Method for creating a network model of a dynamic system of interdependent variables from system observations

A method for creating a network model of a real world system of interacting components having a plurality of expression levels from prior knowledge and a plurality of observations of the real world system comprising the steps of:

• defining N network variables xi, i=0, . . . N−1 having values, vi, i=1, . . . m to represent the components of the real world system, said values defining a network state of said network model;
• defining N network rules ƒi, i=0 . . . N−1 corresponding to said N network variables from a space of possible network rules wherein said N network rules have outputs defining said network model;
• defining N prior distributions corresponding to said N network rules expressing probabilities of said possible network rules from the prior knowledge of the real world system;
• defining at least one likelihood function expressing the probability of making the system observations for said possible network rules;
• determining N posterior distributions defined as a product of said prior distributions and said at least one likelihood function wherein said posterior distributions express the probabilities of said possible network rules given the prior knowledge and the plurality of observations of the real world system;
• and
• selecting one or more of said posterior distributions having the greatest probability to identify said network model of the real world system;
• wherein said defining N prior distributions step comprises the step of defining said N prior probability distributions as an expression of a plurality of abstract properties of said N network rules.

A method for creating a network model of a real world system of interacting components having a plurality of expression levels from prior knowledge and a plurality of observations of the real world system comprising the steps of:

• defining N network variables xi, i=0, . . . N−1 having values, vi, i=1, . . . m to represent the components of the real world system, said values defining a network state of said network model;
• defining N network rules ƒi, i=0 . . . N−1 corresponding to said N network variables from a space of possible network rules wherein said N network rules have outputs defining said network model;
• defining N prior distributions corresponding to said N network rules expressing probabilities of said possible network rules from the prior knowledge of the real world system;
• defining at least one likelihood function expressing the probability of making the system observations for said possible network rules;
• determining N posterior distributions defined as a product of said prior distributions and said at least one likelihood function wherein said posterior distributions express the probabilities of said possible network rules given the prior knowledge and the plurality of observations of the real world system;
• defining a sequence of discrete time steps t, t−1, . . . t−T individually referenced by τ;
• and
• defining said network state {right arrow over (x)}τ of said network model at said discrete time step τ as a vector of said values, xiτε{vi, . . . vm}, i=0, . . . N−1 at said time step τ.

A method for creating a network model of a real world system of interacting components having a plurality of expression levels from prior knowledge and a plurality of observations of the real world system comprising the steps of:

• defining N network variables xi, i=0, . . . N−1 having values, vi, i=1, . . . m to represent the components of the real world system, said values defining a network state of said network model;
• defining N network rules ƒi, i=0, . . . N−1 corresponding to said N network variables from a space of possible network rules wherein said N network rules have outputs defining said network model;
• defining N prior distributions corresponding to said N network rules expressing probabilities of said possible network rules from the prior knowledge of the real world system;
• defining at least one likelihood function expressing the probability of making the system observations for said possible network rules;
• and
• determining N posterior distributions defined as a product of said prior distributions and said at least one likelihood function wherein said posterior distributions express the probabilities of said possible network rules given the prior knowledge and the plurality of observations of the real world system;
• wherein said N network variables, xi, i=0, . . . N−1 have m=2 values.

A method for creating a network model of a real world system of interacting components having a plurality of expression levels from prior knowledge and a plurality of observations of the real world system comprising the steps of:

• defining N network variables xi, i=0, . . . N−1 having values, vi, i−1, . . . m to represent the components of the real world system, said values defining a network state of said network model;
• defining N activation delays Ti0→1, i=0 . . . N−1, corresponding to said network variables xi, i=0 . . . N−1 from a space of possible activation delays;
• and
• defining N deactivation delays Ti0→1, i=0 . . . N−1, corresponding to said N network variables xi, i=0 . . . N−1 from a space of possible deactivation delays;
• defining N network rules ƒi, i=0 . . . N−1 corresponding to said N network variables from a space of possible network rules wherein said N network rules have outputs defining said network model;
• and
• determining at least one posterior distribution wherein said posterior distribution expresses the probabilities of said possible network rules, said possible activation delays and said possible deactivation delays given the prior knowledge and the plurality of observations of the real world system.

Computer executable software code stored on a computer readable medium, the code for creating a network model of a real world system of interacting components having a plurality of expression levels from prior knowledge and a plurality of observations of the real world system, the code comprising:

• code to define N network variables xi, i=0, . . . N−1 having values, vi, i=1, . . . m to represent the components of the real world system, said values defining a network state of said network model;
• code to define N network rules ƒi, i=0, . . . N−1 corresponding to said N network variables from a space of possible network rules wherein said N network rules have outputs defining said network model;
• code to define N prior distributions corresponding to said N network rules expressing probabilities of said possible network rules from the prior knowledge of the real world system;
• code to define at least one likelihood function expressing the probability of making the system observations for said possible network rules;
• code to determine N posterior distributions defined as a product of said prior distributions and said at least one likelihood function wherein said posterior distributions express the probabilities of said possible network rules given the prior knowledge and the plurality of observations of the real world system;
• and
• code to select one or more of said posterior distributions having the greatest probability to identify said network model of the real world system;
• wherein said code to define N prior distributions step comprises code to define said N prior probability distributions as an expression of a plurality of abstract properties of said N network rules.

A programmed computer for creating a network model of a real world system of interacting components having a plurality of expression levels from prior knowledge and a plurality of observations of the real world system comprising a memory having at least one region storing computer executable program code and a processor for executing the program code stored in said memory, wherein the program code includes:

• code to define N network variables xi, i=0, . . . N−1 having values, vi, i=1, . . . m to represent the components of the real world system, said values defining a network state of said network model;
• code to define N network rules ƒi, i=0, . . . N−1 corresponding to said N network variables from a space of possible network rules wherein said N network rules have outputs defining said network model;
• code to define N prior distributions corresponding to said N network rules expressing probabilities of said possible network rules from the prior knowledge of the real world system;
• code to define at least one likelihood function expressing the probability of making the system observations for said possible network rules;
• code to determine N posterior distributions defined as a product of said prior distributions and said at least one likelihood function wherein said posterior distributions express the probabilities of said possible network rules given the prior knowledge and the plurality of observations of the real world system;
• and
• code to select one or more of said posterior distributions having the greatest probability to identify said network model of the real world system;
• wherein said code to define N prior distributions step comprises code to define said N prior probability distributions as an expression of a plurality of abstract properties of said N network rules.

Computer executable software code stored on a computer readable medium, the code for creating a network model of a real world system of interacting components having a plurality of expression levels from prior knowledge and a plurality of observations of the real world system, the code comprising:

• code to define N network variables xi, i=0, . . . N−1 having values, vi, i=1, . . . m to represent the components of the real world system, said values defining a network state of said network model;
• code to define N activation delays Ti0→1, i=0 . . . N−1, corresponding to said N network variables xi, i=0 . . . N−1 from a space of possible activation delays;
• and
• code to define N deactivation delays Ti1→0, i=0 . . . N−1, corresponding to said N network variables xi, i=0, . . . N−1 from a space of possible deactivation delays;
• code to define N network rules ƒi, i=0, . . . N−1 corresponding to said N network variables from a space of possible network rules wherein said N network rules have outputs defining said network model;
• and
• code to determine at least one posterior distribution wherein said posterior distribution expresses the probabilities of said possible network rules, said possible activation delays and said possible deactivation delays given the prior knowledge and the plurality of observations of the real world system.

A programmed computer for creating a network model of a real world system of interacting components having a plurality of expression levels from prior knowledge and a plurality of observations of the real world system comprising a memory having at least one region storing computer executable program code and a processor for executing the program code stored in said memory, wherein the program code includes:

• code to define N network variables xi, i=0, . . . N−1 having values, vi, i=1, . . . m to represent the components of the real world system, said values defining a network state of said network model;
• code to define N activation delays Ti0→1, i=0 . . . N−1, corresponding to said N network variables xi, i=0 . . . N−1 from a space of possible activation delays;
• and
• code to define N deactivation delays Ti0→1, i=0 . . . N−1, corresponding to said N network variables xi, i=0 . . . N−1 from a space of possible deactivation delays;
• code to define N network rules ƒi, i=0 . . . N−1 corresponding to said N network variables from a space of possible network rules wherein said N network rules have outputs defining said network model;
• and
• code to determine at least one posterior distribution wherein said posterior distribution expresses the probabilities of said possible network rules, said possible activation delays and said possible deactivation delays given the prior knowledge and the plurality of observations of the real world system.