Network operator matrix

Network operator matrix (NOM) is a representation of mathematical expressions in computer memory.
NOM is a new approach to the problem of automatic search of mathematical equations. The researcher defines the sets of operations, variables and parameters. The computer program generates a number of mathematical equations that satisfy given restrictions. Then the optimization algorithm finds the structure of appropriate mathematical expression and its parameters.
Network operator is a directed graph that corresponds to some mathematical expressions. Every source nodes of the graph are variables or constants of mathematical expression, inner nodes correspond to binary operations and edges correspond to unary operations. The calculation’s result of mathematical expression is kept in the last sink node.
Example.
Consider the following mathematical expression
The graph for Expression (), is presented in Fig. 1.
On the edges we place unary operations
formula_1<br>
formula_2<br>
formula_3 <br>
formula_4
In the inner and sink nodes we place binary operations<br>
formula_5<br>
formula_6
Expression 1 can be presented in the PC memory as a NOM
Any mathematical expression can be presented as a network operator matrix.
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To calculate the mathematical expression by the network operator matrix the node vector is used.
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Each component of node vector corresponds to the nodes of the network operator graph. Initially each component is equal to the argument for the given node or the unit element of binary operation.
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For addition and multiplication the number of operation equals its unit element. For addition it is 0, for multiplication it is 1.
The node vector for the given example<br>
<br>
formula_8<br>
<br>
The calculation by matrix formula_9 is performed for nonzero nondiagonal elements formula_10 by <br>
<br>
formula_11
Follow the rows of the matrix.<br>
For the Row 1 we have formula_12, that is formula_13, formula_14, formula_15.
Take arguments from formula_8
formula_17, formula_18 then <br>
<br>
formula_19<br>
<br>
Further in Row 1 we have formula_20<br>
<br>
formula_21<br>
<br>
formula_22<br>
<br>
formula_23.<br>
<br>
As a result after Row 1 we have formula_24.<br>
<br>
For the Row 2 we have 
formula_25
<br> 
formula_26<br>
<br>
then follow the rows
formula_27<br>
formula_28
formula_29<br>
<br> 
formula_30
formula_31<br>
<br> 
formula_32
formula_33<br>
<br> 
formula_34
formula_35<br>
<br> 
formula_36.
Josue Ortega

Josue Ortega is a lecturer in economics at Queen's University Belfast. He is the author of a controversial article that suggests that the emergence of online dating has caused an increase in the number of interracial marriages in the US. Ortega's findings have been covered by international media, including "Forbes", "the Times", "New Scientist", "Business Insider" and the "MIT Technology Review". Ortega has been interviewed by "Thinking Allowed" at BBC Radio 4.
Ortega obtained his PhD at the University of Glasgow under the supervision of Professor Hervé Moulin. He received the Catherine Richards prize by the UK Institute for Mathematics and its Applications in 2016. He sits in the editorial board of Palgrave Communications and has published his research in the Journal of Mathematical Economics, the Proceedings of the ACM Conference on Economics and Computation, Economics Letters and .