The half-life of a reaction (t1/2) is the time required for one-half of a given amount of reactant to be consumed. In each succeeding half-life, half of the remaining concentration of the reactant is consumed. For example, during the decomposition of hydrogen peroxide, during the first half-life (from 0.00 hours to 6.00 hours), the concentration of H2O2 decreases from 1.000 M to 0.500 M. During the second half-life (from 6.00 hours to 12.00 hours), the concentration decreases from 0.500 M to...

The “tree of life” describes the evolution of life and the evolutionary relationships between organisms. The root of the tree is the common ancestor to all life on Earth. All other species radiate from this point, much like the branches of a tree. The numerous tips of these branches on the tree of life represent every living, or extant, species. Extinct species, which are species that no longer exist, can be found towards the center of the tree. Currently, these organisms, both extant and...

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.

DNA sequencing is a fundamental technique that is routinely used in the biological sciences. This method can be applied to a range of questions at different scales - from the sequencing of a cloned DNA fragment or the study of a mutation in a gene up to whole-genome sequencing. However, despite the widespread use of sequencing today, it was not until 1977 that Fredrick Sanger and his collaborators developed the chain-termination method to decode DNA sequences. It relies on the separation of a...

In the same year as the discovery of the Sanger sequencing method, another group of scientists, Allan Maxam and Walter Gilbert, demonstrated their chemical-cleavage method for DNA sequencing. The Maxam-Gilbert method relies on using different chemicals that can cleave the DNA sequence at specific sites, the separation of resulting DNA fragments of variable size using electrophoresis, and deciphering the DNA sequence from the resulting gel bands.
Challenges of the Maxam-Gilbert Method
The...

Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.However, realistic environmental conditions limit the number of...