csc 599: computational scientific discovery lecture 7: scientific processes and ids
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Processes
Up until now we have had a mostly static view of science If the Universe did not change much we could:
Assemble database of its attributes Look for patterns among attributes
But the Universe does change! We need to
Assemble hierarchy (or some other structure) of changes
Look for patterns of changes Before and after patterns During patterns Sequence of state patterns
Attributes of a process
Instances of a process described with: Time
Could be a time range (start, finish) Rates of change Previous history
Objects Special cases:
The “doer” (“subject”) The “done-upon” (“direct object”, “indirect object”)John gave flowers to his mother.
Peripheral actors Environment
Location Magnitude
How big (either of process or one of its objects)
Events: Changes between staticness
One way to view processes is that they are about the changes themselves:
Attributes of Events
For events it is natural to ask: For each event
When? What/who? Where? Properties of event (How big?, etc.)
Among events Given the first
When is the next? Who/which will be next? Where will be next? How big will be next?
What is an overall sequence like?(Patterns in time, objects, location and size)
Processes as always active always active principlesprinciples
Another way to view processes is as always active Often opposing forces
cause no net change Macroscopic change
(“events”) result when opposing forces are out of balance
Example: Gravity and Normal Force are “always on”
Attributes of Processes
All processes of events, plus: Quantity of forces as function of time Maximum limit of “homeostatic” forces
Friction Normal force
Additional attributes like opposing forces lets us ask “what is happening during the process”
Example before-during-after
Transition State Theory Energies associated with molecules Energy difference between transition state and
original molecules dictates reaction rate constant Have related a “during attribute” (energy of
transition state) with an “observable” attribute (process rate)
Cycles of States and “Lifecycles”
Birth, adolescence, adulthood, old age, death In living things In stars
Cycles and Periodicity
Period motion Cycle that completely resets itself
Pendulum motion Planetary motion Chemical cycles
Complications Entropy wears things down
Friction eventually stops pendulums Chemical cycles eventually run out of reagents
Apparent period might be symptomatic of deeper relationship
Moon orbits Earth every 28 days Moon slowly receding from Earth due to tidal forces
Cycles within Cycles
The Carbon Cycle(s)
Pools (Black) in Gigatons
Fluxes (Purple) in Gigatons/year
Illustration courtesy NASA Earth Science Enterprise
Multigenerational Lifecycles
Generation 1 makes generation 2 Generation 1 dies Generation 2 makes generation 3 Generation 2 dies Generation 3 makes generation 4 Generation 3 dies Generation 4 makes generation 5 . . .
Timescales and Magnitude
Things look static because they are so slow Growth of plants Motion of plates, recession of moon Lives of stars Growth of rings on Saturn
Use Time lapse photography (plant growth) Very precise measurement (plate motion, moon
recession) Look at whole populations of different ages (lives
of stars) Inferred ages of parts (Saturn's rings)
Timescales and Magnitude (2)
Things look static because they are so fast Motion of air molecules in a breeze-less room
Things blur because they are so fast Engines
Use: High speed photography (hummingbird wings) oscilloscopes, strobe lighting, laser pulses
(engines, chemical reactions) Confirmatory theory (kinetic theory of gases)
Timescales and Magnitude (3a)
Unique processes might also be viewed as continuum of magnitudes
“4500 to 4000 MYA a Mars-sized object hit Earth”
Has not happened since (fortunately!)
Timescales and Magnitude (3b)
Is object hitting Earth unique? Pea-size meteoroids - 10 per hour Walnut-size - 1 per hour Grapefruit-size - 1 every 10 hours Basketball-size - 1 per month 50-m rock that would destroy an area the size of
New Jersey - 1 per 100 years 1-km asteroid - 1 per 100,000 years 2-km asteroid - 1 per 500,000 years Mars-sized object – 1 per 4000 MYA?
Representing Processes
Each is unique Not much generalization
Sets Generalization within set
Single inheritance Limited generalization among sets
Multiple inheritance Fuller generalization among sets
Anything else?
Describing State Sequences
Finite State Machine Perhaps most of science
Push down automaton Natural and computer languages
Turing Machine Besides special cases of natural and computer
languages can you think of any examples?
Describing Changed Attributes
Qualitative Physics Change state when change attribute's derivative
Difference Equationsattr(t+1) = attr(t) + changeFunction(x,y,z)
Ordinary Differential Equations One independent variable (often time):
Newton's 2nd Law: F(x) = d2x(t)/dt2
Partial Differential Equations More than one independent variable:
¶2u/ ¶x2 + ¶2u/ ¶y2 = 0
Integrated Discovery System (IDS)
Pat Langley, Bernd Nordhausen, 1990
Knowledge base Hierarchy of States Continually refined with more data
Input History of descriptions of qualitatively different
states
Output Refined hierarchy of states
IDS Example
IDS is given the following history:State 1:
liquid acid A and liquid base B exist, then combinedState 2:
quantity of acid and base decrease,quantity of salt increases
State 3:Resulting state has some salt and some acid
IDS Example (3)
IDS is next given the following history:State 1:
liquid acid A and liquid base B exist, then combinedState 2:
quantity of acid and base decrease,quantity of salt increases
State 3:Resulting state has some salt and some base
Histories
IDS input is histories Sequence of qualitative states
Each of which as “constant” behavior A qualitative state ends (and new one begins)
when: an increase or decrease of attribute starts or stops
That is, sign of attribute's derivative changes Structural change occurs
For example, substance appears or disappears mass(SUBSTANCE) decreases to 0 mass(SUBSTANCE) increases from 0
Histories (2)
Histories described by: Object description
liquid(C), HCl(C) Structural description
touches(C,D) Successor link
(Which state comes next) Transition condition
Attribute of successor linkTells conditions under which:
Current state ends New state begins
Histories (3)
ExamplesState 1:
Objects: liquid(A), HCl(A), liquid(B), NaOH(B)Structural:Successor: state 2Transition: combine(A,B)
State 2:Objects: liquid(C), HCl(C), liquid(D), NaOH(D),
liquid(E), NaCl(E)Structural: mass(C)<0, mass(D)<0, mass(E)>0Successor: state 3Transition: mass(C)=0
State 3:Objects: liquid(F), NaOH(F), liquid(G), NaCl(G)Structural: n/a Successor: n/a Transition: n/a
IDS State knowledge
Is-a hierarchy No distinction made between abstract and
instance states!State transition constraints:
Transition conditions“When mass HCl reaches 0 reaction state ends and
final state begins” Final conditions
“When water reaches 100 C it starts to boil”
Within state knowledge Eg. Ideal Gas Law
Beginning state/Final state knowledge“For HCl + NaOH -> NaCl, mass(NaCl) =
1.64*mass(HCl)”
IDS Discovery
Hill climbing without backtracking(Where have we seen
this before?)
“Clustering”Put new state in
hierarchyCompare states
lexicographicallyAlso considers merging
nodes
Cluster(SubRoot,NewState){for each child C of SubRoot
compute similarity between C and NewState
Let C_hi be child with highest match score
if (matchScore(C_hi,NewState) > threshold)if not(C_hi covers NewState )
generalize C_hi to cover NewStateCluster(C_hi,NewState)
elseadd NewState as child of SubRootmerge children of SubRoot
}
IDS Merging
Merging does Forms general
knowledge Cuts down on
number of states System not just
“database of histories”
merge_children(SubRoot, NewChild){for each child C of SubRoot but NewChild
Compute similarity between C and NewChildLet C1 = child with highest scoreLet C2 = child with second highest scoreLet C1_NewChild_s = match(NewChild,C1)Let C1_C2_s = match(C1,C2)if (C1_NewChild_s > C1_C2_s)
C1_NewChild = merge(C1,NewChild)if (C1_NewChild != SubRoot)
make C1_NewChild child of SubRootremove SubRoot children C1, NewChildmake C1, NewChild children of
C1_NewChildelse
C1_C2 = merge(C1,C2)if (C1_C2 != SubRoot)
make C1_C2 child of SubRootremove SubRoot children C1, C2make C1, C2 children of C1_C2
Discovering Laws
Qualitative Laws Successor links:
When make new non-leaf node, follow successor links of children generalize up to the most specific node that covers all
Quantitative Laws Use BACON like search for regularities:
Among attributes of given state When going from one state to its successor Between states (e.g. initial and final)
Use numbers at leaf nodes as raw data
IDS Discussion
Among first systems to explicitly be aware of time Qualitative states -> Limits representation's
search space
Room for improvement Needs to be given object hierarchy Qualitative states is a severe limitation!
Ad hoc clustering (sensitive to order that histories presented)
Cannot explicitly parameterize time Assumes single inheritance
How would you fix some of these?
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