A Passage of Time Signal in the Human Brain

Basic continuous-time signals include the unit step function, unit impulse function, and unit ramp function, collectively referred to as singularity functions. Singularity functions are characterized by discontinuities or discontinuous derivatives.
The unit step function, denoted u(t), is zero for negative time values and one for positive time values, exhibiting a discontinuity at t=0. This function often represents abrupt changes, such as the step voltage introduced when turning a car's...

The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is the...

In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...

Despite the protective membrane that separates a cell from the environment, cells need the ability to detect and respond to environmental changes. Additionally, cells often need to communicate with one another. Unicellular and multicellular organisms use a variety of cell signaling mechanisms to communicate to respond to the environment.

Endocrine cells produce hormones to communicate with remote target cells found in other organs. The hormone reaches these distant areas using the circulatory system. This exposes the whole organism to the hormone but only those cells expressing hormone receptors or target cells are affected. Thus, endocrine signaling induces slow responses from its target cells but these effects also last longer.

Bacterial signaling can occur within bacteria (intracellular) or between bacteria (intercellular). At times, a group of bacteria behaves like a community. To achieve this, they engage in quorum sensing, the perception of higher cell density that causes changes in gene expression. Quorum sensing involves both extracellular and intracellular signaling. The signaling cascade starts with a molecule called an autoinducer (AI). Individual bacteria produce AIs that move out of the bacterial cell...