Basic Properties of Periodic Functions

In this article we present definitions, basic properties and some examples of periodic functions according to [5].Li Bo - Qingdao University of Science and Technology, ChinaLi Dailu - Qingdao University of Science and Technology, ChinaMen Yanhong - Qingdao University of Science and Technology, ChinaLiang Xiquan - Qingdao University of Science and Technology, ChinaGrzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Chuanzhang Chen. Mathematical Analysis. Higher Education Press, Beijing, 1978.Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Peng Wang and Bo Li. Several differentiation formulas of special functions. Part V. Formalized Mathematics, 15(3):73-79, 2007, doi:10.2478/v10037-007-0009-4.Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Formalized Mathematics, 7(2):255-263, 1998

Nilpotent Groups

This article describes the concept of the nilpotent group and some properties of the nilpotent groups.Li Dailu - Qingdao University of Science and Technology, ChinaLiang Xiquan - Qingdao University of Science and Technology, ChinaMen Yanhong - Qingdao University of Science and Technology, ChinaGrzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Wojciech A. Trybulec. Classes of conjugation. Normal subgroups. Formalized Mathematics, 1(5):955-962, 1990.Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.Wojciech A. Trybulec. Subgroup and cosets of subgroups. Formalized Mathematics, 1(5):855-864, 1990.Wojciech A. Trybulec. Commutator and center of a group. Formalized Mathematics, 2(4):461-466, 1991.Wojciech A. Trybulec and Michał J. Trybulec. Homomorphisms and isomorphisms of groups. Quotient group. Formalized Mathematics, 2(4):573-578, 1991.Katarzyna Zawadzka. Solvable groups. Formalized Mathematics, 5(1):145-147, 1996

Some Properties of p-Groups and Commutative p-Groups

This article describes some properties of p-groups and some properties of commutative p-groups.Liang Xiquan - Qingdao University of Science and Technology, ChinaLi Dailu - Qingdao University of Science and Technology, ChinaGrzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.Marco Riccardi. The Sylow theorems. Formalized Mathematics, 15(3):159-165, 2007, doi:10.2478/v10037-007-0018-3.Dariusz Surowik. Cyclic groups and some of their properties - part I. Formalized Mathematics, 2(5):623-627, 1991.Wojciech A. Trybulec. Classes of conjugation. Normal subgroups. Formalized Mathematics, 1(5):955-962, 1990.Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.Wojciech A. Trybulec. Subgroup and cosets of subgroups. Formalized Mathematics, 1(5):855-864, 1990.Wojciech A. Trybulec. Commutator and center of a group. Formalized Mathematics, 2(4):461-466, 1991.Wojciech A. Trybulec. Lattice of subgroups of a group. Frattini subgroup. Formalized Mathematics, 2(1):41-47, 1991.Wojciech A. Trybulec and Michał J. Trybulec. Homomorphisms and isomorphisms of groups. Quotient group. Formalized Mathematics, 2(4):573-578, 1991.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990

Transcriptome annotation of 17 porcine tissues using nanopore sequencing technology

The annotation of animal genomes plays an important role in elucidating molecular mechanisms behind the genetic control of economically important traits. Here, we employed long-read sequencing technology, Oxford Nanopore Technology, to annotate the pig transcriptome across 17 tissues from two Yorkshire littermate pigs. More than 9.8 million reads were obtained from a single flow cell, and 69 781 unique transcripts at 50 108 loci were identified. Of these transcripts, 16 255 were found to be novel isoforms, and 22 344 were found at loci that were novel and unannotated in the Ensembl (release 102) and NCBI (release 106) annotations. Novel transcripts were mostly expressed in cerebellum, followed by lung, liver, spleen, and hypothalamus. By comparing the unannotated transcripts to existing databases, there were 21 285 (95.3%) transcripts matched to the NT database (v5) and 13 676 (61.2%) matched to the NR database (v5). Moreover, there were 4324 (19.4%) transcripts matched to the SwissProt database (v5), corresponding to 11 356 proteins. Tissue-specific gene expression analyses showed that 9749 transcripts were highly tissue-specific, and cerebellum contained the most tissue-specific transcripts. As the same samples were used for the annotation of cis-regulatory elements in the pig genome, the transcriptome annotation generated by this study provides an additional and complementary annotation resource for the Functional Annotation of Animal Genomes effort to comprehensively annotate the pig genome.Fil: Li, Jinghui. University of California at Davis; Estados UnidosFil: Guan, Dailu. University of California at Davis; Estados UnidosFil: Halstead, Michelle M.. University of California at Davis; Estados UnidosFil: Islas Trejo, Alma D.. University of California at Davis; Estados UnidosFil: Goszczynski, Daniel Estanislao. University of California at Davis; Estados Unidos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico CONICET- La Plata. Instituto de Genética Veterinaria "Ing. Fernando Noel Dulout". Universidad Nacional de La Plata. Facultad de Ciencias Veterinarias. Instituto de Genética Veterinaria; ArgentinaFil: Ernst, Catherine W.. Michigan State University; Estados UnidosFil: Cheng, Hao. University of California at Davis; Estados UnidosFil: Ross, Pablo. University of California at Davis; Estados UnidosFil: Zhou, Huaijun. University of California at Davis; Estados Unido

On Rough Subgroup of a Group

This article describes a rough subgroup with respect to a normal subgroup of a group, and some properties of the lower and the upper approximations in a group.Liang Xiquan - Qingdao University of Science and Technology, ChinaLi Dailu - Qingdao University of Science and Technology, ChinaWojciech A. Trybulec. Classes of conjugation. Normal subgroups. Formalized Mathematics, 1(5):955-962, 1990.Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.Wojciech A. Trybulec. Subgroup and cosets of subgroups. Formalized Mathematics, 1(5):855-864, 1990.Wojciech A. Trybulec. Lattice of subgroups of a group. Frattini subgroup. Formalized Mathematics, 2(1):41-47, 1991.Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990

Mapping and functional characterization of structural variation in 1060 pig genomes

BACKGROUND: Structural variations (SVs) have significant impacts on complex phenotypes by rearranging large amounts of DNA sequence.RESULTS: We present a comprehensive SV catalog based on the whole-genome sequence of 1060 pigs (Sus scrofa) representing 101 breeds, covering 9.6% of the pig genome. This catalog includes 42,487 deletions, 37,913 mobile element insertions, 3308 duplications, 1664 inversions, and 45,184 break ends. Estimates of breed ancestry and hybridization using genotyped SVs align well with those from single nucleotide polymorphisms. Geographically stratified deletions are observed, along with known duplications of the KIT gene, responsible for white coat color in European pigs. Additionally, we identify a recent SINE element insertion in MYO5A transcripts of European pigs, potentially influencing alternative splicing patterns and coat color alterations. Furthermore, a Yorkshire-specific copy number gain within ABCG2 is found, impacting chromatin interactions and gene expression across multiple tissues over a stretch of genomic region of ~200 kb. Preliminary investigations into SV's impact on gene expression and traits using the Pig Genotype-Tissue Expression (PigGTEx) data reveal SV associations with regulatory variants and gene-trait pairs. For instance, a 51-bp deletion is linked to the lead eQTL of the lipid metabolism regulating gene FADS3, whose expression in embryo may affect loin muscle area, as revealed by our transcriptome-wide association studies.CONCLUSIONS: This SV catalog serves as a valuable resource for studying diversity, evolutionary history, and functional shaping of the pig genome by processes like domestication, trait-based breeding, and adaptive evolution.</p

The Farm Animal Genotype–Tissue Expression (FarmGTEx) Project

Genetic mutation and drift, coupled with natural and human-mediated selection and migration, have produced a wide variety of genotypes and phenotypes in farmed animals. We here introduce the Farm Animal Genotype–Tissue Expression (FarmGTEx) Project, which aims to elucidate the genetic determinants of gene expression across 16 terrestrial and aquatic domestic species under diverse biological and environmental contexts. For each species, we aim to collect multiomics data, particularly genomics and transcriptomics, from 50 tissues of 1,000 healthy adults and 200 additional animals representing a specific context. This Perspective provides an overview of the priorities of FarmGTEx and advocates for coordinated strategies of data analysis and resource-sharing initiatives. FarmGTEx aims to serve as a platform for investigating context-specific regulatory effects, which will deepen our understanding of molecular mechanisms underlying complex phenotypes. The knowledge and insights provided by FarmGTEx will contribute to improving sustainable agriculture-based food systems, comparative biology and eventual human biomedicine

A compendium of genetic regulatory effects across pig tissues

The Farm Animal Genotype-Tissue Expression (FarmGTEx) project has been established to develop a public resource of genetic regulatory variants in livestock, which is essential for linking genetic polymorphisms to variation in phenotypes, helping fundamental biological discovery and exploitation in animal breeding and human biomedicine. Here we show results from the pilot phase of PigGTEx by processing 5,457 RNA-sequencing and 1,602 whole-genome sequencing samples passing quality control from pigs. We build a pig genotype imputation panel and associate millions of genetic variants with five types of transcriptomic phenotypes in 34 tissues. We evaluate tissue specificity of regulatory effects and elucidate molecular mechanisms of their action using multi-omics data. Leveraging this resource, we decipher regulatory mechanisms underlying 207 pig complex phenotypes and demonstrate the similarity of pigs to humans in gene expression and the genetic regulation behind complex phenotypes, supporting the importance of pigs as a human biomedical model.</p

Seismic analysis for the Lanzhou fireball

In this paper, we convert the Lanzhou fireball's trajectory using seismic data according to the analytical method presented in Pujol et al. (2005, 2006). Taking the same assumptions as Pujol et al., the position of the fireball burst at its terminal has been converted using a relative simple independent method. Both the trajectory and the position of burst are roughly coincident.The Meteoritics & Planetary Science archives are made available by the Meteoritical Society and the University of Arizona Libraries. Contact [email protected] for further information.Migrated from OJS platform February 202