October 3, 2022

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# Mathematics of data-realised algorithm – Part 1 – Java Code Geeks As I have said in my blog on “data-realized algorithms”, while we have not used mathematical equations explicitly, data collected using data-realized techniques such as “accumulation of various properties of molecular structures” inherently use mathematical concepts. The expression is in a form that is different from mathematical equations that allows for more complex representation than is possible with the representation as equations. I know this seems like a tall claim, but if we stop to think, after all the language of mathematics has evolved because humans wanted to express what they observed and understood of nature not the other way. So, it should follow that the natural processes that are not specifically arranged by us to follow a specific path, will enact out mathematical concepts, both that which we understand and have represented by equations and that which we do not understand. But, before we get into the mathematical concepts, to summarize what I have said we can do as a design for AI:

The above diagram shows the first set of steps in the data-realized algorithm. As the data passes through various responses and triggers of molecular structures, the sequence and behaviors of the data or the harmonics of the data is automatically established. When we look at the output of the response from the target, we should find that a few things are already done on the data:

• The related data are already grouped together.
• The changes of the relevant data across a duration is already accumulated in the relevant order.
• The sequence is already established through the series of transmission to the target. The specific target can be made to respond and retain the response only for a certain behavior of the data. Thus, using the response from a specific target should give us only that data which has some intended behavior.
• Even though a specific set of parameters could have been created as a single molecular structure, the structure can be broken down to only those relevant ones that contribute to a behavior. Thus a filter is automatically established.
• The fuzziness of data is automatically present because we are not time bound and are accumulation and process trigger bound. Thus, the natural fuzziness which we notice in nature occurs automatically.

If we analyze this further we find that it is nothing but the same if-else clause that we implement. But, it gets implemented without much rigid “if-else” clauses or rigid mathematical functions to be learned. Just a series of triggers of accumulation, formation or split which trigger when some or other condition is met. But, the number of mathematical functions that is realized by this process are many for which we seem to have to write a lot of code and need a very powerful processor to do the computation. And even after all that code and super-computer-based processing we cannot achieve the fuzziness that is already present in the above type of implementation.

So, what are the mathematical concepts that are present in the above? Let us start at the first concept of “encoding changes by accumulation into some molecular structure”. To understand this, let us look in-depth at the steps in the protein synthesis process. At the high level, the process involves transcription, translation, post-translation modification and protein folding. For the first transcription: mRNA needs to be formed from DNA. For this, the denaturation of a part of the DNA to be transcribed has to occur which splits the strands of the DNA. The strands split typically when the hydrogen bonds between the base pairs are broken. One of the various reasons for change in hydrogen bonds is heat. A specific variation in heat induces denaturation which then triggers the process of transcription. If variation in heat represents the data that we want to measure, then, a specific variation in heat splits specific hydrogen bonds in the DNA. The continuity of the heat variation and the duration is encoded in the number of hydrogen bonds split. Thus, the mRNA created from a denatured DNA should encode the variation, the continuity and the duration of heat variation. So what we have encoded is a combination ∆T over ∆s, where T = temperature and s = the space of temperature variance and ∆T over ∆t, where t = time of variance. But this is not just as simple as this, because what we are happening is a combination of both together. If we look at heat variance in time function and map to the structure formed say, we have something as below:

As time progresses, the structure changes based on the heat adding more bonds. It should be realized that while I have taken t1, t2… as discrete time intervals, the bonds get formed because of the continuity that exists between t1 and t2, so variance in heat over transt translates to the bond. So, we can view this as the “continuous variation of heat across time, transforming to the structure”. The structure thus contains all the information from t1 to t9. If we analyze this in the space view at t9, we are looking at just the final structure with the impact from all other time intervals accumulated into it, shown below:

At any instant of time, what we have is an accumulation of all the prior affecting changes contributing to the formation of the structure, continuously growing or decaying by a natural growth factor (e) from that prior time of formation till the current instant. So, if the structure has a variation of some function f