Sequencing in High Definition Drives a Changing Worldview of the Epigenome

Emily Hodges1

  • 1Department of Biochemistry and Vanderbilt Genetics Institute, Vanderbilt University School of Medicine, Nashville, Tennessee 37232.

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Definite Integral01:29

Definite Integral

Consider a real-valued function defined on a closed interval. One of the fundamental objectives in calculus is to determine the area under the graph of such a function. When an exact computation is not readily available, this area can be estimated by dividing the interval into a finite number of equal subintervals. Each subinterval corresponds to a rectangle whose width is the length of the subinterval and whose height is determined by the value of the function at a selected point within that...
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Definition of z-Transform01:26

Definition of z-Transform

The z-transform is a powerful mathematical tool used in the analysis of discrete-time signals and systems. It is an essential analytical tool, analogous to the Laplace transform used in continuous-time systems. It plays a crucial role in the analysis of signals and systems, complementing the discrete-time Fourier transform. Both the z-transform and the Laplace transform convert differential or difference equations into algebraic equations, simplifying the process of solving complex problems.
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Energy to Drive Translocation01:37

Energy to Drive Translocation

Mitochondrial protein import is powered by two distinct energy sources: ATP hydrolysis and electrochemical potential across the inner membrane. Newly synthesized precursors are bound by cytosolic chaperones of the Hsp70 family, which guide them to the import receptors on the mitochondrial surface. Utilizing the energy of ATP hydrolysis, Hsp70 chaperones transfer these precursors to the TOM receptors on the mitochondrial outer membrane.
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Properties of Definite Integral I01:30

Properties of Definite Integral I

A car’s motion over time can be effectively analyzed using integral calculus, particularly through the concept of the definite integral applied to a velocity–time relationship. The definite integral describes how velocity accumulates over a specified time interval to produce total displacement. From a geometric perspective, this displacement is interpreted as the area under the velocity–time curve. Several key properties of definite integrals make it easier to analyze motion...
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The Precise Definition of a Limit01:27

The Precise Definition of a Limit

Understanding the formal definition of a limit is essential for precise mathematical analysis. This concept allows us to rigorously determine how a function behaves near a particular point without relying on ambiguous notions such as "getting close." The ε-δ definition plays a foundational role in calculus, ensuring analytical clarity and logical consistency in limit evaluation.The formal definition states that the limit of a function f(x) as x approaches a is L, written asif for...
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Properties of Definite Integral II01:24

Properties of Definite Integral II

Definite integrals are essential tools in calculus, used to quantify accumulated change over an interval. A common physical application is calculating the total displacement from a velocity-time graph. If a velocity function, v(t), describes the motion of an object over time, the definite integral gives the net displacement between times a and b. This integral corresponds to the signed area under the velocity curve between those two points.Two fundamental properties of definite integrals aid in...
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