On approximations by trigonometric polynomials of classes of functions defined by moduli of smoothness

In this paper, we give a characterization of Nikol'ski\u{\i}-Besov type classes of functions, given by integral representations of moduli of smoothness, in terms of series over the moduli of smoothness. Also, necessary and sufficient conditions in terms of monotone or lacunary Fourier coefficients for a function to belong to a such a class are given. In order to prove our results, we make use of certain recent reverse Copson- and Leindler-type inequalities.Comment: 18 pages. arXiv admin note: substantial text overlap with arXiv:1208.612

Investigating the Effects of Word Substitution Errors on Sentence Embeddings

A key initial step in several natural language processing (NLP) tasks involves embedding phrases of text to vectors of real numbers that preserve semantic meaning. To that end, several methods have been recently proposed with impressive results on semantic similarity tasks. However, all of these approaches assume that perfect transcripts are available when generating the embeddings. While this is a reasonable assumption for analysis of written text, it is limiting for analysis of transcribed text. In this paper we investigate the effects of word substitution errors, such as those coming from automatic speech recognition errors (ASR), on several state-of-the-art sentence embedding methods. To do this, we propose a new simulator that allows the experimenter to induce ASR-plausible word substitution errors in a corpus at a desired word error rate. We use this simulator to evaluate the robustness of several sentence embedding methods. Our results show that pre-trained neural sentence encoders are both robust to ASR errors and perform well on textual similarity tasks after errors are introduced. Meanwhile, unweighted averages of word vectors perform well with perfect transcriptions, but their performance degrades rapidly on textual similarity tasks for text with word substitution errors.Comment: 4 Pages, 2 figures. Copyright IEEE 2019. Accepted and to appear in the Proceedings of the 44th International Conference on Acoustics, Speech, and Signal Processing 2019 (IEEE-ICASSP-2019), May 12-17 in Brighton, U.K. Personal use of this material is permitted. However, permission to reprint/republish this material must be obtained from the IEE

Some reverse lpl_p-type inequalities involving certain quasi monotone sequences

In this paper, we give some $l_p$-type inequalities about sequences satisfying certain quasi monotone type properties. As special cases, reverse $l_p$-type inequalities for non-negative decreasing sequences are obtained. The inequalities are closely related to Copson's and Leindler's inequalities, but the sign of the inequalities is reversed.Comment: 7 pages, Communicated in the Eighth Congress of Romanian Mathematicians, Iasi, Romania, 201

H3F3A (Histone 3.3) G34W Immunohistochemistry: A Reliable Marker Defining Benign and Malignant Giant Cell Tumor of Bone

Giant cell tumor of bone (GCTB) is a locally aggressive subarticular tumor. Having recently reported that H3.3 G34W mutations are characteristic of this tumor type, we have now investigated the sensitivity and specificity of the anti-histone H3.3 G34W rabbit monoclonal antibody in a wide variety of tumors including histologic mimics of GCTB to assess its value as a diagnostic marker. We also determined the incidence of H3.3 G34 mutations in primary malignant bone tumors as assessed by genotype and H3.3 G34W immunostaining. A total of 3163 tumors were tested. Totally, 213/235 GCTB (90.6%) showed nuclear H3.3 p.G34W immunoreactivity. This was not the case for the rare variants, p.G34L, M, and V, which occurred most commonly in the small bones of the hands, patella, and the axial skeleton. If these sites were excluded from the analysis, H3.3 G34W expression was found in 97.8% of GCTB. Malignant bone tumors initially classified as osteosarcomas were the only other lesions (n=11) that showed G34W expression. Notably an additional 2 previously reported osteosarcomas with a p.G34R mutation were not immunoreactive for the antibody. A total of 11/13 of these malignant H3.3-mutant tumors exhibited an osteoclast-rich component: when imaging was available all but one presented at a subarticular site. We propose that subarticular primary malignant bone sarcoma with H3.3 mutations represent true malignant GCTB, even in the absence of a benign GCTB component