Operation of a highly connected system: network, model: probabilistic network

Graph theory is used for network structures, taking advantage of its topological properties, game theory, which is actually a reciprocating interaction that has a certain convergence radius (I know you know...... ）

The most important thing between the layers of the network is coupling or integration, curling up in the same dimension, expressing in multiple dimensions

Granularity, the hierarchy reacts as particles exist, and the concept of statistical mechanics of physics can be introduced

Equilibrium is an inevitable trend, which is actually a process of information transmission, because there is a certain delay in transmission, local imbalance also exists, which satisfies the distribution of equilibrium and imbalance on a larger scale

Connectivity, introduction of the concepts of calculus: path integration, differential equations, surface integrals

Locality is related to the velocity of circulation, and the increase of velocity decreases the proportion of a small number of high-quality information outputs, which actually gives each small node with low connectivity the possibility of becoming a central node with high connectivity

The complexity of the network is reflected in the variability of probability and the diversity of selective expressions of reality, everything is a probabilistic expression, in a long enough time dimension, what may happen will inevitably happen (Murphy's law), the good happens we take for granted, and the bad happens but is shocked, which is unreasonable, but the progress of human beings is reflected in the pursuit of advantages and avoiding disadvantages, that is, to increase the probability of good happening as much as possible, but bad things will definitely happen

The hierarchical decomposition of the network, the connection of single attributes (different evaluation criteria), and the first-order is easy to understand. The relationship between pen, fun, and pavilion www.biquge.info is multi-dimensional, with a network structure such as type, intensity, and so on

The physical properties of the network determine that it must have energy distribution, that is, the distribution of connectivity, there are central nodes and general nodes, the number is inversely proportional to the connectivity, in fact, it can be regarded as local particles, the central node is the nucleus, and the surrounding general nodes are electrons, forming a convergent sublayer. The connection between them is there, just like the relationship between molecules. Electrons, on the other hand, can be represented by a wave function, which has infinite possibilities, and the specific connection is its expression

The expression of properties in the whole, which requires setting a threshold that allows us to make a certain judgment, what percentage of the probability is that the xx hypothesis exists, such as visualization that makes the human mind make a certain judgment

The dynamics of the network, i.e. changes in connections, such as the collision of particles, Brownian motion, these connections are actually wave functions. When the connection of two central nodes exceeds a certain ratio, it can be considered as an atom forming molecule (at this time, the number of connections is equal to energy). The formation of connections makes up the pathways at each level, and its path integral is 0. There are various positive and negative feedbacks inside the pathway, which is the internalization of dynamic equilibrium

The behavior of the individual network is based on the probability expression of the network structure and dynamics, and we can use probability to understand it as a whole, in fact, the behavior of the individual is a fluctuation of the overall behavior of the network, and there is no completely independent individual. It is only when it is regarded as a coupling of the hierarchical circles in which it is located, and its general behavior can be regarded as periodic

The difference in the nature of the different scales of the hierarchy is the result of their selective expression, because their needs can only meet the needs of the collective by constantly rising in the hierarchy (the individual seeks food and clothing, and the collective seeks development)

The six-degree separation is the average or eigenvalue of a whole, which is the possibility of connection, and the transmission of information also needs to consider the strength of the connection, so that the low-quality data can be removed and the quality of the remaining data can be improved

Internet. The nature of the whole is relatively determined, but the individual is the fluctuation of its intrinsic nature, and we should see that any increase in efficiency is the result of sacrificing the possibilities of other parts of the network

Nash equilibrium is a universal trend, a level of fixed points in the whole

As a leader, the rich get richer, and this is because new nodes tend to connect with high connectivity points, which is positive feedback

The contagion of the closed community to the society is a deformation of the network structure. In fact, it is also a hierarchical classification

The nature of the whole stems from the anticipation of the information combination, i.e., the intrinsic, and the multidirectional connections of a single individual form loops and even networks as a whole

Distance, direction, and intensity are the variables that connect the small-world phenomenal functions, the strong connections are the nuclei of the structural formula, and the weak connections are the boundaries of communication with the outside world, i.e., the electrons of the wave function. Selective expression on a large scale seems to be related to boundaries, but in fact it is only related to possibility

The properties of individuals can diverge into a certain network, and different sequence combinations can form different networks

All changes are at the level of probability: when two nodes have a common node, the probability of their connection will increase, and the probability of cohesion can also build a network, which is also the coupling mechanism of the pathway, a probabilistic logical connection

The possibility of leading to movement, multiple small possibilities as antennae, when it encounters an environment that makes its selective expression intense enough to form a new central node

The pathway is the hierarchy, and the shortest path is a tendency of energy distribution, as is the closure

Structural equilibrium, the distribution and proportion of multiple forces (1/0), which is achieved through the formation of sublayers, i.e. particle-like groups

In a triangular relationship, all + or only one + is a balanced relationship. And in the whole, the majority is balanced, and the small part is unbalanced, which is also a distribution. Fixed and variable regions, so that the possibilities of expression are infinite

The equilibrium theorem is the opposition of two groups (internal relations) (political sides are absolute to achieve equilibrium), while in reality they are heterozygous, and multiple dimensions make stratification impossible. It depends on the criteria for division. After the game, the nature of individual choice is biased, and the selective expression of the information transmission relationship according to the proportion forms the opposition of yin and yang. Since it is dynamic, there are also yin and yang roots

Nash equilibrium, the most conservative choice for individuals to maximize their interests in a changing environment, is the intrinsic level of the whole

The median value theorem and the fixed point theorem illustrate the existence of eigenlevels and are also the result of Nash equilibrium

The unit of a network is a path, and each step of it is probabilistic and connected. The coupling of different pathways forms a new dimensional coupling, which enables the new selective expression (also a pathway).

Convolution, multiple integrals, and multiplication are all simplifications of different levels of addition, so that the result is in one dimension that we can understand

Network dynamics, the law of relationship construction of nodes: new nodes tend to establish a connection with the central node of strong circulation, so that there is a Matthew effect, the rich get richer, which is a result of distribution, and the absolute progress led to the distribution of resources. However, this is one-dimensional, and new breakthroughs at different levels can also form new central nodes. This power-law distribution actually reveals its tendency to particleization1/n^2, the distribution of quanta,

Cascade effect

The distribution is omnipresent, with low returns for high probabilities and high returns for low probabilities, which is the form of coupling

The theory of small worlds, the degree of convergence, the radius of convergence, which is the law of large-scale emergence

Combination and expression of inherited genes

My goal is to build a relatively complete architecture of the network

?Watts, Nature, 1998 Small World Model

Barabási, Science, 1999 Scale-free Networks

Construct the concept of network entities from physics, and then return to physical statistics

It should be considered that the connection of edges may have an impact, and the construction of the relationship between the two points is not taken for granted, but probabilistic, with a certain conversion rate. Emphasizing the interaction of edges, which have a certain attenuation radius, only the construction of edges between nodes that are close enough is relatively independent.

To find a relationship to construct a connection in each independent node, it is necessary to select different criteria to construct a connection of different strengths, and form a small circle of various sublayers such as interpersonal communication, which is regarded as a first-order path coupling

The locality of the network, a group of nodes of statistical significance, which can be projected as a high-dimensional cyclic coupling

A node is not a particle, it is a coupling point of a high-dimensional loop

The network topology is a change in the whole and can be seen as a transformation of information, as some loops may break due to path problems or new loops may be built

Network dynamics, new nodes tend to be attached to the central node with high connectivity, which makes it also have a chance to form a central node, which is a conversion rate (find the top and get the middle), of course, this is also a probability distribution, only a very few nodes really become the center node, but the rest are not bad

To integrate the experimental data, it is necessary to choose a better level, and the original knowledge is also a good prior probability

The question is to prove its validity, and my idea is to keep it growable, mature in iterations, and have a large enough resemblance to the complex web of reality. My vector is the biological organism network, and the effect is evaluated through medical or drug experiments

integration, which may exhibit distinct regularities, refers to integrated circuits

The physical statistics of the whole and the disorder of the individual are a pair of contradictions, can we follow the example of our predecessor Planck, introduce the perspective of quantization, and communicate the whole and the individual? Introduce new layers, such as the probability that RNA is considered a structure in a certain time dimension to the DNA as a whole, and the probability that an individual is randomly expressed in a short period of time.

The transformation of the network is the process of transmitting information

The traffic of the network is the process of self-allocation of resources, like a wave function. We determine the inputs and outputs and are confident that the nodes will always move to the destination, which is the connection between the nodes of the higher dimensions. The specific path of reality is the result of selective expression, and the probability collapses

Change is dynamic, and networked changes can reach the goal, but this is not worth the cost: the introduction of new layers will be digested

Introducing the idea of economics, the free market will achieve the purpose of allocation, but this process is uneven and will never reach a steady state; Emphasizing certain rules, individuals can explode into infinite possibilities under a certain framework, and due to the existence of a selection mechanism, there is always a small proportion of people who can survive, but at this time the absolute total has been greatly increased; The multi-dimensional differentiation caused by competition, I repair the car and you farm, and the whole can be formed through market selection in the whole; There is independence, the diversity of choices and the distribution of numbers (fewer central nodes and more nodes in general), which is a kind of coupling, which is necessary for the survival and continuation of the group, proportion and balance

Emergences are multi-level probabilistic ensembles

Big data, probability, and the infinite possibilities of combinations, but what is important is the meaningful combination sequence and distribution, focusing on the construction of patterns, i.e., intrinsics

The overall change of dimensions, the blurring of boundaries, that is, the construction of possibilities is more diverse

Any data is the result of the selective representation of multiple probabilistic networks, such as the hidden Markov model. How to break down epigenetic data into gene levels

Visualizing data is a secondary process that uses the human network

Relationship networks, proportions, and probabilities are their commonalities

The genome is an entity, and the expression is also an entity, and the two should be coupled to each other, forming each other, just like a dynamic equilibrium, and the environment determines k

We always have to look for unchanging entities as a guarantee, and finally find that it is a higher dimensional choice to take the law of change of the changing entity as the immovable point

Quantity is positively correlated with complexity, but the latter is more important

The interaction of large-scale data can derive intrinses based on the coupling hierarchy, such as predicting disease expression patterns

The qualitative selection of descriptive nodes (which are actually selectively expressed in a cycle at a lower level) is measured in elephants

Expressions are expressed in terms of frequency and can be equivalent to circuit network structures

Trends manifest from high-dimensional data, such as high-level leaders may see the impossibility of domination continuation. The derivation of the hierarchy is related to the distance relationship between the nodes, and if a liege's dominance over his own territory begins to decrease, the indirect rule will not appear at all. However, as the effects of this reduced lord's control spread to distant villages - most likely due to technological advances - the network of lordship relationships was gradually simplified and eventually disappeared

Path selection and matching, scoring matrix

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