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Course: ECE 417, Spring 2012School: Ill. Chicago
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Ill. Chicago - ECE - 417
Ill. Chicago - ECE - 417
Ill. Chicago - ECE - 417
Ill. Chicago - ECE - 417
Ill. Chicago - ECE - 417
Complex Analysis Math 147Winter 2006Second MidtermMarch 6, 2006due March 13, 2006Each problem is worth 10 pointsYou are on the honor system to work by yourself1. Let fn be a sequence of functions which are continuous on the closed unit diskcfw_|z | 1
Ill. Chicago - ECE - 417
Ill. Chicago - ECE - 417
Ill. Chicago - ECE - 417
Ill. Chicago - ECE - 417
Ill. Chicago - ECE - 417
Ill. Chicago - ECE - 515
ECE 515: HW9Prof. Jezekiel Ben-Arie1. Design a network that solves the XOR problem. It has an output of +1 for X aTTTT=(1,0), X b = (0,1) and 0 output for X c =(0,0), X d =(1,1).2. What changes are necessary in the network of problem 1 if one want
Ill. Chicago - ECE - 515
HW 6: ECE 515 Image Analysis and Machine Vision IIProf. Jezekiel Ben-Arie1. Show that Eq. (1) and Eq. (2) perform the same function.D j ( x) = x m j , j = 1,2,., M(1)1d j ( x) = x T m j m T m jj2(2)2. Show that the surface given Eq. (3) is the p
Ill. Chicago - ECE - 515
ECE 515 Image Analysis II HW #5: Prof. J. Ben-Arie1) Compute two-dimensional masks of Laplacian of Gaussian (Mexican hat) of size 9x9,7x7 and 5x5. Use a for the Gaussians such that 6 fits in the mask.(a) Print the mask values.(b) Convolve these masks
Ill. Chicago - ECE - 515
Hough transformThe Hough transform is a feature extraction technique used in image analysis, computer vision,and digital image processing.The purpose of the technique is to find imperfect instances of objects within a certain class ofshapes by a votin
Ill. Chicago - ECE - 515
ECE 515 Image Analysis II HW #4: Prof. J. Ben-Arie1. Generate a binary image of the shape in Fig. 1. Pixels which are entirely in the shapeare considered as 1, pixels on the boundary should have values between 0 and 1proportional to their area within t
Ill. Chicago - ECE - 534
i=1 ni=1=i=1 I (Xi ; Xi )(10.166)and (f ) follows from the denition of the distortion rate function. 16. Probability of conditionally typical sequences. In Chapter 7, we calculated the probability that two indep endently drawn sequences X n and Y n
Ill. Chicago - ECE - 534
Entropy of functions of a random variableNational Taiwan Ocean UniversityNational Taiwan Ocean UniversitySolution:FunctionsNational Taiwan Ocean UniversityNational Taiwan Ocean UniversitySolutionSolution cont.National Taiwan Ocean UniversityMut
Ill. Chicago - ECE - 534
ECE 534: Elements of Information Theory, Fall 2010Homework 2Name: Johnson Jonaris GadElkarimUIN 656 312 844Problem 2.28p +pp +pLet pmf P1 (p1 , . . . , pi , . . . , pj , . . . , pm ) and pmf P2 (p1 , . . . , i 2 j , . . . , i 2 j , . . . , pm )H (
Ill. Chicago - ECE - 534
ECE 534: Elements of Information Theory, Fall 2010Homework 3Name: Johnson Jonaris GadElkarimUIN 656 312 844Problem 3.1a) Let X have a probability distribution function f(x)E (X ) =0txf (x) dx =t0xf (x) dx txf (x) dx +txf (x) dxtf (x) dx =
Ill. Chicago - ECE - 534
ECE 534: Elements of Information Theory, Fall 2010Homework 4Name: Johnson Jonaris GadElkarimUIN 656 312 844Problem 4.8We Have X = cfw_1, 2, t = cfw_1, 2, Pr cfw_X = 1 = p1 , Pr cfw_X = 2 = p2 , p1 + p2 = 1H (X ) = p1 log p1 (1 p1 ) log(1 p1 )T (X )
Ill. Chicago - ECE - 534
ECE 534: Elements of Information Theory, Fall 2010Homework 5Name: Johnson Jonaris GadElkarimUIN 656 312 844Problem 5.4a) Binary code:SymbolX1X2X3X4X5X6X7Prob0.490.260.120.040.040.030.020.490.260.120.050.040.040.490.260.120.0
Ill. Chicago - ECE - 534
ECE 534: Elements of Information Theory, Fall 2010Homework 6Name: Johnson Jonaris GadElkarimUIN 656 312 844Problem 7.2Y =X +ZXP r (X )0pP r (Y )0.5p0+a1+a0.5p0.5(1-p)11Y00.5(1-p)1-pWe can see that the value of Y always depend on a.L
Ill. Chicago - ECE - 534
ECE 534: Elements of Information Theory, Fall 2010Homework 7Name: Johnson Jonaris GadElkarimUIN 656 312 844Problem 7.23Y = XZ, X and Z are independent. X = 0, 1, Z = 0, 1Let P (X = 1) = X0101Z0011Y0001P(Y=y)(1 )(1 )(1 )()( )(1 )(
Ill. Chicago - ECE - 534
ECE 534: Elements of Information Theory, Fall 2010Homework 9Name: Johnson Jonaris GadElkarimUIN 656 312 844Problem 9.14a)C = h(Y ) h(Y |X ) = h(Y ) h(Z )But Z has a discrete component, hence h(Z) = -;Since h(Y) is , hence C = .b) We can transmit
Ill. Chicago - ECE - 534
ECE 534: Elements of Information Theory, Fall 2010Homework 9Name: Johnson Jonaris GadElkarimUIN 656 312 844Problem 9.14a)C = h(Y ) h(Y |X ) = h(Y ) h(Z )But Z has a discrete component, hence h(Z) = -;Since h(Y) is , hence C = .b) We can transmit
Ill. Chicago - ECE - 534
ECE 534: Elements of Information Theory, Fall 2010Homework 10Name: Johnson Jonaris GadElkarimUIN 656 312 844Problem 10.1From the lecture we reached that x( 1 ) = E [X |X > 0]x( 1 ) =xf (x)dx =0The above by settingx22202x2 2x2e 2 2 dx =0
Ill. Chicago - ECE - 534
ECE 534: Elements of Information Theory, Fall 2010Homework 11Name: Johnson Jonaris GadElkarimUIN 656 312 844Problem 10.14a) Since X and Y are independent we have:p(x, y, x, y ) = p(x)p(y )p(, y |x, y )xHenceI (X, Y ; X, Y ) = H (X, Y ) H (X, Y, X
Ill. Chicago - ECE - 534
ECE 534: Elements of Information Theory, Fall 2010Homework 12Name: Johnson Jonaris GadElkarimUIN 656 312 844Problem 15.7(1)(1)nLet R1 and R2 be achievable rate pairs, hence we are sure of the existence of a (2nR1 , 2nR2 ), n) codes with Pe1 0(2)
Ill. Chicago - ECE - 534
ECE 534: Elements of Information Theory, Fall 2010Homework 13Name: Johnson Jonaris GadElkarimUIN 656 312 844Problem 15.20a) Exploring the possibilities for the output we can construct the following table:X12424X21122Y24416It is clear
Ill. Chicago - ECE - 534
ECE 534: Elements of Information Theory, Fall 2009Homework 2Johnson Jonaris GadElkarimUIN 656 312 844Problem 2.28p +pp +pLet pmf P1 (p1 , . . . , pi , . . . , pj , . . . , pm ) and pmf P2 (p1 , . . . , i 2 j , . . . , i 2 j , . . . , pm )H (P2 ) H
Ill. Chicago - ECE - 534
ECE 534: Elements of Information Theory, Fall 2010Name: Johnson Jonaris GadElkarimUIN 656 312 844Information theory and Neuroscience:Topic Covered: Neural coding and neural models Tractography fMRI Brain Network Analysis1. C. E. Shannon. A mathem
Ill. Chicago - ECE - 534
12Entropy, Relative Entropy and Mutual Informationsince t log t 0 for 0 t 1 , and is strictly p ositive for t not equal to 0 or 1.Therefore the conditional entropy H (Y |X ) is 0 if and only if Y is a function of X .6. Conditional mutual information v
Ill. Chicago - MATH - 480
Rutgers - RELIGION - 101
Sikhism Midterm List of TermsKhalsa :The word Khalsa means pure, it is a name given by Guru Gobind Singhto all Sikhs who have been baptized by taking Amrit in a ceremonycalled Amrit Sanchar. The ceremony first took place on Ba, isakhi(March 30 , 1699
W. Connecticut - ECON - 100-206
Cha pte r8Comparative Advantageand the Gains fromInternational TradeP re pa re d by:Fe rna ndo & Yvonn Quija no 2008 Prentice Hall Business Publishing Economics R. Glenn Hubbard, Anthony Patrick OBrien, 2e.Is Using Trade Policyto Help U.S. Indust
W. Connecticut - ECON - 100-206
W. Connecticut - ECON - 100-206
Cha pte r10Technology, Production,and CostsP re pa re d by:Fe rna ndo & Yvonn Quija no 2008 Prentice Hall Business Publishing Economics R. Glenn Hubbard, Anthony Patrick OBrien, 2e.Sony Uses a CostCurve to Determine thePrice of RadiosLearning Ob
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Cha pte r13Oligopoly: Firms in LessCompetitive MarketsP re pa re d by:Fe rna ndo & Yvonn Quija no 2008 Prentice Hall Business Publishing Economics R. Glenn Hubbard, Anthony Patrick OBrien, 2e.Competingwith Wal-MartLearning Objectives13.1 Show ho
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Cha pte r12Monopolistic Competition:The Competitive Model ina More Realistic SettingP re pa re d by:Fe rna ndo & Yvonn Quija no 2008 Prentice Hall Business Publishing Economics R. Glenn Hubbard, Anthony Patrick OBrien, 2e.Starbucks: Growththrough
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Cha pte r6Elasticity: TheResponsiveness ofDemand and SupplyP re pa re d by:Fe rna ndo & Yvonn Quija no 2008 Prentice Hall Business Publishing Economics R. Glenn Hubbard, Anthony Patrick OBrien, 2e.Do People Care about thePrices of Books?Learning
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Cha pte r5Externalities,Environmental Policy,and Public GoodsP re pa re d by:Fe rna ndo & Yvonn Quija no 2008 Prentice Hall Business Publishing Economics R. Glenn Hubbard, Anthony Patrick OBrien, 2e.Economic Policy and theEnvironmentLearning Obj
W. Connecticut - ECON - 100-206
Cha pte r7Firms, the Stock Market,and Corporate GovernanceP re pa re d by:Fe rna ndo & Yvonn Quija no 2008 Prentice Hall Business Publishing Economics R. Glenn Hubbard, Anthony Patrick OBrien, 2e.Google: From Dorm Roomto Wall StreetLearning Objec
W. Connecticut - ECON - 100-206
Cha pte r11Firms in PerfectlyCompetitive MarketsP re pa re d by:Fe rna ndo & Yvonn Quija no 2008 Prentice Hall Business Publishing Economics R. Glenn Hubbard, Anthony Patrick OBrien, 2e.Perfect Competitionin the Market forOrganic ApplesLearning
W. Connecticut - ECON - 100-206
CHAPTER2Trade-offs,ComparativeAdvantage, andthe Market SystemTo compete in theautomobile market,the managers ofBMW must makemany strategicdecisions, such aswhether to introducenew car models.Prepared by:e pah CtFernando QuijanoCopyright
W. Connecticut - ECON - 100-206
Cha pte r16The Markets for Laborand Other Factorsof ProductionP re pa re d by:Fe rna ndo & Yvonn Quija no 2008 Prentice Hall Business Publishing Economics R. Glenn Hubbard, Anthony Patrick OBrien, 2e.Why Are the ChicagoCubs Paying AlfonsoSoriano
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CHAPTER15Fiscal PolicyThe tax laws arecomplicatedbecause thegovernmentchanges themrepeatedly,trying to achievesometimesconflictingeconomic,social, andpolitical goals.Prepared by:e pah CtFernando QuijanoCopyright 2010 Pearson Education,
W. Connecticut - ECON - 100-206
CHAPTER10Long-Run EconomicGrowth: Sources andPoliciesGoogles problemshighlight one of theparadoxes of Chinain recent years:very rapid economicgrowth occurring inthe context ofgovernmentregulations that mayultimately stifle thatgrowth.Prepa
W. Connecticut - ECON - 100-206
CHAPTER14Monetary PolicyBeginning in2008, the Fedwas forced toturn to newpolicies to try topull theeconomy out ofrecession.e pah CtPrepared by:FernandoQuijanoCopyright 2010 Pearson Education, Inc. Publishing as Prentice Hall Macroeconomics
W. Connecticut - ECON - 100-206
Cha pte r15Pricing StrategyP re pa re d by:Fe rna ndo & Yvonn Quija no 2008 Prentice Hall Business Publishing Economics R. Glenn Hubbard, Anthony Patrick OBrien, 2e.Getting into WaltDisney World: OnePrice Does Not Fit AllLearning Objectives15.1
W. Connecticut - ECON - 100-206
Chapter 2ComparativeEconomicDevelopmentCopyright 2009 Pearson Addison-Wesley. All rights reserved.Common Characteristics ofdeveloping countriesLower levels of living and productivityLower levels of human capitalHigher levels of inequality and abs
W. Connecticut - ECON - 100-206
Cha pte r18Public Choice, Taxes,and the Distributionof IncomeP re pa re d by:Fe rna ndo & Yvonn Quija no 2008 Prentice Hall Business Publishing Economics R. Glenn Hubbard, Anthony Patrick OBrien, 2e.Should the GovernmentUse the Tax System toRedu
W. Connecticut - ECON - 100-206
CHAPTER1Economics:Foundationsand ModelsBill Gates, chairmanof Microsoft,testified beforeCongress in 2008that limiting thenumber of foreigntechnical workersallowed into theUnited States wasresulting in a criticalshortage ofscientific talent
W. Connecticut - ECON - 100-206
CHAPTER9Economic Growth,the Financial System,and Business CyclesBoeing hasexperiencedgrowth over thelong run, whilebeing affected bythe businesscycle.Prepared by:e pah CtFernando QuijanoCopyright 2010 Pearson Education, Inc. Publishing as
W. Connecticut - ECON - 100-206
Cha pte r17The Economicsof InformationP re pa re d by:Fe rna ndo & Yvonn Quija no 2008 Prentice Hall Business Publishing Economics R. Glenn Hubbard, Anthony Patrick OBrien, 2e.Why Does State FarmCharge Young Men SoMuch More Than YoungWomen for A
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Cha pte r3Where Prices Come From:The Interaction of Demandand SupplyP re pa re d by:Fe rna ndo & Yvonn Quija no 2008 Prentice Hall Business Publishing Economics R. Glenn Hubbard, Anthony Patrick OBrien, 2e.Apple and the Demandfor iPodsLearning O
W. Connecticut - ECON - 100-206
Cha pte r14Monopoly andAntitrust PolicyP re pa re d by:Fe rna ndo & Yvonn Quija no 2008 Prentice Hall Business Publishing Economics R. Glenn Hubbard, Anthony Patrick OBrien, 2e.Time Warner RulesManhattanLearning Objectives14.1 Define monopoly.1
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W. Connecticut - ECON - 100-206
Chapter 5Poverty,Inequality, andDevelopmentCopyright 2009 Pearson Addison-Wesley. All rights reserved.The Growth Controversy:Seven Critical Questions What is the extent of relative inequality, andhow is this related to the extent of poverty? Who
W. Connecticut - ECON - 100-206
Chapter 8Human Capital:Education andHealth inEconomicDevelopmentCopyright 2009 Pearson Addison-Wesley. All rights reserved.The Central Roles of Educationand Health Health and education are importantobjectives of development Health and education