CS 111: Program Design I Lecture 25: Social networks, nothingness. Robert H. Sloan & Richard Warner University of Illinois at Chicago April 24, 2018

Size: px
Start display at page:

Download "CS 111: Program Design I Lecture 25: Social networks, nothingness. Robert H. Sloan & Richard Warner University of Illinois at Chicago April 24, 2018"

Transcription

1 CS 111: Program Desig I Lecture 25: Social etworks, othigess Robert H. Sloa & Richard Warer Uiversity of Illiois at Chicago April 24, 2018

2 SOCIAL MEDIA AND PRIVACY (CONT.)

3 The DHS Example DHS collects social media hadles, aliases, associated idetifiable iformatio, ad search results o immigrats, icludig aturalized citizes ad permaet residets, ad it stores public-source data (icludig iformatio from social media) ad gathers iformatio from commercial data providers ad public sources such as social media, ews media outlets, ad the Iteret.

4 What Relatioships? There are early 40,000 rows

5 This Makes It Easy To See Computatioal Legal jouralist First 200 rows for edge-data [edge_data ['b'] == 'Computatioal Legal']

6 Who Is Chelsea Rider? Predictive Aalytics Computatioal Legal 7096 Chelsea Rider 2607 Legal Tracker 1847 James D. Williams Army Vet Aimal Advocate Sigle Mom JD. Iterests: #laweforcemet/#lesm/#social media, #hockey, #books, #weightliftig, & most importatly, #dogs/#padas

7 Cell Phoe Calls

8 Cell Phoe Calls The structure ca reveal importat iformatio. Moey lauderig Drug distributio Jouralist/source Protesters

9 Network Aalysis Fraud Detectio Desity measures are extremely useful i determiig potetial fraud hotspots i retail bakig from a maze of accout trasactios ad applied cotrol measures. Credit card trasactio moitorig ad moey-lauderig are potetially two areas where desity metrics could trigger the ecessity for deeper ivestigatios. desity = actual coectios (-1)/2 Other useful measures: Degree, closeess, betweeess (extet of a ode s placemet o the shortest paths betwee odes) Degree for the cell phoe etwork

10 The Privacy Problem Privacy of social etwork data is a growig cocer which threates to limit access to this valuable data source. Aalysis of the graph structure of social etworks ca provide valuable iformatio for reveue geeratio ad social sciece research, but ufortuately, esurig this aalysis does ot violate idividual privacy is difficult. Simply aoymizig graphs or eve releasig oly aggregate results of aalysis may ot provide sufficiet protectio. Who is this? Teaches at UIC ad Chicago-Ket College of Law. Has a Ph.D. i Philosophy ad a JD.

11 Relatioal Privacy Privacy is relatioal whe your cotrol over the collectio ad use of iformatio cosists i your reasoable reliace o others volutarily refraiig from collectig ad usig that iformatio. 11

12 Aoucemet: Do the course evaluatio We'll make it worth your while

13 Aoucemet: Witer Fial Exam is Comig Most of you are doig great A small hadful of you are i trouble with reuiremet: You must pass the exam part of the course to pass the exam Meaig average of 2 midterms ad fial exam (weighted eual to both midterms take together) For all: Will use >= 70 fial exam to replace ay lower midterm exams But two midterms i the 30s or 40s ad fial i 50s will fail this course eve with good labs ad projects

14 PANDAS FILE READING ISSUE SOME STUDENTS ENCOUNTERED

15 Are padas reluctat readers? padas.read_csv ca take as its first argumet either file referece (obtaied from ope()) or file ame i uotes Ad optioal sep argumet you kow about sep=',' # Default ad therefore ca be omitted sep=' ' # Space separated sep='\t' # Tab separated CS111 had you usig ope() because that's default i rest of Pytho ad wated you to practice; padas people typically use text file ame ad skip ope()

16 Headers ad commets up top Some graph files start with commets startig with # up top Ad also ca have colum headers Say first 4 lies start with #. Ca tell padas either 1. Start readig at Pytho Lie 3 (0..3) as header header=3 2. or commet='#', header=noe file ame strig type argumet okay with either; fileref oly with 1!

17 padas read_csv Suggestio: use file ame versio of pd.read_csv header: Gives lie umber to treat as lie cotaiig headers, coutig lies Pythoically as 0, 1, 2, 3, Reads headers from that lie; skips earlier lies; reads data from ext lie commet: character for commet to ed of lie; all are igored Next lie after commet always take as header If it's data must specify header=noe

18 NESTED LISTS

19 B = [[1,2,3], [5,10,20]] prit(b[1]) This will prit Clicker A 2 B [1,2,3] C [5,10,20] D E This will cause a error I do t kow

20 How cofidet are you of your aswer? A. Very Highly cofidet: I've got this B. Very cofidet C. Somewhat cofidet D. Not so cofidet: educated guess E. Not cofidet at all: radom guess ad/or bullied ito by the rest of my small group

21 Matrix Famous 1999 Fatasy/Actio movie about Neo ad the elusive Morpheus Way some studets believe that they ca lear Computer Sciece: By pluggig themselves ito it

22 Matrix Famous 1999 Fatasy/Actio movie about Neo ad the elusive Morpheus Way some studets believe that they ca lear Computer Sciece: By pluggig themselves ito it Rectagular array of (usually) umbers, e.g.,

23 Matrices i Pytho Two commo ways to represet: For us: For m-by- matrix, list of m lists, where each ier ested list is of same legth () ad represets oe row (Ca also use umpy module)

24 Creatig ested list Literal otatio: matrix = [ [5, 10, 15, 20, 25], [30, 35, 40, 45, 50], [55, 60, 65, 70, 75], [80, 85, 90, 95, 100], [105, 110, 115, 120, 125] ]

25 Buildig up ested list Create distict list of desired row or row of 0s to chage later for each row apped i: matrix = [ ] for row i rage(umber_rows): ew_row = [ ] for col i rage(umber_cols): ew_row.apped(0) #if startig all-0 matrix.apped(ew_row)

26 Useful fuctio def make_0array(rows, cols): '''returs ew rows x cols 2-d list/array of all 0s''' array = [ ] # Build up array of umbers here for j i rage(rows): ew_blak_row = [ ] # Make a NEW row for i i rage(cols): ew_blak_row.apped(0) array.apped(ew_blak_row) retur array

27 prit fuctio: stayig o oe lie (review) prit() fuctio by default always eds with ewlie. Not ice to prit 2-D m x array 1 umber/lie usig m* lies; wat whole row per lie prit() has optioal argumet ed= that ca give alterate character to put at ed istead of ewlie; e.g., a space: prit (somethig, ed=' ')

28 def ice_prit(a): for i i rage(le(a)): for j i rage(le(a[i])): prit(a[i][j], ed=" ") prit() A = [[2,5,10],[1,17,0]] ice_prit(a) This will prit Clicker A B C D E This will cause a error I do t kow

29 How cofidet are you of your aswer? A. Very Highly cofidet: I've got this B. Very cofidet C. Somewhat cofidet D. Not so cofidet: educated guess E. Not cofidet at all: radom guess ad/or bullied ito by the rest of my small group

30 def col_prit(a): for i i rage(le(a)): for j i rage(le(a[i])): prit(a[j][i], ed=" ") prit() A = [[2,5,10],[1,17,0]] col_prit(a) This will prit Clicker A B C D E This will cause a error I do t kow

31 How cofidet are you of your aswer? A. Very Highly cofidet: I've got this B. Very cofidet C. Somewhat cofidet D. Not so cofidet: educated guess E. Not cofidet at all: radom guess ad/or bullied ito by the rest of my small group

32 Drawig graphs MATPLOTLIB MODULE HIGHLIGHTS

33 A Picture is Worth 1000 Excel cells Year,Aual aomaly,lower 95% cofidece iterval,upper 95% cofidece iterval 1880, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , Ad so o

34 matplotlib: A module for drawig graphs import matplotlab.pyplot as plt matplotlib is super commoly used module for 2-D graphics i Pytho. There are others, but matplotlib is most widely used Style take from MATLAB

35 Fuctios i plt that might be ice to use: plot plt.plot(ls) with oe list iput parameter: Makes a lie graph assumig x's are rage(le(ls)), i.e., 0, 1,, le(ls) -1 With 2: x vs. y Already see: Ca set x ad/or y-axis label, ad the title Importat after CS 111! Exact details of whe ad where plot appears deped heavily o whether you are usig Spyder, cosole, Jupyter, or other, ad o your settigs

36 Basic demo code import matplotlib.pyplot as plt import radom # simple plottig demo of plai lie graph x = [1, 2, 3, 4, 5] ylie =[] # y values will go here for i i rage(le(x)): ylie.apped(radom.radom()) plt.ylabel('some 0 to 1 radom umbers') plt.xlabel('x is 1 to 5') plt.title('lie graph of radom umbers') plt.plot(x, ylie)

37 You probably wat plots i their ow widow Aybody havig plots show up iside the lower-right cosole widow ad havig trouble savig them out?

38 To always get graphs i their ow widow Spyder prefereces (uder Pytho meu o Mac, o Widows maybe uder Tools?) The: Ipytho Cosole à Graphics à Graphics Backed à Backed: "automatic" Reuires you to restart Spyder (oce) to start workig I theory there's also commad ca give at ipytho prompt for this, but Prof. Sloa could't figure it out, ad it's defiitely ot what's stated i official Spyder tutorial (%matplotlib t), which gives error Ad plt.figure(1), plt.figure(2), etc. starts ew plots Util the, plt.whatever() keeps addig to curret plot

39 More specific stylig thigs Described i Zybooks 15.2 ad 15.3, like addig legeds to describe what differet lies o multi-lie lie graph are, makig lies differet colors ad styles (dotted, dashed, solid) that you choose istead of matplotlib choosig automagically Nobody i his or her right mid memorizes this stuff uless you are workig o graphs as full-time job; we would't ask exam uestios about it But you do eed to kow where to fid it if a lab asks you to plot somethig with a gree dashed lie

40 A few examples If last argumet to plot is strig, that's the format 'b-' Solid blue lie; matplotlib default 'r--' Red dashes 'bs' Blue suares 'g^' Gree triagles

41 HEAT MAPS

42 Heat map (or Heatmap) Heat map: Graphical represetatio of data where idividual values i matrix represeted as colors (Word Heatmap was coied ad trademarked i 1991)

43

44 import matplotlib.pyplot as plt x = [1, 2, 3, 4, 5, 6] y = [0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0] itesity = [ [5, 10, 15, 20, 25], [30, 35, 40, 45, 50], [55, 60, 65, 70, 75], [80, 85, 90, 95, 100], [105, 110, 115, 120, 125], [130, 135, 140, 145, 150] ] plt.pcolor(x, y, itesity) # Creates heatmap, origi lower left corer plt.summer() # Color scheme: Gree (low) to Yellow (hi) plt.colorbar() # Adds colorbar so we kow what values mea plt.title("simple Heat Map Example")

45 Heat maps i Pytho Everythig we eed is i matplotlib.pyplot, so import matplotlib.plot as plt plt.pcolor(c) creates heat map from array C of color values Row 0 displayed at bottom of figure Each row displayed left to right So C[0][0] i lower left corer plt.pcolor(x, Y, C) has lists of umbers for X- ad Y-axes

46 Fecepost issue If you wat to specify borders of a ru of rectagles placed side-by-side, eed +1 specificatios left ed of every rectagle, ad right ed of last plt.pcolor(x, Y, C) should have le(x) = 1 + umber of colums of C le(y) = 1 + umber of rows of C I plt.pcolor(c) form labels are supplied startig at 0 for both X ad Y

CS 111: Program Design I Lecture #26: Heat maps, Nothing, Predictive Policing

CS 111: Program Design I Lecture #26: Heat maps, Nothing, Predictive Policing CS 111: Program Desig I Lecture #26: Heat maps, Nothig, Predictive Policig Robert H. Sloa & Richard Warer Uiversity of Illiois at Chicago November 29, 2018 Some Logistics Extra credit: Sample Fial Exam

More information

CS 111: Program Design I Lecture 21: Network Analysis. Robert H. Sloan & Richard Warner University of Illinois at Chicago April 10, 2018

CS 111: Program Design I Lecture 21: Network Analysis. Robert H. Sloan & Richard Warner University of Illinois at Chicago April 10, 2018 CS 111: Program Desig I Lecture 21: Network Aalysis Robert H. Sloa & Richard Warer Uiversity of Illiois at Chicago April 10, 2018 NETWORK ANALYSIS Which displays a graph i the sese of graph/etwork aalysis?

More information

CS 111: Program Design I Lecture 15: Objects, Pandas, Modules. Robert H. Sloan & Richard Warner University of Illinois at Chicago October 13, 2016

CS 111: Program Design I Lecture 15: Objects, Pandas, Modules. Robert H. Sloan & Richard Warner University of Illinois at Chicago October 13, 2016 CS 111: Program Desig I Lecture 15: Objects, Padas, Modules Robert H. Sloa & Richard Warer Uiversity of Illiois at Chicago October 13, 2016 OBJECTS AND DOT NOTATION Objects (Implicit i Chapter 2, Variables,

More information

CS 111: Program Design I Lecture 15: Modules, Pandas again. Robert H. Sloan & Richard Warner University of Illinois at Chicago March 8, 2018

CS 111: Program Design I Lecture 15: Modules, Pandas again. Robert H. Sloan & Richard Warner University of Illinois at Chicago March 8, 2018 CS 111: Program Desig I Lecture 15: Modules, Padas agai Robert H. Sloa & Richard Warer Uiversity of Illiois at Chicago March 8, 2018 PYTHON STANDARD LIBRARY & BEYOND: MODULES Extedig Pytho Every moder

More information

CS 111: Program Design I Lecture # 7: First Loop, Web Crawler, Functions

CS 111: Program Design I Lecture # 7: First Loop, Web Crawler, Functions CS 111: Program Desig I Lecture # 7: First Loop, Web Crawler, Fuctios Robert H. Sloa & Richard Warer Uiversity of Illiois at Chicago September 18, 2018 What will this prit? x = 5 if x == 3: prit("hi!")

More information

CS 111: Program Design I Lecture 16: Module Review, Encodings, Lists

CS 111: Program Design I Lecture 16: Module Review, Encodings, Lists CS 111: Program Desig I Lecture 16: Module Review, Ecodigs, Lists Robert H. Sloa & Richard Warer Uiversity of Illiois at Chicago October 18, 2016 Last time Dot otatio ad methods Padas: user maual poit

More information

CSE 111 Bio: Program Design I Lecture 17: software development, list methods

CSE 111 Bio: Program Design I Lecture 17: software development, list methods CSE 111 Bio: Program Desig I Lecture 17: software developmet, list methods Robert H. Sloa(CS) & Rachel Poretsky(Bio) Uiversity of Illiois, Chicago October 19, 2017 NESTED LOOPS: REVIEW Geerate times table

More information

CS 111: Program Design I Lecture 19: Networks, the Web, and getting text from the Web in Python

CS 111: Program Design I Lecture 19: Networks, the Web, and getting text from the Web in Python CS 111: Program Desig I Lecture 19: Networks, the Web, ad gettig text from the Web i Pytho Robert H. Sloa & Richard Warer Uiversity of Illiois at Chicago April 3, 2018 Goals Lear about Iteret Lear about

More information

CSC 220: Computer Organization Unit 11 Basic Computer Organization and Design

CSC 220: Computer Organization Unit 11 Basic Computer Organization and Design College of Computer ad Iformatio Scieces Departmet of Computer Sciece CSC 220: Computer Orgaizatio Uit 11 Basic Computer Orgaizatio ad Desig 1 For the rest of the semester, we ll focus o computer architecture:

More information

CSC165H1 Worksheet: Tutorial 8 Algorithm analysis (SOLUTIONS)

CSC165H1 Worksheet: Tutorial 8 Algorithm analysis (SOLUTIONS) CSC165H1, Witer 018 Learig Objectives By the ed of this worksheet, you will: Aalyse the ruig time of fuctios cotaiig ested loops. 1. Nested loop variatios. Each of the followig fuctios takes as iput a

More information

CS 111: Program Design I Lecture 20: Web crawling, HTML, Copyright

CS 111: Program Design I Lecture 20: Web crawling, HTML, Copyright CS 111: Program Desig I Lecture 20: Web crawlig, HTML, Copyright Robert H. Sloa & Richard Warer Uiversity of Illiois at Chicago November 8, 2016 WEB CRAWLER AGAIN Two bits of useful Pytho sytax Do't eed

More information

Lecture 9: Exam I Review

Lecture 9: Exam I Review CS 111 (Law): Program Desig I Lecture 9: Exam I Review Robert H. Sloa & Richard Warer Uiversity of Illiois, Chicago September 22, 2016 This Class Discuss midterm topics Go over practice examples Aswer

More information

CS 111: Program Design I Lecture 14: Encodings & Files concluded; Pandas, Modules, legal data analytics

CS 111: Program Design I Lecture 14: Encodings & Files concluded; Pandas, Modules, legal data analytics CS 111: Program Desig I Lecture 14: Ecodigs & Files cocluded; Padas, Modules, legal data aalytics Robert H. Sloa & Richard Warer Uiversity of Illiois at Chicago October 16, 2018 Recall: ASCII Ecodig characters

More information

CS 111 Green: Program Design I Lecture 27: Speed (cont.); parting thoughts

CS 111 Green: Program Design I Lecture 27: Speed (cont.); parting thoughts CS 111 Gree: Program Desig I Lecture 27: Speed (cot.); partig thoughts By Nascarkig - Ow work, CC BY-SA 4.0, https://commos.wikimedia.org/w/idex.php?curid=38671041 Robert H. Sloa (CS) & Rachel Poretsky

More information

CS 111: Program Design I Lecture 18: Web and getting text from it

CS 111: Program Design I Lecture 18: Web and getting text from it CS 111: Program Desig I Lecture 18: Web ad gettig text from it Robert H. Sloa & Richard Warer Uiversity of Illiois at Chicago October 25, 2016 Goals Lear about Iteret ad how to access it directly from

More information

The number n of subintervals times the length h of subintervals gives length of interval (b-a).

The number n of subintervals times the length h of subintervals gives length of interval (b-a). Simulator with MadMath Kit: Riema Sums (Teacher s pages) I your kit: 1. GeoGebra file: Ready-to-use projector sized simulator: RiemaSumMM.ggb 2. RiemaSumMM.pdf (this file) ad RiemaSumMMEd.pdf (educator's

More information

Parabolic Path to a Best Best-Fit Line:

Parabolic Path to a Best Best-Fit Line: Studet Activity : Fidig the Least Squares Regressio Lie By Explorig the Relatioship betwee Slope ad Residuals Objective: How does oe determie a best best-fit lie for a set of data? Eyeballig it may be

More information

CS 111: Program Design I Lecture # 7: Web Crawler, Functions; Open Access

CS 111: Program Design I Lecture # 7: Web Crawler, Functions; Open Access CS 111: Program Desig I Lecture # 7: Web Crawler, Fuctios; Ope Access Robert H. Sloa & Richard Warer Uiversity of Illiois at Chicago September 13, 2016 Lab Hit/Remider word = "hi" word.upper() à "HI" Questio

More information

Pattern Recognition Systems Lab 1 Least Mean Squares

Pattern Recognition Systems Lab 1 Least Mean Squares Patter Recogitio Systems Lab 1 Least Mea Squares 1. Objectives This laboratory work itroduces the OpeCV-based framework used throughout the course. I this assigmet a lie is fitted to a set of poits usig

More information

Python Programming: An Introduction to Computer Science

Python Programming: An Introduction to Computer Science Pytho Programmig: A Itroductio to Computer Sciece Chapter 6 Defiig Fuctios Pytho Programmig, 2/e 1 Objectives To uderstad why programmers divide programs up ito sets of cooperatig fuctios. To be able to

More information

Python Programming: An Introduction to Computer Science

Python Programming: An Introduction to Computer Science Pytho Programmig: A Itroductio to Computer Sciece Chapter 1 Computers ad Programs 1 Objectives To uderstad the respective roles of hardware ad software i a computig system. To lear what computer scietists

More information

Ones Assignment Method for Solving Traveling Salesman Problem

Ones Assignment Method for Solving Traveling Salesman Problem Joural of mathematics ad computer sciece 0 (0), 58-65 Oes Assigmet Method for Solvig Travelig Salesma Problem Hadi Basirzadeh Departmet of Mathematics, Shahid Chamra Uiversity, Ahvaz, Ira Article history:

More information

The VSS CCD photometry spreadsheet

The VSS CCD photometry spreadsheet The VSS CCD photometry spreadsheet Itroductio This Excel spreadsheet has bee developed ad tested by the BAA VSS for aalysig results files produced by the multi-image CCD photometry procedure i AIP4Wi v2.

More information

Intermediate Statistics

Intermediate Statistics Gait Learig Guides Itermediate Statistics Data processig & display, Cetral tedecy Author: Raghu M.D. STATISTICS DATA PROCESSING AND DISPLAY Statistics is the study of data or umerical facts of differet

More information

n Some thoughts on software development n The idea of a calculator n Using a grammar n Expression evaluation n Program organization n Analysis

n Some thoughts on software development n The idea of a calculator n Using a grammar n Expression evaluation n Program organization n Analysis Overview Chapter 6 Writig a Program Bjare Stroustrup Some thoughts o software developmet The idea of a calculator Usig a grammar Expressio evaluatio Program orgaizatio www.stroustrup.com/programmig 3 Buildig

More information

One advantage that SONAR has over any other music-sequencing product I ve worked

One advantage that SONAR has over any other music-sequencing product I ve worked *gajedra* D:/Thomso_Learig_Projects/Garrigus_163132/z_productio/z_3B2_3D_files/Garrigus_163132_ch17.3d, 14/11/08/16:26:39, 16:26, page: 647 17 CAL 101 Oe advatage that SONAR has over ay other music-sequecig

More information

Solution printed. Do not start the test until instructed to do so! CS 2604 Data Structures Midterm Spring, Instructions:

Solution printed. Do not start the test until instructed to do so! CS 2604 Data Structures Midterm Spring, Instructions: CS 604 Data Structures Midterm Sprig, 00 VIRG INIA POLYTECHNIC INSTITUTE AND STATE U T PROSI M UNI VERSI TY Istructios: Prit your ame i the space provided below. This examiatio is closed book ad closed

More information

Chapter 10. Defining Classes. Copyright 2015 Pearson Education, Ltd.. All rights reserved.

Chapter 10. Defining Classes. Copyright 2015 Pearson Education, Ltd.. All rights reserved. Chapter 10 Defiig Classes Copyright 2015 Pearso Educatio, Ltd.. All rights reserved. Overview 10.1 Structures 10.2 Classes 10.3 Abstract Data Types 10.4 Itroductio to Iheritace Copyright 2015 Pearso Educatio,

More information

CS 11 C track: lecture 1

CS 11 C track: lecture 1 CS 11 C track: lecture 1 Prelimiaries Need a CMS cluster accout http://acctreq.cms.caltech.edu/cgi-bi/request.cgi Need to kow UNIX IMSS tutorial liked from track home page Track home page: http://courses.cms.caltech.edu/courses/cs11/material

More information

EM375 STATISTICS AND MEASUREMENT UNCERTAINTY LEAST SQUARES LINEAR REGRESSION ANALYSIS

EM375 STATISTICS AND MEASUREMENT UNCERTAINTY LEAST SQUARES LINEAR REGRESSION ANALYSIS EM375 STATISTICS AND MEASUREMENT UNCERTAINTY LEAST SQUARES LINEAR REGRESSION ANALYSIS I this uit of the course we ivestigate fittig a straight lie to measured (x, y) data pairs. The equatio we wat to fit

More information

IMP: Superposer Integrated Morphometrics Package Superposition Tool

IMP: Superposer Integrated Morphometrics Package Superposition Tool IMP: Superposer Itegrated Morphometrics Package Superpositio Tool Programmig by: David Lieber ( 03) Caisius College 200 Mai St. Buffalo, NY 4208 Cocept by: H. David Sheets, Dept. of Physics, Caisius College

More information

MOTIF XF Extension Owner s Manual

MOTIF XF Extension Owner s Manual MOTIF XF Extesio Ower s Maual Table of Cotets About MOTIF XF Extesio...2 What Extesio ca do...2 Auto settig of Audio Driver... 2 Auto settigs of Remote Device... 2 Project templates with Iput/ Output Bus

More information

1.2 Binomial Coefficients and Subsets

1.2 Binomial Coefficients and Subsets 1.2. BINOMIAL COEFFICIENTS AND SUBSETS 13 1.2 Biomial Coefficiets ad Subsets 1.2-1 The loop below is part of a program to determie the umber of triagles formed by poits i the plae. for i =1 to for j =

More information

Lecture Notes 6 Introduction to algorithm analysis CSS 501 Data Structures and Object-Oriented Programming

Lecture Notes 6 Introduction to algorithm analysis CSS 501 Data Structures and Object-Oriented Programming Lecture Notes 6 Itroductio to algorithm aalysis CSS 501 Data Structures ad Object-Orieted Programmig Readig for this lecture: Carrao, Chapter 10 To be covered i this lecture: Itroductio to algorithm aalysis

More information

Which movie we can suggest to Anne?

Which movie we can suggest to Anne? ECOLE CENTRALE SUPELEC MASTER DSBI DECISION MODELING TUTORIAL COLLABORATIVE FILTERING AS A MODEL OF GROUP DECISION-MAKING You kow that the low-tech way to get recommedatios for products, movies, or etertaiig

More information

Administrative UNSUPERVISED LEARNING. Unsupervised learning. Supervised learning 11/25/13. Final project. No office hours today

Administrative UNSUPERVISED LEARNING. Unsupervised learning. Supervised learning 11/25/13. Final project. No office hours today Admiistrative Fial project No office hours today UNSUPERVISED LEARNING David Kauchak CS 451 Fall 2013 Supervised learig Usupervised learig label label 1 label 3 model/ predictor label 4 label 5 Supervised

More information

CSE 111 Bio: Program Design I Class 11: loops

CSE 111 Bio: Program Design I Class 11: loops SE 111 Bio: Program Desig I lass 11: loops Radall Muroe, xkcd.com/1411/ Robert H. Sloa (S) & Rachel Poretsky (Bio) Uiversity of Illiois, hicago October 2, 2016 Pytho ets Loopy! he Pytho, Busch ardes Florida

More information

Math Section 2.2 Polynomial Functions

Math Section 2.2 Polynomial Functions Math 1330 - Sectio. Polyomial Fuctios Our objectives i workig with polyomial fuctios will be, first, to gather iformatio about the graph of the fuctio ad, secod, to use that iformatio to geerate a reasoably

More information

CS 111: Program Design I Lecture 5: US Law when others have encryption keys; if, for

CS 111: Program Design I Lecture 5: US Law when others have encryption keys; if, for CS 111: Program Desig I Lecture 5: US Law whe others have ecryptio keys; if, for Robert H. Sloa & Richard Warer Uiversity of Illiois at Chicago September 8, 2016 Lavabit ad Sowde Lavabit was a ecrypted

More information

Recursion. Computer Science S-111 Harvard University David G. Sullivan, Ph.D. Review: Method Frames

Recursion. Computer Science S-111 Harvard University David G. Sullivan, Ph.D. Review: Method Frames Uit 4, Part 3 Recursio Computer Sciece S-111 Harvard Uiversity David G. Sulliva, Ph.D. Review: Method Frames Whe you make a method call, the Java rutime sets aside a block of memory kow as the frame of

More information

Project 2.5 Improved Euler Implementation

Project 2.5 Improved Euler Implementation Project 2.5 Improved Euler Implemetatio Figure 2.5.10 i the text lists TI-85 ad BASIC programs implemetig the improved Euler method to approximate the solutio of the iitial value problem dy dx = x+ y,

More information

Optimal Mapped Mesh on the Circle

Optimal Mapped Mesh on the Circle Koferece ANSYS 009 Optimal Mapped Mesh o the Circle doc. Ig. Jaroslav Štigler, Ph.D. Bro Uiversity of Techology, aculty of Mechaical gieerig, ergy Istitut, Abstract: This paper brigs out some ideas ad

More information

Computers and Scientific Thinking

Computers and Scientific Thinking Computers ad Scietific Thikig David Reed, Creighto Uiversity Chapter 15 JavaScript Strigs 1 Strigs as Objects so far, your iteractive Web pages have maipulated strigs i simple ways use text box to iput

More information

Basic allocator mechanisms The course that gives CMU its Zip! Memory Management II: Dynamic Storage Allocation Mar 6, 2000.

Basic allocator mechanisms The course that gives CMU its Zip! Memory Management II: Dynamic Storage Allocation Mar 6, 2000. 5-23 The course that gives CM its Zip Memory Maagemet II: Dyamic Storage Allocatio Mar 6, 2000 Topics Segregated lists Buddy system Garbage collectio Mark ad Sweep Copyig eferece coutig Basic allocator

More information

9.1. Sequences and Series. Sequences. What you should learn. Why you should learn it. Definition of Sequence

9.1. Sequences and Series. Sequences. What you should learn. Why you should learn it. Definition of Sequence _9.qxd // : AM Page Chapter 9 Sequeces, Series, ad Probability 9. Sequeces ad Series What you should lear Use sequece otatio to write the terms of sequeces. Use factorial otatio. Use summatio otatio to

More information

How do we evaluate algorithms?

How do we evaluate algorithms? F2 Readig referece: chapter 2 + slides Algorithm complexity Big O ad big Ω To calculate ruig time Aalysis of recursive Algorithms Next time: Litterature: slides mostly The first Algorithm desig methods:

More information

Area As A Limit & Sigma Notation

Area As A Limit & Sigma Notation Area As A Limit & Sigma Notatio SUGGESTED REFERENCE MATERIAL: As you work through the problems listed below, you should referece Chapter 5.4 of the recommeded textbook (or the equivalet chapter i your

More information

Term Project Report. This component works to detect gesture from the patient as a sign of emergency message and send it to the emergency manager.

Term Project Report. This component works to detect gesture from the patient as a sign of emergency message and send it to the emergency manager. CS2310 Fial Project Loghao Li Term Project Report Itroductio I this project, I worked o expadig exercise 4. What I focused o is makig the real gesture recogizig sesor ad desig proper gestures ad recogizig

More information

Lecture 28: Data Link Layer

Lecture 28: Data Link Layer Automatic Repeat Request (ARQ) 2. Go ack N ARQ Although the Stop ad Wait ARQ is very simple, you ca easily show that it has very the low efficiecy. The low efficiecy comes from the fact that the trasmittig

More information

University of Waterloo Department of Electrical and Computer Engineering ECE 250 Algorithms and Data Structures

University of Waterloo Department of Electrical and Computer Engineering ECE 250 Algorithms and Data Structures Uiversity of Waterloo Departmet of Electrical ad Computer Egieerig ECE 250 Algorithms ad Data Structures Midterm Examiatio ( pages) Istructor: Douglas Harder February 7, 2004 7:30-9:00 Name (last, first)

More information

Lower Bounds for Sorting

Lower Bounds for Sorting Liear Sortig Topics Covered: Lower Bouds for Sortig Coutig Sort Radix Sort Bucket Sort Lower Bouds for Sortig Compariso vs. o-compariso sortig Decisio tree model Worst case lower boud Compariso Sortig

More information

Alpha Individual Solutions MAΘ National Convention 2013

Alpha Individual Solutions MAΘ National Convention 2013 Alpha Idividual Solutios MAΘ Natioal Covetio 0 Aswers:. D. A. C 4. D 5. C 6. B 7. A 8. C 9. D 0. B. B. A. D 4. C 5. A 6. C 7. B 8. A 9. A 0. C. E. B. D 4. C 5. A 6. D 7. B 8. C 9. D 0. B TB. 570 TB. 5

More information

Message Integrity and Hash Functions. TELE3119: Week4

Message Integrity and Hash Functions. TELE3119: Week4 Message Itegrity ad Hash Fuctios TELE3119: Week4 Outlie Message Itegrity Hash fuctios ad applicatios Hash Structure Popular Hash fuctios 4-2 Message Itegrity Goal: itegrity (ot secrecy) Allows commuicatig

More information

Chapter 4. Procedural Abstraction and Functions That Return a Value. Copyright 2015 Pearson Education, Ltd.. All rights reserved.

Chapter 4. Procedural Abstraction and Functions That Return a Value. Copyright 2015 Pearson Education, Ltd.. All rights reserved. Chapter 4 Procedural Abstractio ad Fuctios That Retur a Value Copyright 2015 Pearso Educatio, Ltd.. All rights reserved. Overview 4.1 Top-Dow Desig 4.2 Predefied Fuctios 4.3 Programmer-Defied Fuctios 4.4

More information

. Written in factored form it is easy to see that the roots are 2, 2, i,

. Written in factored form it is easy to see that the roots are 2, 2, i, CMPS A Itroductio to Programmig Programmig Assigmet 4 I this assigmet you will write a java program that determies the real roots of a polyomial that lie withi a specified rage. Recall that the roots (or

More information

n Maurice Wilkes, 1949 n Organize software to minimize errors. n Eliminate most of the errors we made anyway.

n Maurice Wilkes, 1949 n Organize software to minimize errors. n Eliminate most of the errors we made anyway. Bjare Stroustrup www.stroustrup.com/programmig Chapter 5 Errors Abstract Whe we program, we have to deal with errors. Our most basic aim is correctess, but we must deal with icomplete problem specificatios,

More information

Exceptions. Your computer takes exception. The Exception Class. Causes of Exceptions

Exceptions. Your computer takes exception. The Exception Class. Causes of Exceptions Your computer takes exceptio s s are errors i the logic of a program (ru-time errors). Examples: i thread mai java.io.filenotfoud: studet.txt (The system caot fid the file specified.) i thread mai java.lag.nullpoiter:

More information

Workflow model GM AR. Gumpy. Dynagump. At a very high level, this is what gump does. We ll be looking at each of the items described here seperately.

Workflow model GM AR. Gumpy. Dynagump. At a very high level, this is what gump does. We ll be looking at each of the items described here seperately. Workflow model GM AR Gumpy RM Dyagump At a very high level, this is what gump does. We ll be lookig at each of the items described here seperately. User edits project descriptor ad commits s maitai their

More information

Overview Chapter 12 A display model

Overview Chapter 12 A display model Overview Chapter 12 A display model Why graphics? A graphics model Examples Bjare Stroustrup www.stroustrup.com/programmig 3 Why bother with graphics ad GUI? Why bother with graphics ad GUI? It s very

More information

top() Applications of Stacks

top() Applications of Stacks CS22 Algorithms ad Data Structures MW :00 am - 2: pm, MSEC 0 Istructor: Xiao Qi Lecture 6: Stacks ad Queues Aoucemets Quiz results Homework 2 is available Due o September 29 th, 2004 www.cs.mt.edu~xqicoursescs22

More information

Lecturers: Sanjam Garg and Prasad Raghavendra Feb 21, Midterm 1 Solutions

Lecturers: Sanjam Garg and Prasad Raghavendra Feb 21, Midterm 1 Solutions U.C. Berkeley CS170 : Algorithms Midterm 1 Solutios Lecturers: Sajam Garg ad Prasad Raghavedra Feb 1, 017 Midterm 1 Solutios 1. (4 poits) For the directed graph below, fid all the strogly coected compoets

More information

( n+1 2 ) , position=(7+1)/2 =4,(median is observation #4) Median=10lb

( n+1 2 ) , position=(7+1)/2 =4,(median is observation #4) Median=10lb Chapter 3 Descriptive Measures Measures of Ceter (Cetral Tedecy) These measures will tell us where is the ceter of our data or where most typical value of a data set lies Mode the value that occurs most

More information

CS 111: Program Design I Lecture 20: Web crawling, HTML, Copyright

CS 111: Program Design I Lecture 20: Web crawling, HTML, Copyright CS 111: Program Desig I Lecture 20: Web crawlig, HTML, Copyright Robert H. Sloa & Richard Warer Uiversity of Illiois at Chicago November 8, 2016 Most importat thig If you have ot yet voted (ad are a US

More information

ENGR Spring Exam 1

ENGR Spring Exam 1 ENGR 300 Sprig 03 Exam INSTRUCTIONS: Duratio: 60 miutes Keep your eyes o your ow work! Keep your work covered at all times!. Each studet is resposible for followig directios. Read carefully.. MATLAB ad

More information

Lecture 1: Introduction and Strassen s Algorithm

Lecture 1: Introduction and Strassen s Algorithm 5-750: Graduate Algorithms Jauary 7, 08 Lecture : Itroductio ad Strasse s Algorithm Lecturer: Gary Miller Scribe: Robert Parker Itroductio Machie models I this class, we will primarily use the Radom Access

More information

n n B. How many subsets of C are there of cardinality n. We are selecting elements for such a

n n B. How many subsets of C are there of cardinality n. We are selecting elements for such a 4. [10] Usig a combiatorial argumet, prove that for 1: = 0 = Let A ad B be disjoit sets of cardiality each ad C = A B. How may subsets of C are there of cardiality. We are selectig elemets for such a subset

More information

ENGR 132. Fall Exam 1

ENGR 132. Fall Exam 1 ENGR 3 Fall 03 Exam INSTRUCTIONS: Duratio: 60 miutes Keep your eyes o your ow work. Keep your work covered at all times.. Each studet is resposible for followig directios. Read carefully.. MATLAB ad Excel

More information

CHAPTER IV: GRAPH THEORY. Section 1: Introduction to Graphs

CHAPTER IV: GRAPH THEORY. Section 1: Introduction to Graphs CHAPTER IV: GRAPH THEORY Sectio : Itroductio to Graphs Sice this class is called Number-Theoretic ad Discrete Structures, it would be a crime to oly focus o umber theory regardless how woderful those topics

More information

JoLetter 6.7. JoLauterbach Software GmbH. Mail and merge with QuarkXPress. JoLauterbach Software GmbH. Stolzingstraße 4a Bayreuth Germany

JoLetter 6.7. JoLauterbach Software GmbH. Mail and merge with QuarkXPress. JoLauterbach Software GmbH. Stolzingstraße 4a Bayreuth Germany JoLetter 6.7 Mail ad merge with QuarkXPress JoLauterbach Software GmbH Stolzigstraße 4a 95445 Bayreuth Germay Telefo: +49-921-730 3363 Fax: +49-921-730 3394 E-Mail: ifo@jolauterbach.com Iteret: http://www.jolauterbach.com

More information

Customer Portal Quick Reference User Guide

Customer Portal Quick Reference User Guide Customer Portal Quick Referece User Guide Overview This user guide is iteded for FM Approvals customers usig the Approval Iformatio Maagemet (AIM) customer portal to track their active projects. AIM is

More information

Our second algorithm. Comp 135 Machine Learning Computer Science Tufts University. Decision Trees. Decision Trees. Decision Trees.

Our second algorithm. Comp 135 Machine Learning Computer Science Tufts University. Decision Trees. Decision Trees. Decision Trees. Comp 135 Machie Learig Computer Sciece Tufts Uiversity Fall 2017 Roi Khardo Some of these slides were adapted from previous slides by Carla Brodley Our secod algorithm Let s look at a simple dataset for

More information

CMSC Computer Architecture Lecture 10: Caches. Prof. Yanjing Li University of Chicago

CMSC Computer Architecture Lecture 10: Caches. Prof. Yanjing Li University of Chicago CMSC 22200 Computer Architecture Lecture 10: Caches Prof. Yajig Li Uiversity of Chicago Midterm Recap Overview ad fudametal cocepts ISA Uarch Datapath, cotrol Sigle cycle, multi cycle Pipeliig Basic idea,

More information

Floristic Quality Assessment (FQA) Calculator for Colorado User s Guide

Floristic Quality Assessment (FQA) Calculator for Colorado User s Guide Floristic Quality Assessmet (FQA) Calculator for Colorado User s Guide Created by the Colorado atural Heritage Program Last Updated April 2012 The FQA Calculator was created by Michelle Fik ad Joaa Lemly

More information

K-NET bus. When several turrets are connected to the K-Bus, the structure of the system is as showns

K-NET bus. When several turrets are connected to the K-Bus, the structure of the system is as showns K-NET bus The K-Net bus is based o the SPI bus but it allows to addressig may differet turrets like the I 2 C bus. The K-Net is 6 a wires bus (4 for SPI wires ad 2 additioal wires for request ad ackowledge

More information

Normal Distributions

Normal Distributions Normal Distributios Stacey Hacock Look at these three differet data sets Each histogram is overlaid with a curve : A B C A) Weights (g) of ewly bor lab rat pups B) Mea aual temperatures ( F ) i A Arbor,

More information

Octahedral Graph Scaling

Octahedral Graph Scaling Octahedral Graph Scalig Peter Russell Jauary 1, 2015 Abstract There is presetly o strog iterpretatio for the otio of -vertex graph scalig. This paper presets a ew defiitio for the term i the cotext of

More information

Chapter 1. Introduction to Computers and C++ Programming. Copyright 2015 Pearson Education, Ltd.. All rights reserved.

Chapter 1. Introduction to Computers and C++ Programming. Copyright 2015 Pearson Education, Ltd.. All rights reserved. Chapter 1 Itroductio to Computers ad C++ Programmig Copyright 2015 Pearso Educatio, Ltd.. All rights reserved. Overview 1.1 Computer Systems 1.2 Programmig ad Problem Solvig 1.3 Itroductio to C++ 1.4 Testig

More information

Avid Interplay Bundle

Avid Interplay Bundle Avid Iterplay Budle Versio 2.5 Cofigurator ReadMe Overview This documet provides a overview of Iterplay Budle v2.5 ad describes how to ru the Iterplay Budle cofiguratio tool. Iterplay Budle v2.5 refers

More information

Numerical Methods Lecture 6 - Curve Fitting Techniques

Numerical Methods Lecture 6 - Curve Fitting Techniques Numerical Methods Lecture 6 - Curve Fittig Techiques Topics motivatio iterpolatio liear regressio higher order polyomial form expoetial form Curve fittig - motivatio For root fidig, we used a give fuctio

More information

Announcements. Reading. Project #4 is on the web. Homework #1. Midterm #2. Chapter 4 ( ) Note policy about project #3 missing components

Announcements. Reading. Project #4 is on the web. Homework #1. Midterm #2. Chapter 4 ( ) Note policy about project #3 missing components Aoucemets Readig Chapter 4 (4.1-4.2) Project #4 is o the web ote policy about project #3 missig compoets Homework #1 Due 11/6/01 Chapter 6: 4, 12, 24, 37 Midterm #2 11/8/01 i class 1 Project #4 otes IPv6Iit,

More information

Morgan Kaufmann Publishers 26 February, COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Interface. Chapter 5

Morgan Kaufmann Publishers 26 February, COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Interface. Chapter 5 Morga Kaufma Publishers 26 February, 28 COMPUTER ORGANIZATION AND DESIGN The Hardware/Software Iterface 5 th Editio Chapter 5 Set-Associative Cache Architecture Performace Summary Whe CPU performace icreases:

More information

Designing a learning system

Designing a learning system CS 75 Machie Learig Lecture Desigig a learig system Milos Hauskrecht milos@cs.pitt.edu 539 Seott Square, x-5 people.cs.pitt.edu/~milos/courses/cs75/ Admiistrivia No homework assigmet this week Please try

More information

CMPT 125 Assignment 2 Solutions

CMPT 125 Assignment 2 Solutions CMPT 25 Assigmet 2 Solutios Questio (20 marks total) a) Let s cosider a iteger array of size 0. (0 marks, each part is 2 marks) it a[0]; I. How would you assig a poiter, called pa, to store the address

More information

Recursive Procedures. How can you model the relationship between consecutive terms of a sequence?

Recursive Procedures. How can you model the relationship between consecutive terms of a sequence? 6. Recursive Procedures I Sectio 6.1, you used fuctio otatio to write a explicit formula to determie the value of ay term i a Sometimes it is easier to calculate oe term i a sequece usig the previous terms.

More information

Chapter 5. Functions for All Subtasks. Copyright 2015 Pearson Education, Ltd.. All rights reserved.

Chapter 5. Functions for All Subtasks. Copyright 2015 Pearson Education, Ltd.. All rights reserved. Chapter 5 Fuctios for All Subtasks Copyright 2015 Pearso Educatio, Ltd.. All rights reserved. Overview 5.1 void Fuctios 5.2 Call-By-Referece Parameters 5.3 Usig Procedural Abstractio 5.4 Testig ad Debuggig

More information

What are we going to learn? CSC Data Structures Analysis of Algorithms. Overview. Algorithm, and Inputs

What are we going to learn? CSC Data Structures Analysis of Algorithms. Overview. Algorithm, and Inputs What are we goig to lear? CSC316-003 Data Structures Aalysis of Algorithms Computer Sciece North Carolia State Uiversity Need to say that some algorithms are better tha others Criteria for evaluatio Structure

More information

Descriptive Statistics Summary Lists

Descriptive Statistics Summary Lists Chapter 209 Descriptive Statistics Summary Lists Itroductio This procedure is used to summarize cotiuous data. Large volumes of such data may be easily summarized i statistical lists of meas, couts, stadard

More information

10/23/18. File class in Java. Scanner reminder. Files. Opening a file for reading. Scanner reminder. File Input and Output

10/23/18. File class in Java. Scanner reminder. Files. Opening a file for reading. Scanner reminder. File Input and Output File class i Java File Iput ad Output TOPICS File Iput Exceptio Hadlig File Output Programmers refer to iput/output as "I/O". The File class represets files as objects. The class is defied i the java.io

More information

FREQUENCY ESTIMATION OF INTERNET PACKET STREAMS WITH LIMITED SPACE: UPPER AND LOWER BOUNDS

FREQUENCY ESTIMATION OF INTERNET PACKET STREAMS WITH LIMITED SPACE: UPPER AND LOWER BOUNDS FREQUENCY ESTIMATION OF INTERNET PACKET STREAMS WITH LIMITED SPACE: UPPER AND LOWER BOUNDS Prosejit Bose Evagelos Kraakis Pat Mori Yihui Tag School of Computer Sciece, Carleto Uiversity {jit,kraakis,mori,y

More information

CSE 417: Algorithms and Computational Complexity

CSE 417: Algorithms and Computational Complexity Time CSE 47: Algorithms ad Computatioal Readig assigmet Read Chapter of The ALGORITHM Desig Maual Aalysis & Sortig Autum 00 Paul Beame aalysis Problem size Worst-case complexity: max # steps algorithm

More information

15-859E: Advanced Algorithms CMU, Spring 2015 Lecture #2: Randomized MST and MST Verification January 14, 2015

15-859E: Advanced Algorithms CMU, Spring 2015 Lecture #2: Randomized MST and MST Verification January 14, 2015 15-859E: Advaced Algorithms CMU, Sprig 2015 Lecture #2: Radomized MST ad MST Verificatio Jauary 14, 2015 Lecturer: Aupam Gupta Scribe: Yu Zhao 1 Prelimiaries I this lecture we are talkig about two cotets:

More information

CS : Programming for Non-Majors, Summer 2007 Programming Project #3: Two Little Calculations Due by 12:00pm (noon) Wednesday June

CS : Programming for Non-Majors, Summer 2007 Programming Project #3: Two Little Calculations Due by 12:00pm (noon) Wednesday June CS 1313 010: Programmig for No-Majors, Summer 2007 Programmig Project #3: Two Little Calculatios Due by 12:00pm (oo) Wedesday Jue 27 2007 This third assigmet will give you experiece writig programs that

More information

Package RcppRoll. December 22, 2014

Package RcppRoll. December 22, 2014 Type Package Package RcppRoll December 22, 2014 Title Fast rollig fuctios through Rcpp ad RcppArmadillo Versio 0.1.0 Date 2013-01-10 Author Kevi Ushey Maitaier Kevi Ushey RcppRoll

More information

Investigation Monitoring Inventory

Investigation Monitoring Inventory Ivestigatio Moitorig Ivetory Name Period Date Art Smith has bee providig the prits of a egravig to FieArt Gallery. He plas to make just 2000 more prits. FieArt has already received 70 of Art s prits. The

More information

Random Graphs and Complex Networks T

Random Graphs and Complex Networks T Radom Graphs ad Complex Networks T-79.7003 Charalampos E. Tsourakakis Aalto Uiversity Lecture 3 7 September 013 Aoucemet Homework 1 is out, due i two weeks from ow. Exercises: Probabilistic iequalities

More information

Force Network Analysis using Complementary Energy

Force Network Analysis using Complementary Energy orce Network Aalysis usig Complemetary Eergy Adrew BORGART Assistat Professor Delft Uiversity of Techology Delft, The Netherlads A.Borgart@tudelft.l Yaick LIEM Studet Delft Uiversity of Techology Delft,

More information

Global Support Guide. Verizon WIreless. For the BlackBerry 8830 World Edition Smartphone and the Motorola Z6c

Global Support Guide. Verizon WIreless. For the BlackBerry 8830 World Edition Smartphone and the Motorola Z6c Verizo WIreless Global Support Guide For the BlackBerry 8830 World Editio Smartphoe ad the Motorola Z6c For complete iformatio o global services, please refer to verizowireless.com/vzglobal. Whether i

More information

Goals of the Lecture UML Implementation Diagrams

Goals of the Lecture UML Implementation Diagrams Goals of the Lecture UML Implemetatio Diagrams Object-Orieted Aalysis ad Desig - Fall 1998 Preset UML Diagrams useful for implemetatio Provide examples Next Lecture Ð A variety of topics o mappig from

More information

Sharing Collections. Share a Collection via . Share a Collection via Google Classroom. Quick Reference Guide

Sharing Collections. Share a Collection via  . Share a Collection via Google Classroom. Quick Reference Guide Quick Referece Guide Share a Collectio via Email Sharig your collectio with others is a great way to collaborate. You ca easily sed a lik to your colleagues, studets, classmates ad frieds. Recipiets do

More information

An Efficient Algorithm for Graph Bisection of Triangularizations

An Efficient Algorithm for Graph Bisection of Triangularizations A Efficiet Algorithm for Graph Bisectio of Triagularizatios Gerold Jäger Departmet of Computer Sciece Washigto Uiversity Campus Box 1045 Oe Brookigs Drive St. Louis, Missouri 63130-4899, USA jaegerg@cse.wustl.edu

More information