CN104598748A - Calculating method of restrictive boolean network degeneracy - Google Patents

Abstract

The invention provides a calculating method of restrictive boolean network degeneracy. The calculating method of the restrictive boolean network degeneracy comprises the following steps of carrying out set partitioning on all nodes in a transduction layer, grouping partitioned sets; in each group, calculating function contribution overlap amount, as shown in the figure, between each set and a complementary set thereof, and averaging to obtain a mean as shown in the figure; summing the function contribution overlap amount mean of each group, wherein the obtained result is the degeneracy of a restrictive boolean network. The calculation formula of the restrictive boolean network degeneracy is shown in the figure. According to the calculating method of the restrictive boolean network degeneracy provided by the invention, knowledge on biology degeneracy is step up to quantitative depiction from qualitative description, and a degeneracy phenomenon in a complex biological network can be cognized accurately and conveniently.

Description

A kind of computing method of suppressive Boolean network degeneracy

Technical field

The present invention relates to a kind of degeneracy computing method, specifically a kind of computing method of suppressive Boolean network degeneracy.

Background technology

The made rapid progress of microelectric technique, substantially increases the integrated, intelligent of electronic equipment and precision level, makes it play more and more important effect in communication, traffic, finance and the field such as military.But increasing electronic equipment also intentional or unintentionally can launch the electromagnetic wave of high density, high field intensity, wide spectrum, in addition the natural forceful electric power magnetic source such as Lightning Electromagnetic Pulse, static discharge electromagnetic pulse, and the artificial forceful electric power magnetic source such as nuclear electromagnetic pulse, High-Power Microwave, ultra broadband, make space electromagnetic environment become day by day complicated, severe.Although take such as shielding, filtering, ground connection, transient suppression device and the various technological means such as insensitiveness device and electromagnetic protection new material, existing electronic system often still can not resist the attack of strong electromagnetic pulse, traditional electromagnetic protection technology is faced with new challenges, threatens reliability and the adaptability of equipment.

Review the biosome of occurring in nature, the infosystem moment in their bodies all suffer from continual " the signal bombing " of various environmental factor, as radiation, illumination, temperature, noise and electromagnetic field etc.But through the baptism of long-term evolution, biosome has possessed certain resistivity and adaptive faculty to environmental stimulus.Such as, the neurocyte of brain has part apoptosis every day, and the olfactory cell of dog monthly all can all change one time, but its physiological function is still normal, also never as electronic system, because the damage of a certain assembly of elements causes paralysis or the degradation of entire system.Neural information process can be subject to the interference of polytype noise, but neural calculating is still reliable, effectively can utilize noise signal even in some cases.The biological anti-interference phenomenon of these excellences is that electromagnetic protection field brings brand-new enlightenment, and " electromagnetic protection is bionical " research is just arisen at the historic moment.

The target of electromagnetic protection bionics fiber is the anti-interference and selfreparing mechanism by exploring Bioinformatics, biomechanism is introduced electromagnetic protection field, the key scientific problems of breakthrough conversion, research electromagnetic protection bionic principle, bionic model, bionical device and bionic system, the bionical new principle of electromagnetic protection and new method are proposed, for improving the reliability of electronics under complex electromagnetic environment and adaptability, a kind of brand-new Theory and technology is provided to support.This studies the problem in science faced and can be summarized as:

(1) the anti-interference mechanism of Bioinformatics;

(2) from biological anti-interference mechanism to the conversion method in electronic system electromagnetic protection field;

(3) application oriented bionical anti-jamming circuit design and implementation methods.

The electromagnetic protection technical research of mimic biology degeneracy is the bionical research direction of electromagnetic protection.Degeneracy is the important mechanisms that biological nervous system resists interference and damage.In bio-networks, degeneracy refers to that the node set of different structure in system has identical function in certain circumstances or produces an attribute of identical output.Degeneracy is a kind of system property instead of specific structure objects, and it is prevalent in the but unfixing version at all levels of biosystem.Such as, different codeword triplets can be encoded same amino acid; Different protein can react by catalysis the same enzyme; Different genotype can regulate and control to produce identical phenotype; Different antibodies can retrain same antigen; Different neuronal circuits can affect same movement output; Different signal transduction pathways can express identical information etc.Therefore, according to the degeneracy feature of bio-networks, mathematical method is utilized to measure the degeneracy of bio-networks, find the computing method of bio-networks degeneracy, and then these computing method are generalized to field of electronic systems, just become reference and mimic biology degeneracy phenomenon, realize the important channel from biological anti-interference mechanism to the conversion of electronic system electromagnetic protection field.

Summary of the invention

An object of the present invention is just to provide a kind of computing method of suppressive Boolean network degeneracy, adopting the method can make to rise to quantitative portraying to the understanding of biological degeneracy from describing qualitatively, being convenient to the degeneracy phenomenon in cognitive complex biological network exactly.

Two of object of the present invention is just to provide a kind of computing formula of suppressive Boolean network degeneracy, adopts this formula can calculate the degeneracy of suppressive Boolean network.

An object of the present invention is achieved in that a kind of computing method of suppressive Boolean network degeneracy, it is characterized in that, comprises the steps:

The first step, calculates the objective function truth table of suppressive Boolean network; Described suppressive Boolean network comprises input layer, transduction layer and output layer, and described input layer has l node, and described transduction layer has m node, and described output layer has t node;

Second step, carries out set to m node in described transduction layer and divides, mark off altogether individual set, k is the number of contained node in a set, 1≤k≤m; Divide into groups to divided set, set identical for contained node number is classified as one group, and each group is denoted as X ^k; Comprise in each group individual set, is denoted as z set in each group set supplementary set be denoted as

3rd step, determines each independent action network gathered, and calculates the virtual condition truth table of each set independent action network;

4th step, according to the virtual condition truth table of each set independent action network, and complete function degree function, calculate the complete function degree of each set, the complete function degree of each set is the individual contributions amount of each set to described suppressive Boolean network allomeric function;

The expression formula of described complete function degree function is:

$\begin{array}{c}\mathrm{Fun}(X;O)=(1-\frac{1}{2^l\·t}\·\underset{i=1}{\overset{2^l}{\mathrm{\Σ}}}\underset{j=1}{\overset{t}{\mathrm{\Σ}}}|o_{\mathrm{ij}}-d_{\mathrm{ij}}\left|\right)\·100\%\end{array}----\left(1\right)$

In above formula, d _ijfor the i-th row of the corresponding truth table of output layer node in the objective function truth table of suppressive Boolean network, the numerical value of jth row, o _ijfor the i-th row of the corresponding truth table of output layer node in virtual condition truth table, the numerical value of jth row; 1≤i≤2 ^l, 1≤j≤t; X is lumped parameter, and O is under set X independent action, the truth table that in virtual condition truth table, output layer node is corresponding;

5th step, in each group divided, calculates the function contribution lap between each set and its supplementary set in second step and in each group, function contribution lap is averaged, obtain fun (X _all; O) for all transduction node layers are to the contribution amount of described suppressive Boolean network allomeric function, X _allfor comprising the set of all nodes in transduction layer;

6th step, result of calculation in the 5th step substituted in the computing formula of suppressive Boolean network degeneracy and calculate, the computing formula of suppressive Boolean network degeneracy is as follows:

$D_m(V;O)=1/2\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}[<\mathrm{Fun}(X_z^k;O)+\mathrm{Fun}(\stackrel{\&OverBar;}{X_z^k};O)-\mathrm{Fun}(X_{\mathrm{all}};O)>]---\left(2\right)$

The result of calculation D of formula (2) _m(V; O) be the degeneracy of suppressive Boolean network, V is the set that in suppressive Boolean network, all nodes are formed.

The described first step is specially:

Described suppressive Boolean network is feedforward network, and namely all nodes only accept the regulation and control from its front node layer relative, and all internodal regulation relationships form regulation and control matrix W, arbitrary regulation relationship weight w in regulation and control matrix W _pqthere are ﹣ 1,0 and 1 three kind of state value, i.e. w _pq∈ {-1,0,1}, w _pq=-1 representation node q makes node p inactivation, w _pq=0 representation node q does not affect node p, w _pq=1 representation node q makes node p activate; Node p has 0 and 1 two states value, i.e. v _p∈ { 0,1}, v _p=1 representation node p activates, v _p=0 representation node p inactivation;

In described suppressive Boolean network, all node state value synchronized update; The state value v of any node p _pjointly determined by the state value of all nodes participating in regulation and control node p, v _pcomputing formula as follows:

$v_p=\left\{\begin{array}{cc}1,& \underset{q<p}{\mathrm{\&Sigma;}}{w}_{\mathrm{pq}}\&CenterDot;v_q>0\\ 0,& \underset{q<p}{\mathrm{\&Sigma;}}{w}_{\mathrm{pq}}\&CenterDot;v_q\&le;0\end{array}\right.---\left(3\right)$

In formula (3), 1≤p≤n, 1≤q≤n, n=l+m+t;

According to regulation and control matrix W and formula (3), calculate the state value of all nodes in suppressive Boolean network, namely draw the objective function truth table of suppressive Boolean network.

Described 3rd step is specially:

For any one set by its supplementary set the node comprised and the annexation of input layer disconnect, and the annexation of all isolated nodes produced owing to disconnecting relation with relative node layer are thereafter also disconnected, thus are gathered independent action network;

According to regulation and control matrix W and formula (3), calculate the virtual condition value of each set independent action nodes, namely draw the virtual condition truth table of each set independent action network.

Two of object of the present invention is achieved in that a kind of computing formula of suppressive Boolean network degeneracy, and it is characterized in that, described computing formula is as follows:

$D_m(V;O)=1/2\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}[<\mathrm{Fun}(X_z^k;O)+\mathrm{Fun}(\stackrel{\&OverBar;}{X_z^k};O)-\mathrm{Fun}(X_{\mathrm{all}};O)>]---\left(2\right)$

The result of calculation D of formula (2) _m(V; O) degeneracy of suppressive Boolean network is; Described suppressive Boolean network comprises input layer, transduction layer and output layer, and in formula (2), m is the number of described transduction layer interior joint, and described input layer has l node, and described output layer has t node; V is the set that in suppressive Boolean network, all nodes are formed;

Carry out set to m node in described transduction layer to divide, can mark off individual set, k is the number of contained node in a set, 1≤k≤m; Divide into groups to divided set, set identical for contained node number is classified as one group, and each group is denoted as X ^k; Comprise in each group individual set, is denoted as z set in each group set supplementary set be denoted as x _allfor comprising the set of all nodes in transduction layer; for set to the individual contributions amount of described suppressive Boolean network allomeric function, for set supplementary set to the individual contributions amount of described suppressive Boolean network allomeric function, Fun (X _all; O) for all transduction node layers are to the contribution amount of described suppressive Boolean network allomeric function; Sign of operation <*> represent calculate the average of likely value;

Gather the complete function degree namely gathered the individual contributions amount of described suppressive Boolean network allomeric function, the complete function degree of set is calculated by complete function degree function, and the computing formula of complete function degree function is as follows:

$\begin{array}{c}\mathrm{Fun}(X;O)=(1-\frac{1}{2^l\&CenterDot;t}\&CenterDot;\underset{i=1}{\overset{2^l}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{t}{\mathrm{\&Sigma;}}}|o_{\mathrm{ij}}-d_{\mathrm{ij}}\left|\right)\&CenterDot;100\%\end{array}----\left(1\right)$

In formula (1), X is lumped parameter, and O is under set X independent action, the truth table that in virtual condition truth table, output layer node is corresponding; d _ijfor the i-th row of the corresponding truth table of output layer node in the objective function truth table of suppressive Boolean network, the numerical value of jth row, o _ijfor the i-th row of the corresponding truth table of output layer node in virtual condition truth table, the numerical value of jth row.

Degeneracy in bio-networks refers to that the node set of different structure in system has identical function in certain circumstances or produces a kind of system property of identical output, is the important mechanisms ensureing Biological Robustness.Degeneracy evaluates the quantizating index of bio-networks degeneracy.Suppressive Boolean network is a kind of network model general in bio-networks modeling.The main thought of suppressive Boolean network degeneracy tolerance is: measure the lap (or claim function contribution lap) of all node set to described suppressive Boolean network allomeric function contribution amount.Divide by carrying out set to all nodes in transduction layer, and divided set is divided into groups, in each group, calculate the function contribution lap between each set and its supplementary set fun (X; O) be complete function degree function, Fun (X; O) result of calculation is the complete function degree of each set, and namely each set is to the individual contributions amount of described suppressive Boolean network allomeric function; Computing function contribution lap average in each group and the function contribution lap average of each group is sued for peace, acquired results is the degeneracy of suppressive Boolean network.The computing formula of suppressive Boolean network degeneracy is: $D_m(V;O)=1/2\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}[<\mathrm{Fun}(X_z^k;O)+\mathrm{Fun}(\stackrel{\&OverBar;}{X_z^k};O)-\mathrm{Fun}(X_{\mathrm{all}};O)>],$ Due to when traveling through all node set, each set has calculated twice, therefore has coefficient 1/2 in formula.

The present invention has the following advantages and good effect:

The computing method of suppressive Boolean network degeneracy that the present invention proposes, make to rise to quantitative portraying to the understanding of biological degeneracy from describing qualitatively, are convenient to the degeneracy phenomenon in cognitive complex biological network accurately.And, the method can be generalized to the degeneracy tolerance of the digital circuit equally with Boolean network feature, therefore, in the electromagnetic protection bionics fiber of mimic biology degeneracy, the digital circuit that the method design robustness is higher can be utilized, to strengthen the ability of the electromagnetism interference of electronic circuit.

Accompanying drawing explanation

Fig. 1 is the structural representation of suppressive Boolean network in the embodiment of the present invention 2.

Fig. 2 is the regulation and control matrix W schematic diagram of regulation relationship weight sequence composition in suppressive Boolean network.

Fig. 3 is the objective function truth table schematic diagram of suppressive Boolean network.

Fig. 4 is the structural representation of the independent action network of single set.

Fig. 5 is the structural representation that in the embodiment of the present invention 3, has a suppressive Boolean network of specific input/output function.

Fig. 6 gathers in Fig. 5 schematic network structure after annexation between the node comprised and input layer disconnects.

Fig. 7 is the schematic network structure after being disconnected with the annexation of relative node layer thereafter with 5 by isolated node in Fig. 64.

Fig. 8 is the schematic diagram of the function contribution lap average in each group of table 3 between set and its supplementary set.

Embodiment

Embodiment 1, a kind of computing formula of suppressive Boolean network degeneracy.

The main thought of suppressive Boolean network degeneracy tolerance is: measure the lap (or claim function contribution lap) of all node set to described suppressive Boolean network allomeric function contribution amount.

Suppressive Boolean network comprises input layer, transduction layer and output layer, if input layer has l node, transduction layer has m node, and output layer has t node.Carry out set to m node in transduction layer to divide, mark off altogether individual set (or claiming node set), k is set size, represents the number of contained node in a set, 1≤k≤m; Divide into groups by set size to divided set, the set identical by contained node number is classified as one group, and the grouping being k for set size is denoted as X ^k; Comprise in each group individual set, is denoted as z set in each group set supplementary set be denoted as complete or collected works are the set that in transduction layer, all nodes are formed, and are denoted as X _all.

For any one set with its supplementary set the summation of standalone feature contribution amount be greater than the function contribution amount of the set (i.e. complete or collected works) of all nodes composition, both differences are set with its supplementary set between function contribution lap.And then, by calculating the average of each group interior joint consolidation function contribution lap, and the average of each group of function contribution lap being sued for peace, obtaining the degeneracy of suppressive Boolean network.Therefore, the computing formula of suppressive Boolean network degeneracy provided by the present invention is:

$D_m(V;O)=1/2\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}[<\mathrm{Fun}(X_z^k;O)+\mathrm{Fun}(\stackrel{\&OverBar;}{X_z^k};O)-\mathrm{Fun}(X_{\mathrm{all}};O)>]---\left(2\right)$

The result of calculation D of formula (2) _m(V; O) degeneracy of suppressive Boolean network is.V is the set that in suppressive Boolean network, all nodes are formed in formula (2), sign of operation <*> represent calculate the average of likely value, namely * refers to all possible value. for set to the individual contributions amount of suppressive Boolean network allomeric function, for set supplementary set to the individual contributions amount of suppressive Boolean network allomeric function, Fun (X _all; O) for all transduction node layers are to the contribution amount of suppressive Boolean network allomeric function, for set with its supplementary set to the contribution lap of suppressive Boolean network allomeric function, for one group of X that set size is k ^kin function contribution lap average between all set supplementary set corresponding to it.Due to when traveling through all node set, each set has calculated twice, therefore has coefficient 1/2 in formula (2).

Wherein, the complete function degree that namely the individual contributions amount gathered is gathered, the complete function degree of set is calculated by complete function degree function (Fun), the implication of complete function degree function is: under map network set X (X is a lumped parameter) independent action, Hamming distance under described set independent action between the state truth table O of all output nodes of overall network node and the truth table D of objective function output node, complete function degree function is such as formula shown in (1).

$\begin{array}{c}\mathrm{Fun}(X;O)=(1-\frac{1}{2^l\&CenterDot;t}\&CenterDot;\underset{i=1}{\overset{2^l}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{t}{\mathrm{\&Sigma;}}}|o_{\mathrm{ij}}-d_{\mathrm{ij}}\left|\right)\&CenterDot;100\%\end{array}----\left(1\right)$

In formula (1), l and t is respectively the interstitial content of objective function input and output, namely the number of input layer and output layer node; d _ijrepresent the numerical value of the i-th row in the truth table of objective function output node, jth row, o _ijrepresent the numerical value of the i-th row in the truth table of actual output node, jth row.

Embodiment 2, a kind of computing method of suppressive Boolean network degeneracy.

The computing method of suppressive Boolean network degeneracy provided by the present invention, comprise the steps:

The first step, for suppressive Boolean network model general in bio-networks modeling, specifies the allomeric function of suppressive Boolean network (as shown in Figure 1), calculates the objective function truth table of suppressive Boolean network.

As shown in Figure 1, suppressive Boolean network is designated as vectorial F=(V, W), and V represents the set that in network, all nodes are formed, regulation relationship weight matrix between W representation node.Suppressive Boolean network is divided into input layer 10, transduction layer 11 and output layer 12.In bio-networks, the signal perception acceptor of input layer 10 node on behalf cell surface, stimulates for experiencing external environment condition; Transduction layer 11 node on behalf intracellular signal transduction courier, for the treatment of and transmission of signal; The intracellular effect target protein of output layer 12 node on behalf, makes response to outside stimulus, as regulated metabolic pathway, regulate gene expression and adjustment cell quality.Wherein, internodal regulation relationship is restricted to feedforward and connects, and the network formed is called feedforward network, and namely all nodes can only accept the regulation and control from its front node layer relative.

If the total number of the node of suppressive Boolean network is n, input layer 10 nodes is l, and transduction layer 11 nodes is m, and output layer 12 nodes is t, then have n=l+m+t.The state value of all nodes is Boolean variable v _p{ 0,1}, regulation relationship weight (being called for short regulation and control weight) has boolean properties w to ∈ equally _pq{-1,0,1}, variable implication defines identical with Boolean network ∈.V _p=1 representation node p activates, v _p=0 representation node p inactivation; w _pq=-1 representation node q makes node p inactivation (or claiming to suppress), w _pq=0 representation node q does not affect node p, w _pq=1 representation node q makes node p activate, and sees that in Fig. 1, front node layer is to the regulation relationship of rear node layer.

In suppressive Boolean network, all node state value synchronized update.The state value v of any node p _pjointly determined by the state value of all nodes participating in regulation and control node p, and adopt to add and calculate with computing, threshold operation (see Fig. 1).V _pspecific formula for calculation is such as formula shown in (3):

$v_p=\left\{\begin{array}{cc}1,& \underset{q<p}{\mathrm{\&Sigma;}}{w}_{\mathrm{pq}}\&CenterDot;v_q>0\\ 0,& \underset{q<p}{\mathrm{\&Sigma;}}{w}_{\mathrm{pq}}\&CenterDot;v_q\&le;0\end{array}\right.---\left(3\right)$

In formula (3), p and q is integer, and 1≤p≤n, 1≤q≤n, n=l+m+t; Limit q < p in sum formula, namely show the state value v of node p _pjointly determined by the state value of all front node layer participating in regulation and control node p.W _pqrepresent variable v _qto v _pregulation and control weight, all regulation and control weight sequences composition regulation and control matrix W, is shown in Fig. 2.

According to regulation and control matrix W and formula (3), the state value of all nodes in suppressive Boolean network just can be calculated, thus the objective function truth table of the type Boolean network that can be inhibited, see Fig. 3.

Second step, carries out set to suppressive Boolean network transfer conducting shell node and divides, and divides into groups dividing all set obtained by set size.

The transduction layer 11 of suppressive Boolean network has m node, first, carries out set and divides, can be divided into m node in transduction layer 11 individual set, wherein, k is set size, represents in a set and comprises k (1≤k≤m) individual node.Secondly, divide into groups dividing all set obtained by set size, the set identical by contained node number is classified as one group, and the grouping being k for set size is denoted as X ^k; Comprise in each group set size is that z set in a group of k is denoted as by individual set carry out set to m node in transduction layer 11 to divide, acquired results is in table 1.

Table 1: transduction layer m node carries out gathering the grouping sheet after dividing

3rd step, according to the set dividing condition of second step transfer conducting shell node, determine the independent action network of each set, and calculate the virtual condition truth table of overall network node under each set independent action respectively according to the method calculating objective function truth table in the first step.

For arbitrary collection in transduction layer (also node set can be claimed ), as shown in Figure 4, if set the node comprised by ellipse is formed, by its supplementary set the node comprised and the annexation of input layer disconnect, in figure, namely annexation shown in dotted line represents the annexation be disconnected, and the annexation of all isolated nodes produced owing to disconnecting relation with relative node layer thereafter is also disconnected, gathered independent action network.Dotted line represents that annexation disconnects, and the regulation relationship weight of its representative is 0, i.e. w=0.This operation makes supplementary set the information of input layer can not be obtained alone, shield supplementary set unique individualities to the contribution amount of described suppressive Boolean network allomeric function, highlight set independent action.

After determining the independent action network of each set, according to the method for objective function truth table calculating suppressive Boolean network in the first step, according to regulation and control matrix W and formula (3), calculate the virtual condition value of each set independent action nodes, namely draw the virtual condition truth table of each set independent action network.

4th step, according to the virtual condition truth table of each set independent action network, and complete function degree function (Fun), calculate the complete function degree of each set, the complete function degree of each set is the individual contributions amount of each set to described suppressive Boolean network allomeric function.

The expression formula of complete function degree function is:

$\begin{array}{c}\mathrm{Fun}(X;O)=(1-\frac{1}{2^l\&CenterDot;t}\&CenterDot;\underset{i=1}{\overset{2^l}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{t}{\mathrm{\&Sigma;}}}|o_{\mathrm{ij}}-d_{\mathrm{ij}}\left|\right)\&CenterDot;100\%\end{array}----\left(1\right)$

In formula (1), d _ijfor the i-th row of the corresponding truth table of output layer node in the objective function truth table of suppressive Boolean network, the numerical value of jth row, o _ijfor the i-th row of the corresponding truth table of output layer node in virtual condition truth table, the numerical value of jth row; I and j is integer, and 1≤i≤2 ^l, 1≤j≤t; X is node set parameter, and O is under node set X independent action, the truth table that in virtual condition truth table, output layer node is corresponding.By arbitrary collection lumped parameter X in alternate form (1), obtains be set to the individual contributions amount of described suppressive Boolean network allomeric function.

5th step, according to the individual contributions amount of each set of the 4th step gained to described suppressive Boolean network allomeric function, calculates the function contribution lap between each set and its supplementary set and in each group, function contribution lap is averaged, obtain

Sign of operation <*> represent calculate the average of likely value, * is all possible value, refer at set size to be in that group of k, the function contribution lap between all set supplementary set corresponding to it is averaged, Fun (X _all; O) for all transduction node layers are to the contribution amount of described suppressive Boolean network, X _allfor comprising the set of all nodes in transduction layer, namely meet

6th step, result of calculation in the 5th step substituted in the computing formula of suppressive Boolean network degeneracy and calculate, the computing formula of suppressive Boolean network degeneracy is as follows:

$D_m(V;O)=1/2\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}[<\mathrm{Fun}(X_z^k;O)+\mathrm{Fun}(\stackrel{\&OverBar;}{X_z^k};O)-\mathrm{Fun}(X_{\mathrm{all}};O)>]---\left(2\right)$

The result of calculation D of formula (2) _m(V; O) be the degeneracy of suppressive Boolean network, V is the set that in suppressive Boolean network, all nodes are formed.Due to when traveling through all node set, each set has calculated twice, therefore has coefficient 1/2 in formula (2).

The computing method of suppressive Boolean network degeneracy in the present invention are described below in detail with an object lesson.

Embodiment 3, a kind of computing method of suppressive Boolean network degeneracy.

A known suppressive Boolean network, input layer has l=2 node, transduction layer has m=7 node, and output layer has t=3 node, and network topology as shown in Figure 5.

The first step, the state value of each node in suppressive Boolean network according to formula (3) calculating chart 5 in embodiment 2, obtains the objective function truth table of the Boolean network of suppressive shown in Fig. 5, in table 2.

The objective function truth table of all nodes of table 2: Fig. 5

Second step, carries out set to the Boolean network of suppressive shown in Fig. 5 transfer conducting shell node and divides, and divides into groups dividing all set obtained by set size.

The transduction layer of the Boolean network of suppressive shown in Fig. 5 has 7 nodes (node serial number is 1-7), and therefore, transduction node layer has plant set to divide.Set size k has 7 kinds of values, thus forms 7 groups; Contain in one group that each set size k is formed plant different set.And for the arbitrary set in a group that is made up of set size k, all having one is a set in a group of 7-k supplementary set each other with it by set size.Divide into groups dividing all set obtained by set size, as shown in table 3.

Table 3: the grouping sheet after Fig. 5 transfer conducting shell node set divides

In table 3, the node in the suppressive Boolean network corresponding to digitized representation numbering in arbitrary set.

3rd step, according to the set dividing condition of second step transfer conducting shell node, determine the independent action network of each set, and calculate the virtual condition truth table of overall network node under each set independent action respectively according to the method calculating objective function truth table in the first step.

For arbitrary collection in transduction layer by its supplementary set the node comprised and the annexation of input layer disconnect, and the annexation of all isolated nodes produced owing to disconnecting relation with relative node layer are thereafter also disconnected, and are namely gathered independent action network.

Now with set for example is described.First will gather supplementary set { annexation between In1, In2} disconnects, and as shown in Figure 6, in figure, dotted line represents that annexation disconnects, and produces isolated node 4 and 5 for the node comprised and input layer.Then, isolated node 4 is also disconnected with the annexation of relative node layer thereafter with 5, as shown in Figure 7, is gathered independent action network.

Gather according to Fig. 7 independent action network and embodiment 2 in formula (3), set of computations under independent action, the virtual condition value of overall network node, is gathered the virtual condition truth table of independent action network, in table 4.

Table 4: set effect lower node virtual condition truth table

Table 4 is compared with table 2, and black overstriking numeral indicates the functional status position changed.

In like manner, the virtual condition truth table of overall network node under each set independent action can be calculated.

4th step, according to the virtual condition truth table of overall network node under each set independent action of the 3rd step gained, and complete function degree function (Fun) (see formula (1)), calculate the individual contributions amount of each set to suppressive Boolean network allomeric function respectively.

Equally, to gather for example is described.The complete degree function of binding function, according to set the virtual condition truth table (see table 4) of overall network node and its objective function state truth table (see table 2) under independent action, set of computations individual contributions amount to suppressive Boolean network allomeric function:

$\begin{array}{c}\mathrm{Fun}(X_1^3;O)=(1-\frac{1}{2^l\&CenterDot;t}\&CenterDot;\underset{i=1}{\overset{2^l}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{t}{\mathrm{\&Sigma;}}}|o_{\mathrm{ij}}-d_{\mathrm{ij}}\left|\right)\&CenterDot;100\%\\ =(1-\frac{2}{2^2\&CenterDot;3}\&CenterDot;\underset{i=1}{\overset{2^2}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{3}{\mathrm{\&Sigma;}}}|o_{\mathrm{ij}}-d_{\mathrm{ij}}\left|\right)\&CenterDot;100\%\\ =(1-\frac{1}{12}\&times;1)\&CenterDot;100\%\\ =91.7\%\end{array}$

In like manner, the individual contributions amount of all set to suppressive Boolean network allomeric function can be calculated.

5th step, according to each set of the 4th step gained to the individual contributions amount of suppressive Boolean network allomeric function, under calculating often kind of set size k, the function contribution lap average between complementary set $\begin{array}{c}<\mathrm{Fun}(X_z^k;O)+\mathrm{Fun}(\stackrel{\&OverBar;}{X_z^k};O)-\mathrm{Fun}(X_{\mathrm{all}};O)>.\end{array}$

For set size k=1, the computation process of the function contribution lap average between complementary set is described.

$\begin{array}{c}<\mathrm{Fun}(X_z^k;O)+\mathrm{Fun}(\stackrel{\&OverBar;}{X_z^k};O)-\mathrm{Fun}(X_{\mathrm{all}};O)>\\ =\frac{1}{C_m^k}\underset{z=1}{\overset{C_m^k}{\mathrm{\&Sigma;}}}(\mathrm{Fun}(X_z^k;O)+\mathrm{Fun}(\stackrel{\&OverBar;}{X_z^k};O)-\mathrm{Fun}(X_{\mathrm{all}};O))\\ =\frac{1}{7}\underset{z=1}{\overset{7}{\mathrm{\&Sigma;}}}(\mathrm{Fun}(X_z^1;O)+\mathrm{Fun}(\stackrel{\&OverBar;}{X_z^1};O)-\mathrm{Fun}(X_{\mathrm{all}};O))\\ =0.726\end{array}$

According to computing method during set size k=1, the function contribution lap average under calculating all set size between (namely in each group) complementation set, result of calculation is as shown in table 5 and Fig. 8.

Table 5: the function contribution lap average in each group of table 3 between complementary set

6th step, 5th step is calculated the function contribution lap average between gained complementation set, substitute in suppressive Boolean network degeneracy computing formula (see formula (2)), result of calculation is 2.444, then the degeneracy of suppressive Boolean network shown in known Fig. 5 is 2.444.

Claims (4)

1. computing method for suppressive Boolean network degeneracy, is characterized in that, comprise the steps:

The first step, calculates the objective function truth table of suppressive Boolean network; Described suppressive Boolean network comprises input layer, transduction layer and output layer, and described input layer has l node, and described transduction layer has m node, and described output layer has t node;

Second step, carries out set to m node in described transduction layer and divides, mark off altogether individual set, k is the number of contained node in a set, 1≤k≤m; Divide into groups to divided set, set identical for contained node number is classified as one group, and each group is denoted as X ^k; Comprise in each group individual set, is denoted as z set in each group set supplementary set be denoted as

3rd step, determines each independent action network gathered, and calculates the virtual condition truth table of each set independent action network;

4th step, according to the virtual condition truth table of each set independent action network, and complete function degree function, calculate the complete function degree of each set, the complete function degree of each set is the individual contributions amount of each set to described suppressive Boolean network allomeric function;

The expression formula of described complete function degree function is:

$\mathrm{Fum}(X;O)=(1-\frac{1}{2^l\&CenterDot;t}\&CenterDot;\underset{i=1}{\overset{2^l}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{t}{\mathrm{\&Sigma;}}}|o_{\mathrm{ij}}-d_{\mathrm{ij}}\left|\right)\&CenterDot;100\%---\left(1\right)$

In above formula, d _ijfor the i-th row of the corresponding truth table of output layer node in the objective function truth table of suppressive Boolean network, the numerical value of jth row, o _ijfor the i-th row of the corresponding truth table of output layer node in virtual condition truth table, the numerical value of jth row; 1≤i≤2 ^l, 1≤j≤t; X is lumped parameter, and O is under set X independent action, the truth table that in virtual condition truth table, output layer node is corresponding;

5th step, in each group divided, calculates the function contribution lap between each set and its supplementary set in second step and in each group, function contribution lap is averaged, obtain $<\mathrm{Fum}(X_z^k;O)+\mathrm{Fum}(\stackrel{\&OverBar;}{X_z^k};O)-\mathrm{Fum}(X_{\mathrm{all}};O)>;$ for all transduction node layers are to the contribution amount of described suppressive Boolean network allomeric function, X _allfor comprising the set of all nodes in transduction layer;

6th step, result of calculation in the 5th step substituted in the computing formula of suppressive Boolean network degeneracy and calculate, the computing formula of suppressive Boolean network degeneracy is as follows:

$D_m(V;O)=1/2\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}[<\mathrm{Fun}(X_z^k;O)+\mathrm{Fun}(\stackrel{\&OverBar;}{X_z^k};O)-\mathrm{Fun}(X_{\mathrm{all}};O)>]---\left(2\right)$

The result of calculation D of formula (2) _m(V; O) be the degeneracy of suppressive Boolean network, V is the set that in suppressive Boolean network, all nodes are formed.

2. the computing method of suppressive Boolean network degeneracy according to claim 1, it is characterized in that, the described first step is specially:

Described suppressive Boolean network is feedforward network, and namely all nodes only accept the regulation and control from its front node layer relative, and all internodal regulation relationships form regulation and control matrix W, arbitrary regulation relationship weight w in regulation and control matrix W _pqthere are ﹣ 1,0 and 1 three kind of state value, i.e. w _pq∈ {-1,0,1}, w _pq=-1 representation node q makes node p inactivation, w _pq=0 representation node q does not affect node p, w _pq=1 representation node q makes node p activate; Node p has 0 and 1 two states value, i.e. v _p∈ { 0,1}, v _p=1 representation node p activates, v _p=0 representation node p inactivation;

In described suppressive Boolean network, all node state value synchronized update; The state value v of any node p _pjointly determined by the state value of all nodes participating in regulation and control node p, v _pcomputing formula as follows:

$v_p=\left\{\begin{array}{cc}1,& \underset{q<p}{\mathrm{\&Sigma;}}{w}_{\mathrm{pq}}\&CenterDot;v_q>0\\ 0,& \underset{q<p}{\mathrm{\&Sigma;}}{w}_{\mathrm{pq}}\&CenterDot;v_q\&le;0\end{array}\right.---\left(3\right)$

In formula (3), 1≤p≤n, 1≤q≤n, n=l+m+t;

According to regulation and control matrix W and formula (3), calculate the state value of all nodes in suppressive Boolean network, namely draw the objective function truth table of suppressive Boolean network.

3. the computing method of suppressive Boolean network degeneracy according to claim 2, is characterized in that, described 3rd step is specially:

For any one set by its supplementary set the node comprised and the annexation of input layer disconnect, and the annexation of all isolated nodes produced owing to disconnecting relation with relative node layer are thereafter also disconnected, thus are gathered independent action network;

According to regulation and control matrix W and formula (3), calculate the virtual condition value of each set independent action nodes, namely draw the virtual condition truth table of each set independent action network.

4. a computing formula for suppressive Boolean network degeneracy, is characterized in that, described computing formula is as follows:

$D_m(V;O)=1/2\underset{k=1}{\overset{m}{\mathrm{\&Sigma;}}}[<\mathrm{Fun}(X_z^k;O)+\mathrm{Fun}(\stackrel{\&OverBar;}{X_z^k};O)-\mathrm{Fun}(X_{\mathrm{all}};O)>]---\left(2\right)$

The result of calculation D of formula (2) _m(V; O) degeneracy of suppressive Boolean network is; Described suppressive Boolean network comprises input layer, transduction layer and output layer, and in formula (2), m is the number of described transduction layer interior joint, and described input layer has l node, and described output layer has t node; V is the set that in suppressive Boolean network, all nodes are formed;

Carry out set to m node in described transduction layer to divide, can mark off individual set, k is the number of contained node in a set, 1≤k≤m; Divide into groups to divided set, set identical for contained node number is classified as one group, and each group is denoted as X ^k; Comprise in each group individual set, is denoted as z set in each group set supplementary set be denoted as x _allfor comprising the set of all nodes in transduction layer; for set to the individual contributions amount of described suppressive Boolean network allomeric function, for set supplementary set to the individual contributions amount of described suppressive Boolean network allomeric function, Fun (X _all; O) for all transduction node layers are to the contribution amount of described suppressive Boolean network allomeric function; Sign of operation <*> represent calculate the average of likely value;

Gather the complete function degree namely gathered the individual contributions amount of described suppressive Boolean network allomeric function, the complete function degree of set is calculated by complete function degree function, and the computing formula of complete function degree function is as follows:

$\mathrm{Fum}(X;O)=(1-\frac{1}{2^l\&CenterDot;t}\&CenterDot;\underset{i=1}{\overset{2^l}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{t}{\mathrm{\&Sigma;}}}|o_{\mathrm{ij}}-d_{\mathrm{ij}}\left|\right)\&CenterDot;100\%---\left(1\right)$

In formula (1), X is lumped parameter, and O is under set X independent action, the truth table that in virtual condition truth table, output layer node is corresponding; d _ijfor the i-th row of the corresponding truth table of output layer node in the objective function truth table of suppressive Boolean network, the numerical value of jth row, o _ijfor the i-th row of the corresponding truth table of output layer node in virtual condition truth table, the numerical value of jth row.