Topological measures

Degree: The number of edges connected to the node

Maximum Components: The largest components in the network that are connected to each other

Clustering coefficient: ci=2n/ki (ki-1), ki refers to the number of adjacent nodes of node i, and n refers to the number of edges between ki nodes. The pen "Biquge" Pavilion www.biquge.infoci=1 indicates that it is the center of this fully connected class.

The yeast two-hybrid system utilizes hybrid genes to probe protein-protein interactions by activating the expression of reporter genes

The relationship between drug targets and disease-related gene products on PPI is used to find disease-related genes through drug guidance, and the minimum distance between pairings is found in disease-related genes.

The coupling, collision, and intersection of the network are regulated by distance, and the coupling of the number of targets is like a+b=a*b, and the drug combination is 2

Similar drugs have a relatively high local clustering coefficient and use macroscopic attributes

Multiple targets—multi-level, i.e., different clustering coefficients--

Targeting genes, protein levels

The distribution of quantum levels such as network tendencies, nodes, distances, clustering coefficients, etc

Stochastic based patterns emerge

Disease is a network of different patterns, attributes: number of nodes, average path, clustering coefficient, etc., and the same is true for organ systems

Consider the differences and the pathway structure of the upper layers

Linearity, splitting and coupling of substructures. The path connection of nodes, the information redundancy and the eigenvalue of the complementary node group, and the degree of contribution. Weight allocation

The first six genes can represent more than 80% of the subpathway state, six degrees of space

Is the average at the gene and protein level a geometric mean or something else

Interaction, non-isotopic

Force is proportional

The interrelationship of fine structures, the interaction between subsystems and substructures at all levels, and the interaction between the whole system and local regions

The global invariance and the definition domain invariance of the high-rise structure when the local space is continuously transformed

Whether the extension and expansion of the concept itself can produce a new unknown result—and whether this new result can be contained and accommodated by the old structural form, a linear structure

The fractal dimension of the overall structure, the hierarchy

Space is high-dimensional, containing combined information

The information structure is correlated as a whole, the measurable subspace is homogeneous after segmentation, and the domain invariance of the linear combination is defined

All elements in a space are compatible with each other, and all incompatible elements do not belong to the same space.

Linearity is a Taylor decomposition like a step derivative, which allows any element A and the e-neighborhood of a to contain or imply all the neighbors of a or all neighborhood systems, or even the entire space

Elements, their properties, their coordinates or positions in space, and the spatial structure of holographic space are compatible and adaptable to each other

The overall or overall spatial structure of a space determines the nature of the elements at any isolated point, as well as the spatial structure of any part of the subspace or local area

Distribution and distribution

Nonlinearity is the selective expression of linearity, and the selection of the hierarchy of the network, such as the addition of the distributive layers, is also a kind of quantization. The similarity of the hierarchy can be similar to the formation of sequence matching, sublayers, motifs. The search for relationships, evolutionary relationships, and different selective behaviors are also linear and distributed. Approximation of the multi-approximation method. Look for preferences.

Data model thinking

Signaling and data crossing. The coupling of pathways is the coupling of sequence complementarity and pan-correspondence.

The properties of the external body depend on the relationship between the internal genes and their expression

Boolean algebras of 1 and 0 are quantum, which reduces everything to the most basic binary operations, at the level of one life two, one is an all-encompassing electron cloud, and the third is a two-based structure, and when the order of magnitude is large enough, it can perform complex operations, which is the emergence of probability

The probabilistic nature of the network, the different orientations of the relationship between concepts

Space is represented in a coordinate system, and distance is equal to the sum of squares of the coordinates

The vertical relationship of the vector: the product is 0, and the sum of the respective products of the quantities of the corresponding coordinate axes is 0

Projection, dimensionality reduction, first-order operations

The inner product is the absolute value of the vector multiplied by its absolute angle

The vector product (cross product, outer product) c=a*b, is a vector perpendicular to the third dimension of the two vectors a and b, which can be represented by a matrix, and a parallel relationship can be obtained

The product of the vector is the area of that parallelogram, ascending dimension

Networks are also vectors, which not only do not satisfy the law of elimination, but also do not satisfy the commutative law as a type of matrix

The mixed product is the result of multiplying multiple vectors, and the cross product is followed by a dot product

Multivariate equals multidimensionality, and its projection is its defining domain

Can a multivariate function exist only if there is a limit?

Continuous vs. Limit

The partial function is a relative proportion, which is the change in dimensionality reduction

The equivalence of the hybrid partial function, commutative

Real function (or real analysis) is a problem that is not solved by mathematical analysis. It's the integrability of the function, and then it comes out to enjoy a rigorous system. Starting with set theory, measures are introduced, and then integrals are introduced. The integrals of the real function are all Lebesgue integrals, because this range is wider, and the set of Riemannian integrables is not as large as the set of Lebegus integrables.

In the initial stage, you quickly get in touch with enough concepts, deepen your understanding in practical terms, and wait until you reach the advanced stage, choose the part as the main line, and focus on development (the pyramid distribution of the hierarchy of probability networks)

Complicated formulas, difficult theories: based on simple ideas

Economics is a kind of communication network, which has a certain similarity with the complex system of the world, and its mathematical theories such as Nash equilibrium can also be applied to the composition of probability networks

The state of the quantum is a description of the orbit of the network

The uncertainty principle of network nodes, different orders of magnitude at different levels, the similarity of their sequences and the coupling of quanta form orbitals/loops (one-dimensional relations of the network)

Vector - Curve Integral - Tensor, simplification of operators

Fourier analysis, the understanding of new directions

A matrix is seen as a hierarchical representation of a network, and its two-dimensional form is a probabilistic network (physical reality) that decomposes vectors into quantum levels. The multiplication of the matrix is a kind of traversal, and the different levels are different expressions of the network (I recognize that the essence of the world is the complex connection of the network). A determinant is a simplification of the mathematical structure of a matrix, and its rules of operation are related to the properties of the matrix. The chunked operation of the matrix is the embodiment of the relative opposition of the network hierarchy. The eigengen, which is the result of the overall computation of the network, is a target.

A network is a space, (defined by length, angle, etc.), that can accommodate motion, i.e., various transformations. Matrices describe motion, and both its motion and the representation of its own existence (coordinate system) are forms of matrix description of the network. Related to the relativity of motion, mapping is the essence of motion.

Probability multiplication is a linear transformation of different bases

Continuity has its limit, and matrices are the points of transition

An object can be expressed as a linear solution to other objects (different weights are different probabilities), a mathematical form of a probabilistic network, Fourier analysis

Matrix change, derivative

Linear algebra and loop construction, eigenvalue solving

A neural circuit is a network structure, and severing a certain connection may interfere with a variety of neural circuits, and there may be a certain compensation, which stems from the intrinsic similarity of probabilistic networks

Big data for system analysis and system optimization

Coupling of pathways, operation at the overall level, emergence of patterns, similarity of levels

The abstract beauty of formal operations (the repetition of simple laws leads to complex results) - ingenious design - the theoretical system at the heart of mathematics - the intuition and motivation of mathematics (the pattern of selective expression, the perception of similarity makes the path connection of different positions the shortest)

Invisible, unknowable, all are probabilistic networks. Like a wave function, it can only be understood as a whole, and once understood concretely, it can collapse into a specific path

Experience and knowledge are a couple

Combining the obvious facts with each other, it is possible to find a path that makes the whole coupling (the assumption based on the network) because it has a certain internal structure. Geometry is a two-dimensional, self-consistent structure

The decomposition of simple steps, which is the differentiation of paths, is part of the high-dimensional structure (by iterative proximity)

Concretization: extreme cases, simplifications, derivation of theories that are included or included, formal substitution, similar problems, generalization problems

The relationship of number theory is a network of decimal relations, the distribution of prime numbers may be a kind of convergence, and the whole number is a quantized description: it can be regarded as a tendency to collapse;

A hierarchical game, constrained by various constraints, according to the change of rules, like a Turing machine

;