Identification and prediction problem of nonlinear time-series generated by discrete dynamic system is considered via Kernel Method approach. A unified approach to recurrent kernel identification algorithms design is proposed. In such a way a recurrent modification of initial Kernel Method with growing windows is considered. In order to prevent the model complexity increasing under on-line iden...

Clinical datasets typically contain continuous, ordinal, categorical and binary variables. To model this type of datasets, linear kernel methods are generally used. However, the linear kernel has some disadvantages, which were tackled by the introduction of a clinical one. This work shows that the use of a clinical kernel can improve the performance of support vector machine survival models. In...

In this paper we define a new type of modular object and construct explicit examples of such functions. Our functions are closely related to cusp forms constructed by Zagier [37] which played an important role in the construction by Kohnen and Zagier [26] of a kernel function for the Shimura and Shintani lifts between half-integral and integral weight cusp forms. Although our functions share ma...

We study interior Lp-regularity theory, also known as Calderon-Zygmund of the equation〈Lsu,φ〉:=∫Rn∫RnK(x,y)(u(x)−u(y))(φ(x)−φ(y))|x−y|n+2sdxdy=〈f,φ〉,∀φ∈Cc∞(Rn). prove that for s∈(0,1), t∈[s,2s], p∈[2,∞), K an elliptic, symmetric, and K(⋅,y) is uniformly Hölder continuous, solution u belongs to Hloc2s−t,p(Ω) long 2s−t<1 f∈(H00t,p′(Ω))⁎. The increase in differentiability integrability independent...

The appearance of massive data has become increasingly common in contemporary scientific research. When sample size n is huge, classical learning methods become computationally costly for the regression purpose. Recently, the orthogonal greedy algorithm (OGA) has been revitalized as an efficient alternative in the context of kernel-based statistical learning. In a learning problem, accurate and...

The Semantic Textual Similarity (STS) task aims to exam the degree of semantic equivalence between sentences (Agirre et al., 2012). This paper presents the work of the Hong Kong Polytechnic University (PolyUCOMP) team which has participated in the STS core and typed tasks of SemEval2013. For the STS core task, the PolyUCOMP system disambiguates words senses using contexts and then determine sen...

The Rankin-Cohen bracket of two Eisenstein series provides a kernel yielding products of the periods of Hecke eigenforms at critical values. Extending this idea leads to a new type of Eisenstein series built with a double sum. We develop the properties of these series and their nonholomorphic analogs and show their connection to values of L-functions outside the critical strip.