The evolution, genetics, and robustness of the network structure of the system are related to the coupling level of the network. The formation of patterns is the basis of all subsequent changes, but the ability to express is the result of selective expression, like dominant and recessive inheritance.

Data optimization to remove background noise based on high-dimensional structures, i.e. distributions. The introduction of multi-dimensionality helps to improve the accuracy and make the expression of the sequence more precise. Then there is the discrete operation of sequence matching, i.e., dynamic programming that makes the score matrix numerous.

Sequence matching and equilibrium construction, matching transfer of similarity sequences.

The inevitability of hierarchical convergence, any process can be expanded to represent a certain level, and any particular level is a selective expression of other levels. Generally speaking, the higher-order derivatives can be ignored, and due to the multi-level coupling point characteristics of the network, the operation is multiple iterations, and there may be chaotic states, that is, the effective operation range is limited.

Different equilibrium is at the global level, and the equilibrium we can observe is a high-dimensional structure, which is based on more low-dimensional equilibrium, and the latter operation keeps the equilibrium of the network within a certain range (robustness), and finally accumulates to a certain extent that there will be an overall state transition. This is the coupling of stability and evolutionary mutation.

The organization of the pathway stems from the fact that it is more in line with the adaptation to the environment (not necessarily the minimization of energy, but the optimization of efficiency) than the poorly organized pathway, and the emergence of the organization is based on the selection and elimination of non-organization, like the behavior of the free market, the survival of the fittest.

The definition of hierarchy is a kind of customization, which is essentially a description of a certain clustering of the network, which is regarded as a relatively independent hierarchy, but in fact it is a multi-level coupling. This may seem like a trap of circular definition, but my original intention was to construct a self-justifying and compatible system, which is a qualitative description, and the specific quantitative description depends on the anchor point chosen.

The coupling of sequences forms a matrix of high-dimensional structures, and then the matrices selectively express a certain sequence structure. It's an optimization.

The regulatory element and the regulatory mechanism are the expressions of different levels of the coupling structure of the network, and the latter is a high-dimensional structure, which is the sequence matching operation at the pathway level constructed by the former.

The similarity of systems, the similarity of levels, is understood in terms of the fractal theory of mathematics. It is also the basis for hierarchical coupling. It is also the basis of chemotaxis or resonance, distribution.

THE MULTI-LEVEL COUPLING OF THE REGULATORY MECHANISM, THE REGULATION OF THE MULTIPLE LINKS OF THE CENTRAL LAW OF DN~RNA~PROTEIN, JUST LIKE THE RECIPROCATION OF THE CHAIN OF SUSPICION, HAS A CERTAIN CONVERGENCE AS A WHOLE, THAT IS, THE ESSENCE OF THE DISTRIBUTION FUNCTION: ANTIBODY ~ ANTI-ANTIBODY ~ ANTI-ANTIBODY...... Here's an example, and I want to emphasize that these relationships are not one-way. Depending on the nature of the network, it is mostly convergent, which maintains the stability of the network, and a small part is non-convergent, which provides the possibility of variation that allows the network to evolve. (The inevitability of a small probability expressed on a sufficiently large scale)

Mutants provide the intrinsic nature of change, while hybridization similar to orthogonal experiments allows sequence matching operations to construct matrices that can express certain behaviors, i.e., sequences. This is related to the double helix structure of DNA, the dominant recessive expression of heredity.

The representation of the laws of biology and the rigorous mathematical derivation are an idealization. Because real mathematics emphasizes precision and accuracy, the construction of its Euclidean system is essentially an aetology expression, an elaboration of the unknown that exists, and a kind of discovery, while the biological network emphasizes more on the adaptation to the environment, that is, a certain distribution can be diffused on the basis of mathematical principles, and then the path collapses, and the requirements for accuracy are limited.

The final expression of the sequence is the equilibrium point of the hierarchical game.

The potential change is a multi-level coupling, that is, the sequential expression of different proteins, and the equivalence of the network can be used to express specific mechanisms using a circuit system composed of various components. This is an exploration of implicit structures, or high-dimensional structures. Multi-level coupling is not only the achievement of equilibrium points, but also the high-dimensional structure of computation, the processing of information.

Modeling is a simplification, hoping to deduce the most basic eigens from the distribution of the network, and build a model with certain predictive ability on this basis, and we know that the specific network is based on the distribution of its certain fluctuation range.

The feedback mechanism of the system is the pattern that inevitably emerges from hierarchical coupling. This is a requirement for the boundary formation of a self-justifying system.

The significance of feedback to the formation of homeostasis.

Both positive and negative feedback are selective expressions of the network, and their distribution makes the whole maintain a certain steady state. Therefore, its coexistence makes sense. Its distribution may conform to a power-law distribution.

The cyclic pathway is used as a hidden structure, just like atoms also satisfy a certain Boltzmann distribution. This is the basis for the self-justification of the network. Mathematically, it can be understood that the curvature is negative.

Multi-level coupling can be expressed as a representation of the Fourier series, which is the coordination of different frequencies, like a song. And this presupposes the existence of fundamental primitives: all aperiodic functions can be decomposed into superpositions of periodic functions.

The specific mechanism emergence, which is the multiplication of these Fourier series, i.e., a traversal, and then the emergence of some meaningful patterns. Like the concept of the parent function in combinatorics, the coefficient of the result of multiplying a polynomial is the possibility of combination, which is also a distribution. This is the power of the organization. This is also a reflection of the importance of probability, which is the emergence of infinite combinations of patterns.

Life comes from resistance to change. The distribution of potential difference is a form of organization that carries certain high-dimensional information. Such as genetic mechanisms. This is a mechanism of convergence resistance to the individual, and the information of the network is perpetuated by constructing groups. See Richard's selfish genes, which is a kind of idea that uses genes as a structure for operation.

The multi-level coupling provides a certain stability and can resist certain fluctuations. This is a buffering mechanism, which can also explain feedback formation. Resistance to change and even resistance to change caused by this resistance is like a first- and second-order derivative of the series expansion, which can preliminarily describe a certain network. For example, the cell membrane needs to maintain a potential difference in the concentration of a certain substance, so there are certain channel proteins, and there is also a certain differentiation in these channel proteins, that is, there are pumps in and out. Finally, a certain pattern can be formed.

The high degree of differentiation of the system allows it to play a very delicate role, which in turn reduces its resistance to environmental changes (which is decoupled with stability). So there will be a change in resistance to this tendency, in the case of biology, the formation of information systems, DNA and RNA. In my view of life, the formation of life precedes the formation of genetic information, and the mechanism of the genetic system is an accident that appears in the infinite combination of the earth, and then multiplies and expands due to its superiority. The process is a complex game. Once formed, the original life activities can be adjusted in turn, that is, new life can be formed. I see it as a revolution. The same is true for network regulation, because the combination of levels forms a meaningful cyclic regulation mechanism, as a high-dimensional structure, it will in turn adjust the original hierarchy for the operation of the overall mechanism. (Although behaving like life, it is essentially a trend) is what I understand as self-organization. At this level, there is also competition between different mechanisms, and there is also a certain equilibrium. This trend can be traversed upwards and upwards.

Relative proportions, relative relationships of levels, probability, partial derivatives.

The properties caused by the combination emerge and at the same time lead to the disappearance of certain properties in order to achieve the balance of the whole.

The critical point of the system and the explosion of the network are all manifestations of the power law distribution. The functionality of the network topology is related to this structure.

The power-law distribution is not just a global tendency, but can lead to a certain inference: a particular hierarchy is regarded as a variable, and its relationship is represented by the ln form of various variables.

The universality of variation and the integration of new modules into the overall system may be like the combinatorial arrangement of DNA sequences, and then a certain new pattern is formed at the level of expression, like the lactose operon of bacteria.

The necessity of high-throughput data for network understanding: the network is decomposed into sequences at different levels, and the matching and even traversal between sequences can be understood as a certain hybridization, and the resulting effect is the selective expression of the network.