Let B be a set of real numbers of size n. We prove that the length of the longest arithmetic progression contained in the product set B.B={bibj|bi,bj∈B} cannot be greater than O(n1+1/loglogn) an ...arithmetic progression of length Ω(nlogn), so the obtained upper bound is close to the optimal.
ON ITERATED PRODUCT SETS WITH SHIFTS Hanson, Brandon; Roche-Newton, Oliver; Zhelezov, Dmitrii
Mathematika,
2019, Letnik:
65, Številka:
4
Journal Article
Recenzirano
Odprti dostop
We prove that, for any finite set
$A\subset \mathbb{Q}$
with
$|AA|\leqslant K|A|$
and any positive integer
$k$
, the
$k$
-fold product set of the shift
$A+1$
satisfies the bound
...$$\begin{eqnarray}|\{(a_{1}+1)(a_{2}+1)\cdots (a_{k}+1):a_{i}\in A\}|\geqslant \frac{|A|^{k}}{(8k^{4})^{kK}}.\end{eqnarray}$$
This result is essentially optimal when
$K$
is of the order
$c\log |A|$
, for a sufficiently small constant
$c=c(k)$
. Our main tool is a multiplicative variant of the
$\unicodeSTIX{x1D6EC}$
-constants used in harmonic analysis, applied to Dirichlet polynomials.
OpenBiodiv is a biodiversity database—knowledge graph based on Resource Description Framework (RDF)—that contains information extracted from the scientific literature. It provides access to an ...ecosystem of tools and services, including a Linked Open Dataset, an ontology (OpenBiodiv-O) and а website (Dimitrova et al. 2021).
Using the available data, OpenBiodiv discovers links between various biodiversity data types (e.g., taxon names, treatments, specimens, sequences, people and institutions), to answer a user’s questions about specific taxa, scientific articles, materials examined and others.
The full-text XML content is converted into Linked Open Data from journals on the ARPHA Publishing Platform and treatments extracted by Plazi’s TreatmentBank (stored in the Biodiversity Literature Repository at Zenodo). The database is updated and indexed daily using a workflow based on the Apache Kafka event-streaming platform. The workflow was developed during the European Union-funded
Biodiversity Community Integrated Knowledge Library
(BiCIKL) project (Penev et al. 2022b). By 1 of August 2023, the graph consisted of 24,939 articles; 167,471 treatments; 130,359 authors; 736,809 taxon names; 129,257 sequences; 1,390 institutions and collections, 117,854 figures; 18,585 tables, and 90,008 materials examined sections.
Each semantic statement (e.g., authors, articles, treatments, taxonomic names, localities) has its own globally unique, persistent and resolvable identifier (GUPRI).
There are four ways a user can explore the data on OpenBiodiv:
General search
The search engine is accessible from the OpenBiodiv homepage. The user needs to type in a key term, (e.g., a taxonomic name, authority or an article title), and the system retrieves information about it. Errors caused by misspellings are avoided due to the Elasticsearch index. It can also determine the semantic type of the searched entity.
Application Programing Interface (API)
OpenBiodiv can be used through a RESTful API for programmatic access. The documentation of the API is described on Swagger. The API construction and functionalities follow the recommendations elaborated by the Technical Research Infrastructures forum of the BiCIKL project (Addink et al. 2023).
User applications based on a query algorithm
This function can be applied for any data class. The method uses the relationships between an element type (e.g., taxon name) and the type of the section, where it can be found.
An application example is
Literature exploration
, designed to answer the question:
Give me information about X mentioned within article section type Y.
The results show the number of mentions of the entity (e.g., taxon name) in the section(s) of interest (e.g., Title, Abstract, Treatment). A click navigates the user to the place in the article that mentions the item (Fig. 1).
SPARQL queries in a thematic context
OpenBiodiv provides a SPARQL endpoint through the Ontotext GraphDB solution*1. Several sample SPARQL queries*2 are also available on the OpenBiodiv website.
This paper presents the process of degradation of the surface layer of Si3N4−TiN ceramics induced by a pulsed Nd:YAG laser. The dissociation of silicon nitride and titanium nitride in the irradiation ...zone is turned out to yield in a silicon depletion and so the zone becomes enriched with titanium, which, in turn, leads to the formation of TiSi2. This process of the TiSi2 formation can be considered as a ceramics metallization and its concentration depends on the energy delivered by the laser. The expansion of dissociation/evaporation products through the atmosphere is accompanied by the formation of SiO2 and TiO2, which are then deposited on the substrate as an amorphous film of complex composition.
Hundreds of years of biodiversity research have resulted in the accumulation of a substantial pool of communal knowledge; however, most of it is stored in silos isolated from each other, such as ...published articles or monographs. The need for a system to store and manage collective biodiversity knowledge in a community-agreed and interoperable open format has evolved into the concept of the Open Biodiversity Knowledge Management System (OBKMS). This paper presents OpenBiodiv: An OBKMS that utilizes semantic publishing workflows, text and data mining, common standards, ontology modelling and graph database technologies to establish a robust infrastructure for managing biodiversity knowledge. It is presented as a Linked Open Dataset generated from scientific literature. OpenBiodiv encompasses data extracted from more than 5000 scholarly articles published by Pensoft and many more taxonomic treatments extracted by Plazi from journals of other publishers. The data from both sources are converted to Resource Description Framework (RDF) and integrated in a graph database using the OpenBiodiv-O ontology and an RDF version of the Global Biodiversity Information Facility (GBIF) taxonomic backbone. Through the application of semantic technologies, the project showcases the value of open publishing of Findable, Accessible, Interoperable, Reusable (FAIR) data towards the establishment of open science practices in the biodiversity domain.
Abstract
We prove that finite sets of real numbers satisfying $|AA| \leq |A|^{1+\epsilon}$ with sufficiently small $\epsilon > 0$ cannot have small additive bases nor can they be written as a set of ...sums $B+C$ with $|B|, |C| \geq 2$. The result can be seen as a real analog of the conjecture of Sárközy that multiplicative subgroups of finite fields of prime order are additively irreducible.
To the best of our knowledge, OpenBiodiv is the first production-stage semantic system running on top of a reasonably-sized biodiversity knowledge graph. It stores biodiversity data in a semantic ...interlinked format and offers facilities for working with it (Senderov et Penev 2016, Senderov et al. 2018, Penev et al. 2019, Dimitrova et al. 2021). It is a dynamic system that continuously updates its database as new biodiversity information becomes available by several international biodiversity publishers. It also allows its users to ask complex queries via SPARQL (a query language for semantic graph databases) and a simplified semantic search interface.OpenBiodiv was created during two EU-funded Marie Sklodowska-Curie PhD projects: BIG4 (Grant Agreement No 642241) and IGNITE (Grant Agreement No 764840). During those projects, the backend Ontology-0, the first versions of RDF converters and the basic website functionalities have been created (see Dimitrova et al. 2021 for overview).After the start of the BiCIKL project, the entire workflow for processing and RDF conversion of full-text articles in XML and Plazi’s treatments in XML has been re-built using up-to-date technological solutions (such as Apache Kaka and Elasticsearch) to fully automatise and speed up the conversion process and to make it trackable and efficient. As a result, the entire graph content has been re-processed and indexed. New user applications described in Milestone MS27 App specifications have been discussed and implemented.The present deliverable describes the newly built workflow and tools for data extraction, conversion and indexing and the user applications, created in the BiCIKL project.
The aim of the study – to evaluate the role of expression of specific connective tissue proteins in the formation of the scar on the uterus.
Materials and Methods. The study was performed on the ...basis of the regional perinatal center and KU PB No. 5 during 2017–2019. 426 women with a scar on the uterus were examined, including 115 (27.0 %) with two or more scars. The mean age of the subjects was (33.4±1.1) years. The results of sonographic studies were analyzed. For pathomorphological examination, three cases of intranatal rupture of the uterine wall along the “old” scar after cesarean section from middle-aged women with a gestational age of 33 to 40 weeks are presented. The expression of collagen types 1 and 3 and the protein of the intermediate filaments of the muscle tissue of desmin was determined using a semi-quantitative method with the calculation of H-score.
Results and Discussion. Analysis of ultrasound data showed that the average assessment of the degree of insolvency of the scar on the uterus was in the examined women X=(1.3±0.2) points, a high level of insolvency was found in 114 (26.8 %) pregnant women. At the same time, 225 (52.8 %) pregnant women showed no signs of scar failure at all. In 87 (20.4 %) one sign of uterine scar failure was found, in 76 (17.8 %) – two signs, in 20 (4.7 %) – three signs, and in 18 (4.2 %) – four signs. Subsequently, 44 (10.3 %) women were born operatively, the rest gave birth per via naturales. Local myometrial defect after ultrasound delivery was detected in 25 of 182 (13.7 %) women who gave birth independently.
Conclusions. A high level of scar failure risk is found in 26.8 % of pregnant women. H-score valuesfor collagen types 1 and 3 averaged (212±24) and (188±22), for desmin – (193±17). Thus, reparative processes at the site of previous surgery on the uterine wall are by incomplete regeneration (substitution) and compensatory hyperplasia of structural tissue elements.
OpenBiodiv is a complex ecosystem of tools and services for RDF conversion of XML narratives of biodiversity articles including Darwin Core data into Linked Open Data (LOD), running on top of a graph ...database. OpenBiodiv provides four main types of services:
Searching named entities (e.g., taxon names, taxon concepts, treatments, specimens, occurrences, gene sequences, bibliographic information, institutions, persons) in context, within and between articles.
Answering questions based on the presence of certain named entities within specific article sections (e.g., titles, abstracts, introduction or other sections, taxon treatments).
Identifying article sections for further text processing (NLP) and providing contextual information, stored in MongoDB.
Federating the SPARQL endpoint with other triple stores to enrich the discovered knowledge.
Searching named entities (e.g., taxon names, taxon concepts, treatments, specimens, occurrences, gene sequences, bibliographic information, institutions, persons) in context, within and between articles.
Answering questions based on the presence of certain named entities within specific article sections (e.g., titles, abstracts, introduction or other sections, taxon treatments).
Identifying article sections for further text processing (NLP) and providing contextual information, stored in MongoDB.
Federating the SPARQL endpoint with other triple stores to enrich the discovered knowledge.
Conversion of such data into RDF follows a general semantic model expressed in the OpenBiodiv-O ontology, an extension of the Treatment Ontology for knowledge representation of current and legacy biodiversity publications (Senderov et al. 2018) and uses two main sources, the full-text article XML published on the ARPHA Publishing Platform and the taxon treatments extracted by Plazi’s TreatmentBank from more than 100 biodiversity journals, stored in the Biodiversity Literature Repository at Zenodo. To ensure efficiency, quality control and fast tracking of all stages of the entire process of extraction, conversion to RDF and indexing of the content has been re-built on the Apache Kafka event streaming platform (Fig. 1). In this new format, OpenBiodiv provides not only a GraphDB SPARQL query endpoint but also indexes the named entities through Elasticsearch and additional provision of data to end users through a RESTful API and a number of user applications.
OpenBiodiv is designed for a wide range of users who are interested in a deep-level bibliographic exploration, an ontology-linked search of various data elements (e.g., specimens, sequences, taxon concepts, persons), or co-existence of named entities (e.g., taxon names with a possible biotic relationships between them, or taxon names and potential habitats of occupation) in pre-defined sections of the articles. The SPARQL endpoint allows complex queries of various kinds (Dimitrova et al. 2021).
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