Below I've included description of my theoretical contributions that I believe to be important for many different applications. Please use the links on the left and colored links in the main text to navigate.
Imagine that the state of a certain object is constantly modified by a series of elementary changes with zero mean and intensity (amplitude times frequency) determined by the objects state. Every modification is a micro-step. Then, on a macro-step time scale, the object’s state will appear as though driven by a “kinetic force” toward a state domain that corresponds to smaller intensity of modifications. In other words, a systematic component in the object’s state trajectory will be observed with the magnitude proportional to the gradient of modification intensity and direction opposite to that gradient. In general, KFP can be viewed as the main mathematical basis of time arrow-type phenomena.
KFP is a very general principle. After I discovered KFP, I was thinking a lot about and looking for examples of its natural applications. Given the ubiquity of stochastic fluctuations throughout the universe, it must be possible to find evidence for KFP utilization in many diverse areas of nature (Shimansky, 2007). Below is a list of such examples I found so far.
That natural regulation of mutation rate is exactly what one would expect knowing KFP. In fact, I predicted existence of such regulation before knowing anything about it, and that hypothesis prompted me to search the related literature for evidence supporting it. The hypothesis seemed to me so likely at the time that I was not even surprised when I found such evidence.
Intuitively, it seems likely that KFP can be used to explain many more natural phenomena, and the above list will be appended. For instance, given Erik Verlinde’s hypothesis that gravity is an entropic force and the fact that the law of entropy increase can be derived from KFP, it can be imagined (as a tempting, although rather raw, hypothesis) that KFP might be useful for explaining gravity, and, since KFP is perfectly compatible with quantum mechanics, it could serve as a basis for quantum gravity.
In many cases, data describing the behavior of a system are collected as sets of waveforms. The degree of similarity between the waveforms is a fundamental characteristic reflecting important properties of the system’s dynamics. For example, the degree of coordination among state variables of a control system is a measure of its optimality. The amount of mutual inter-correlations within a set of waveforms describing the price dynamics of a given set of stocks can be important for financial forecast.
I developed a novel method for measuring significant linear dimensionality that produces is a theoretically correct estimate of the degree of linear independence within a given set of waveforms viewed as vectors (Shimansky, 2000; 2006).