Claims
- 1. A method for analyzing a system, the system being representable as a plurality of nodes connected by edges to form a graph, the method comprising:
analyzing the graph to form a plurality of sub-graphs, each sub-graph containing a plurality of nodes connected by at least one edge; and analyzing said plurality of sub-graphs to detect a type of sub-graph occurring at a threshold frequency in the graph, said type of sub-graph forming a motif of the system.
- 2. The method of claim 1, wherein said analyzing said plurality of sub-graphs further comprises:
constructing a randomized graph; comparing a frequency of appearance of said type of sub-graph in said randomized graph with a frequency of appearance of said type of sub-graph in the graph; and if a difference between said frequency of appearance of said type of sub-graph in said randomized graph and said frequency of appearance of said type of sub-graph in the graph is significant, forming said motif with said type of sub-graph.
- 3. The method of claim 2, wherein said randomized graph has at least one feature similar to said network graph.
- 4. The method of claim 3, wherein a plurality of characteristics of said nodes of said randomized graph is identical to said plurality of said characteristics of said nodes of said network graph.
- 5. The method of claim 1, wherein a type of sub-graph is determined as having a particular set of said plurality of nodes and of said at least one edge.
- 6. The method of claim 1, wherein a type of sub-graph is determined according to an equivalence of a plurality of nodes and of at least one edge
- 7. The method of claim 1, wherein said analyzing the graph further comprises:
constructing a connectivity matrix for representing the graph, wherein each node is represented by an element of said connectivity matrix.
- 8. The method of claim 7, wherein said analyzing said graph further comprises:
examining each row i of said connectivity matrix; within each row i, examining each element (i,j); for each element (i,j), examining each connected element existing as a node in the graph; and if a plurality of connected elements exist as nodes in the graph, repeating recursively for said plurality of connected elements.
- 9. The method of claim 7, wherein said analyzing said graph further comprises:
at least sampling said connectivity matrix to detect said type of sub-graph.
- 10. The method of claim 7, wherein said analyzing said graph further comprises:
exhaustively searching said connectivity matrix to detect said type of sub-graph.
- 11. The method of claim 7, wherein said analyzing said graph further comprises:
constructing a plurality of connectivity matrices, wherein each connectivity matrix represents a different discrete value in time for at least one edge between a plurality of nodes of the graph.
- 12. The method of claim 1, wherein the system comprises a gene transcription regulatory network.
- 13. The method of claim 1, wherein the system comprises an ecological food web.
- 14. The method of claim 1, wherein the system comprises a plurality of connected neurons.
- 15. The method of claim 1, wherein the system comprises at least one of a computer network, and a software program.
- 16. The method of claim 15, wherein said computer network is the World Wide Web.
- 17. The method of claim 1, wherein the system comprises an electronic circuit.
- 18. A method for analyzing a system, the system comprising a plurality of components, the method comprising:
constructing a connectivity matrix for representing the components of the system, said connectivity matrix comprising a plurality of elements, wherein a value for each element represents at least one characteristic of a relationship between a plurality of components; and examining at least a portion of said connectivity matrix for analyzing the system.
- 19. The method of claim 18, wherein a network motif is detected after examining said at least a portion of said connectivity matrix.
- 20. The method of claim 19, wherein said at least a portion of said connectivity matrix is examined by analyzing a connection between a plurality of n elements, said connection being analyzed by examining a sub-matrix of n×n elements of said connectivity matrix.
- 21. The method of claim 20, wherein an element (i,j) of said connectivity matrix equals one if a first component j has a connection to a second component i, and wherein otherwise said element is equal to zero.
- 22. The method of claim 21, wherein a plurality of submatrices is detected by recursively searching for nonzero elements (i,j), and scanning row i and column j for non-zero elements.
- 23. The method of claim 21, wherein a search is performed for identical rows of said connectivity matrix for detecting a “fan-out”, wherein a plurality of the components of the system is related to a single component.
- 24. The method of claim 21, wherein the system is a gene transcription regulatory network, such that said element (i,j) is equal to one if operon j encodes for a transcription factor that transcriptionally regulates operon i and is equal to zero otherwise.
- 25. The method of claim 18, further comprising:
locating a gate array of a plurality of components of the system according to a distance between components belonging to said group.
- 26. The method of claim 25, wherein said distance is determined according to a distance measure, said distance measure being selected according to at least one characteristic of the system.
- 27. The method of claim 18, further comprising:
detecting at least a portion of the system operating at a lower efficiency than at least a second portion of the system.
- 28. The method of claim 18, wherein the system comprises a plurality of dynamic processes, such that analyzing the system includes analyzing said dynamic processes.
- 29. The method of claim 18, wherein the system comprises a healthcare system, a traffic system or a business process.
- 30. A computer software program, operative to analyze a system, the system being representable as a plurality of nodes connected by edges to form a graph, the program being capable of at least performing the processes of:
analyzing the graph to form a plurality of sub-graphs, each sub-graph containing a plurality of nodes connected by at least one edge; and analyzing said plurality of sub-graphs to detect a type of sub-graph occurring at a threshold frequency in the graph, said type of sub-graph forming a motif of the system.
- 31. A method for analyzing a network, the network containing a plurality of sub-components, comprising selecting at least one sub-component according to a simplicity measure.
- 32. The method of claim 31 further comprising analyzing said selected at least one sub-component for determining relationship between said sub-component and the network.
- 33. The method of claim 31, wherein said simplicity measure comprises finding a minimum number of Structurally Independent Units (SIUs).
- 34. The method of claim 33, wherein said SIUs have a minimal optimized number of mixed nodes.
- 35. The method of claim 33, wherein said simplicity measure comprises counting the ports for each said SIU according to the function H=I+O+2M where I is the number of input nodes, O is the number of output nodes, and M is the number of mixed nodes.
- 36. The method of claim 31, wherein said selecting at least one sub-component according to said simplicity measure further comprises finding a maximum of a scoring function.
- 37. The method of claim 36, wherein said finding said maximum comprises applying a combinatorial optimization process to said scoring function.
- 38. The method of claim 37, wherein said combinatorial optimization process comprises a simulated annealing process.
- 39. The method of claim 38, wherein said applying said simulated annealing further comprises determining the probability that a less maximal result is accepted during said simulated annealing process, according to a Metropolis Monte-Carlo procedure.
- 40. The method of claim 31, wherein said sub-components are sub-graphs.
- 41. The method of claim 32, wherein said analyzing said sub-components further comprises:
selecting a plurality of sub-components; and creating a dictionary of said selected sub-components.
- 42. The method of claim 31, wherein said selecting said sub-components further comprises minimizing a number of selected sub-components.
- 43. The method of claim 32, wherein said analyzing said sub-components further comprises:
creating a coarse-grain network of said system to obtain a plurality of sub-components; and repeating said creating said coarse-grain network at least once.
- 44. The method of claim 43, wherein said repeating said creating said coarse-grain network comprises performing said repeating iteratively until a goal is reached.
- 45. The method of claim 44, wherein said goal comprises reaching a threshold for a minimum size of the network.
- 46. The method of claim 44, wherein said goal comprises obtaining a network lacking an optimal coarse graining reduction.
- 47. The method of claim 31, wherein said network comprises an electronic circuit.
- 48. The method of claim 31, wherein said network comprises a protein signaling pathway.
- 49. The method of claim 48, wherein said protein signaling pathway is human.
- 50. A method for analyzing a system, the system being representable as a plurality of nodes connected by edges to form a complex network, the method comprising:
analyzing said system to detect a plurality of types of sub-graphs occurring at a threshold frequency in the graph, each said type of sub-graph forming a network motif of the system, said network motifs forming a plurality of sub-components; selecting a plurality of sub-components from said detected plurality of network motifs, each sub-component containing at least one node, according to a simplicity measure; and applying a maximizing function to select one or more of said sub-components.
- 51. The method of claim 50, wherein said selecting said plurality of sub-components further comprises partitioning said selected sub-components according to a binary measure.
- 52. The method of claim 51, wherein said partitioning said sub-components further comprises assigning a spin variable to each said sub-component.
- 53. The method of claim 50, wherein said maximizing function further comprises applying simulated annealing.
- 54. A method for analyzing a network to obtain a set of a plurality of simpler sub-components, the method comprising iteratively applying a coarse-graining method to the network to obtain a plurality of sub-components.
- 55. The method of claim 54, wherein in each said iteration said selected sub-components contain at least one sub-component selected in the previous iteration.
- 56. The method of claim 54, wherein said set of sub-components is chosen according to a simplicity measure for reducing the number of connections of said sub-components to other components of the network.
- 57. The method of claim 56, wherein said reducing the number of connections comprises maximizing the scoring function
- 58. The method of claim 54, wherein said sub-components occur at a threshold frequency in the graph, which is significantly higher than the occurrence of said sub-components in a randomized graph.
Parent Case Info
[0001] This is a Continuation in Part Application (CIP) of PCT Application No. PCT/IL03/00053, filed Jan. 22, 2003, which claims priority from U.S. Provisional Application No. 60/420,730, filed Oct. 24, 2002, and from U.S. Provisional Application No. 60/349,365, filed Jan. 22, 2002. All of these applications are hereby incorporated by reference as if fully set forth herein.
Provisional Applications (2)
|
Number |
Date |
Country |
|
60420730 |
Oct 2002 |
US |
|
60349365 |
Jan 2002 |
US |
Continuation in Parts (1)
|
Number |
Date |
Country |
Parent |
PCT/IL03/00053 |
Jan 2003 |
US |
Child |
10746277 |
Dec 2003 |
US |