# PRC

The following method describes how can one obtain the phase reset curve (PRC) as a function of timings of pulses. It turns out using the PRC of a system we could basically say a lot about the interactions between neurons without actually simulating the whole differential equations taking the maps route. I thought I will write this as a note for the future stupid me wondering why I chose this route.

Let a neuron be spiking and

\[\begin{align} T_1&=\text{normal time period}\\ T_2&=\text{perturbed time period} \end{align}\]The perturbation is happening at time \(t_s\), therefore,

\[\begin{align} t_s/T_1&=\text{phase before perturbation}\\ T_2-t_s&=\text{time to next spike} \end{align}\]Then, the phase has become \((T_1-(T_2-t_s))/T_1\)

This therefore gives the following phase difference,

\[\begin{align} \Delta \phi &= \text{new phase} - \text{old phase}\\ &=((T_1-(T_2-t_s))/T_1)-t_s/T_1\\ &=(T_1-T_2)/T_1 \end{align}\]Here, \(T_1\), \(T_2\) are the timings. \(t_s\) is the time of perturbation. \(T_1\) is the free running period and \(T_2\) is the perturbed period.

## Posts

### Notes on Inverse transform sampling

### Eigenvalues and poles

### Back Prop Algorithm - What remains constant in derivatives

### Wordpress to Jekyll Conversion

### Phase functions

### Solving Dynamical Systems in Javascript

### Javascript on markdown file

### Walking data

### Walking, it is complicated

### PRC

### Isochrone

### Walking, it's complicated

### Newtons iteration as a map - Part 2

### Newton's iteration as map - Part 1

### ChooseRight

### Mathematica for machine learning - Learning a map

### Prediction and Detection, A Note

### Why we walk ?

### The equations that fall in love!

### Oru cbi diarykkuripp(ഒരു സിബിഐ ഡയറിക്കുറിപ്പ്)

### A way to detect your stress levels!!

### In search of the cause in motor control

### Compressive sensing - the most magical of signal processing.

### Machine Learning using python in 5 lines

### Can we measure blood pressure from radial artery pulse?

subscribe via RSS