ON THE SMARANDACHE FUNCTION AND SQUARE COMPLEMENTS

The main purpose of this paper is using the elementary method to study the mean value properties of the Smarandache function, and give an interesting asymptotic formula

On a problem of D.H. Lehmer over short intervals

AbstractLet p be an odd prime and a be an integer coprime to p. Denote by N(a,p) the number of pairs of integers b,c with bc≡a (mod p), 1⩽b,c⩽(p−1)2 and with b,c having different parity. The main purpose of this paper is to study the sum ∑a=1p−1(N(a,p)−(p−1)8)2, and obtain a sharp asymptotic formula

On the order of the high-dimensional Cochrane sum and its mean value

AbstractThe main purpose of this paper is to study the high-dimensional Cochrane sum and give a sharp estimate of its order by using properties of hyper-Kloosterman sum and the mean value theorems of Dirichlet L-functions

Mining Word Boundaries in Speech as Naturally Annotated Word Segmentation Data

Inspired by early research on exploring naturally annotated data for Chinese word segmentation (CWS), and also by recent research on integration of speech and text processing, this work for the first time proposes to mine word boundaries from parallel speech/text data. First we collect parallel speech/text data from two Internet sources that are related with CWS data used in our experiments. Then, we obtain character-level alignments and design simple heuristic rules for determining word boundaries according to pause duration between adjacent characters. Finally, we present an effective complete-then-train strategy that can better utilize extra naturally annotated data for model training. Experiments demonstrate our approach can significantly boost CWS performance in both cross-domain and low-resource scenarios.Comment: latest versio

Mining Density Contrast Subgraphs

Dense subgraph discovery is a key primitive in many graph mining applications, such as detecting communities in social networks and mining gene correlation from biological data. Most studies on dense subgraph mining only deal with one graph. However, in many applications, we have more than one graph describing relations among a same group of entities. In this paper, given two graphs sharing the same set of vertices, we investigate the problem of detecting subgraphs that contrast the most with respect to density. We call such subgraphs Density Contrast Subgraphs, or DCS in short. Two widely used graph density measures, average degree and graph affinity, are considered. For both density measures, mining DCS is equivalent to mining the densest subgraph from a "difference" graph, which may have both positive and negative edge weights. Due to the existence of negative edge weights, existing dense subgraph detection algorithms cannot identify the subgraph we need. We prove the computational hardness of mining DCS under the two graph density measures and develop efficient algorithms to find DCS. We also conduct extensive experiments on several real-world datasets to evaluate our algorithms. The experimental results show that our algorithms are both effective and efficient.Comment: Full version of an ICDE'18 pape

Drosophila Perlecan Regulates Intestinal Stem Cell Activity via Cell-Matrix Attachment

SummaryStem cells require specialized local microenvironments, termed niches, for normal retention, proliferation, and multipotency. Niches are composed of cells together with their associated extracellular matrix (ECM). Currently, the roles of ECM in regulating niche functions are poorly understood. Here, we demonstrate that Perlecan (Pcan), a highly conserved ECM component, controls intestinal stem cell (ISC) activities and ISC-ECM attachment in Drosophila adult posterior midgut. Loss of Pcan from ISCs, but not other surrounding cells, causes ISCs to detach from underlying ECM, lose their identity, and fail to proliferate. These defects are not a result of a loss of epidermal growth factor receptor (EGFR) or Janus kinase/signal transducer and activator of transcription (JAK/STAT) signaling activity but partially depend on integrin signaling activity. We propose that Pcan secreted by ISCs confers niche properties to the adjacent ECM that is required for ISC maintenance of stem cell identity, activity, and anchorage to the niche

A tomato HD-Zip homeobox protein, LeHB-1, plays an important role in floral organogenesis and ripening

Ethylene is required for climacteric fruit ripening. Inhibition of ethylene biosynthesis genes, 1-aminocyclopropane-1-carboxylate (ACC) synthase and ACC oxidase, prevents or delays ripening, but it is not known how these genes are modulated during normal development. LeHB-1, a previously uncharacterized tomato homeobox protein, was shown by gel retardation assay to interact with the promoter of LeACO1, an ACC oxidase gene expressed during ripening. Inhibition of LeHB-1 mRNA accumulation in tomato fruit, using virus-induced gene silencing, greatly reduced LeACO1 mRNA levels, and inhibited ripening. Conversely, ectopic overexpression of LeHB-1 by viral delivery to developing flowers elsewhere on injected plants triggered altered floral organ morphology, including production of multiple flowers within one sepal whorl, fusion of sepals and petals, and conversion of sepals into carpel-like structures that grew into fruits and ripened. Our findings suggest that LeHB-1 is not only involved in the control of ripening but also plays a critical role in floral organogenesis

How Well Do Large Language Models Understand Syntax? An Evaluation by Asking Natural Language Questions

While recent advancements in large language models (LLMs) bring us closer to achieving artificial general intelligence, the question persists: Do LLMs truly understand language, or do they merely mimic comprehension through pattern recognition? This study seeks to explore this question through the lens of syntax, a crucial component of sentence comprehension. Adopting a natural language question-answering (Q&A) scheme, we craft questions targeting nine syntactic knowledge points that are most closely related to sentence comprehension. Experiments conducted on 24 LLMs suggest that most have a limited grasp of syntactic knowledge, exhibiting notable discrepancies across different syntactic knowledge points. In particular, questions involving prepositional phrase attachment pose the greatest challenge, whereas those concerning adjectival modifier and indirect object are relatively easier for LLMs to handle. Furthermore, a case study on the training dynamics of the LLMs reveals that the majority of syntactic knowledge is learned during the initial stages of training, hinting that simply increasing the number of training tokens may not be the `silver bullet' for improving the comprehension ability of LLMs.Comment: 20 pages, 6 figure