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Abstract. In this paper we consider the Cauchy problem for the Novikov equation. We prove that the Cauchy problem for the Novikov equation is not locally well-posed in the Sobolev spaces H s ( ) with s < 3 2 in the sense that its solutions do not depend uniformly continuously on the initial data. Since the Cauchy problem for the Novikov equation is locally well-posed in H s ( ) with s > 3/2 in the sense of Hadamard, our result implies that s = 3/2 is the critical Sobolev index for well-posedness. We also present two blow-up results of strong solution to the Cauchy problem for the Novikov equation in H s ( ) with s > 3/2.Mathematics Subject Classification (2010). Primary 35G25, 35L05; Secondary 35R25.

Mitochondrial DNA (mtDNA) mutations have been associated with Leber’s hereditary optic neuropathy (LHON) and their pathophysiology remains poorly understood. In this study, we investigated the pathophysiology of a LHON susceptibility allele (m.3394T&gt;C, p.30Y&gt;H) in the Mitochondrial (MT)-ND1 gene. The incidence of m.3394T&gt;C mutation was 2.7% in the cohort of 1741 probands with LHON. Extremely low penetrances of LHON were observed in 26 pedigrees carrying only m.3394T&gt;C mutation, while 21 families bearing m.3394T&gt;C, together with m.11778G&gt;A or m.14484T&gt;C mutation, exhibited higher penetrance of LHON than those in families carrying single mtDNA mutation(s). The m.3394T&gt;C mutation disrupted the specific electrostatic interactions between Y30 of p.MT-ND1 with the sidechain of E4 and backbone carbonyl group of M1 of NDUFA1 (NADH dehydrogenase [ubiquinone] 1 alpha subcomplex subunit 1) of complex I, thereby altering the structure and function of complex I. We demonstrated that these cybrids bearing only m.3394T&gt;C mutation caused mild mitochondrial dysfunctions and those harboring both m.3394T&gt;C and m.11778G&gt;A mutations exhibited greater mitochondrial dysfunctions than cybrids carrying only m.11778G&gt;A mutation. In particular, the m.3394T&gt;C mutation altered the stability of p.MT-ND1 and complex I assembly. Furthermore, the m.3394T&gt;C mutation decreased the activities of mitochondrial complexes I, diminished mitochondrial ATP levels and membrane potential and increased the production of reactive oxygen species in the cybrids. These m.3394T&gt;C mutation-induced alterations aggravated mitochondrial dysfunctions associated with the m.11778G&gt;A mutation. These resultant biochemical defects contributed to higher penetrance of LHON in these families carrying both mtDNA mutations. Our findings provide new insights into the pathophysiology of LHON arising from the synergy between mitochondrial ND1 and ND4 mutations.

Jamming is a big threat to radar system survival and anti-jamming is a part of the solution. The classification of radar jamming signal is the first step toward to anti-jamming. Recently, as an important part of deep learning, convolutional neural network (CNN) based methods have shown their capability in discriminant feature extraction and accurate classification. In this study, in order to harness the powerfulness of deep learning, CNN based methods are proposed to classify radar jamming signal acting on pulse compression radar. Specifically, a 1D-CNN is designed for radar jamming signal classification under the condition of sufficient training samples. Furthermore, due to the fact that the collection of sufficient training samples is time-consuming and expensive, a CNN-based siamese network is proposed for radar jamming signal classification to deal with the issue of limited training samples. The experimental results with sufficient and limited training samples show that the CNN-based classification methods obtain good classification performance in terms of classification accuracy and show a huge potential for radar jamming signal classification. INDEX TERMS Radar jamming signal, convolutional neural network (CNN), sufficient and limited training samples, siamese network.

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