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In this talk, I will review several classes of higher-order generalizations of the integrable Camassa-Holm equation in the Hamiltonian forms. Then, I talk about some new results for one generalized Ca...
It is well-known that modern neural networks are vulnerable to adversarial examples. To mitigate this problem, a series of robust learning algorithms have been proposed. However, although the robust t...
This report consists of two parts associated with graph neural networks: generalization and graph structural learning. We first study the Rademacher complexity of GNNs, as one of independent-algorithm...
Since the celebrated work by Cartan, distributions with small growth vector (2,3,5) have been studied extensively. In the holomorphic setting, there is a natural correspondence between holomorphic (2,...
With the globalization and rapid development every filed is taking an increasing interest in physical geography and human economics. There is a surging demand for small scale world map in large format...
Route maps, which depict a path from one location to another, have emerged as one of the most popular applications on the Web. Current computer-generated route maps, however, are often very diffi- ...
We generalize a construction of the Neron model for a family of intermediate Jacobians due to Green, Griths and Kerr by using the theory of mixed Hodge modules. It is a topological group de ned ov...
In 1912 Bieberbach proved that every compact flat Riemannian manifold M is finitely covered by a flat torus. More precisely, M has the form (F\G)/H where G is a group of translations of Euclidean ...
A generalization of Blaschke’s Rolling Theorem for not necessarily convex sets is proved that exhibits an intimate connection between a generalized notion of convexity, various concepts in mathematic...
The paper concerns the generalization of DTM extracted from LiDAR data. The essence of generalization is reducing details while enhancing important features at the same time; so for the purpose of te...
We show that a simple network model of associative learning can reproduce three findings that arise from particular training and testing procedures in generalization experiments: the effect of 1) ``er...
We demonstrate the generalizability of the Extended Baum-Welch (EBW) algorithm not only for HMM parameter estimation but for decoding as well. We show that there can exist a general function associate...
An analog of the spectral analysis of time series is developed for data in general spaces. This is applied to data from an election in which 5738 people rank ordered five candidates. Group theoret...
Map generalization simplifies the details of map representation. Automatic generalization has been a hot research topic for decades, but there does not exist a set of universal rules or algorithms th...
Automating the map generalization process has traditionally been a major focus of research in cartography and GIS environment. Many algorithms and models have been developed over the past three decad...

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