Browsing by Subject "regularity"

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  • Niu, Pingping; Helin, Tapio; Zhang, Zhidong (2020)
    In this work the authors consider an inverse source problem the stochastic fractional diffusion equation. The interested inverse problem is to reconstruct the unknown spatial functions f and g (the latter up to the sign) in the source by the statistics of the final time data u(x, T). Some direct problem results are proved at first, such as the existence, uniqueness, representation and regularity of the solution. Then a reconstruction scheme for f and g up to the sign is given. To tackle the ill-posedness, Tikhonov regularization is adopted and some numerical results are displayed.
  • Yli-Jyrä, Anssi Mikael (The Association for Computational Linguistics, 2017)
    A recently proposed encoding for non- crossing digraphs can be used to imple- ment generic inference over families of these digraphs and to carry out first-order factored dependency parsing. It is now shown that the recent proposal can be substantially streamlined without information loss. The improved encoding is less dependent on hierarchical processing and it gives rise to a high-coverage bounded-depth approximation of the space of non- crossing digraphs. This subset is presented elegantly by a finite-state machine that recognises an infinite set of encoded graphs. The set includes more than 99.99% of the 0.6 million noncrossing graphs obtained from the UDv2 treebanks through planarisation. Rather than taking the low probability of the residual as a flat rate, it can be modelled with a joint probability distribution that is factorised into two underlying stochastic processes – the sentence length distribution and the related conditional distribution for deep nesting. This model points out that deep nesting in the streamlined code requires extreme sentence lengths. High depth is categorically out in common sentence lengths but emerges slowly at infrequent lengths that prompt further inquiry.