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7 Pages

### challset1sol

Course: BIO 510, Fall 2006
School: Carnegie Mellon
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Word Count: 1967

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344 Mat Solution Sketch for Challenge Set 1 1. a. The positive integers less than or equal to 100 are the integers 1,2,3,...,100. There are 50 even integers and 50 odd integers. b. Let S={1,2,3,...,100}. Let A = {x: x is an even positive integer}, B={x: x is a positive integer divisible by 5}, and C={x: x is a positive integer divisible by 11}. Let N(A or B)= {x: x is an integer divisible by 2 or 5}. The number of...

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Carnegie Mellon - BIO - 510
MAT 344 Challenge Set #2 The following is a selection of problems that you will find useful to test your understanding of the enumeration concepts we have been studying. There are more in the text that are also worthwhile, and you are encouraged to select
Carnegie Mellon - BIO - 510
1Mat 344F challenge set #2 Solutions1. Put two balls into box 1, one ball into box 2 and three balls into box 3.The remaining 4 balls can now be distributed in any way among the three remaining boxes. This can be done in C(4+3-1,4)=C(6,4)=15 ways. Plea
Carnegie Mellon - BIO - 510
Mat 344 Challenge Set 3 The following is a selection of problems that you will find useful to test your understanding of the generating function concepts we have been studying. Try to do as many as you can; there are more in the text that are also worthwh
Carnegie Mellon - BIO - 510
Carnegie Mellon - BIO - 510
Back to MAT 344Tucker 6.3: Selected Solutions3. Find a generating function for the number of ways to write the integer r as a sum of positive integers in which no integer appears more than three times. Solution. This is the same as the number of integer
Carnegie Mellon - BIO - 510
Carnegie Mellon - BIO - 510
Carnegie Mellon - BIO - 510
Carnegie Mellon - BIO - 510
MAT 344 CHALLENGE SET #4 The following is a selection of problems that you will find useful to test your understanding of the generating function and recurrence relation concepts we have been studying. Try to do as many as you can; there are more in the t
Carnegie Mellon - BIO - 510
Carnegie Mellon - BIO - 510
Carnegie Mellon - BIO - 510
Carnegie Mellon - BIO - 510
MAT 344F Challenge Set #5The following is a selection of problems that you will find useful to test your understanding of the recurrence relation, and inclusion-exclusion concepts we have been studying. Try to do as many as you can; there are more in the
Carnegie Mellon - BIO - 510
Carnegie Mellon - BIO - 510
Carnegie Mellon - BIO - 510
Sheet1Demonstration: Dynamic Programming with Similarity Matrix and Constant Gap PenaltyAuthor: R.F. Murphy, Feb. 27, 2005, Revised January 25, 2007The sequences are entered here: 1: acdcdefg 2: acdefghiThis demonstration illustrates the three steps o
Carnegie Mellon - BIO - 510
Sheet1Demonstration: Dynamic Programming with Similarity Matrix and Constant Gap PenaltyAuthor: R.F. Murphy, Feb. 27, 2005The sequences are entered here: 1: acdcdefg 2: acdefghiThis demonstration illustrates the three steps of the basic dynamic progra
Carnegie Mellon - BIO - 510
Dynamic Programming Illustration Figure 39 from Mount Bioinformaticsgap gap b1 b2 b3 b4 0 1 gap 2 gaps 3 gaps 4 gaps gap gap b1 b2 b3 b4 0 1 gap 2 gaps 3 gaps 4 gaps gap gap b1 b2 b3 b4 0 1 gap 2 gaps 3 gaps 4 gaps gap gap b1 b2 b3 b4 0 1 gap 2 gaps 3 ga
Carnegie Mellon - BIO - 510
EvenEmissionDemonstration: Viterbi AlgorithmAuthor: R.F. Murphy, Feb. 8, 2007This demonstration illustrates the Viterbi algorithm without storing the traceback. See Lectures, Part 7 for details on the method. Suggestions: Change the sequence in cells B
Carnegie Mellon - BIO - 510
Sheet1 (2)Demonstration: XY plots and Categorical plotsAuthor: R.F. Murphy, April 27, 1995 x 0.5 1 2 4 8 y 1 2 4 8 1620 Axis Title 10 0 0.5Categorical Plot12 category4820 Axis Title 15 10 5 0 0 1 2XY Plot34 X56789Page 1
Carnegie Mellon - BIO - 510
Sheet1Demonstration: Smoothing data using Fourier transforms Author: Robert F. Murphy, March 29, 1995sine: cosine: amplitude period &lt; This section contains constants for generating a 0.2 1.570796327 &lt; periodic function with two components differing 1 0.
Carnegie Mellon - BIO - 510
Computational Biology 03-310/311/510/710, Spring 2006R. F. MurphyRequirements for obtaining extra-credit by writing a summary of a Computational Biology seminarYou may obtain 5 extra credit points by attending a computational biology seminar at Carnegi
Carnegie Mellon - BIO - 510
Computational Biology 03-510/710 &amp; 42-434/734 Homework 1 (revised January 25, 2009)Spring 2009 R. F. MurphyHomework 1 Dynamic Programming Alignment Due: January 29, 2009 50 pointsYour task is to write and test a program in C, C+, Java, Perl, Python or
Carnegie Mellon - BIO - 510
Computational Biology 03-510/710 &amp; 42-434/734 Homework 2 (revised February 12, 2009)Spring 2009 R. F. MurphyHomework 2 Building Profile HMMs Due: February 19, 2009 50 pointsYour task is to write and test a program in C, C+, Java, Perl, Python or Matlab
Carnegie Mellon - BIO - 510
Getting StartedCopyright statementCopyright 2001 Accelrys, a subsidiary of Pharmacopeia Inc. All rights reserved. This document contains proprietary information of Accelrys and its licensors. It is their exclusive property. It may not be reproduced or t
Carnegie Mellon - BIO - 510
CURRICULUM VITAERobert F. Murphy Ray and Stephanie Lane Professor of Computational Biology Professor of Biological Sciences, Biomedical Engineering and Machine Learning Carnegie Mellon University 5000 Forbes Avenue Pittsburgh, Pennsylvania 15213 EDUCATIO
Carnegie Mellon - BIO - 510
Computational Biology 03-310/311/510/710 &amp; 42-334/534/734 Problem A1Spring 2005 Robert F. MurphyProblem A1 Simple Sequence Analysis Operations Due: January 20, 2005Hand in written answers to the questions or submit via Blackboard a single Word or PDF d
Carnegie Mellon - BIO - 510
Computational Biology 03-310/311 &amp; 42-334 Problem A1Spring 2006 Robert F. MurphyProblem A1 Simple Sequence Analysis Operations Due: January 26, 2006Hand in written answers to the questions or submit via Blackboard a single Word or PDF document containi
Carnegie Mellon - BIO - 510
Computational Biology 03-310/311/510/710 &amp; 42-334/534/734 Problem A1Spring 2004 Robert F. MurphyProblem A1 Simple Sequence Analysis Operations Due: January 20, 2004There are a number of sequence analysis packages that run on a variety of platforms. Thi
Carnegie Mellon - BIO - 510
Carnegie Mellon - BIO - 510
Computational Biology 03-310/311 &amp; 42-334 Problem A2Spring 2004 Robert F. MurphyProblem A2 Finding coding sequences and PCR primers Due: February 3, 2004Use MacVector to complete the following. Hand in requested printouts and written answers to the que
Carnegie Mellon - BIO - 510
Computational Biology 03-310/311/510/710 &amp; 42-334/534/734 Problem A2Spring 2005 Robert F. MurphyProblem A2 BLAST Due: February 8, 2005In this assignment, you are given a sequence of a mouse cDNA in the file ProbA2.txt on the homeworks web page. Your go
Carnegie Mellon - BIO - 510
Computational Biology 03-310/311/510/710 &amp; 42-334/534/734 Problem A2Spring 2006 Robert F. MurphyProblem A2 BLAST Due: February 9, 2006In this assignment, you are given a sequence of a mouse cDNA in the file ProbA2.txt on the homeworks web page. Your go
Carnegie Mellon - BIO - 510
Computational Biology 03-310/311/510/710 &amp; 42-334/534/734 Problem A3Spring 2004 Robert F. MurphyProblem A3 BLAST Due: February 17, 2004In this assignment, you are given a sequence of a mouse cDNA. Your goal is perform initial sequence analysis and comp
Carnegie Mellon - BIO - 510
Computational Biology 03-310/311/510/710, Spring 2005R. F. MurphyProblem A3 Predicting and viewing protein structure Due: March 1, 2005For this assignment you are given the amino acid sequence of a chimeric protein (a chimera in this context is defined
Carnegie Mellon - BIO - 510
Computational Biology 03-310, Spring 2006R. F. MurphyProblem A3 Predicting and viewing protein structure Due: February 28, 2006For this assignment you are given the amino acid sequence of a chimeric protein (a chimera in this context is defined as a ma
Carnegie Mellon - BIO - 510
Computational Biology 03-310/311/510/710, Spring 2004R. F. MurphyProblem A4 Predicting and viewing protein structure Due: March 4, 2004For this assignment you are given the amino acid sequence of a chimeric protein (a chimera in this context is defined
Carnegie Mellon - BIO - 510
Computational Biology 03-310, Spring 2006R. F. MurphyProblem C1 Modeling Acid-Base Equilibria Due: April 4, 2006In this assignment you will make a model of the net charge on an amino acid by considering the pK's of its ionizable groups and entering app
Carnegie Mellon - BIO - 510
Computational Biology 03-310/510, Spring 2004R. F. MurphyProblem C2 Spreadsheet Model of a Biochemical Reaction Due: April 6, 2004For this assignment you may use any spreadsheet program that you have access to (the assignment has been tested using Exce
Carnegie Mellon - BIO - 510
Computational Biology 03-310/510/710, Spring 2005R. F. MurphyProblem C2 Spreadsheet Model of a Biochemical Reaction Due: April 5, 2005For this assignment you may use any spreadsheet program that you have access to (the assignment has been tested using
Carnegie Mellon - BIO - 510
Computational Biology 03-310/510/710, Spring 2006R. F. MurphyProblem C2 Kinetic Model of a Biochemical Reaction Due: April 13, 2006For this assignment you may use any spreadsheet program that you have access to (the assignment has been tested using Exc
Carnegie Mellon - BIO - 510
Computational Biology 03-310, Spring 2004R. F. MurphyProblem C3 Modeling compartmental systems Due: April 30, 2004 (accepted without penalty until May 11, 2004)In this assignment we will solve simple compartmental systems using MAPLE. Consider the foll
Carnegie Mellon - BIO - 510
Computational Biology 03-310/510/710, Spring 2005R. F. MurphyProblem C3 Modeling compartmental systems Due: April 19, 2005In this assignment we will solve simple compartmental systems using MAPLE. Consider the following compartmental system (system 1)
Carnegie Mellon - BIO - 510
Computational Biology 03-310/510/710, Spring 2004R. F. MurphyProblem D1 Finding objects in images Due: April 30, 2004 (accepted without penalty until May 11)You should use NIH Image or ImageJ public domain image analysis packages, and/or Matlab, for th
Carnegie Mellon - BIO - 510
Computational Biology 03-310, Spring 2005R. F. MurphyProblem D1 Finding objects in images Due: April 28, 2005 (accepted without penalty until 8:30 AM May 10)(510/710 students can submit for extra credit but only if assignment B4 is completed) You shoul
Carnegie Mellon - BIO - 510
Computational Biology 03-310, Spring 2006R. F. MurphyProblem D1 Finding objects in images Due: May 2, 2006You should use NIH Image or ImageJ public domain image analysis packages, and/or Matlab, for this assignment. You will also need to download file(
Carnegie Mellon - BIO - 510
Computational Biology 03-310/510/710, Spring 2005R. F. MurphyExtra Credit E1 Modeling a Biological System Due: May 10, 2005 at 8:30 AM Find a published journal paper(s) that describe(s) a biological or biochemical system Build a model of the system us
Carnegie Mellon - BIO - 510
Computational Biology 03-310/510/710, Spring 2004R. F. MurphyExtra Credit E1 Modeling a Biological System Due: May 11, 2004 Find a published journal paper that describe a biological or biochemical system Build a model of the system using Excel, Maple,
Carnegie Mellon - BIO - 510
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Carnegie Mellon - BIO - 510
S. Tanny Subsets of a Set [n] 1) How many k-subsets of [n] are there? k 0, integer n=4 k=2 12 34 13 23 14 24MAT 344FFall, 1997let x be the # of k-subsets Each such subset can be arranged in k! ways. Thus, xk! counts the number of ordered k-subsets of [
Carnegie Mellon - BIO - 510
S. Tanny c)MAT 344FFall, 1997r distinct balls into n nondistinct boxes:k= 1nS (r, k)where S(r,k) = number of ways to partition an r-set into k (non-empty) parts. S(r,k) is called a Stirling number of the Second Kind. Try to compute some S(r,k): eg:
Carnegie Mellon - BIO - 510
GENERATING FUNCTIONS Solve an infinite number of related problems in one swoop. *Code the problems, manipulate the code, then decode the answer! Really an algebraic concept but can be extended to analytic basis for interesting results. (i) Ordinary Genera
Carnegie Mellon - BIO - 510
S. Tanny Recurrence Relations Tower of Hanoi Let TnMAT 344Spring 1999be the minimum number of moves required. T0 = 0, T1 = 1 T n = 2 Tn - 1 + 1 7 Initial Conditions n\$2*Tn is a sequence (fn. on integers). Solve for Tn? * is a recurrence, difference e
Carnegie Mellon - BIO - 510
S. Tanny Non-Linear DFE Exercise 1 YnYn+2 = Y2 n + 1 Y0 =1, Y1 = 2MAT 344Spring 1999Follows that Yn . 0 oen. ^ Yn % Yn %2 1'Yn % 1 YnLet Wn =Yn % 1 Yn. Then Wn + 1 = Wn , W0 = 2 (Y0 = 1)^ Wn = 2 Y Yn + 1 = 2Yn Y Yn = 2n N.B. Could also linearize
Carnegie Mellon - BIO - 510
S. TannyMAT 344Spring, 1999N(aN1 aN2 aN3 aN4) = N - j N(ai) % j N(ai a j) - j N(ai a j ak) Here N = 21 34 % 10&amp; 1 N(ai) = 10(Just put 8 balls in box i and fill arbitrarily for the remaining 10) (Put 8 balls in both i and j, fill arbitrarily from here
Harvey Mudd College - ECON - 201
Domain XValueFunction Tangent X Y=f(x) Y=L(X) 10 1025 1025 9.9 995.3 1017.5 9.8 966.19 1010 9.7 937.67 1002.5 9.6 909.74 995 9.5 882.38 987.5 9.4 855.58 980 9.3 829.36 972.5 9.2 803.69 965 9.1 778.57 957.5 9 754 950 8.9 729.97 942.5 8.8 706.47 935 8.7 68
Tyler College - CS - 1405
Bent CyclingAuthorDatePurposeToestimatethereturnofaninvestmentincurrentdollarsBentCyclingDepreciationofAssetsBent CyclingPrepared:11/7/2009ReturnontheBuildingProjectInitialInvestment(\$1,200,000)CumulativeNetCashFlow07/19/2011Year1\$150,000
Tyler College - CS - 1405
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Tyler College - CS - 1405
Bent CyclingAuthorDateYournamegoeshereCurrentDatePurposeToanalyzedifferentinvestmentandloanscenariosBentCyclingSavingsProposals07/19/2011Bent CyclingPrepared:InvestmentAnalysisInitialInvestment InvestmentCalculate(PV)Goal(FV)AnnualMonths
Tyler College - CS - 1405
Bent CyclingAuthorDateYournamegoeshereCurrentDatePurposeToprojectBentCycling'sincomestatementsforthenextfivefiscalyearsBentCyclingProjectedFiveYearIncomeStatementBent CyclingPreparedProjectedFiveYearIncomeStatementSalesRevenueCostofGoodsSold
Tyler College - CS - 1405
Bent CyclingAuthorDatePurposeYour name goes hereCurrent DateTo analyze different investment and loan scenariosBent CyclingSavings ProposalsBent Cycling4/6/2010Prepared: 04/06/2010Investment AnalysisCalculateMonthly Payment (PMT)Investment G