Reduced dimensions form

In biophysics and related fields, reduced dimension forms (RDFs) are unique on-off mechanisms for random walks that generate two-state trajectories (see Fig.

Two-state time trajectories are very common in measurements in chemistry, physics, and the biophysics of individual molecules[2][3] (e.g. measurements of protein dynamics and DNA and RNA dynamics,[4][5][6][7][8][9][10] activity of ion channels,[11][12][13] enzyme activity,[14][15][16][17][18][19][20][21][22][23][24] quantum dots [25][26][27][28][29][30][31][32]), thus making RDFs an important tool in the analysis of data in these fields.

Since RDFs are uniquely obtained from the data,[33][34] they have many advantages over other mathematical and statistical methods that were developed for solving two-state trajectories.

A RDF can have irreversible connections, yet, it generates an on-off trajectory that has the property of microscopic reversibility, meaning that the physical system fluctuates around equilibrium.

In principle, there are 4 independent types of correlations in two-state trajectories: on-on, on-off, off-on, and off-off.

Figure 1 A 3on3 RDF
Figure 2 Two-state trajectories
Figure3 A two-state trajectory, RDFs and kinetic schemes, and the relations among these.
Figure 4 Here, shown are the stages of the software: first, take a noisy trajectory and clean it; then, find the RDF from the cleaned data. Finally, suggest a set of kinetic schemes that may be related with the found RDF. The software should also present the possibility of numerical simulations of noisy time trajectories.