introduction to geographic information systems spring 2013 (inf 385t-28437) dr. david arctur...

69
Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures 8 & 9 Feb 28, 2013 8 - Spatial Analysis 9 - Geocoding

Upload: sebastian-ventre

Post on 31-Mar-2015

219 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437)

Dr. David ArcturLecturer, Research Fellow

University of Texas at Austin

Lectures 8 & 9Feb 28, 2013

8 - Spatial Analysis9 - Geocoding

Page 2: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

ArcInfo coverages (from Lecture 5)

Created using ESRI’s ArcInfo software (prior to version 8)

Older format (import/export as “.e00”) Set of files within a folder or directory called

a workspace Files represent different types of topology or

feature types Coverages have geometry: Arcs (lines), Nodes

(points), or Polygons, and associated attribute tables

Coverages also have Tics (spatial registration points), and may have Labels and Annotation

INF385T(28437) – Spring 2013 – Lecture 5

Review

Page 3: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Inside a coverage…

INF385T(28437) – Spring 2013 – Lecture 8

View from the operating system:

Page 4: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Coverage attribute table

Area and perimeter

Coverage_ and Coverage_ID

4INF385T(28437) – Spring 2013 – Lecture 5

Page 5: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

5

Labels vs. Annotation

Labels are based on one or more attributes of features.

Annotation is a way to store text to place on your maps

independent of features. Each piece of text stores its

own position, text string, and display properties.

Annotation can also be linked to individual features, for

positional or existence dependency.

If the exact position of each piece of text is important, you

should store your text as annotation in a geodatabase.

Annotation provides flexibility in the appearance and

placement of your text because you can select individual

pieces of text and edit them.

You can convert labels to create new annotation features.INF385T(28437) – Spring 2013 – Lecture 8

Page 6: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Spatial Analysis Outline (Tutorial Ch.9)

Proximity buffers

Site suitability example

Basic apportionment (on your own)

Advanced apportionment (on your

own)

Then… Geocoding (Tutorial Ch.7)

6INF385T(28437) – Spring 2013 – Lecture 8

Lecture 8

Page 7: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

PROXIMITY BUFFERSLecture 8

7INF385T(28437) – Spring 2013 – Lecture 8

Page 8: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Proximity buffers Points

Circular buffers with user supplied radius

Lines Looks like worm based on line feature

8INF385T(28437) – Spring 2013 – Lecture 8

Page 9: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Proximity buffers Polygons

Extends polygons outward and rounds off corners

Created by assigning a buffer distance around polygon

9INF385T(28437) – Spring 2013 – Lecture 8

Page 10: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Point buffer example Polluting company buffers

Added schools Added population

INF385T(28437) – Spring 2013 – Lecture 8 10

Page 11: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Point buffer example

Crimes near schools

INF385T(28437) – Spring 2013 – Lecture 8 11

Page 12: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Line buffer example Businesses within .25 miles of a

selected street

12INF385T(28437) – Spring 2013 – Lecture 8

Page 13: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Select features in buffer

INF385T(28437) – Spring 2013 – Lecture 8 13

Page 14: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Spatial join to count

Join business points to buffer polygon

INF385T(28437) – Spring 2013 – Lecture 8 14

Page 15: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Polygon buffer example River buffer to analyze environmental

conditions, flooding, etc.

15INF385T(28437) – Spring 2013 – Lecture 8

Page 16: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Polygon buffer example

Parcels within 150′ of selected property

16INF385T(28437) – Spring 2013 – Lecture 8

Page 17: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Select features in buffer

INF385T(28437) – Spring 2013 – Lecture 8 17

Page 18: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

SITE SUITABILITYLecture 8

18INF385T(28437) – Spring 2013 – Lecture 8

Page 19: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Locate new police station

Criteria Must be centrally located in each car beat

(within a 0.33-mile radius buffer of car beat centroids)

Must be in retail/commercial areas (within 0.10 mile of at least one retail business)

Must be within 0.05 mile of major streets

19INF385T(28437) – Spring 2013 – Lecture 8

Page 20: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Starting map Lake Precinct of the Rochester, New

York, Police Department Police car beats Retail business points Street centerlines

20INF385T(28437) – Spring 2013 – Lecture 8

Page 21: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Create car beat centroids

XY centroids for police beats

21INF385T(28437) – Spring 2013 – Lecture 8

Page 22: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Buffer car beat centroids

.33 mile buffer

INF385T(28437) – Spring 2013 – Lecture 8 22

Page 23: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Buffer retail businesses

0.1 mile buffer

INF385T(28437) – Spring 2013 – Lecture 8 23

Page 24: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Select major streets

Select by attribute

INF385T(28437) – Spring 2013 – Lecture 8 24

Page 25: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Buffer major streets

0.05 mile buffer

INF385T(28437) – Spring 2013 – Lecture 8 25

Page 26: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Intersect buffers

Can only intersect two at a time Car beat and businesses Streets

INF385T(28437) – Spring 2013 – Lecture 8 26

Page 27: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Site suitability result Map showing possible sites for police

station

INF385T(28437) – Spring 2013 – Lecture 8 27

Page 28: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Spatial Analysis Summary

Proximity buffers (Tutorial exercise 9-1)

Site suitability example (Tutorial exercise

9-2)

Basic apportionment (optional)

Advanced apportionment (optional)

Assignments: 9-1, 9-2 (9-3 optional)

Next up today - Geocoding28INF385T(28437) – Spring 2013 – Lecture 8

Page 29: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

INF385T(28437) – Spring 2013 – Lecture 8

Page 30: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

BASIC APPORTIONMENTLecture 8

30INF385T(28437) – Spring 2013 – Lecture 8

Page 31: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Apportionment example

Population by voting district You want to know the population of a

voting district but only have census tracts Voting districts and census tracts are not

contiguous Approximate the population of voting using

census tracts and blocks

31INF385T(28437) – Spring 2013 – Lecture 8

Page 32: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Population by voting district

Start with census tracts

32INF385T(28437) – Spring 2013 – Lecture 8

Page 33: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Population by voting district Overlay voting districts (not contiguous

with tracts)

INF385T(28437) – Spring 2013 – Lecture 8 33

Page 34: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Population by voting district Better to use block centroids for population

Smaller than tracts

34INF385T(28437) – Spring 2013 – Lecture 8

Page 35: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Spatially join centriods

Join centroids to voting districts

INF385T(28437) – Spring 2013 – Lecture 8 35

Page 36: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Other simple apportionments

Population by

Neighborhoods

Zip Codes

Historic sites

Others?

36INF385T(28437) – Spring 2013 – Lecture 8

Page 37: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Census data to apportion Short form SF1 data (tract, block group,

block) Population Age Race Housing Units Others?

Long form SF3 data (tract and block group) Educational attainment Income Poverty status Others?

37INF385T(28437) – Spring 2013 – Lecture 8

Page 38: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

ADVANCED APPORTIONMENTLecture 8

38INF385T(28437) – Spring 2013 – Lecture 8

Page 39: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Advanced Apportionment

Chapter 9 example Police want to know the number of under-

educated persons in their car beats Under-educated data is located SF3 tables,

census tracts or block groups (not car beat polygons)

39INF385T(28437) – Spring 2013 – Lecture 8

Page 40: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Data to apportion

Car beats

Census tracts

Beats and tracts

Not contiguous

40INF385T(28437) – Spring 2013 – Lecture 8

Page 41: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Beats and tracts zoomed

Tracts clearly cut across beats

INF385T(28437) – Spring 2013 – Lecture 8 41

Page 42: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Tract attribute table Tracts contain undereducated data

No high school degree

INF385T(28437) – Spring 2013 – Lecture 8 42

Page 43: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Math of apportionment Simple census data (e.g. population) is

not a problem Can use block centroids

Problem Block centroids don’t

contain undereducatedpopulation

Tracts contain thisinformation

INF385T(28437) – Spring 2013 – Lecture 8 43

Page 44: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Math of apportionment Tract 360550002100 Car beats 261 and 251

INF385T(28437) – Spring 2013 – Lecture 8 44

Page 45: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Math of apportionment

One approach Assume that the target population is

uniformly distributed across the tract You could split undereducated population

up by the fraction of the area of the tract in each car beat

What if, however, the tract has a cemetery, park, or other unoccupied areas? Then the apportionment could have sizable errors

INF385T(28437) – Spring 2013 – Lecture 8 45

Page 46: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Math of apportionment A better approach

Use a block-level, short-form census attribute as the basis of apportionment

Assume that the long-form attribute of interest is uniformly distributed across the short-form population (accounts for unoccupied areas)

One limitation of the block-level data is that the break points for age categories do not match those of the educational attainment data (persons 25 or older)

The best that can be done with the block data is to tabulate persons aged 22 or older

Close enough for approximationINF385T(28437) – Spring 2013 – Lecture 8 46

Page 47: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Math of apportionment Tract 360550002100 has 39 block

centroids that span 2 beats

Of the 26 blocks making up the tract, the 13 that lie in car beat 261 have 1,177 people aged 22 or older.

The other 13 blocks in car beat 251 have 1,089 such people for a total of 2,266 for the tract.

47INF385T(28437) – Spring 2013 – Lecture 8

Page 48: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Math of apportionment Apportionment assumes that the

fraction of undereducated people aged 25 or older is the same as that for the general population aged 22 or older This fraction, called the weight, is 1,177 ÷

2,266 = 0.519. For the other car beat, the weight is 1,089 ÷ 2,266 = 0.481

Thus, we estimate the contribution of tract 36055002100 to car beat 261’s undereducated population to be (1,177 ÷ 2,266) × 205 = 106. For car beat 251, it is (1,089 ÷ 2,266) × 205 = 99

INF385T(28437) – Spring 2013 – Lecture 8 48

Page 49: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Math of apportionment Eventually, by apportioning all tracts,

we can sum up the total undereducated population for car beats 261 and 251

INF385T(28437) – Spring 2013 – Lecture 8 49

Page 50: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

BACKGROUND STEPSLecture 8

50INF385T(28437) – Spring 2013 – Lecture 8

Page 51: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Background steps1.) Download census data

Download census block and tract polygons from the census Web sites for the county containing the administrative area polygons

Download the short-form census data for blocks that are the basis of apportionment, in this case the population of age 22 and greater

Download the long-form census attribute(s) at the tract level that you wish to apportion to the administrative area, in this case the population aged 25 or greater with less than high school education

51INF385T(28437) – Spring 2013 – Lecture 8

Page 52: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Background steps2.) Create new tract layer

That intersects administrative boundaries

If a tract is only partially inside the administrative area, you must include the entire tract for apportionment to work correctly

An example tract is the southerly-most tract in Tutorial9-3.mxd

INF385T(28437) – Spring 2013 – Lecture 8 52

Page 53: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Background steps

3.) Prepare block centroids Create a new centroid point layer for blocks Clip the centroids with the new intersected tract

layer Join census short-form data to the clipped block

centroids This is the layer that is the basis for apportionment

INF385T(28437) – Spring 2013 – Lecture 8 53

Page 54: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Background steps4.) Sum the short-form census attributes in age

categories to create Age22Plus in the clipped block centroids table

This step is unique to this problem Also, this table has a new TractID attribute which

concatenates FIPSSTCO & TRACT2000 to create an ID matching the Tracts map layer

INF385T(28437) – Spring 2013 – Lecture 8 54

Page 55: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Background steps5.) In the attribute table for block centroids,

sum the field for persons aged 22 or older by TractID to create a new table, SumAge22Plus. This table provides the denominator for the weight used in apportionment

INF385T(28437) – Spring 2013 – Lecture 8 55

Page 56: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

APPORTIONMENT STEPSLecture 8

56INF385T(28437) – Spring 2013 – Lecture 8

Page 57: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Apportionment steps1.)Intersect tracts and car beats to create new

polygons that each have a tract ID and car beat number

INF385T(28437) – Spring 2013 – Lecture 8 57

Page 58: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Apportionment steps2.) Spatially join the new layer of tracts and car

beats with the block centroids to assign all the tract attributes (including the attribute of interest: undereducated population) and car beat attributes to each block’s centroid

INF385T(28437) – Spring 2013 – Lecture 8 58

Page 59: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Apportionment steps

2.)

INF385T(28437) – Spring 2013 – Lecture 8 59

Page 60: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Apportionment steps3.) Join SumAge22Plus to block centroids to

make the apportionment weight denominator, total population aged 22 or older by tract, available to each block centroid

INF385T(28437) – Spring 2013 – Lecture 8 60

Page 61: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Apportionment steps3.) Export the join as a precaution

INF385T(28437) – Spring 2013 – Lecture 8 61

Page 62: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Apportionment steps4.) For each block centroid, create new fields to

store apportionment weight and apportioned undereducated population values, then calculate these values

INF385T(28437) – Spring 2013 – Lecture 8 62

Page 63: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Apportionment steps4.) Calculate values

INF385T(28437) – Spring 2013 – Lecture 8 63

Page 64: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Apportionment steps5.) Sum the apportionment weights by tract as

a check for accuracy (they should sum to 1.0 for each tract)

INF385T(28437) – Spring 2013 – Lecture 8 64

Page 65: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Apportionment steps5.) Each tract that is totally within car beats will

have weights summing to 1. Those partially within car beats sum to less than 1

INF385T(28437) – Spring 2013 – Lecture 8 65

Page 66: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Apportionment steps5.) Sum the undereducated population per car

beat

INF385T(28437) – Spring 2013 – Lecture 8 66

Page 67: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Join apportionment results The last task is to join

the table containing undereducated population by car beat to the car beats layer, then symbolize the data for map display

INF385T(28437) – Spring 2013 – Lecture 8 67

Page 68: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Finished map

INF385T(28437) – Spring 2013 – Lecture 8 68

Page 69: Introduction to Geographic Information Systems Spring 2013 (INF 385T-28437) Dr. David Arctur Lecturer, Research Fellow University of Texas at Austin Lectures

Summary

Proximity buffers

Site suitability example

Basic apportionment

Advanced apportionment

69INF385T(28437) – Spring 2013 – Lecture 8