Genomics is the science of genomes: it is the study of all the genetic material of an organism. In humans, the genome consists of information carried in 23 pairs of chromosomes in the nucleus, as well as mitochondrial DNA. In genomics, both coding and non-coding DNA is sequenced and analyzed. Genomics allows a better understanding of all living things, their evolution, and their diversity. It has a myriad of uses: for example, to build phylogenetic trees, to improve productivity and...

Diploid organisms inherit genetic material through chromosomes from both parents. Copies of the same gene are known as alleles. In most cases, both alleles are simultaneously expressed and allow various cellular processes to function optimally. If one of the alleles is missing or mutated, the expression of the other allele can compensate; however, this is not true for all genes.
The expression of some genes depends on which parent passed the gene to the offspring, through a phenomenon known as...

Integration by parts is a fundamental technique in calculus for evaluating integrals involving the product of two functions. It is particularly useful when direct integration is not feasible. The method is based on the product rule for differentiation, which states that the derivative of a product equals the derivative of the first function times the second, plus the first function times the derivative of the second. By integrating this identity and rearranging terms, the integration by parts...

While every living organism has a genome of some kind (be it RNA, or DNA), there is considerable variation in the sizes of these blueprints. One major factor that impacts genome size is whether the organism is prokaryotic or eukaryotic. In prokaryotes, the genome contains little to no non-coding sequence, such that genes are tightly clustered in groups or operons sequentially along the chromosome. Conversely, the genes in eukaryotes are punctuated by long stretches of non-coding sequence.

Definite integrals involving the product of two functions over a fixed interval can be evaluated using integration by parts. This method rewrites the integral as the difference of a product evaluated at the endpoints and a remaining definite integral that is often simpler to compute.A representative example is the definite integral of the inverse tangent function. Since there is no direct integration formula for arctan ⁡x, the integrand is rewritten as a product of arctan⁡ x and the...

The present-day mitochondrial and chloroplast genomes have retained some of the characteristics of their ancestral prokaryotes and also have acquired new attributes during their evolution within eukaryotic cells. Like prokaryotic genomes, mitochondrial and chloroplast genomes neither bind with histone-like proteins nor show complex packaging into chromosome-like structures, as observed in eukaryotes. Unlike mitotic cell divisions observed in eukaryotic cells, mitochondria and chloroplasts...