Figurate primes and Hilbert's 8th problem

In this paper, by using the theory of elliptic curves, we discuss several Diophantine equations related with the so-called figurate primes. Meanwhile, we raise several conjectures related with figurate primes and Hilbert's 8th problem, including Goldbach's conjecture, twin primes conjecture and Catalan's conjecture as well.Comment: 7 pages, 1 figur

CSCWD technologies, applications and challenges [Editorial]

As CSCWD (Computer Supported Cooperative Work in Design) has involved the cooperation of multidisciplinary design teams, traditionally the communication among different design teams has been facilitated by the Intranet or Extranet, which makes the applications of CSCWD more expensive and hardly accessible to most organizations, especially small and medium enterprises. The Internet which can be accessed anywhere and at anytime has changed the whole world as well as CSCWD communities. The phenomenon of Internet has significantly reshaped the research of CSCWD. The universal and nearly free accessibility has made it much easier for people to coordinate and do collaborative design jobs without any physical location boundaries. The new technologies and applications from CSCWD have significantly contributed to the multidisciplinary design teams. Over the past thirteen years, CSCWD communities have been actively involved in the dynamic researches and practical developments from both academia and industry. In order to address the new challenges that CSCWD communities are facing, we carefully selected 15 manuscripts from 198 papers (from 360 original submissions) presented at the 12th International Conference on Computer Supported Cooperative Work in Design (CSCWD 2008), Xi�an, China on April 16-18, 2008, to forge this J.UCS special issue. It is intended for researchers and practitioners interested in CSCWD Technologies, Applications and Challenges. All selected papers have been revised and extended into current versions by three rigorous review rounds

Wasserstein Distance Guided Representation Learning for Domain Adaptation

Domain adaptation aims at generalizing a high-performance learner on a target domain via utilizing the knowledge distilled from a source domain which has a different but related data distribution. One solution to domain adaptation is to learn domain invariant feature representations while the learned representations should also be discriminative in prediction. To learn such representations, domain adaptation frameworks usually include a domain invariant representation learning approach to measure and reduce the domain discrepancy, as well as a discriminator for classification. Inspired by Wasserstein GAN, in this paper we propose a novel approach to learn domain invariant feature representations, namely Wasserstein Distance Guided Representation Learning (WDGRL). WDGRL utilizes a neural network, denoted by the domain critic, to estimate empirical Wasserstein distance between the source and target samples and optimizes the feature extractor network to minimize the estimated Wasserstein distance in an adversarial manner. The theoretical advantages of Wasserstein distance for domain adaptation lie in its gradient property and promising generalization bound. Empirical studies on common sentiment and image classification adaptation datasets demonstrate that our proposed WDGRL outperforms the state-of-the-art domain invariant representation learning approaches.Comment: The Thirty-Second AAAI Conference on Artificial Intelligence (AAAI 2018