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Class presentations, Epilogue
CS 249B: Science of NetworksWeek 15: Monday, 05/05/08Daniel BilarWellesley CollegeSpring 2008
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Goals today
� Epilogue of CS249B and review
� (Network science redux: Up one level of scale to Motifs)
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Epilogue: Have we done what we set out to do?
Metrics, models, processes and algorithms of networks
� Graph theory� Probability theory� Power laws � Phenomenological models
� Random graphs (Erdos-Reniy)� Small world (Watts-Strogatz)
� Generative (dynamic) models� Preferential attachment (aka Yule
process , Gibrat principle, Matthew effect)
� Hierarchy generation (fractal, self-similarity)
� [Self-organized criticality, EOC]� HOT systems
� Processes and Consequences� Attack, Error tolerances� Diffusion, Epidemics
Learning to learn� Dealing with unknowns,
confusion, abundance of new material
� Efficient reading of difficult papers
� Mind maps/ Concept maps� Presentation to audience� Culminating project
Scientific paradigm� Witness the unfolding of the
scientific paradigm� Course material� Self
� A first-hand look at the acquisition, discussion, correction and evaluation of scientific models to explain phenomena
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You� You showed consistent progress and development, application of our class concepts, and most of all inquisitive couragein your final project
� You took chances, dared to be bold, staked out a position, then argued scientifically, empirically and logically – this is key
� Imagination as the first step is much more important than knowledge “Think like Einstein”
� Don’t fear being wrong, you cannot grow if you do not take that chance
It was a pleasure and a real treat to work with you this semester ☺
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Have a great summer!� You might forget most material of this course in time -> not so tragic� More important are practice of skills that you learned are universally
applicable� Dealing with unknowns, confusion, abundance of new material� Efficient reading of difficult papers, negotiating unknowns, impasses� Clearly expressing yourself in English
� The Scientific Paradigm: In order of importance� Being bold, Primacy of data, “Consillience of Induction” and logic
looks like a duckquacks like a duckhas duck genome
hangs out with ducksPope tells you it is a duck
lives in waterdoes ducky things“I am your father” Duck Vader ☺
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Comparing Apples with Oranges
� A spectrographic analysis of ground, desiccated samples of a Granny Smith apple and a Sunkist navel orange
Sandford S. Apples and oranges: a comparison. Annals of Improbable Research 1995;1(3)
Read other ground breaking research: “Is Kansas flatter than a pancake?” at
http://www.improbable.com/airchives/paperair/volume9/v9i3/kansas.html
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Addendum
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Motifs
� We discussed some properties of network and some conclusions that researchers drew
� Some processes (which are temporal, i.e. over time) may be driven or influenced by re-occurring structures or subgraphpatterns
� In the network context, these structures are called motifs
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Recurring Patterns are motifsIdea: If a pattern occurs more often in real world
networks than random networks, it is called a motifWhere have we seen this type of approach before?
Technique:1. Construct many random graphs with the same number of
nodes and edges ( and same node degree distribution)
2. Count the number of motifs in those graphs
3. Calculate the Z score: the probability that the given number of motifs in the real world network could have occurred by chance
� Software available:� http://www.weizmann.ac.il/mcb/UriAlon/
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Motif count criteria
� Three concepts are considered for the determination of motif frequency, which have different applications and restrictions on counting overlapping matches (i.e. matches sharing edges or vertices) for motif frequency.
� F1 has no restrictions
� F2 allows the sharing of vertices, but not of edges
� F3 does not allow any sharing of network elements
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Application of F1, F2 and F3
motif matches in the target graph
motif to be foundgraph
one of {M1,M2,M3,M4,M5}
F3
{M1,M4} or {M3,M4}F2
{M1,M2,M3,M4,M5}F1
MatchConcept
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3-node Feed-forward loop
Idea: Processes decision-making based on fluctuating external signals
Shen-Orr, Milo, Mangan, Alon. Network motifs in the transcriptional regulation network of Escherichia coli. Nature Genetics, 31:64-68 (2002)
“coherent FF loop act as a circuit that rejects transient activation signals from the general transcription factor and responds only to persistent signals, while allowing a rapid system shutdown”
What does this mean in English?
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4-node: Single-Input module
“motif can show a temporal program of expression according to a hierarchy of activation thresholds of the genes”
What does this mean in English?
Shen-Orr, Milo, Mangan, Alon. Network motifs in the transcriptional regulation network of Escherichia coli. Nature Genetics, 31:64-68 (2002)
Idea: Temporal ordering useful in processes that require several stages to complete
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What is a Z-score?
� A common statistical way of standardizing data on one scale so a ‘normalized’ comparison can take place� “yard stick” for all types of data
� Each z-score corresponds to a point in a normal distribution
� z-score will describe how much a point deviates from a mean or specification point.
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What the Z score meansµ =mean number of times the motifappeared in the random graph
# of times motif
appeared in random graph
zx=x - µµµµx
σσσσx
σ standard deviationthe probability observing a Z
score of 2 is 0.02275
In the context of motifs:
Z > 0, motif occurs more often
than for random graphs
Z < 0, motif occurs less often
than in random graphs
|Z| > 1.65, only a 5% chance of
random occurence
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Z-scores and motif profiling
Milo et al. Superfamilies of designed and evolved networks.Science, 303:1538-42 (2004)
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General motif detection approach
Milo, Shen-Orr, Itzkovitz, Kashtan, Chklovskii & Alon. Network Motifs: Simple Building Blocks of Complex NetworksScience, 298:824-827 (2002)
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Milo (2002) Motif discovery� Discovery of recurring patterns – motifs in broad empirical networks
� Can randomly remove, add, change 20% of edges and set of significant motifs do not change!
� Speculation on classification of network families based on motifs
� “Information processing”, computational circuits?
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Mangan (2003) FFL motif
� Investigation of one motif, the Feed Forward loop� Most significant network motifs in both E. coli and yeast� A three-gene pattern, is composed of two input transcription factors, one of which
regulates the other, both jointly regulating a target gene.� The FFL has eight possible structural types (why?), because each of the three
interactions in the FFL can be activating or repressing� Mathematically modeled the 8 types
� All are sign sensitive� Both coherent and incoherent types delay responses to stimulus steps, but only in one
direction
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Milo (2004) Family classification� Superfamilies can be constructed
based on Triad Significance Profile (TSP) acting as a “Motif signature”� Motif and antimotif
� Examples
Sensory transcription networks� “rate limited networks” by
individual component, faster� FFL over-, 3-chain under-
represented
Signal transduction networks� Not “rate limited”, slower� Triads 7,9,10 (+), 1,2,4,5 (-)
Social networks, languageWWW
Similarities between networks visualized bylooking at the correlation between theTSPs of different networks. Correlationsused to cluster the networks into distinctsuperfamilies
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Finding classes on graphs based on motif signatures
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Papers of interest
� Shen-Orr (2002) “Network motifs in the transcriptional regulation network of Escherichia coli”
� Przulj (2006) “Biological Network Comparison Using Graphlet Degree Distribution”
� Gupta (2007) “Quantifying similarities betweeen motifs”
� Learn more at http://www.weizmann.ac.il/mcb/UriAlon
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Comparing Apples with Oranges
� A spectrographic analysis of ground, desiccated samples of a Granny Smith apple and a Sunkist navel orange
Sandford S. Apples and oranges: a comparison. Annals of Improbable Research 1995;1(3)
Read other ground breaking research: “Is Kansas flatter than a pancake?” at
http://www.improbable.com/airchives/paperair/volume9/v9i3/kansas.html