Topic
Dual representation
About: Dual representation is a research topic. Over the lifetime, 325 publications have been published within this topic receiving 4721 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: The theory of quasitriangular Hopf algebras and its connections with physics are reviewed in this paper. But the main focus of this paper is on the Yang-Baxter equations.
Abstract: This is an informal introduction to the theory of quasitriangular Hopf algebras and its connections with physics. Basic properties and applications of Hopf algebras and Yang-Baxter equations are reviewed, with the quantum group Uq(sl2) as a frequent example. The development builds up to the representation theory of quasitriangular Hopf algebras. Much of the abstract representation theory is new, including a formula for the rank of a representation.
482 citations
TL;DR: In this paper, the Bethe ansatz technique is applied for the calculation of the observables in the strong coupling region of the sine-Gordon model and the results are in the exact agreement with ones following from the sigma model action, which is a two-parameter U (1) ⊗ ( 1) symmetrical deformation of the O(4) non-finear sigma Model.
224 citations
Posted Content•
TL;DR: In this article, a sparse convex framework for solving Canonical Correlation Analysis (CCA) was proposed, which minimizes the number of features used in both the primal and dual projections while maximising the correlation between the two views.
Abstract: We present a novel method for solving Canonical Correlation Analysis (CCA) in a sparse convex framework using a least squares approach. The presented method focuses on the scenario when one is interested in (or limited to) a primal representation for the first view while having a dual representation for the second view. Sparse CCA (SCCA) minimises the number of features used in both the primal and dual projections while maximising the correlation between the two views. The method is demonstrated on two paired corpuses of English-French and English-Spanish for mate-retrieval. We are able to observe, in the mate-retreival, that when the number of the original features is large SCCA outperforms Kernel CCA (KCCA), learning the common semantic space from a sparse set of features.
216 citations
TL;DR: In this paper, the notion of O-operator is introduced for differential Lie algebras, where the standard definitions are shown to be deficient, and a definition suitable to differential (-difference) Lie algesbras is proposed, which has all the natural properties one would expect form it, but lacks those which are artifacts of finite-dimensional isomorpisms such as not true in differential generality relations.
Abstract: To my friend and colleague K.C. Reddy on occasion of his retirement. The notion of classical r-matrix is re-examined, and a definition suitable to differential (-difference) Lie algebras, – where the standard definitions are shown to be deficient, – is proposed, the notion of an O-operator. This notion has all the natural properties one would expect form it, but lacks those which are artifacts of finite-dimensional isomorpisms such as not true in differential generality relation End (V ) V ∗ ⊗ V for a vector space V . Examples considered include a quadratic Poisson bracket on the dual space to a Lie algebra; generalized symplectic-quadratic models of such brackets (aka Clebsch representations); and Drinfel’d’s 2-cocycle interpretation of nondegenate classical r-matrices.
182 citations
Patent•
16 May 1996TL;DR: In this paper, the dual representation mathematical principle is used for the design of decision systems, which permits some decision functions that are weighted sums of predefined functions to be represented as memory-based decision functions.
Abstract: A method is described wherein the dual representation mathematical principle is used for the design of decision systems. This principle permits some decision functions that are weighted sums of predefined functions to be represented as memory-based decision function. Using this principle a memory-based decision system with optimum margin is designed wherein weights and prototypes of training patterns of a memory-based decision function are determined such that the corresponding dual decision function satisfies the criterion of margin optimality.
129 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 8 |
| 2024 | 13 |
| 2023 | 13 |
| 2022 | 14 |
| 2021 | 17 |
| 2020 | 16 |