Extending sequence-class membership with matching to sample

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Introduction to Sequences01:26

Introduction to Sequences

The ancient Greek philosopher Zeno of Elea proposed a series of paradoxes to challenge prevailing notions of motion and continuity. One such paradox imagines a man walking toward a door but only ever covering half the remaining distance with each step. This sequence of movements—first one-half, then one-quarter, then one-eighth of the total distance, and so on—forms a mathematical concept known as a geometric sequence. Each term is half of the previous one and can be written...
Per-Unit Sequence Models01:26

Per-Unit Sequence Models

An ideal Y-Y transformer, grounded through neutral impedances, displays per-unit sequence networks akin to those of a single-phase ideal transformer when subjected to balanced positive- or negative-sequence currents. These currents do not produce neutral currents, and their associated voltage drops.
Zero-sequence currents, which are identical in magnitude and phase, generate a neutral current, resulting in voltage drops across the neutral impedance and the low-voltage winding. If the...
Sequences01:29

Sequences

Sequences are fundamental mathematical objects consisting of ordered lists of numbers that follow a specific rule or pattern. Sequences are critical in various mathematical concepts, including calculus, series, and number theory. They can model real-world phenomena such as population growth, financial investments, and physical processes like the diminishing height of a bouncing ball.Each number in a sequence is referred to as a term. Typically, the terms are denoted as a1, a2, a3,…, where the...
Multi-species Conserved Sequences02:51

Multi-species Conserved Sequences

Next-generation sequencing technologies have created large genomic databases of a variety of animals and plants. Ever since the human genome project was completed, scientists studied the genome of primates, mammals, and other phylogenetically distant living beings. Such large-scale  studies have provided new insights into the evolutionary relationship between organisms.
Although the genome of each species varies greatly from each other, a few sequences are highly conserved. Such conserved DNA...
Maxam-Gilbert Sequencing01:05

Maxam-Gilbert Sequencing

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...
Next-generation Sequencing03:00

Next-generation Sequencing

The first human genome sequencing project cost $2.7 billion and was declared complete in 2003, after 15 years of international cooperation and collaboration between several research teams and funding agencies. Today, with the advent of next-generation sequencing technologies, the cost and time of sequencing a human genome have dropped over 100 fold.
Next-Generation Sequencing Methods
Although all next-generation methods use different technologies, they all share a set of standard features.