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### datarep

Course: ASTR 415, Fall 2008
School: Maryland
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Word Count: 562

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Representations Computers Data store data as different variable types, e.g. integer, floating point, complex, etc. Different machines have different wordlengths, e.g. 4-byte ints on a 32-bit machine (Pentium), 8-byte ints on a 64-bit machine (Alpha). This makes (binary) data non-portable. Integers All data types represented by 0's and 1's. An integer value: = = N = # of bits in word si = value of bit i...

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Representations Computers Data store data as different variable types, e.g. integer, floating point, complex, etc. Different machines have different wordlengths, e.g. 4-byte ints on a 32-bit machine (Pentium), 8-byte ints on a 64-bit machine (Alpha). This makes (binary) data non-portable. Integers All data types represented by 0's and 1's. An integer value: = = N = # of bits in word si = value of bit i in binary string s 2 1 e.g. 0 0 0 0 0 1 1 0 = 2 + 2 = 6 for 8-bit word. Use "two's complement" method for sign. Integers, Cont'd Largest value that can be represented is 2N - 1. For 32-bit word this is 4,294,967,295. Arithmetic with integers is exact, except: When division results in remainder. Result exceeds largest representable integer e.g. 2 109 + 3 109 = overflow error Note multiplication by 2's can be achieved by left-shift, which is very fast (in C: "<<" operator). Two's Complement Exploits finite size of data representations (cyclic groups) and properties of binary arithmetic. To get negative of binary number, invert all bits and add 1 to the result. e.g. 1 = 0 0 0 0 0 0 0 1 in 8-bit invert bits: 1 1 1 1 1 1 1 0 add 1: 00000001 result: 1 1 1 1 1 1 1 1 = -1 In 8 bits, signed char ranges from -128 to +127. Negative Powers of 2 Binary notation can be extended to cover negative powers of 2, e.g. "110.101" is: 1 22 + 1 21 + 1 2-1 + 1 2-3 = 6.625 Can represent real numbers by specifying some location in the word as the "binary point" fixed-point representation. In practice, use some bits for an exponent floating-point representation. Floats For most machines these days, real numbers are represented by floating-point format: = s M E = sign B = base (usually 2, sometimes 16) = mantissa e = exponent = bias, usually 127. In past, manufacturers used different number of bits for each of M and e non-portable code. Floats, Cont'd Currently, manufacturers most adopt IEEE standard: s = 1st bit Next 8 bits are e Last 23 bits are M, expressed as a binary fraction, either 1.F, or, if e=0, 0.F, where F is in base 2. Largest single-precision float fmax = 2127 1038. Smallest (and least precise!) fmin = 2-149 10-45. Round-off Error Not all values along real axis can be represented. There are 10 integers between fmin & fmax, but only 232 109 bit patterns. 38 Values < |10-45| result in "underflow" error. If value cannot be represented, next nearest value is produced. Difference between desired and actual value is called "round-off error" (RE). Round-off Error, Cont'd Smallest value em for which 1 + em > 1 is called "machine accuracy", typically 10-7 for 32 bits. Double precision greatly reduces em (~ 10 ). RE accumulates in a calculation: -16 Random walk: total error N1/2 em after N operations. But algorithms rarely random linear error N em. Round-off Error, Cont'd Subtraction of two very nearly equal numbers can give rise to large RE. e.g. Solution of quadratic equation... = ...can go badly wrong whenever ac << b2 ...

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Maryland - ASTR - 415
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Numerical Linear Algebra Probably the simplest kind of problem. Occurs in many contexts, often as part of larger problem. Symbolic manipulation packages can do linear algebra &quot;analytically&quot; (e.g. Mathematica, Maple). Numerical methods needed when:
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Nonlinear EquationsOften (most of the time?) the relevant system of equations is not linear in the unknowns. Then, cannot decompose as Ax = b. Oh well. Instead write as:(1) (2) f(x) = 0 f(x) = 0function of one variable (1-D) x = (x1,x2,.,xn
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Statistical Description of Data Cf. NRiC, Chapter 14. Statistics provides tools for understanding data.In the wrong hands these tools can be dangerous! Apply some formula to data to compute a &quot;statistic&quot;. Find where value falls in a probability
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Modeling of Data NRiC Chapter 15. Model depends on adjustable parameters. Can be used for &quot;constrained interpolation&quot;. Basic approach:1. 2. 3. 4.Choose figure-of-merit function (e.g. 2). Adjust best-fit parameters: minimize merit function. Co
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Random Numbers NRiC Chapter 7. Frequently needed to generate initial conditions. Often used to solve problems statistically. How can a computer generate a random number? It can't! Generators are pseudo-random. Generators are deterministic: i
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Numerical Integration (Quadrature) NRiC Chapter 4. Already seen Monte Carlo integration. Can cast problem as a differential equation (DE): = is equivalent to solving for I y(b) the DE dy/dx = f(x) with the boundary condition (BC) y(a) =
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Ordinary Differential Equations (ODEs) NRiC Chapter 16. ODEs involve derivatives wrt one independent variable, e.g. time t. ODEs can always be reduced to a set of firstorder equations (involving only first derivatives).e.g. = is
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MATH 241 CALCULUS III FIRST MIDTERM EXAM Instructions. Answer each question on a separate answer sheet. Show all your work. Be sure your name, section number, and problem number are on each answer sheet, and that you have copied and signed the honor
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Center for Satellite and Hybrid Communication NetworksIntegrated Security Services for Dynamic Coalition ManagementHimanshu Khurana Electrical and Computer Engineering Department, University of Maryland College Park, Maryland 20742 DARPA DC PI Mee
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Center for Satellite and Hybrid Communication NetworksIntegrated Security Services for Dynamic Coalition ManagementVirgil D. Gligor and John S. Baras Electrical and Computer Engineering Department, University of Maryland College Park, Maryland 207
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Center for Satellite and Hybrid Communication NetworksIntegrated Security Services for Dynamic Coalition ManagementHimanshu Khurana and Vijay Bharadwaj Electrical and Computer Engineering Department, University of Maryland College Park, Maryland 2
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DK6037 FLPraveen K. MurthyFujitsu Laboratories of America, Sunnyvale, California, USAShuvra S. BhattacharyyaUniversity of Maryland, College Park, USAEffective Strategies for Aggressive Memory OptimizationAlthough programming in memory restri
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INTRODUCTION TO PHYSICAL GEOLOGY GEOL100 -Section: 0102 -Fall 2004Professor: Bill McDonough Office Hours: Wednesday, 9-10 AM Office: Chemistry Bldg (091), room 0229 Phone: 301-405-5561 Email: mcdonough@geol.umd.edu (preferred communication medium)
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Homework #2Chapter 3 Q25 The dividing line between the illuminated and unilluminated halves of the Moon is called the terminator. The terminator appears curved when there is a crescent or gibbous moon, but appears straight when there is a first qu
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ASTR120 Homework #3 (Hamilton) due Thursday Sept. 27 (20 Points)Finish reading Chapter 4! Now you are cleared for this homework (from Chapter 3, page 92). Try to start early if you can - there are some interesting (but tricky!) problems this week.
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ASTR120 Homework #4 (Hamilton) due Thursday Oct. 4 (30 Points)Denitely nish reading Chapters 4 and 7! These rst ve problems are from Chapter 4. W4. Do problem W4 from http:/www.astro.umd.edu/hamilton/ASTR120/webexp.html. 46. A satellite is said to
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ASTR120 Homework #8 (Hamilton) due Thursday Nov. 8 (20 Points)Finish reading Chapters 11 and 12! This is the last graded homework before Exam 2 on Nov. 15. These problems are from Chapter 11. 56. The Mariner 2 spacecraft detected more microwave rad
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ASTR120 Homework #9 (Hamilton) due Thursday Nov. 29 (20 Points)Finish reading Chapter 12 and 13! These problems are from Chapter 12. 49. When Saturn is at dierent points in its orbit, we see dierent aspects of its rings because the planet has a 27
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ASTR120 Homework #10 (Hamilton) due Thursday Dec. 6 (20 Points)Finish reading Chapters 14, 15, and 28! These problems are from Chapter 14. 30. At certain points in its orbit, a stellar occultation by Uranus would not reveal the existence of the rin
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Vol 436|28 July 2005NEWS &amp; VIEWSKAMLAND/LBNLEARTH SCIENCESGhosts from withinWilliam F. McDonough The first detection of geoneutrinos from beneath our feet is a landmark result. It will allow better estimation of the abundances and distributio
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2.15 Compositional Model for the Earths CoreW. F. McDonough University of Maryland, College Park, USA2.15.1 INTRODUCTION 2.15.2 FIRST-ORDER GEOPHYSICS 2.15.3 CONSTRAINING THE COMPOSITION OF THE EARTHS CORE 2.15.3.1 Observations from Meteorites and
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Chemical Geology 145 1998. 153159Geochemical Earth Reference Model GERM/ : description of the initiativeHubert Staudigel a , Francis Albarede b,) , Janne Blichert-Toft b, John Edmond c , ` d Bill McDonough , Stein B. Jacobsen d , Ralph Keeling e,
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Earth and Planetary Science Letters 208 (2003) 279^290 www.elsevier.com/locate/epslExtremely light Li in orogenic eclogites: The role of isotope fractionation during dehydration in subducted oceanic crust Thomas Zack , Paul B. Tomascak, Roberta L
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Precambrian Research 118 (2002) 267 /283 www.elsevier.com/locate/precamresRe /Os and U /Pb geochronological constraints on the eclogite/tonalite connection in the Archean Man Shield, West AfricaMatthias G. Barth a,1, Roberta L. Rudnick a,1, Richar
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PergamonGeochimica et Cosmochimica Acta, Vol. 66, No. 24, pp. 4325 4345, 2002 Copyright 2002 Elsevier Science Ltd Printed in the USA. All rights reserved 0016-7037/02 \$22.00 .00PII S0016-7037(00)01004-9Geochemistry of xenolithic eclogites from
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Earth and Planetary Science Letters 198 (2002) 307^322 www.elsevier.com/locate/epslRe^Os evidence for replacement of ancient mantle lithosphere beneath the North China cratonShan Gao a;b , Roberta L. Rudnick c; , Richard W. Carlson d , William F.
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Chemical Geology 183 (2002) 43 61 www.elsevier.com/locate/chemgeoDepleted melt inclusions in MORB plagioclase: messages from the mantle or mirages from the magma chamber?Peter J. Michael a,*, William F. McDonough b, Roger L. Nielsen c, Winton C.
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ASTR121 Homework #1 (Hamilton) due Thursday Feb. 7 (15 Points)Start this homework by nishing the relevant reading: Chapter 5. I also recommend testing yourself on the Review Questions at the end of each chapter. This is an excellent way to see if y
Maryland - ASTR - 121
ASTR121 Homework #2 (Hamilton) due Thursday Feb. 14 (15 Points)This problem is from Chapter 5. 40. The wavelength of H in the spectrum of the star Megrez in the Big Dipper (part of the constellation Ursa Major, the Great Bear) is 486.112 nm. Labora
Maryland - ASTR - 121
ASTR121 Homework #3 (Hamilton) due Thursday Feb. 21 (15 Points)Finishing reading Chapter 16. These problems are from that chapter. 29. Calculate how much energy would be released if each of the following masses were converted entirely into their eq
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ASTR121 Homework #4 (Hamilton) due Thursday Feb. 28 (15 Points)Finishing reading Chapter 17. These problems are from that chapter. *36. Kapteyns star (named after the Dutch astronomer who found it) has a parallax of 0.255 arcsec, a proper motion of