removes the issue on possible exchange disorders in YbMgGaO4. More excitingly, the rich diversity of the family members allows tunable charge gaps, variable exchange coupling, and many other advantages. This makes the family an ideal platform for fundamental research of QSLs and its promising applications.PACS numbers: 75.10. Kt, 75.30.Et, 75.30.Gw Introduction.-The concept of quantum spin liquids (QSLs) was originally proposed by P. W. Anderson theoretically over 40 years ago [1]. It describes a highly entangled quantum state for spin degrees of freedom and was initially constructed with a superposition of spin singlets on the triangular antiferromagnet, so-called resonatingvalence-bond state [1]. Later on, the possible connection between QSLs and high-temperature superconductivity was theoretically established through doping a QSL Mott insulator [2]. Although the underlying mechanism for the high-temperature superconductivity has not yet come into a consensus, our understanding of QSLs has greatly improved, both from exactly solvable models [3,4] and several classification schemes [4,5]. On the experimental side, various frustrated magnetic materials, particularly the triangular-lattice-based antiferromagnets, were considered to be the most promising systems to realize QSLs [6]. So far, a number of compounds have been reported to host QSLs. Among them, the well-known ones include herbertsmithite and its derived compounds [7][8][9][10][11][12][13][14], and triangular organics [15][16][17][18][19]. The magnetic ions in most of these compounds are 3d transition metal ions Cu 2+ with S = 1/2, which may be crucial to enhance quantum fluctuations.Quite recently, frustrated materials with magnetic rare-earth ions are proposed to be promising QSL candidates [20]. These include the well-known pyrochlore ice materials [21][22][23][24][25][26][27][28][29][30], the kagome magnet [31,32], and the triangular lattice magnets [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]. The local degree

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Clustering is a long-standing important research problem, however, remains challenging when handling large-scale image data from diverse sources. In this paper, we present a novel Binary Multi-View Clustering (BMVC) framework, which can dexterously manipulate multi-view image data and easily scale to large data. To achieve this goal, we formulate BMVC by two key components: compact collaborative discrete representation learning and binary clustering structure learning, in a joint learning framework. Specifically, BMVC collaboratively encodes the multi-view image descriptors into a compact common binary code space by considering their complementary information; the collaborative binary representations are meanwhile clustered by a binary matrix factorization model, such that the cluster structures are optimized in the Hamming space by pure, extremely fast bit-operations. For efficiency, the code balance constraints are imposed on both binary data representations and cluster centroids. Finally, the resulting optimization problem is solved by an alternating optimization scheme with guaranteed fast convergence. Extensive experiments on four large-scale multi-view image datasets demonstrate that the proposed method enjoys the significant reduction in both computation and memory footprint, while observing superior (in most cases) or very competitive performance, in comparison with state-of-the-art clustering methods.

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This paper presents a weighted optimization framework that unifies the binary, multivalued, and continuous treatment—as well as mixture of discrete and continuous treatment—under a unconfounded treatment assignment. With a general loss function, the framework includes the average, quantile, and asymmetric least squares causal effect of treatment as special cases. For this general framework, we first derive the semiparametric efficiency bound for the causal effect of treatment, extending the existing bound results to a wider class of models. We then propose a generalized optimization estimator for the causal effect with weights estimated by solving an expanding set of equations. Under some sufficient conditions, we establish the consistency and asymptotic normality of the proposed estimator of the causal effect and show that the estimator attains the semiparametric efficiency bound, thereby extending the existing literature on efficient estimation of causal effect to a wider class of applications. Finally, we discuss estimation of some causal effect functionals such as the treatment effect curve and the average outcome. To evaluate the finite sample performance of the proposed procedure, we conduct a small‐scale simulation study and find that the proposed estimation has practical value. In an empirical application, we detect a significant causal effect of political advertisements on campaign contributions in the binary treatment model, but not in the continuous treatment model.

Abstract-In this paper, we aim at learning compact and discriminative linear regression models. Linear regression has been widely used in different problems. However, most of the existing linear regression methods exploit the conventional zeroone matrix as the regression targets, which greatly narrows the flexibility of the regression model. Another major limitation of theses methods is that the learned projection matrix fails to precisely project the image features to the target space due to their weak discriminative capability. To this end, we present an elastic-net regularized linear regression (ENLR) framework, and develop two robust linear regression models which possess the following special characteristics. First, our methods exploit two particular strategies to enlarge the margins of different classes by relaxing the strict binary targets into a more feasible variable matrix. Second, a robust elastic-net regularization of singular values is introduced to enhance the compactness and effectiveness of the learned projection matrix. Third, the resulting optimization problem of ENLR has a closed-form solution in each iteration, which can be solved efficiently. Finally, rather than directly exploiting the projection matrix for recognition, our methods employ the transformed features as the new discriminate representations to make final image classification. Compared with the traditional linear regression model and some of its variants, our method is much more accurate in image classification. Extensive experiments conducted on publicly available datasets well demonstrate that the proposed framework can outperform the state-of-the-art methods. The MATLAB codes of our methods can be available at http://www.yongxu.org/lunwen.html.

We develop an algorithm that decomposes a long alignment into sub-alignments that avoid these potential imperfections. Our algorithm runs in time proportional to the original alignment's length. Practical applications to alignments of genomic DNA sequences are described.