1. Karl Lieberherr CCIS/PRL Northeastern University
Correlations in Computer Science: an approach based on Noise Elimination
Karl Lieberherr
CCIS/PRL
Northeastern University
11/28/2018
Correlations

2. Technique for building a correlation paradigm
Noise Elimination
Requirements-level techniques to separate crosscutting concerns: reductions
Specker Derivative Game (SDG)
Programming-level techniques to separate crosscutting concerns: AP-F/ DemeterF
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3. Connections to Quantum Computing
Phase transitions are important to play the game well. SDG phase transitions separate P from NP.
Entanglement is connected to phase transitions.
SDG deals with hiding secrets.
Entanglement is used to hide secrets.
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4. Kochen-Specker Theorem / Specker Derivative Game
It is the same Ernst Specker.
The Kochen-Specker theorem is an important, but subtle, topic in the foundations of quantum mechanics. The theorem provides a powerful argument against the possibility of interpreting QM in terms of hidden variables.
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5. Outline Specker Derivative Game (SDG) history top-down
derivatives, raw materials, finished products
example, bottom up
Risk analysis for a derivative
Problem reductions – noise elimination
SDG(MAX-SAT): risk analysis using polynomials
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6. History
Around 1975: I was working on non-chronological backtracking for MAX-SAT for my PhD at ETH Zurich with Erwin Engeler.
With Ernst Specker (co-advisor) I analyzed MAX-SAT which lead to the Golden Ratio Result: joint FOCS 79 and JACM 1981 paper. Ideas applicable to MAX-CSP. J. Algorithms 1982.
2006: sabbatical at Novartis reactivated my interest in MAX-CSP.
2007: Turned Golden Ratio Result into a game SDG(Max) parameterized by a maximization problem Max.
2007/2008: Taught SDG to students who had a lot of fun trying to produce a winning robot (class size 30).
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7. The SDG Game: Two high level views
Financial: Implement trading robots that survive in an artificial derivative market through offering derivatives, and buying and processing derivatives produced by other trading robots.
Biological: Implement organisms that survive in an artificial world through offering outsourced services, and consuming and processing outsourced services produced by other organisms.
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8. Buyer makes profit of 0.8 - 0.7 = 0.1
(p2,0.9,s)
Buyer b
Seller s O
0.8 O
0.8 R R
(p1,0.7,s)
sold
Derivatives
R satisfies p1
0.7
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9. Derivative: (pred, p, s) bought by b
Max is an NP-hard combinatorial maximization problem with objective function range [0,1].
Buyer b buys derivative at price p.
Seller s delivers raw material R (instance of Max) satisfying predicate pred.
Raw material R is finished by buyer with outcome O of quality q and seller pays q to buyer.
Buyer only buys if she thinks q > p.
Uncertainty for buyer: which raw material R will I get? Only know the predicate! What is the quality of the solution of Max I can achieve for R?
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10. Survive in an artificial market
Each robot contains a:
Derivative buying agent
Derivative offering agent
Raw material production agent
Finished product agent (solves Max)
Game is interesting even if robots are far from perfect.
Focus today: how to play the game perfectly (never losing)
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11. SDG Example
derivative based on simplified 3-SAT: S3-SAT = all clauses of length 3, except that all clauses of length 1 contain one positive literal.
derivative(S3-SAT, 0.70) =
derivative(CNF{(3,0),(3,1),(3,2),(3,3),(2,0),(2,1),(2,2),(1,1)}, 0.70)
4 variables maximum
would you like to buy it?
you will get two rights
you will receive a CNF R of the given type.
if you can satisfy the fraction q of clauses in R, I will pay back q to you.
CNF = SEQUENCE of clauses
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12. SDG Example Noise Elimination
derivative(CNF{(3,0),(3,1),(3,2),(3,3),(2,0),(2,1),(2,2),(1,1)}, p) “=“ derivative(CNF{(2,0),(1,1)}, p)
If the seller acts rationally, only clause types {(2,0),(1,1)} will be used in the raw material.
CNF = SEQUENCE of clauses
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13. CNF{(2,0),(1,1)} raw materials
2: b
2: c
1: !a !b
1: !b !c
2: a
2: b
3: c
1: d
3: !a !b
9: !a !c
7: !b !c
1: !a !d
6: !b !d
6: !c !d
2: a
3: b
1: c
8: !a !b
6: !b !c
Find best
satisfaction
ratio
1: a
1: b
8: !a !b
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14. CNF{(2,0),(1,1)} raw materials, finished products
2: b
2: c
1: !a !b
1: !b !c
2: a
2: b
3: c
1: d
3: !a !b
9: !a !c
7: !b !c
1: !a !d
6: !b !d
6: !c !d
6/8=0.75
2: a
3: b
1: c
8: !a !b
6: !b !c
17/20=0.85
price of 0.7
seems fair!?
1: a
1: b
8: !a !b
9/10=0.9
35/40 = 0.875
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15. Oops!! Our analysis was not thorough enough! 2 kinds of uncertainty:
worst formula?
best assignment?
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16. Playing with the weights
x: a
x: b
x: c
x: d
y: !a !b
y: !a !c
y: !b !c
y: !a !d
y: !b !d
y: !c !d
x =1, y=1
best assignment
a=1, b=0, c=0, d=0: (1+6)/10=7/10=0.7
x = 2, y=1
a=1, b=1, c=0, d=0: (4+5)/14=9/14=0.64
derivative(CNF{(2,0),(1,1)}, 0.70)
LOSS: 0.06
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17. To play well: solve min max
maximum
solutions
instances
selected
by predicate
(an infinite set)
0.91
0.62
0.8
0.618
0.619
minimum
Analysis for one Derivative
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18. Concerns Win the game. Seller: Buyer offering:
too expensive or too cheap?
raw material construction
how well can I hide the best assignment?
how can I keep the satisfaction ratio low?
efficiency
Buyer
buying
how well will the best assignment be hidden?
how low can the satisfaction ratio be?
finishing: efficiency
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19. Concerns: SDG(Max) tpred = lim n -> ∞ min
all raw materials rm of size n
satisfying predicate pred
max
all finished products fp
produced for rm
q(fp)
The better the Seller hides the maximum,
the harder the Buyer has to work to find it.
Seller approximates
minimum efficiently
Buyer approximates
Max efficiently
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20. To play well: solve min max
maximum
solutions
instances
selected
by predicate
(an infinite set)
0.91
0.62
0.8
0.62
0.618
0.619
minimum
small subset of
raw materials
guaranteed to contain
minimum of maxima
Analysis for one Derivative
Noise
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21. Raw material selected all possible finished products 0.7 0.7 0.7
small subset of finished products
guaranteed to contain maximum
Noise
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22. Risk analysis Life cycle of a derivative (pred,p) Two uncertainties
offer
risk high if I can find rm and fp with q(fp) > p
buy
risk high if I can find rm and fp with q(fp) < p
raw material (rm)
finished product (fp ,quality q(fp))
Two uncertainties
raw material is not the worst (uncertainty_rm)
finished product is not the best (uncertainty_fp)
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23. To play SDG perfectly eliminate risk
buy
break-even price
sell
produce
efficiently find worst-case example
process
efficiently achieve break-even quality
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24. Goal: never lose with offer/buy
Choose algorithms RM and FP
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25. More Concerns for SDG(Max)
Robot communication
exchange language for derivatives, raw material, finished product
centralized game with administrator managing store of derivatives
decentralized game
Winning in the market
clever algorithm design
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26. Analysis of SDG(Max) tpred = lim n -> ∞ min
all raw materials rm of size n
satisfying predicate pred
max
all finished products fp
produced for rm
q(fp)
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27. Spec for RM and FP tpred = lim n -> ∞ min
all raw materials rm of size n
satisfying predicate pred and
having property WORST(rm)
max
small subset of all finished products fp
produced for rm
q(fp)
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28. Analysis of SDG(Max) tpred = lim n -> ∞ min
all raw materials rm of size n produced by RM
satisfying predicate pred
max
all finished products fp
produced for rm by FP
q(fp)
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29. Hope
Max is NP-hard
SDG(Max) simplifies Max if our goal is to never lose.
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30. SDG(MAX-SAT) Predicates using clause types.
Example predicate S3-SAT = All CNFs with clauses of length at most 3 but clauses of length 1 must contain one positive literal.
What is the right price p for derivative (S3-SAT, p, Specker)
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31. SDG(MAX-SAT) Predicate space: any subset of clause types of S3-SAT:
t S3-SAT = (√5 -1)/2
t {(2,0),(1,1)} = (√5 -1)/2
t {(100,50), (3,2), (2,0),(1,1)} = (√5 -1)/2
Noise for the purpose of constructing raw material.
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32. SDG(MAX-SAT) t {(2,0),(1,1)} = t SYM{(2,0),(1,1)} = (√5 -1)/2
SYM stands for Symmetrization: Idea: if you give me a CNF with a satisfaction ratio f, I give you a symmetric CNF with a satisfaction ratio <= f.
For a CNF in SYM{(2,0),(1,1)}, the MAX-SAT problem reduces to maximizing a polynomial.
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33. Reductions Noise Elimination
Abstraction: What is important to play the game well.
Derivative reduction: to play well with derivative d, it is sufficient to play the game well with a simpler derivative d1 (pred(d1) => pred(d)).
Raw Material Construction Reduction: to construct raw material for a derivative d, it is sufficient to construct only symmetric formulas.
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34. Complexity theory connection
Break-even prices are not only interesting for the SDG game.
They also have complexity-theoretic significance: they are phase transition points separating P from NP (for “most” predicates).
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35. General Dichotomy Theorem
MAX-CSP(G,f): For each finite set G of relations
there exists an algebraic number tG
For f ≤ tG: MAX-CSP(G,f) has polynomial solution
For f ≥ tG+ e: MAX-CSP(G,f) is NP-complete, e>0. 1
hard (solid)
NP-complete
polynomial solution:
Use optimally biased coin.
Derandomize.
P-Optimal.
tG = phase transition point
easy (fluid)
Polynomial
due to Lieberherr/Specker (1979, 1982)
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36. Other break-even prices (Lieberherr/Specker (1982))
G = {R0,R1,R2,R3}; Rj : rank 3, exactly j of 3 variables are true. tG= ¼
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37. Other break-even prices (Lieberherr/Specker (1982))
G(p,q) = {Rp,q = disjunctions containing at least p positive or q negative literals (p,q≥1)}
Let a be the solution of (1-x)p=xq in (0,1). tG(p,q)=1-aq
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Correlations

38. Lessons learned from SDG / correlation perspective
Noise elimination is essential to separate the concerns.
Noise elimination leads to tractable minimization and maximization problems.
Noise elimination is key to come up with needed correlations: Combination Generator, Randomized Algorithm and its Derandomized version, etc.
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39. A model for correlations? The Socrates programming model
A program in the Socrates core language consists of
messages, representing abstract operations,
branches, representing concrete units of behavior that implement parts of one or more operations, and
fields, representing associations between data values.
During the execution of a Socrates program, decision points, objects, and contexts are created and manipulated.
These six entities are all first-class values.
Socrates = Predicate Dispatch + …
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40. Socrates Reference http://socrates-lang.sourceforge.net/
@INPROCEEDINGS{doug:aosd-2002, AUTHOR = "Doug Orleans", TITLE = "Incremental Programming with Extensible Decisions", BOOKTITLE = "First International Conference on Aspect-Oriented Software Developm ent", YEAR = "2002", ADDRESS = "Enschede, The Netherlands", PAGES = "", EDITOR = "Gregor Kiczales", PUBLISHER = "ACM Press”}
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Correlations

41. crosscutting concerns
public class Shape
implements ShapeI {
protected AdjustableLocation loc;
protected AdjustableDimension dim;
public Shape() {
loc = new AdjustableLocation(0, 0);
dim = new AdjustableDimension(0, 0); }
double get_x() throws RemoteException {
return loc.x(); }
void set_x(int x) throws RemoteException {
loc.set_x(); }
double get_y() throws RemoteException {
return loc.y(); }
void set_y(int y) throws RemoteException {
loc.set_y(); }
double get_width() throws RemoteException {
return dim.width(); }
void set_width(int w) throws RemoteException {
dim.set_w(); }
double get_height() throws RemoteException {
return dim.height(); }
void set_height(int h) throws RemoteException {
dim.set_h(); }
void adjustLocation() throws RemoteException {
loc.adjust();
void adjustDimensions() throws RemoteException {
dim.adjust();
class AdjustableLocation {
protected double x_, y_;
public AdjustableLocation(double x, double y) {
x_ = x; y_ = y;
synchronized double get_x() { return x_; }
synchronized void set_x(int x) {x_ = x;}
synchronized double get_y() { return y_; }
synchronized void set_y(int y) {y_ = y;}
synchronized void adjust() {
x_ = longCalculation1();
y_ = longCalculation2();
class AdjustableDimension {
protected double width_=0.0, height_=0.0;
public AdjustableDimension(double h, double w) {
height_ = h; width_ = w;
synchronized double get_width() { return width_; }
synchronized void set_w(int w) {width_ = w;}
synchronized double get_height() { return height_; }
synchronized void set_h(int h) {height_ = h;}
width_ = longCalculation3();
height_ = longCalculation4();
interface ShapeI extends Remote {
double get_x() throws RemoteException ;
void set_x(int x) throws RemoteException ;
double get_y() throws RemoteException ;
void set_y(int y) throws RemoteException ;
double get_width() throws RemoteException ;
void set_width(int w) throws RemoteException ;
double get_height() throws RemoteException ;
void set_height(int h) throws RemoteException ;
void adjustLocation() throws RemoteException ;
void adjustDimensions() throws RemoteException ;
Modularization of
crosscutting concerns
public class Shape {
protected double x_= 0.0, y_= 0.0;
protected double width_=0.0, height_=0.0;
double get_x() { return x_(); }
void set_x(int x) { x_ = x; }
double get_y() { return y_(); }
void set_y(int y) { y_ = y; }
double get_width(){ return width_(); }
void set_width(int w) { width_ = w; }
double get_height(){ return height_(); }
void set_height(int h) { height_ = h; }
void adjustLocation() {
x_ = longCalculation1();
y_ = longCalculation2(); }
void adjustDimensions() {
width_ = longCalculation3();
height_ = longCalculation4();
coordinator Shape {
selfex adjustLocation, adjustDimensions;
mutex {adjustLocation, get_x, set_x,
get_y, set_y};
mutex {adjustDimensions, get_width, get_height,
set_width, set_height};
portal Shape {
double get_x() {} ;
void set_x(int x) {};
double get_y() {};
void set_y(int y) {};
double get_width() {};
void set_width(int w) {};
double get_height() {};
void set_height(int h) {};
void adjustLocation() {};
void adjustDimensions() {};
Write
this
Instead of
writing this
© Crista Lopes
11/28/2018
Correlations

42. A Safe Form of Aspects: Adaptive Programming (AP)
General Aspects (96)
Base: any program
join points
pointcuts
advice
AP (92)
Base: any traversal
before / after events
method signatures
method bodies
Connection to Theo:
DemeterF was developed
in the context of language
interpreters and compilers.
See DemeterF home page.
AP is a special case of AOP.
AP-F is a special case of AP.
DemeterF is an implementation of AP-F (Java, C#)
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43. Theme: noise elimination
leads to better separation of concerns and better correlations.
requirements: problem reductions eliminate noise
irrelevant information is eliminated. Correlations: minimizing and maximizing continuous functions.
programming: traversal abstractions eliminate noise
irrelevant classes are not mentioned. Correlations: WhereToGo, WhatToDo.
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44. Noise Elimination SDG (specific to SDG Game) DemeterF (very general)
Only a subset of the formulas of the MAX-CSP problem is relevant to find a good raw material.
Only a subset of the assignments is relevant to find a good finished product.
DemeterF (very general)
Only a subset of the classes is relevant to implement an object collaboration.
Only a subset of the classes is relevant to specify
WhereToGo
WhatToDo
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45. find all persons waiting at any bus stop on a bus route
WhereToGo: Strategy
first try: from BusRoute to Person
busStops
BusRoute
BusStopList
buses
0..*
BusStop
BusList
waiting
0..*
passengers
Bus
PersonList
Person
0..*
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46. find all persons waiting at any bus stop on a bus route
WhereToGo: Strategy
from BusRoute via BusStop to Person
busStops
BusRoute
BusStopList
buses
0..*
BusStop
BusList
waiting
0..*
passengers
Bus
PersonList
Person
0..*
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47. find all persons waiting at any bus stop on a bus route
WhereToGo: Strategy
Altern.: from BusRoute bypassing Bus to Person
busStops
BusRoute
BusStopList
buses
0..*
BusStop
BusList
waiting
0..*
passengers
Bus
PersonList
Person
0..*
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48. Robustness of Strategy
find all persons waiting at any bus stop on a bus route
Robustness of Strategy
from BusRoute via BusStop to Person
villages
BusRoute
BusStopList
busses
VillageList
busStops
0..*
0..*
BusStop
BusList
Village
waiting
0..*
passengers
Bus
PersonList
Person
0..*
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49. Filter out noise in class diagram
only three out of seven classes
are mentioned in traversal
strategy!
from BusRoute via BusStop to Person
explain why strategy better
replaces traversal methods for the classes
BusRoute VillageList Village BusStopList BusStop
PersonList Person
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50. WhatToDo: Type-Unifying
Return 1 for each Person-object.
Return 0 for other leafs.
Sum for lists: int up(ConsI c, int f, int r) {return f+r;}
Pass for one part: int up(Object o, int p) {return p;}
Processing works for many class graphs.
Static type-checking protects against some bad changes to the class graph.
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51. Genericity Works for a family of object graphs WhereToGo WhatToDo
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52. Comparing Noise Elimination
Noise elimination in SDG: have to prove theorems to show that nothing is lost and we get the correct result.
Noise elimination in DemeterF: have to prove (or approximate it through testing) that the noise elimination leads to correct generalizations.
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53. Other Benefit of AP-F
If you want to take advantage of multi-core computers, it is beneficial to write programs in a style that is amenable to parallel execution.
I will present such a style: AP-F and its implementation in Java and C#, called DemeterF.
AP-F has other benefits: easier software variability.
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54. Outline AP-F/DemeterF
DemeterF: a traversal abstraction tool that supports structure-shy software
Generalized data abstraction
Intro to AP-F
Intro to DemeterF
4 important classes (ID, Bc, EdgeControl, Traversal)
3 important methods (down, up, traverse)
Examples
Composition in DemeterF
Conclusions
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55. AP-F/DemeterF: a useful tool to process objects
OOP and Functional Adaptive Programming
Traversal abstraction library
similar to a library supporting the visitor design pattern
new: better traversal abstraction through multi-methods and traversal control
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56. Builds on
Adaptive Programming (AP): Graph-based traversal control based on expansions, separation of concerns into ClassGraph, WhereToGo, WhatToDo. Mostly the separation of functionality (WhatToDo) and traversal (WhereToGo). Functions don't need to traverse, and traversals don't mention any specific function.
Functional Programming (FP): Side-effect-free programming, WhatToDo without local state. Programming with map and fold. Generalized fold.
Generic functions (GF): dynamic dispatch for down and up methods. Predicate Dispatch. Socrates. PolyD.
Scrap Your Boilerplate (SYB): separation into type preserving and type unifying computations.
Datatype-Generic Programming (DGP): Polytypic Programming.
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57. Recent related activity
Attribute Grammars (AG): AOSD 2008 (Oxford paper).
(Functional) Visitor Pattern (VP): OOPSLA 2008 (Oxford paper). Bruno Oliveira,  Jeremy Gibbons.
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58. Important Software Topic To Which We Contribute with AP-F
Generalizing the Data Abstraction Problem
Through Better Abstractions for Traversals
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59. Generalizing Data Abstraction
well-accepted, since 70s
Data Abstraction Principle: the implementation of objects can be changed without affecting clients provided the interface holds.
Adaptive Programming (AP) Principle: the interface of objects can be changed without affecting clients provided the generalized interface holds.
since 90s
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60. Motto of AP-F Law of Demeter: Talk only to your friends.
Law of AP-F: Listen only to your friends and selectively receive information from your superiors.
You might not need all the information you get from your friends. You only take what you need and what the communication protocol requires.
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61. What happens if you don’t use traversal abstraction?
You write a lot of boiler plate code! Related work: Scrap Your Boilerplate (SYB) started by Ralf Laemmel and Simon Peyton-Jones.
You tightly couple structure (changes frequently) and computation (more stable). That is against common sense.
You always deal with the worst-case scenario of AP-F.
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62. A Quick Intro to AP-F
An AP-F program is defined by two sets of functions which adapt behavior of a predefined traversal with a multiple dispatch function. The two sets of functions:
down up
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63. crosscutting concerns
public class Shape
implements ShapeI {
protected AdjustableLocation loc;
protected AdjustableDimension dim;
public Shape() {
loc = new AdjustableLocation(0, 0);
dim = new AdjustableDimension(0, 0); }
double get_x() throws RemoteException {
return loc.x(); }
void set_x(int x) throws RemoteException {
loc.set_x(); }
double get_y() throws RemoteException {
return loc.y(); }
void set_y(int y) throws RemoteException {
loc.set_y(); }
double get_width() throws RemoteException {
return dim.width(); }
void set_width(int w) throws RemoteException {
dim.set_w(); }
double get_height() throws RemoteException {
return dim.height(); }
void set_height(int h) throws RemoteException {
dim.set_h(); }
void adjustLocation() throws RemoteException {
loc.adjust();
void adjustDimensions() throws RemoteException {
dim.adjust();
class AdjustableLocation {
protected double x_, y_;
public AdjustableLocation(double x, double y) {
x_ = x; y_ = y;
synchronized double get_x() { return x_; }
synchronized void set_x(int x) {x_ = x;}
synchronized double get_y() { return y_; }
synchronized void set_y(int y) {y_ = y;}
synchronized void adjust() {
x_ = longCalculation1();
y_ = longCalculation2();
class AdjustableDimension {
protected double width_=0.0, height_=0.0;
public AdjustableDimension(double h, double w) {
height_ = h; width_ = w;
synchronized double get_width() { return width_; }
synchronized void set_w(int w) {width_ = w;}
synchronized double get_height() { return height_; }
synchronized void set_h(int h) {height_ = h;}
width_ = longCalculation3();
height_ = longCalculation4();
interface ShapeI extends Remote {
double get_x() throws RemoteException ;
void set_x(int x) throws RemoteException ;
double get_y() throws RemoteException ;
void set_y(int y) throws RemoteException ;
double get_width() throws RemoteException ;
void set_width(int w) throws RemoteException ;
double get_height() throws RemoteException ;
void set_height(int h) throws RemoteException ;
void adjustLocation() throws RemoteException ;
void adjustDimensions() throws RemoteException ;
Modularization of
crosscutting concerns
In AP-F:
concern 1: class graph
concern 2: WhereToGo (down,up)
concern 3: WhatToDo
public class Shape {
protected double x_= 0.0, y_= 0.0;
protected double width_=0.0, height_=0.0;
double get_x() { return x_(); }
void set_x(int x) { x_ = x; }
double get_y() { return y_(); }
void set_y(int y) { y_ = y; }
double get_width(){ return width_(); }
void set_width(int w) { width_ = w; }
double get_height(){ return height_(); }
void set_height(int h) { height_ = h; }
void adjustLocation() {
x_ = longCalculation1();
y_ = longCalculation2(); }
void adjustDimensions() {
width_ = longCalculation3();
height_ = longCalculation4();
coordinator Shape {
selfex adjustLocation, adjustDimensions;
mutex {adjustLocation, get_x, set_x,
get_y, set_y};
mutex {adjustDimensions, get_width, get_height,
set_width, set_height};
portal Shape {
double get_x() {} ;
void set_x(int x) {};
double get_y() {};
void set_y(int y) {};
double get_width() {};
void set_width(int w) {};
double get_height() {};
void set_height(int h) {};
void adjustLocation() {};
void adjustDimensions() {};
Write
this
Instead of
writing this
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64. Motto of AP-F down A object graph Listen to C and D Receive from A Bup
Does NOT Receive from A C
Receive from A D E
Receive from A
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65. Illustration of up 19a 19 :C (w1+w2+w3+w4,2) :Cons (w1+w2+w3+w4,1) :E20 2
18a 3 18 3a
13a
:Cons
(w1+w2+w3,1)
after blue arrow
up is
active (like after)
17a :C
(w2+w3,1) 4
12a 17
:Cons
(w1,0) 5 13 14 12
16a
:Cons
(w2+w3,0)
15a 6 :E
(w1,0)
:Empty
(0,0)
11a 7a 15 16 11 :E
(w3,0)
:Cons
(w2,0) 8 7
10a 9a :E
(w2,0)
:Empty
(0,0) 9
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Correlations 10

66. DemeterF
A significant class of applications can be coded modularly without tangled code and without having to write boiler plate code.
DemeterF has an optional code generation tool to generate Java classes from grammars (data binding) and traversal strategies (navigation binding).
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67. DemeterF Function Objects
up methods
several parameters (from your friends)
default: reconstruct using (new) parameters
down methods
three parameters (where, which field/path, what came from above)
default: identity (return third parameter)
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68. What is new with DemeterF
easy generalization of functionality thanks to multimethods: exploit similarities between up methods at different nodes. Type-checking captures missing methods.
easy generalization of traversals
easy parallelization
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69. What Hinders Creation of Flexible Software
Manually following rules like: Follow the structure, follow the grammar.
Actively call traversal methods (explicit traversal problem).
Also leads to manual passing of arguments (explicit argument problem).
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70. Still follow the grammar?
Might have to write customized methods for every node. Extreme case.
Encode local information about structure in customized methods.
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71. The 4 most important classes in DemeterF
WhatToDo:
ID: you take responsibility for writing sufficiently many up methods covering your objects. Type Unifying.
Bc: you let the system write default up methods that rebuild the object and you override some of them. Type Preserving.
WhereToGo: EdgeControl.
For using ID, Bc and EdgeControl: Traversal
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72. The 4 most important classes in DemeterF
ID == id-for-trav-arguments and
id-for-prims (int,String, etc.) ID
inherits Bc
Bc == ID + rebuild
Use ID for type-unifying processing.
Use Bc for type-preserving processing.
Traversal(ID, EdgeControl) Traversal(WhatToDo, WhereToGo)
EdgeControl
which edges to avoid
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73. The 3 most important methods in DemeterF
for initiating a traversal: traverse
for modifying a traversal (WhatToDo):
down:
method is activated when the down method of the parent is complete.
up:
method is activated when all subtraversals have returned.
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74. Type-unifying: ID, Traversal up, traverse
// Produces a string representation of the tree
static class Str extends ID {
String up(leaf l) { return ""; }
String up(node n, int d, String l, String r) {
return "("+d+" "+l+" "+r+")"; }
public static String doStr(bst t){
return new Traversal(new Str()).<String>traverse(t);
how generic? positions 2 and 3 are important
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75. Example: Class Graph bst
right
left
is-a
is-a
leaf
node
data
int
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Correlations

76. Example: Class Graph bst
middle
right
left
is-a
is-a y x
leaf
node
is-a
data
node2
int
data2
float
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Correlations

77. Type-preserving: Bc, Traversal up, traverse
// Increments each int element and rebuilds the
// resulting tree
static class Incr extends Bc {
int up(int i) { return i+1; }
public static String doIncr(bst t){
return new Traversal(new Incr()).
<bst>traverse(t); }
how generic? very general
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78. ID, Traversal, EdgeControl up, traverse
// Find the minimum data element in the BST... keep going left
static class Min extends ID {
int up(node n, int d, leaf l) { return d; }
int up(node n, int d, int l) { return l; }
public static int min(bst t){
EdgeControl ec = EdgeControl.create(
new Edge(node.class,"right"));
ec.addBuiltIn(leaf.class);
return new Traversal(new Min(), ec).<Integer>traverse(t); }
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Correlations

79. ID, Traversal down, up, traverse
// Produces a list of strings representing the paths to each
// leaf element in the tree
static class Paths extends ID {
String down(node n, node.left f, String path)
{ return path+".left"; }
String down(node n, node.right f, String path)
{ return path+".right"; }
List<String> up(leaf l)
{ return new Empty<String>(); }
List<String> up(node n, int d, List<String> l, List<String> r, String p)
{ return l.append(r).push(" "+d+" : "+p); }
public static String doPaths(bst t){
return new Traversal(new Paths()).
< List<String>>traverse(t, “root”); } }
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Correlations

80. Type-unifying Tree Height, bottom up: Unifying type: (int height)
fold: max + 1
class Height extends ID{
int up(node t, int d,
int l, int r){ return
Math.max(l,r)+1; }
int up(leaf l){return 0;} }
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81. Dispatch function of DemeterF
chooses most specific method
more information means more specific
only list arguments up to last one that is needed
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82. Traversal Constructors
Traversal(ID ba)           Takes an ID function object
Traversal(ID ba, EdgeControl eb)           In addition takes a traversal control object.
Edge control may be specified using domain-specific language.
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83. Unifying Type
The unifying type which may contain many more elements than only what we need to compute.
We want a type T = (U1, U2, ...) so that T carries just enough information to implement up: T up (X x, T t1, T t2, ...) at all nodes in the structure.
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84. Type-unifying Examples
Binary Search Tree Property:
Given a binary tree of ints, are all nodes in the left tree smaller than the root and all nodes in the right subtree greater to or equal than the root.
Consider the maximum max of the left subtree and the minimum min of the right subtree to do the max < d <= min check.
Unifying type: (boolean BSTproperty, int min, int max)
Base case: Empty tree: (true, +oo, -oo)
fold: operation on two triples.
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Correlations

85. Check BST Property
An integer tree T, with integer n at its root, is a binary search tree if (all must hold)
the left and right tree of T are a BST
the maximum of all nodes in the left tree of T is smaller than n
the minimum of all nodes in the right tree of T is greater than or equal to n
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86. Why do we need the last 2? 8 10 3 BST 1 9 BST not BST 11/28/2018
Correlations

87. Check for BST Property class Check extends ID{
Pack up(leaf l){ return new Pack(true); }
Pack up(node t, int d, Pack lt, Pack rt){
return new Pack((lt.good && rt.good &&
(lt.max < d) && (d <= rt.min)),
Math.min(lt.min,d),
Math.max(rt.max,d)); }
static boolean check(bst tree){
return new Traversal(new Check())
.<Pack>traverse(tree).good; }}
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Correlations

88. Pack Helper Class class Pack{ boolean good; int min,max;
Pack(boolean g, int mn, int mx)
{ good = g; min = mn; max = mx; }
Pack(boolean g){ this(g,
Integer.MAX_VALUE,
Integer.MIN_VALUE); } }
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89. Example 5 (t,1,7) (t,1,3) 3 7 (t,7,7) E 1 E E (t,1,1) (t,+∞,-∞)
(t/f,min,max) for entire tree.
min and max are only valid if tree is BST.
(t,+∞,-∞)
(t,+∞,-∞)
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Correlations

90. Conclusions: A Technique for Finding Correlations
Noise Elimination
Requirements-level techniques to separate crosscutting concerns: reductions
Specker Derivative Game (SDG)
Programming-level techniques to separate crosscutting concerns: AP-F/ DemeterF
Are the connections to Quantum Computing of any value?
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91. 11/28/2018
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92. Composition
How to compose traversals?
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93. Tree Diameter
The diameter of a tree T is the largest of the following quantities:
(1) diameter of T’s left subtree
(2) diameter of T’s right subtree
(3) the longest path between two leaves that goes through the root of T (computed from the heights of the subtrees of T)
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94. Why do we need 1 and 2? 5 4 6 3 2 9 1 diameter 9, NOT through root
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95. 11/28/2018
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96. Correlations in the SDG World
Consider organisms that need to survive in an artificial world through producing outsourced services, and consuming and processing outsourced services produced by other organisms.
Consider simple trading robots that need to survive in an artificial derivative market through offering derivatives, and consuming and processing derivatives produced by other trading robots.
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Correlations

97. Services: Correlations in the SDG World
Consider organisms that need to survive in an artificial world through offering services, and consuming and processing services produced by other organisms.
Consider simple trading robots that need to survive in an artificial derivative market through offering derivatives, and consuming and processing derivatives produced by other trading robots.
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Correlations

98. (food,price,producer))
organisms need to decide whether to absorb a food based on partial information. Hopes to gain energy by absorption and processing of food.
(food,price,producer))
energy gained where deducted? producing organism is nearby? seller and buyer of food meet.
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99. correlations in SDG
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Correlations

100. Model SDG(Max) organisms: move around partial information = predicate
food in organism: still connected to owner?
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Correlations

101. want to absorb a “kind” of food.
inside: organism: food of the promised kind is delivered.
food is digested with quality q. energy q belongs to consuming organism; deducted from providing organism.
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Correlations

102. correlations in biology: prices don’t have to come down.
slightly different rules.
organisms meet, explore each others food/service offers, choose and move on
not a global store; distributed version
in biology: “being” costs energy: need to consume and produce to generate energy; another way to make game interesting.
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Correlations

103. correlations in SDG(Max)
think kind of: food, service, raw material
what kind of skills make the organisms survive?
buy, sell, produce, process
what cuts across those 4?
symmetrization, Polya’s inventor paradox
problem solving techniques cut across 4 agents
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Correlations

104. buy sell produce process break-even price
efficiently find worst case example
process
efficiently achieve break-even quality
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Correlations

105. Cutting across classes
find polynomial for a maximization instance
de-randomization
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106. Cutting across problems
symmetrization
randomization
de-randomization
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Correlations

107. A different form of crosscutting
Problem solving techniques applicable in many domains.
specific ways to solve problems are applicable in many sub problems of the same problem
reductions and correlations
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108. Demeter Interface
Bus example: want no shortcuts, except list shortcuts. Or want one path with multiplicities allowed.
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109. Variant SDG for CSP
derivative: (predicate1 (on instances), predicate2 (on assignments and instances), price, creator)
worst formula satisfying predicate1 and with assignment satisfying predicate2 we can satisfy fraction p.
Example: independent set: predicate1 = relation q(x,y) = !(x = y). predicate2 = 2/3 of variables set to 1.
Example: vertex cover: predicate1 = relation q(x,y) = {(1,0),(0,1),(1,1)} = x or y. predicate2 = 2/3 of variables set to 1.
Example: maximum cut: predicate1 = relation q(x,y) = {(1,0).(0,1)} = x xor y. predicate2 = true.
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Correlations

110. 11/28/2018
Correlations

111. Lefteris Rolling Stones: I can get no Satisfaction
Beatles: yesterday, all you need is love.
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Correlations

112. Positive votes 15
Negative votes 7
Passes 2
Erik Ernst
The notion of being an inherently cross-cutting concern does not exist.
Posted by Erik Ernst, Friday, March 28, 2008 on aosd.net.
It is a matter of (1) the power of the available abstraction mechanisms, and (2) the choice of organizational principles in the design of the software system under scrutiny whether or not the set of software elements associated with a given concern is cross-cutting or not. Such a set of software elements may be distributed in a cross-cutting manner in a concrete system written using one or more concrete languages. As soon as somebody manages to express the concern modularly by reshaping the architecture or creating and using new abstraction mechanisms, this concern becomes non-cross-cutting, so it was never *inherently* cross-cutting. The notion of being a *currently* cross-cutting concern does exist, though, and the really interesting issue is how we can move concrete concerns out of this sad state by means of improvements of the basic theories and technologies. ;-)
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Correlations

113. Theme: noise elimination
leads to better separation of concerns and better correlations.
requirements: problem reductions eliminate noise
irrelevant information is eliminated. Correlations: minimizing and maximizing continuous functions.
programming: traversal abstractions eliminate noise
irrelevant classes are not mentioned. Correlations: WhereToGo, WhatToDo.
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114. Example: class node // Functional Nodes
public static class node extends bst {
int data;
bst left, right;
public node(int d, bst l, bst r) { data = d; left = l; right = r; }
public bst insert(int d) {
if(d <= data)
return new node(data, left.insert(d), right);
return new node(data, left, right.insert(d)); }
// Field classes... Must be public+static.
public static class data { }
public static class left { }
public static class right { }
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115. Difference: Coplien Abstraction (loses information) Generalization
(Abstraction is here defined as the ability to perceive a concept irrespective of its concrete embodiment.)
if appropriate conceptual abstraction (promoted by perceptual variability) and generalization (promoted by mathematical variability) are to occur.
It seems reasonable to suggest that a child has truly learned a mathematical concept only when s(he) is able to abstract it from its physical context and generalize it to new situations.
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116. the point of concern is that the psychological factors (abstraction and generalization) to which the perceptual and mathematical variability principles address themselves
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Correlations

117. A model for correlations? The Socrates programming model
A program in the Socrates core language consists of
messages, representing abstract operations,
branches, representing concrete units of behavior that implement parts of one or more operations, and
fields, representing associations between data values.
During the execution of a Socrates program, decision points, objects, and contexts are created and manipulated.
These six entities are all first-class values.
Socrates = Predicate Dispatch + …
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118. Socrates Reference http://socrates-lang.sourceforge.net/
@INPROCEEDINGS{doug:aosd-2002, AUTHOR = "Doug Orleans", TITLE = "Incremental Programming with Extensible Decisions", BOOKTITLE = "First International Conference on Aspect-Oriented Software Developm ent", YEAR = "2002", ADDRESS = "Enschede, The Netherlands", PAGES = "", EDITOR = "Gregor Kiczales", PUBLISHER = "ACM Press”}
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119. Noise reduction: important topic
To implement trading robots, we use a tool called DemeterF which is good at noise reduction during the programming process: focus on important classes and eliminate noise classes.
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120. Positive votes 15
Negative votes 7
Passes 2
Erik Ernst
The notion of being an inherently cross-cutting concern does not exist.
Posted by Erik Ernst, Friday, March 28, 2008 on aosd.net.
It is a matter of (1) the power of the available abstraction mechanisms, and (2) the choice of organizational principles in the design of the software system under scrutiny.
11/28/2018
Correlations

121. Positive votes 15
Negative votes 7
Passes 2
Erik Ernst
The notion of being an inherently cross-cutting concern does not exist.
Posted by Erik Ernst, Friday, March 28, 2008 on aosd.net.
It is a matter of (1) the power of the available abstraction mechanisms, and (2) the choice of organizational principles in the design of the software system under scrutiny whether or not the set of software elements associated with a given concern is cross-cutting or not. Such a set of software elements may be distributed in a cross-cutting manner in a concrete system written using one or more concrete languages. As soon as somebody manages to express the concern modularly by reshaping the architecture or creating and using new abstraction mechanisms, this concern becomes non-cross-cutting, so it was never *inherently* cross-cutting. The notion of being a *currently* cross-cutting concern does exist, though, and the really interesting issue is how we can move concrete concerns out of this sad state by means of improvements of the basic theories and technologies. ;-)
11/28/2018
Correlations