Signal-flow graphs offer a streamlined and intuitive approach to representing control systems, providing an alternative to traditional block diagrams. These graphs use branches to symbolize systems and nodes to represent signals, effectively illustrating the relationships and interactions within the system.
In a signal-flow graph, branches denote the system's transfer functions, while nodes represent the signals. The direction of signal flow is indicated by arrows, with the corresponding...

In Signal Flow Graph (SFG) algebra, the value a node represents is determined by the sum of all signals entering that node. This summed value is then transmitted through every branch leaving the node, making the SFG a powerful tool for visualizing and analyzing control systems.
Each node in an SFG corresponds to a variable, and the interactions between nodes are represented by branches with associated gains. When multiple branches lead into a node, the value at that node is the sum of the...

Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...

The Hedgehog gene (Hh) was first discovered due to its control of the growth of disorganized, hair-like bristles phenotype in Drosophila, much like hedgehog spines. Hh plays a crucial role in the development of organs and the maintenance of homeostasis in both invertebrates and vertebrates. However, while Drosophila has only one Hh protein, mammals have multiple functional Hedgehog proteins - Sonic (Shh), Desert (Dhh), and Indian Hedgehog (Ihh). All of these homologous proteins have adapted to...

Membrane lipids such as phosphatidylinositol (PI) are precursors for several membrane-bound and soluble second messengers. Specific kinases phosphorylate PI and produce phosphorylated inositol phospholipids. One such inositol phospholipids are the  phosphatidylinositol-4,5 bisphosphate [PI(4,5)P2], present in the inner half of the lipid bilayer. Upon ligand binding, GPCR stimulates Gq proteins to turn on phospholipase Cꞵ. Activated phospholipase Cꞵ cleaves PI(4,5)P2 and...

An ogive graph is sometimes called a cumulative frequency polygon. It is one type of frequency polygon that shows cumulative frequency. In other words, the cumulative percentages are added to the graph from left to right. An ogive graph plots cumulative frequency on the vertical y-axis and class boundaries along the horizontal x-axis. It’s very similar to a histogram; only instead of rectangles, an ogive displays a single point where the top right of the rectangle would be. Creating this...