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Redmond, WA, United States

Hanson J.,DigiPen Institute of Technology
General Relativity and Gravitation | Year: 2013

The canonical decomposition of a Lorentz algebra element into a sum of orthogonal simple (decomposable) Lorentz bivectors is defined and discussed. This decomposition on the Lie algebra level leads to a natural decomposition of a proper orthochronous Lorentz transformation into a product of commuting Lorentz transformations, each of which is the exponential of a simple bivector. While this later result is known, we present novel formulas that are independent of the form of the Lorentz metric chosen. As an application of our methods, we obtain an alternative method of deriving the formulas for the exponential and logarithm for Lorentz transformations. © 2012 Springer Science+Business Media New York. Source

Ming Z.-Y.,DigiPen Institute of Technology | Chua T.S.,National University of Singapore
Information Sciences | Year: 2015

Names are important atomic information carriers in unstructured text. Matching names that refer to the same entities is an important issue in text analysis and a key component in many real world applications. Generally referred to as entity linking, it is defined as a task that aligns a name mentioned in free text to its corresponding entry in a Knowledge Base (KB). The difficulty of the task lies in the many-to-many correspondence between names and entities, causing the pseudonymity and polysemy issues. Existing work usually focuses on resolving polysemy by aggregating large numbers of loosely arranged features in supervised learning frameworks, with very few targeting the pseudonymity or both issues with the same depth. In this work, we tackle both issues by comprehensive modeling of an entity's name and context: we tackle the pseudonymity by modeling name variants on the query name and the KB title; and polysemy by modeling heterogeneous aspects of the query and KB context. Specially, we harness entity coreferences within query and KB documents together with the external alias resources for modeling name variants, and further use the name variants to identify focused context. Moreover, we propose a recall-boosted retrieval method for efficient candidate entity generation. Experimental results show that our proposed approach outperforms the state-of-the-art systems on the benchmark data. © 2015 Elsevier Inc. All rights reserved. Source

Coroianu L.,University of Oradea | Gal S.G.,University of Oradea | Bede B.,DigiPen Institute of Technology
Fuzzy Sets and Systems | Year: 2014

In this paper firstly we extend to an arbitrary compact interval the definition of the nonlinear Bernstein operators of max-product kind, by proving that their order of uniform approximation is the same as in the particular case of the unit interval. Then, similarly to the particular case of the unit interval, we will prove that these operators preserve the quasi-concavity too. Since these properties will help us to generate in a simple way fuzzy numbers of the same support, it turns out that these results are very suitable in the approximation of fuzzy numbers. Moreover, these operators approximate the (non-degenerate) segment core with a good order of approximation. In addition, in the case when the fuzzy numbers are given in parametric form, the Bernstein max-product operator generates a sequence of fuzzy numbers whose widths, expected intervals, ambiguities and values, approximate with a convergent rate the width, the expected interval, the ambiguity and the value of the approximated fuzzy number. Finally, we obtain a quantitative approximation with respect to a well-known integral type metric for some subclasses of functions, leading to applications to the approximation of some subclasses of fuzzy numbers. © 2013 Elsevier B.V. All rights reserved. Source

Ye J.,MOZAT PTE. LTD of Singapore | Ming Z.Y.,DigiPen Institute of Technology | Chua T.S.,National University of Singapore
ACM Transactions on Intelligent Systems and Technology | Year: 2016

Document summarization is playing an important role in coping with information overload on the Web. Many summarization models have been proposed recently, but few try to adjust the summary length and sentence order according to application scenarios. With the popularity of handheld devices, presenting key information first in summaries of flexible length is of great convenience in terms of faster reading and decision-making and network consumption reduction. Targeting this problem, we introduce a novel task of generating summaries of incremental length. In particular, we require that the summaries should have the ability to automatically adjust the coverage of general-detailed information when the summary length varies. We propose a novel summarization model that incrementally maximizes topic coverage based on the document's hierarchical topic model. In addition to the standard Rouge-1 measure, we define a new evaluation metric based on the similarity of the summaries' topic coverage distribution in order to account for sentence order and summary length. Extensive experiments on Wikipedia pages, DUC 2007, and general noninverted writing style documents from multiple sources show the effectiveness of our proposed approach. Moreover, we carry out a user study on a mobile application scenario to show the usability of the produced summary in terms of improving judgment accuracy and speed, as well as reducing the reading burden and network traffic. © 2016 ACM 2157-6904/2016/02-ART29 $15.00. Source

Bede B.,DigiPen Institute of Technology | O'Regan D.,National University of Ireland
Knowledge-Based Systems | Year: 2013

In the present paper we develop a theory of pseudo-linear operators. A generalization of the classical Lp spaces to the setting of pseudo-analysis is constructed. We obtain a Riesz representation theorem together with a Lax-Milgram type lemma. © 2012 Elsevier B.V. All rights reserved. Source

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