The Role of the Scientific Method in Software Development. Robert Sedgewick Princeton University

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "The Role of the Scientific Method in Software Development. Robert Sedgewick Princeton University"

Transcription

1 The Role of he Scienific Mehod in Sofware Developmen Rober Sedgewick Princeon Univeriy

2 The cienific mehod i neceary in algorihm deign and ofware developmen Scienific mehod creae a model decribing naural world ue model o develop hypohee run experimen o validae hypohee refine model and repea model hypohei experimen Algorihm deigner who doe no experimen ge lo in abracion Sofware developer who ignore co rik caarophic conequence

3 Fir hypohei (need checking) Modern ofware developmen require huge amoun of code

4 Fir hypohei (need checking) Modern ofware developmen require huge amoun of code bu performance-criical code implemen relaively few fundamenal algorihm

5 Warmup: random number generaion Problem: wrie a program o generae random number model: claical probabiliy and aiic hypohei: frequency value hould be uniform weak experimen: generae random number check for uniform frequencie model hypohei experimen beer experimen: generae random number ue x 2 e o check frequency value again uniform diribuion beer hypohee/experimen ill needed many documened diaer acive area of cienific reearch applicaion: imulaion, crypography in k = 0; V = 10 connec o core iue in heory of compuaion while ( rue ) Syem.ou.prin(k++ % V); in k = 0; random? while ( rue ) { } k = k* ); Syem.ou.prin(k % V); exbook algorihm ha flunk x 2 e

6 Warmup (coninued) Q. I a given equence of number random? A. No. average probe unil duplicae i abou 24 Q. Doe a given equence exhibi ome propery ha random number equence exhibi? V = 365 Birhday paradox Average coun of random number generaed unil a duplicae happen i abou pv/2 Example of a beer experimen: generae number unil duplicae check ha coun i cloe o pv/2 even beer: repea many ime, check again diribuion ill beer: run many imilar e for oher properie Anyone who conider arihmeical mehod of producing random digi i, of coure, in a ae of in John von Neumann

7 Deailed example: pah in graph A lecure wihin a lecure

8 Finding an -pah in a graph i a fundamenal operaion ha demand underanding Ground rule for hi alk work in progre (more queion han anwer) baic reearch ave deep dive for he righ problem Applicaion graph-baed opimizaion model nework percolaion compuer viion ocial nework (many more) Baic reearch fundamenal abrac operaion wih numerou applicaion worh doing even if no immediae applicaion rei empaion o premaurely udy impac

9 : maxflow Ford-Fulkeron maxflow cheme find any - pah in a (reidual) graph augmen flow along pah (may creae or delee edge) ierae unil no pah exi Goal: compare performance of wo baic implemenaion hore augmening pah maximum capaciy augmening pah Key ep in analyi How many augmening pah? Wha i he co of finding each pah? reearch lieraure hi alk

10 : max flow Compare performance of Ford-Fulkeron implemenaion hore augmening pah maximum-capaciy augmening pah Graph parameer number of verice V number of edge E maximum capaciy C How many augmening pah? hore max capaciy wor cae upper bound VE/2 VC 2E lg C How many ep o find each pah? E (wor-cae upper bound)

11 : max flow Compare performance of Ford-Fulkeron implemenaion hore augmening pah maximum-capaciy augmening pah Graph parameer for example graph number of verice V = 177 number of edge E = 2000 maximum capaciy C = 100 How many augmening pah? hore wor cae upper bound VE/2 VC for example 177,000 17,700 max capaciy 2E lg C 26,575 How many ep o find each pah? 2000 (wor-cae upper bound)

12 : max flow Compare performance of Ford-Fulkeron implemenaion hore augmening pah maximum-capaciy augmening pah Graph parameer for example graph number of verice V = 177 number of edge E = 2000 maximum capaciy C = 100 How many augmening pah? wor cae upper bound for example acual hore VE/2 VC 177,000 17, max capaciy 2E lg C 26,575 7 How many ep o find each pah? < 20, on average oal i a facor of a million high for houand-node graph!

13 : max flow Compare performance of Ford-Fulkeron implemenaion hore augmening pah maximum-capaciy augmening pah Graph parameer number of verice V number of edge E maximum capaciy C Toal number of ep? hore max capaciy wor cae upper bound VE 2 /2 VEC 2E 2 lg C WARNING: The Algorihm General ha deermined ha uing uch reul o predic performance or o compare algorihm may be hazardou.

14 : leon Goal of algorihm analyi predic performance (running ime) guaranee ha co i below pecified bound wor-cae bound Common widom random graph model are unrealiic average-cae analyi of algorihm i oo difficul wor-cae performance bound are he andard Unforunae ruh abou wor-cae bound ofen uele for predicion (ficional) ofen uele for guaranee (oo high) ofen miued o compare algorihm Bound are ueful in many applicaion: which one?? Open problem: Do beer! acual co

15 Finding an -pah in a graph i a baic operaion in a grea many applicaion Q. Wha i he be way o find an -pah in a graph? A. Several well-udied exbook algorihm are known Breadh-fir earch (BFS) find he hore pah Deph-fir earch (DFS) i eay o implemen Union-Find (UF) need wo pae BUT all hree proce all E edge in he wor cae divere kind of graph are encounered in pracice Wor-cae analyi i uele for predicing performance Which baic algorihm hould a praciioner ue???

16 Algorihm performance depend on he graph model complee random grid neighbor mall-world Iniial choice: grid graph ufficienly challenging o be inereing found in pracice (or imilar o graph found in pracice) calable poenial for analyi Ground rule algorihm hould work for all graph... (many appropriae candidae) if verice have poiion we can find hor pah quickly wih A* (ay uned) algorihm hould no ue any pecial properie of he model

17 Applicaion of grid graph conduciviy concree granular maerial porou media polymer fore fire epidemic Inerne reior nework evoluion ocial influence Fermi paradox fracal geomery ereo viion image reoraion objec egmenaion cene reconrucion... Example 1: Saiical phyic percolaion model exenive imulaion ome analyic reul arbirarily huge graph Example 2: Image proceing model pixel in image maxflow/mincu energy minimizaion huge graph

18 Finding an -pah in a grid graph M by M grid of verice undireced edge connecing each verex o i HV neighbor ource verex a cener of op boundary deinaion verex a cener of boom boundary Find any pah connecing o M 2 verice abou 2M 2 edge M verice edge Co meaure: number of graph edge examined

19 Finding an -pah in a grid graph Similar problem are covered exenively in he lieraure Percolaion Random walk Nonelfinerecing pah in grid Graph covering?? Which baic algorihm hould a praciioner ue o find a pah in a grid-like graph?

20 Finding an -pah in a grid graph Elemenary algorihm are found in exbook Deph-fir earch (DFS) Breadh-fir earch (BFS) Union-find?? Which baic algorihm hould a praciioner ue o find a pah in a grid-like graph?

21 Abrac daa ype eparae clien from implemenaion A daa ype i a e of value and he operaion performed on hem An abrac daa ype i a daa ype whoe repreenaion i hidden Clien Inerface Implemenaion invoke operaion pecifie how o invoke op code ha implemen op Implemenaion hould no be ailored o paricular clien Develop implemenaion ha work properly for all clien Sudy heir performance for he clien a hand

22 Graph abrac daa ype Verice are ineger beween 0 and V-1 Edge are verex pair Graph ADT implemen Graph(Edge[]) o conruc graph from array of edge findpah(in, in) o conduc earch from o (in) o reurn predeceor of v on pah found Example: clien code for grid graph in e = 0; Edge[] a = new Edge[E]; for (in i = 0; i < V; i++) { if (i < V-M) a[e++] = new Edge(i, i+m); if (i >= M) a[e++] = new Edge(i, i-m); if ((i+1) % M!= 0) a[e++] = new Edge(i, i+1); if (i % M!= 0) a[e++] = new Edge(i, i-1); } GRAPH G = new GRAPH(a); G.findPah(V-1-M/2, M/2); for (in k = ; k!= ; k = G.(k)) Syem.ou.prinln( ); M =

23 DFS: andard implemenaion graph ADT conrucor code for (in k = 0; k < E; k++) { in v = a[k].v, w = a[k].w; adj[v] = new Node(w, adj[v]); adj[w] = new Node(v, adj[w]); } graph repreenaion verex-indexed array of linked li wo node per edge DFS implemenaion (code o ave pah omied) void findpahr(in, in ) { if ( == ) reurn; viied() = rue; for(node x = adj[]; x!= null; x = x.nex) if (!viied[x.v]) earchr(x.v, ); } void findpah(in, in ) { viied = new boolean[v]; earchr(, ); }

24 Baic flaw in andard DFS cheme co rongly depend on arbirary deciion in clien code!... for (in i = 0; i < V; i++) { if ((i+1) % M!= 0) a[e++] = new Edge(i, i+1); if (i % M!= 0) a[e++] = new Edge(i, i-1); if (i < V-M) a[e++] = new Edge(i, i+m); if (i >= M) a[e++] = new Edge(i, i-m); }... order of hee aemen deermine order in li we, ea, norh, ouh ouh, norh, ea, we order in li ha draic effec on running ime ~E/2 ~E 1/2 bad new for ANY graph model

25 Addreing he baic flaw Advie he clien o randomize he edge? no, very poor ofware engineering lead o nonrandom edge li (!) Randomize each edge li before ue? no, may no need he whole li Soluion: Ue a randomized ieraor andard ieraor in N = adj[x].lengh; for(in i = 0; i < N; i++) { proce verex adj[x][i]; } x i N repreen graph wih array, no li randomized ieraor in N = adj[x].lengh; for(in i = 0; i < N; i++) { exch(adj[x], i, i + (in) Mah.random()*(N-i)); } proce verex adj[x][i]; exchange random verex from adj[x][i..n-1] wih adj[x][i] x x i i N

26 Ue of randomized ieraor urn every graph algorihm ino a randomized algorihm Imporan pracical effec: abilize algorihm performance co depend on problem no i repreenaion Yield well-defined and fundamenal analyic problem Average-cae analyi of algorihm X for graph family Y(N)? Diribuion? Full employmen for algorihm analy

27 (Revied) andard DFS implemenaion graph ADT conrucor code for (in k = 0; k < E; k++) { in v = a[k].v, w = a[k].w; adj[v][deg[v]++] = w; adj[w][deg[w]++] = v; } graph repreenaion verex-indexed array of variablelengh array DFS implemenaion (code o ave pah omied) void findpahr(in, in ) 4 7 { in N = adj[].lengh; if ( == ) reurn; viied() = rue; for(in i = 0; i < N; i++) 7 4 { in v = exch(adj[], i, i+(in) Mah.random()*(N-i)); } } if (!viied[v]) earchr(v, ); void findpah(in, in ) { viied = new boolean[v]; findpahr(, ); }

28 BFS: andard implemenaion Ue a queue o hold fringe verice while Q i nonempy ge x from Q done if x = for each unmarked v adj o x pu v on Q mark v ree verex fringe verex uneen verex void findpah(in, in ) FIFO queue for BFS { Queue Q = new Queue(); Q.pu(); viied[] = rue; while (!Q.empy()) { in x = Q.ge(); in N = adj[x].lengh; if (x == ) reurn; randomized ieraor for (in i = 0; i < N; i++) { in v = exch(adj[x], i, i + (in) Mah.random()*(N-i)); if (!viied[v]) { Q.pu(v); viied[v] = rue; } } } } Generalized graph earch: oher queue yield A* and oher graph-earch algorihm

29 Union-Find implemenaion 1. Run union-find o find componen conaining and iniialize array of ieraor iniialize UF array while and no in ame componen chooe random ieraor chooe random edge for union 2. Build ubgraph wih edge from ha componen 3. Ue DFS o find -pah in ha ubgraph

30 Animaion give inuiion on performance BFS DFS UF and ugge hypohee o verify wih experimenaion

31 Experimenal reul for baic algorihm DFS i ubanially faer han BFS and UF on he average M V E BFS DFS UF UF DFS BFS Analyic proof? Faer algorihm available?

32 A faer algorihm for finding an -pah in a graph Ue wo deph-fir earche one from he ource one from he deinaion inerleave he wo M V E BFS DFS UF wo Examine 13% of he edge 3-8 ime faer han andard implemenaion No loglog E, bu no bad!

33 Are oher approache faer? Oher earch algorihm randomized? farhe-fir? Muliple earche? inerleaving raegy? merge raegy? how many? which algorihm? Hybrid algorihm which combinaion? probabiliic rear? merge raegy? randomized choice? Beer han conan-facor improvemen poible? Proof?

34 Experimen wih oher approache Randomized earch ue random queue in BFS eay o implemen Reul: no much differen from BFS Muliple earcher ue N earcher one from he ource one from he deinaion N-2 from random verice Addiional facor of 2 for N>2 Reul: no much help anyway 1.40 BFS Be mehod found (by far): DFS wih 2 earcher DFS

35 Small-world graph are a widely udied graph model wih many applicaion Small-world graph A mall-world graph ha large number of verice low average verex degree (pare) low average pah lengh local cluering Example: Add random edge o grid graph Add random edge o any pare graph wih local cluering Many cienific model Q. How do we find an -pah in a mall-world graph?

36 Small-world graph model he ix degree of eparaion phenomenon Small-world graph Caligola Parick Allen Dial M for Murder Grace Kelly John Gielguld Glenn Cloe Porrai of a Lady The Sepford Wive Nicole Kidman The Eagle ha Landed To Cach a Thief High Noon Lloyd Bridge Murder on he Orien Expre Cold Mounain Donald Suherland Kahleen Quinlan Joe Veru he Volcano Hamle Enigma Eernal Sunhine of he Spole Mind Vernon Dobcheff Jude Kae Winle An American Hauning The Woodman Wild Thing John Beluhi Meryl Sreep Animal Houe Kevin Bacon The River Wild Tianic Apollo 13 Bill Paxon Paul Herber Yve Auber Tom Hank The Da Vinci Code Shane Zaza Audrey Tauou A iny porion of he movie-performer relaionhip graph Example: Kevin Bacon number

37 Applicaion of mall-world graph ocial nework airline road neurobiology evoluion ocial influence proein ineracion percolaion inerne elecric power grid poliical rend... Example 1: Social nework infeciou dieae exenive imulaion ome analyic reul huge graph Example 2: Proein ineracion mall-world model naural proce experimenal validaion Hamle John Gielguld Enigma Murder on he Orien Expre Eernal Sunhine of he Spole Mind Caligola Vernon Dobcheff Glenn Cloe Porrai of a Lady Jude Kae Winle Cold Mounain An American Hauning Small-world graph The Sepford Wive Nicole Kidman The Woodman Wild Thing John Beluhi Meryl Sreep Parick Allen The Eagle ha Landed Donald Suherland Animal Houe Kevin Bacon The River Wild Tianic Dial M for Murder To Cach a Thief Kahleen Quinlan Apollo 13 Bill Paxon Paul Herber Yve Auber A iny porion of he movie-performer relaionhip graph Grace Kelly The Da Vinci Code High Noon Lloyd Bridge Joe Veru he Volcano Tom Hank Shane Zaza Audrey Tauou

38 Finding a pah in a mall-world graph i a heavily udied problem Small-world graph Milgram experimen (1960) Small-world graph model Random (many varian) Wa-Srogaz Kleinberg add V random horcu o grid graph and oher A* ue ~ log E ep o find a pah How doe 2-way DFS do in hi model? no change a all in graph code ju a differen graph model Experimen: add M ~ E 1/2 random edge o an M-by-M grid graph ue 2-way DFS o find pah Surpriing reul: Find hor pah in ~ E 1/2 ep!

39 Finding a pah in a mall-world graph i much eaier han finding a pah in a grid graph Conjecure: Two-way DFS find a hor -pah in ublinear ime in any mall-world graph Small-world graph Evidence in favor 1. Experimen on many graph 2. Proof kech for grid graph wih V horcu ep 1: 2 E 1/2 ep ~ 2 V 1/2 random verice ep 2: like birhday paradox Pah lengh? Muliple earcher reviied? wo e of 2V 1/2 randomly choen verice are highly unlikely o be dijoin Nex ep: refine model, more experimen, deailed proof

40 More queion han anwer Anwer Randomizaion make co depend on graph, no repreenaion. DFS i faer han BFS or UF for finding pah in grid graph. Two DFS are faer han 1 DFS or N of hem in grid graph. We can find hor pah quickly in mall-world graph Queion Wha are he BFS, UF, and DFS conan in grid graph? I here a ublinear algorihm for grid graph? Which mehod adap o direced graph? Can we preciely analyze and quanify co for mall-world graph? Wha i he co diribuion for DFS for any inereing graph family? How effecive are hee mehod for oher graph familie? Do hee mehod lead o faer maxflow algorihm? How effecive are hee mehod in pracice?...

41 Leon We know much le han you migh hink abou mo of he algorihm ha we ue The cienific mehod i neceary in algorihm deign and ofware developmen

42 The cienific mehod i neceary in algorihm deign and ofware developmen Scienific mehod creae a model decribing naural world ue model o develop hypohee run experimen o validae hypohee refine model and repea model hypohei experimen Algorihm deigner who doe no experimen ge lo in abracion Sofware developer who ignore co rik caarophic conequence

The Role of Science and Mathematics in Software Development

The Role of Science and Mathematics in Software Development The cienific mehod i eenial in applicaion of compuaion A peronal opinion formed on he bai of decade of experience a a The Role of Science and Mahemaic in Sofware Developmen CS educaor auhor algorihm deigner

More information

Chapter 13. Network Flow III Applications. 13.1 Edge disjoint paths. 13.1.1 Edge-disjoint paths in a directed graphs

Chapter 13. Network Flow III Applications. 13.1 Edge disjoint paths. 13.1.1 Edge-disjoint paths in a directed graphs Chaper 13 Nework Flow III Applicaion CS 573: Algorihm, Fall 014 Ocober 9, 014 13.1 Edge dijoin pah 13.1.1 Edge-dijoin pah in a direced graph 13.1.1.1 Edge dijoin pah queiong: graph (dir/undir)., : verice.

More information

2.4 Network flows. Many direct and indirect applications telecommunication transportation (public, freight, railway, air, ) logistics

2.4 Network flows. Many direct and indirect applications telecommunication transportation (public, freight, railway, air, ) logistics .4 Nework flow Problem involving he diribuion of a given produc (e.g., waer, ga, daa, ) from a e of producion locaion o a e of uer o a o opimize a given objecive funcion (e.g., amoun of produc, co,...).

More information

How Much Can Taxes Help Selfish Routing?

How Much Can Taxes Help Selfish Routing? How Much Can Taxe Help Selfih Rouing? Tim Roughgarden (Cornell) Join wih Richard Cole (NYU) and Yevgeniy Dodi (NYU) Selfih Rouing a direced graph G = (V,E) a ource and a deinaion one uni of raffic from

More information

Acceleration Lab Teacher s Guide

Acceleration Lab Teacher s Guide Acceleraion Lab Teacher s Guide Objecives:. Use graphs of disance vs. ime and velociy vs. ime o find acceleraion of a oy car.. Observe he relaionship beween he angle of an inclined plane and he acceleraion

More information

A Comparative Study of Linear and Nonlinear Models for Aggregate Retail Sales Forecasting

A Comparative Study of Linear and Nonlinear Models for Aggregate Retail Sales Forecasting A Comparaive Sudy of Linear and Nonlinear Model for Aggregae Reail Sale Forecaing G. Peer Zhang Deparmen of Managemen Georgia Sae Univeriy Alana GA 30066 (404) 651-4065 Abrac: The purpoe of hi paper i

More information

Chabot College Physics Lab RC Circuits Scott Hildreth

Chabot College Physics Lab RC Circuits Scott Hildreth Chabo College Physics Lab Circuis Sco Hildreh Goals: Coninue o advance your undersanding of circuis, measuring resisances, currens, and volages across muliple componens. Exend your skills in making breadboard

More information

CHARGE AND DISCHARGE OF A CAPACITOR

CHARGE AND DISCHARGE OF A CAPACITOR REFERENCES RC Circuis: Elecrical Insrumens: Mos Inroducory Physics exs (e.g. A. Halliday and Resnick, Physics ; M. Sernheim and J. Kane, General Physics.) This Laboraory Manual: Commonly Used Insrumens:

More information

Rotational Inertia of a Point Mass

Rotational Inertia of a Point Mass Roaional Ineria of a Poin Mass Saddleback College Physics Deparmen, adaped from PASCO Scienific PURPOSE The purpose of his experimen is o find he roaional ineria of a poin experimenally and o verify ha

More information

On the Connection Between Multiple-Unicast Network Coding and Single-Source Single-Sink Network Error Correction

On the Connection Between Multiple-Unicast Network Coding and Single-Source Single-Sink Network Error Correction On he Connecion Beween Muliple-Unica ework Coding and Single-Source Single-Sink ework Error Correcion Jörg Kliewer JIT Join work wih Wenao Huang and Michael Langberg ework Error Correcion Problem: Adverary

More information

The Role of the Scientific Method in Programming. Robert Sedgewick Princeton University

The Role of the Scientific Method in Programming. Robert Sedgewick Princeton University The Role of the Scientific Method in Programming Robert Sedgewick Princeton University The scientific method is essential in applications of computation A personal opinion formed on the basis of decades

More information

Heat demand forecasting for concrete district heating system

Heat demand forecasting for concrete district heating system Hea demand forecaing for concree diric heaing yem Bronilav Chramcov Abrac Thi paper preen he reul of an inveigaion of a model for hor-erm hea demand forecaing. Foreca of hi hea demand coure i ignifican

More information

Fortified financial forecasting models: non-linear searching approaches

Fortified financial forecasting models: non-linear searching approaches 0 Inernaional Conference on Economic and inance Reearch IPEDR vol.4 (0 (0 IACSIT Pre, Singapore orified financial forecaing model: non-linear earching approache Mohammad R. Hamidizadeh, Ph.D. Profeor,

More information

SKF Documented Solutions

SKF Documented Solutions SKF Documened Soluions Real world savings and we can prove i! How much can SKF save you? Le s do he numbers. The SKF Documened Soluions Program SKF is probably no he firs of your supplier parners o alk

More information

How has globalisation affected inflation dynamics in the United Kingdom?

How has globalisation affected inflation dynamics in the United Kingdom? 292 Quarerly Bullein 2008 Q3 How ha globaliaion affeced inflaion dynamic in he Unied Kingdom? By Jennifer Greenlade and Sephen Millard of he Bank Srucural Economic Analyi Diviion and Chri Peacock of he

More information

Issues Using OLS with Time Series Data. Time series data NOT randomly sampled in same way as cross sectional each obs not i.i.d

Issues Using OLS with Time Series Data. Time series data NOT randomly sampled in same way as cross sectional each obs not i.i.d These noes largely concern auocorrelaion Issues Using OLS wih Time Series Daa Recall main poins from Chaper 10: Time series daa NOT randomly sampled in same way as cross secional each obs no i.i.d Why?

More information

The Application of Multi Shifts and Break Windows in Employees Scheduling

The Application of Multi Shifts and Break Windows in Employees Scheduling The Applicaion of Muli Shifs and Brea Windows in Employees Scheduling Evy Herowai Indusrial Engineering Deparmen, Universiy of Surabaya, Indonesia Absrac. One mehod for increasing company s performance

More information

17 Laplace transform. Solving linear ODE with piecewise continuous right hand sides

17 Laplace transform. Solving linear ODE with piecewise continuous right hand sides 7 Laplace ransform. Solving linear ODE wih piecewise coninuous righ hand sides In his lecure I will show how o apply he Laplace ransform o he ODE Ly = f wih piecewise coninuous f. Definiion. A funcion

More information

The Chase Problem (Part 2) David C. Arney

The Chase Problem (Part 2) David C. Arney The Chae Problem Par David C. Arne Inroducion In he previou ecion, eniled The Chae Problem Par, we dicued a dicree model for a chaing cenario where one hing chae anoher. Some of he applicaion of hi kind

More information

Chapter 2 Kinematics in One Dimension

Chapter 2 Kinematics in One Dimension Chaper Kinemaics in One Dimension Chaper DESCRIBING MOTION:KINEMATICS IN ONE DIMENSION PREVIEW Kinemaics is he sudy of how hings moe how far (disance and displacemen), how fas (speed and elociy), and how

More information

Making a Faster Cryptanalytic Time-Memory Trade-Off

Making a Faster Cryptanalytic Time-Memory Trade-Off Making a Faser Crypanalyic Time-Memory Trade-Off Philippe Oechslin Laboraoire de Securié e de Crypographie (LASEC) Ecole Polyechnique Fédérale de Lausanne Faculé I&C, 1015 Lausanne, Swizerland philippe.oechslin@epfl.ch

More information

Performance Center Overview. Performance Center Overview 1

Performance Center Overview. Performance Center Overview 1 Performance Cener Overview Performance Cener Overview 1 ODJFS Performance Cener ce Cener New Performance Cener Model Performance Cener Projec Meeings Performance Cener Execuive Meeings Performance Cener

More information

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees

More information

Chapter 8: Regression with Lagged Explanatory Variables

Chapter 8: Regression with Lagged Explanatory Variables Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One

More information

The Grantor Retained Annuity Trust (GRAT)

The Grantor Retained Annuity Trust (GRAT) WEALTH ADVISORY Esae Planning Sraegies for closely-held, family businesses The Granor Reained Annuiy Trus (GRAT) An efficien wealh ransfer sraegy, paricularly in a low ineres rae environmen Family business

More information

Process Modeling for Object Oriented Analysis using BORM Object Behavioral Analysis.

Process Modeling for Object Oriented Analysis using BORM Object Behavioral Analysis. Proce Modeling for Objec Oriened Analyi uing BORM Objec Behavioral Analyi. Roger P. Kno Ph.D., Compuer Science Dep, Loughborough Univeriy, U.K. r.p.kno@lboro.ac.uk 9RMW FKMerunka Ph.D., Dep. of Informaion

More information

Morningstar Investor Return

Morningstar Investor Return Morningsar Invesor Reurn Morningsar Mehodology Paper Augus 31, 2010 2010 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion

More information

Analogue and Digital Signal Processing. First Term Third Year CS Engineering By Dr Mukhtiar Ali Unar

Analogue and Digital Signal Processing. First Term Third Year CS Engineering By Dr Mukhtiar Ali Unar Analogue and Digial Signal Processing Firs Term Third Year CS Engineering By Dr Mukhiar Ali Unar Recommended Books Haykin S. and Van Veen B.; Signals and Sysems, John Wiley& Sons Inc. ISBN: 0-7-380-7 Ifeachor

More information

Calculation of variable annuity market sensitivities using a pathwise methodology

Calculation of variable annuity market sensitivities using a pathwise methodology cuing edge Variable annuiie Calculaion of variable annuiy marke eniiviie uing a pahwie mehodology Under radiional finie difference mehod, he calculaion of variable annuiy eniiviie can involve muliple Mone

More information

Capacity Planning and Performance Benchmark Reference Guide v. 1.8

Capacity Planning and Performance Benchmark Reference Guide v. 1.8 Environmenal Sysems Research Insiue, Inc., 380 New York S., Redlands, CA 92373-8100 USA TEL 909-793-2853 FAX 909-307-3014 Capaciy Planning and Performance Benchmark Reference Guide v. 1.8 Prepared by:

More information

µ r of the ferrite amounts to 1000...4000. It should be noted that the magnetic length of the + δ

µ r of the ferrite amounts to 1000...4000. It should be noted that the magnetic length of the + δ Page 9 Design of Inducors and High Frequency Transformers Inducors sore energy, ransformers ransfer energy. This is he prime difference. The magneic cores are significanly differen for inducors and high

More information

Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613.

Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613. Graduae School of Business Adminisraion Universiy of Virginia UVA-F-38 Duraion and Convexiy he price of a bond is a funcion of he promised paymens and he marke required rae of reurn. Since he promised

More information

cooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)

cooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins) Alligaor egg wih calculus We have a large alligaor egg jus ou of he fridge (1 ) which we need o hea o 9. Now here are wo accepable mehods for heaing alligaor eggs, one is o immerse hem in boiling waer

More information

Optimal Investment and Consumption Decision of Family with Life Insurance

Optimal Investment and Consumption Decision of Family with Life Insurance Opimal Invesmen and Consumpion Decision of Family wih Life Insurance Minsuk Kwak 1 2 Yong Hyun Shin 3 U Jin Choi 4 6h World Congress of he Bachelier Finance Sociey Torono, Canada June 25, 2010 1 Speaker

More information

Automatic measurement and detection of GSM interferences

Automatic measurement and detection of GSM interferences Auomaic measuremen and deecion of GSM inerferences Poor speech qualiy and dropped calls in GSM neworks may be caused by inerferences as a resul of high raffic load. The radio nework analyzers from Rohde

More information

AP Calculus BC 2010 Scoring Guidelines

AP Calculus BC 2010 Scoring Guidelines AP Calculus BC Scoring Guidelines The College Board The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in, he College Board

More information

Chapter 7. Response of First-Order RL and RC Circuits

Chapter 7. Response of First-Order RL and RC Circuits Chaper 7. esponse of Firs-Order L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural

More information

Principal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya.

Principal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya. Principal componens of sock marke dynamics Mehodology and applicaions in brief o be updaed Andrei Bouzaev, bouzaev@ya.ru Why principal componens are needed Objecives undersand he evidence of more han one

More information

The Transport Equation

The Transport Equation The Transpor Equaion Consider a fluid, flowing wih velociy, V, in a hin sraigh ube whose cross secion will be denoed by A. Suppose he fluid conains a conaminan whose concenraion a posiion a ime will be

More information

CHAPTER 11 NONPARAMETRIC REGRESSION WITH COMPLEX SURVEY DATA. R. L. Chambers Department of Social Statistics University of Southampton

CHAPTER 11 NONPARAMETRIC REGRESSION WITH COMPLEX SURVEY DATA. R. L. Chambers Department of Social Statistics University of Southampton CHAPTER 11 NONPARAMETRIC REGRESSION WITH COMPLEX SURVEY DATA R. L. Chamber Deparmen of Social Saiic Univeriy of Souhampon A.H. Dorfman Office of Survey Mehod Reearch Bureau of Labor Saiic M.Yu. Sverchkov

More information

RC, RL and RLC circuits

RC, RL and RLC circuits Name Dae Time o Complee h m Parner Course/ Secion / Grade RC, RL and RLC circuis Inroducion In his experimen we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors.

More information

Equity Valuation Using Multiples. Jing Liu. Anderson Graduate School of Management. University of California at Los Angeles (310) 206-5861

Equity Valuation Using Multiples. Jing Liu. Anderson Graduate School of Management. University of California at Los Angeles (310) 206-5861 Equiy Valuaion Uing Muliple Jing Liu Anderon Graduae School of Managemen Univeriy of California a Lo Angele (310) 206-5861 jing.liu@anderon.ucla.edu Doron Niim Columbia Univeriy Graduae School of Buine

More information

Information Systems for Business Integration: ERP Systems

Information Systems for Business Integration: ERP Systems Informaion Sysems for Business Inegraion: ERP Sysems (December 3, 2012) BUS3500 - Abdou Illia, Fall 2012 1 LEARNING GOALS Explain he difference beween horizonal and verical business inegraion. Describe

More information

Physical Topology Discovery for Large Multi-Subnet Networks

Physical Topology Discovery for Large Multi-Subnet Networks Phyical Topology Dicovery for Large Muli-Subne Nework Yigal Bejerano, Yuri Breibar, Mino Garofalaki, Rajeev Raogi Bell Lab, Lucen Technologie 600 Mounain Ave., Murray Hill, NJ 07974. {bej,mino,raogi}@reearch.bell-lab.com

More information

Top-K Structural Diversity Search in Large Networks

Top-K Structural Diversity Search in Large Networks Top-K Srucural Diversiy Search in Large Neworks Xin Huang, Hong Cheng, Rong-Hua Li, Lu Qin, Jeffrey Xu Yu The Chinese Universiy of Hong Kong Guangdong Province Key Laboraory of Popular High Performance

More information

Explore the Application of Financial Engineering in the Management of Exchange Rate Risk

Explore the Application of Financial Engineering in the Management of Exchange Rate Risk SHS Web o Conerence 17, 01006 (015) DOI: 10.1051/ hcon/01517 01006 C Owned by he auhor, publihed by EDP Science, 015 Explore he Applicaion o Financial Engineering in he Managemen o Exchange Rae Rik Liu

More information

Max Flow, Min Cut. Maximum Flow and Minimum Cut. Soviet Rail Network, 1955. Minimum Cut Problem

Max Flow, Min Cut. Maximum Flow and Minimum Cut. Soviet Rail Network, 1955. Minimum Cut Problem Maximum Flow and Minimum u Max Flow, Min u Max flow and min cu. Two very rich algorihmic problem. ornerone problem in combinaorial opimizaion. eauiful mahemaical dualiy. Minimum cu Maximum flow Max-flow

More information

Two-Group Designs Independent samples t-test & paired samples t-test. Chapter 10

Two-Group Designs Independent samples t-test & paired samples t-test. Chapter 10 Two-Group Deign Independen ample -e & paired ample -e Chaper 0 Previou e (Ch 7 and 8) Z-e z M N -e (one-ample) M N M = andard error of he mean p. 98-9 Remember: = variance M = eimaed andard error p. -

More information

Three Dimensional Grounding Grid Design

Three Dimensional Grounding Grid Design Three Dimenional Grounding Grid Deign Fikri Bari Uzunlar 1, Özcan Kalenderli 2 1 Schneider Elecric Turkey, Ianbul, Turkey bari.uzunlar@r.chneider-elecric.com 2 Ianbul Technical Univeriy, Elecrical-Elecronic

More information

Optimal Path Routing in Single and Multiple Clock Domain Systems

Optimal Path Routing in Single and Multiple Clock Domain Systems IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN, TO APPEAR. 1 Opimal Pah Rouing in Single and Muliple Clock Domain Syem Soha Haoun, Senior Member, IEEE, Charle J. Alper, Senior Member, IEEE ) Abrac Shrinking

More information

Table of contents Chapter 1 Interest rates and factors Chapter 2 Level annuities Chapter 3 Varying annuities

Table of contents Chapter 1 Interest rates and factors Chapter 2 Level annuities Chapter 3 Varying annuities Table of conens Chaper 1 Ineres raes and facors 1 1.1 Ineres 2 1.2 Simple ineres 4 1.3 Compound ineres 6 1.4 Accumulaed value 10 1.5 Presen value 11 1.6 Rae of discoun 13 1.7 Consan force of ineres 17

More information

Appendix A: Area. 1 Find the radius of a circle that has circumference 12 inches.

Appendix A: Area. 1 Find the radius of a circle that has circumference 12 inches. Appendi A: Area worked-ou s o Odd-Numbered Eercises Do no read hese worked-ou s before aemping o do he eercises ourself. Oherwise ou ma mimic he echniques shown here wihou undersanding he ideas. Bes wa

More information

Strategic Optimization of a Transportation Distribution Network

Strategic Optimization of a Transportation Distribution Network Sraegic Opimizaion of a Transporaion Disribuion Nework K. John Sophabmixay, Sco J. Mason, Manuel D. Rossei Deparmen of Indusrial Engineering Universiy of Arkansas 4207 Bell Engineering Cener Fayeeville,

More information

An approach for designing a surface pencil through a given geodesic curve

An approach for designing a surface pencil through a given geodesic curve An approach for deigning a urface pencil hrough a given geodeic curve Gülnur SAFFAK ATALAY, Fama GÜLER, Ergin BAYRAM *, Emin KASAP Ondokuz Mayı Univeriy, Faculy of Ar and Science, Mahemaic Deparmen gulnur.affak@omu.edu.r,

More information

Task is a schedulable entity, i.e., a thread

Task is a schedulable entity, i.e., a thread Real-Time Scheduling Sysem Model Task is a schedulable eniy, i.e., a hread Time consrains of periodic ask T: - s: saring poin - e: processing ime of T - d: deadline of T - p: period of T Periodic ask T

More information

Empirical heuristics for improving Intermittent Demand Forecasting

Empirical heuristics for improving Intermittent Demand Forecasting Empirical heuriic for improving Inermien Demand Forecaing Foio Peropoulo 1,*, Konanino Nikolopoulo 2, Georgio P. Spihouraki 1, Vailio Aimakopoulo 1 1 Forecaing & Sraegy Uni, School of Elecrical and Compuer

More information

Vector Autoregressions (VARs): Operational Perspectives

Vector Autoregressions (VARs): Operational Perspectives Vecor Auoregressions (VARs): Operaional Perspecives Primary Source: Sock, James H., and Mark W. Wason, Vecor Auoregressions, Journal of Economic Perspecives, Vol. 15 No. 4 (Fall 2001), 101-115. Macroeconomericians

More information

Section 7.1 Angles and Their Measure

Section 7.1 Angles and Their Measure Secion 7.1 Angles and Their Measure Greek Leers Commonly Used in Trigonomery Quadran II Quadran III Quadran I Quadran IV α = alpha β = bea θ = hea δ = dela ω = omega γ = gamma DEGREES The angle formed

More information

Measuring macroeconomic volatility Applications to export revenue data, 1970-2005

Measuring macroeconomic volatility Applications to export revenue data, 1970-2005 FONDATION POUR LES ETUDES ET RERS LE DEVELOPPEMENT INTERNATIONAL Measuring macroeconomic volailiy Applicaions o expor revenue daa, 1970-005 by Joël Cariolle Policy brief no. 47 March 01 The FERDI is a

More information

Improvement of a TCP Incast Avoidance Method for Data Center Networks

Improvement of a TCP Incast Avoidance Method for Data Center Networks Improvemen of a Incas Avoidance Mehod for Daa Cener Neworks Kazuoshi Kajia, Shigeyuki Osada, Yukinobu Fukushima and Tokumi Yokohira The Graduae School of Naural Science and Technology, Okayama Universiy

More information

TSG-RAN Working Group 1 (Radio Layer 1) meeting #3 Nynashamn, Sweden 22 nd 26 th March 1999

TSG-RAN Working Group 1 (Radio Layer 1) meeting #3 Nynashamn, Sweden 22 nd 26 th March 1999 TSG-RAN Working Group 1 (Radio Layer 1) meeing #3 Nynashamn, Sweden 22 nd 26 h March 1999 RAN TSGW1#3(99)196 Agenda Iem: 9.1 Source: Tile: Documen for: Moorola Macro-diversiy for he PRACH Discussion/Decision

More information

Appendix D Flexibility Factor/Margin of Choice Desktop Research

Appendix D Flexibility Factor/Margin of Choice Desktop Research Appendix D Flexibiliy Facor/Margin of Choice Deskop Research Cheshire Eas Council Cheshire Eas Employmen Land Review Conens D1 Flexibiliy Facor/Margin of Choice Deskop Research 2 Final Ocober 2012 \\GLOBAL.ARUP.COM\EUROPE\MANCHESTER\JOBS\200000\223489-00\4

More information

Part 1: White Noise and Moving Average Models

Part 1: White Noise and Moving Average Models Chaper 3: Forecasing From Time Series Models Par 1: Whie Noise and Moving Average Models Saionariy In his chaper, we sudy models for saionary ime series. A ime series is saionary if is underlying saisical

More information

Journal Of Business & Economics Research September 2005 Volume 3, Number 9

Journal Of Business & Economics Research September 2005 Volume 3, Number 9 Opion Pricing And Mone Carlo Simulaions George M. Jabbour, (Email: jabbour@gwu.edu), George Washingon Universiy Yi-Kang Liu, (yikang@gwu.edu), George Washingon Universiy ABSTRACT The advanage of Mone Carlo

More information

Capacitors and inductors

Capacitors and inductors Capaciors and inducors We coninue wih our analysis of linear circuis by inroducing wo new passive and linear elemens: he capacior and he inducor. All he mehods developed so far for he analysis of linear

More information

SELF-EVALUATION FOR VIDEO TRACKING SYSTEMS

SELF-EVALUATION FOR VIDEO TRACKING SYSTEMS SELF-EVALUATION FOR VIDEO TRACKING SYSTEMS Hao Wu and Qinfen Zheng Cenre for Auomaion Research Dep. of Elecrical and Compuer Engineering Universiy of Maryland, College Park, MD-20742 {wh2003, qinfen}@cfar.umd.edu

More information

Caring for trees and your service

Caring for trees and your service Caring for rees and your service Line clearing helps preven ouages FPL is commied o delivering safe, reliable elecric service o our cusomers. Trees, especially palm rees, can inerfere wih power lines and

More information

5.8 Resonance 231. The study of vibrating mechanical systems ends here with the theory of pure and practical resonance.

5.8 Resonance 231. The study of vibrating mechanical systems ends here with the theory of pure and practical resonance. 5.8 Resonance 231 5.8 Resonance The sudy of vibraing mechanical sysems ends here wih he heory of pure and pracical resonance. Pure Resonance The noion of pure resonance in he differenial equaion (1) ()

More information

The Greek financial crisis: growing imbalances and sovereign spreads. Heather D. Gibson, Stephan G. Hall and George S. Tavlas

The Greek financial crisis: growing imbalances and sovereign spreads. Heather D. Gibson, Stephan G. Hall and George S. Tavlas The Greek financial crisis: growing imbalances and sovereign spreads Heaher D. Gibson, Sephan G. Hall and George S. Tavlas The enry The enry of Greece ino he Eurozone in 2001 produced a dividend in he

More information

Multiprocessor Systems-on-Chips

Multiprocessor Systems-on-Chips Par of: Muliprocessor Sysems-on-Chips Edied by: Ahmed Amine Jerraya and Wayne Wolf Morgan Kaufmann Publishers, 2005 2 Modeling Shared Resources Conex swiching implies overhead. On a processing elemen,

More information

INTRODUCTION TO EMAIL MARKETING PERSONALIZATION. How to increase your sales with personalized triggered emails

INTRODUCTION TO EMAIL MARKETING PERSONALIZATION. How to increase your sales with personalized triggered emails INTRODUCTION TO EMAIL MARKETING PERSONALIZATION How o increase your sales wih personalized riggered emails ECOMMERCE TRIGGERED EMAILS BEST PRACTICES Triggered emails are generaed in real ime based on each

More information

9. Capacitor and Resistor Circuits

9. Capacitor and Resistor Circuits ElecronicsLab9.nb 1 9. Capacior and Resisor Circuis Inroducion hus far we have consider resisors in various combinaions wih a power supply or baery which provide a consan volage source or direc curren

More information

11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements

11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements Inroducion Chaper 14: Dynamic D-S dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuing-edge

More information

4 Convolution. Recommended Problems. x2[n] 1 2[n]

4 Convolution. Recommended Problems. x2[n] 1 2[n] 4 Convoluion Recommended Problems P4.1 This problem is a simple example of he use of superposiion. Suppose ha a discree-ime linear sysem has oupus y[n] for he given inpus x[n] as shown in Figure P4.1-1.

More information

Stability. Coefficients may change over time. Evolution of the economy Policy changes

Stability. Coefficients may change over time. Evolution of the economy Policy changes Sabiliy Coefficiens may change over ime Evoluion of he economy Policy changes Time Varying Parameers y = α + x β + Coefficiens depend on he ime period If he coefficiens vary randomly and are unpredicable,

More information

Robust Bandwidth Allocation Strategies

Robust Bandwidth Allocation Strategies Robu Bandwidh Allocaion Sraegie Oliver Heckmann, Jen Schmi, Ralf Seinmez Mulimedia Communicaion Lab (KOM), Darmad Univeriy of Technology Merckr. 25 D-64283 Darmad Germany {Heckmann, Schmi, Seinmez}@kom.u-darmad.de

More information

AP Calculus AB 2010 Scoring Guidelines

AP Calculus AB 2010 Scoring Guidelines AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in 1, he College

More information

Information Theoretic Evaluation of Change Prediction Models for Large-Scale Software

Information Theoretic Evaluation of Change Prediction Models for Large-Scale Software Informaion Theoreic Evaluaion of Change Predicion Models for Large-Scale Sofware Mina Askari School of Compuer Science Universiy of Waerloo Waerloo, Canada maskari@uwaerloo.ca Ric Hol School of Compuer

More information

Differential Equations and Linear Superposition

Differential Equations and Linear Superposition Differenial Equaions and Linear Superposiion Basic Idea: Provide soluion in closed form Like Inegraion, no general soluions in closed form Order of equaion: highes derivaive in equaion e.g. dy d dy 2 y

More information

Model-Based Monitoring in Large-Scale Distributed Systems

Model-Based Monitoring in Large-Scale Distributed Systems Model-Based Monioring in Large-Scale Disribued Sysems Diploma Thesis Carsen Reimann Chemniz Universiy of Technology Faculy of Compuer Science Operaing Sysem Group Advisors: Prof. Dr. Winfried Kalfa Dr.

More information

Capital Budgeting and Initial Cash Outlay (ICO) Uncertainty

Capital Budgeting and Initial Cash Outlay (ICO) Uncertainty Financial Decisions, Summer 006, Aricle Capial Budgeing and Iniial Cash Oulay (ICO) Uncerainy Michael C. Ehrhard and John M. Wachowicz, Jr. * * The Paul and Beverly Casagna Professor of Finance and Professor

More information

Topic Overview. Learning Objectives. Capital Budgeting Steps: WHAT IS CAPITAL BUDGETING?

Topic Overview. Learning Objectives. Capital Budgeting Steps: WHAT IS CAPITAL BUDGETING? Chaper 10: THE BASICS OF CAPITAL BUDGETING Should we build his plan? Topic Overview Projec Types Capial Budgeing Decision Crieria Payback Period Discouned Payback Period Ne Presen Value () Inernal Rae

More information

The Real Business Cycle paradigm. The RBC model emphasizes supply (technology) disturbances as the main source of

The Real Business Cycle paradigm. The RBC model emphasizes supply (technology) disturbances as the main source of Prof. Harris Dellas Advanced Macroeconomics Winer 2001/01 The Real Business Cycle paradigm The RBC model emphasizes supply (echnology) disurbances as he main source of macroeconomic flucuaions in a world

More information

Q-SAC: Toward QoS Optimized Service Automatic Composition *

Q-SAC: Toward QoS Optimized Service Automatic Composition * Q-SAC: Toward QoS Opimized Service Auomaic Composiion * Hanhua Chen, Hai Jin, Xiaoming Ning, Zhipeng Lü Cluser and Grid Compuing Lab Huazhong Universiy of Science and Technology, Wuhan, 4374, China Email:

More information

Subsistence Consumption and Rising Saving Rate

Subsistence Consumption and Rising Saving Rate Subience Conumpion and Riing Saving Rae Kenneh S. Lin a, Hiu-Yun Lee b * a Deparmen of Economic, Naional Taiwan Univeriy, Taipei, 00, Taiwan. b Deparmen of Economic, Naional Chung Cheng Univeriy, Chia-Yi,

More information

1.2 Goals for Animation Control

1.2 Goals for Animation Control A Direc Manipulaion Inerface for 3D Compuer Animaion Sco Sona Snibbe y Brown Universiy Deparmen of Compuer Science Providence, RI 02912, USA Absrac We presen a new se of inerface echniques for visualizing

More information

Single-machine Scheduling with Periodic Maintenance and both Preemptive and. Non-preemptive jobs in Remanufacturing System 1

Single-machine Scheduling with Periodic Maintenance and both Preemptive and. Non-preemptive jobs in Remanufacturing System 1 Absrac number: 05-0407 Single-machine Scheduling wih Periodic Mainenance and boh Preempive and Non-preempive jobs in Remanufacuring Sysem Liu Biyu hen Weida (School of Economics and Managemen Souheas Universiy

More information

Usefulness of the Forward Curve in Forecasting Oil Prices

Usefulness of the Forward Curve in Forecasting Oil Prices Usefulness of he Forward Curve in Forecasing Oil Prices Akira Yanagisawa Leader Energy Demand, Supply and Forecas Analysis Group The Energy Daa and Modelling Cener Summary When people analyse oil prices,

More information

The Time Value of Money

The Time Value of Money THE TIME VALUE OF MONEY CALCULATING PRESENT AND FUTURE VALUES Fuure Value: FV = PV 0 ( + r) Presen Value: PV 0 = FV ------------------------------- ( + r) THE EFFECTS OF COMPOUNDING The effecs/benefis

More information

A Component-Based Navigation-Guidance-Control Architecture for Mobile Robots

A Component-Based Navigation-Guidance-Control Architecture for Mobile Robots A Componen-Based Navigaion-Guidance-Conrol Archiecure for Mobile Robos Nicolas Gobillo Charles Lesire David Doose Onera - The French Aerospace Lab, Toulouse, France firsname.lasname a onera.fr Absrac In

More information

1 HALF-LIFE EQUATIONS

1 HALF-LIFE EQUATIONS R.L. Hanna Page HALF-LIFE EQUATIONS The basic equaion ; he saring poin ; : wrien for ime: x / where fracion of original maerial and / number of half-lives, and / log / o calculae he age (# ears): age (half-life)

More information

Statistical Analysis with Little s Law. Supplementary Material: More on the Call Center Data. by Song-Hee Kim and Ward Whitt

Statistical Analysis with Little s Law. Supplementary Material: More on the Call Center Data. by Song-Hee Kim and Ward Whitt Saisical Analysis wih Lile s Law Supplemenary Maerial: More on he Call Cener Daa by Song-Hee Kim and Ward Whi Deparmen of Indusrial Engineering and Operaions Research Columbia Universiy, New York, NY 17-99

More information

GoRA. For more information on genetics and on Rheumatoid Arthritis: Genetics of Rheumatoid Arthritis. Published work referred to in the results:

GoRA. For more information on genetics and on Rheumatoid Arthritis: Genetics of Rheumatoid Arthritis. Published work referred to in the results: For more informaion on geneics and on Rheumaoid Arhriis: Published work referred o in he resuls: The geneics revoluion and he assaul on rheumaoid arhriis. A review by Michael Seldin, Crisopher Amos, Ryk

More information

Double Entry System of Accounting

Double Entry System of Accounting CHAPTER 2 Double Enry Sysem of Accouning Sysem of Accouning \ The following are he main sysem of accouning for recording he business ransacions: (a) Cash Sysem of Accouning. (b) Mercanile or Accrual Sysem

More information

Torsion of Closed Thin Wall (CTW) Sections

Torsion of Closed Thin Wall (CTW) Sections 9 orsion of losed hin Wall (W) Secions 9 1 Lecure 9: ORSION OF LOSED HIN WALL (W) SEIONS ALE OF ONENS Page 9.1 Inroducion..................... 9 3 9.2 losed W Secions.................. 9 3 9.3 Examples......................

More information

Working Paper No. 482. Net Intergenerational Transfers from an Increase in Social Security Benefits

Working Paper No. 482. Net Intergenerational Transfers from an Increase in Social Security Benefits Working Paper No. 482 Ne Inergeneraional Transfers from an Increase in Social Securiy Benefis By Li Gan Texas A&M and NBER Guan Gong Shanghai Universiy of Finance and Economics Michael Hurd RAND Corporaion

More information

Present Value Methodology

Present Value Methodology Presen Value Mehodology Econ 422 Invesmen, Capial & Finance Universiy of Washingon Eric Zivo Las updaed: April 11, 2010 Presen Value Concep Wealh in Fisher Model: W = Y 0 + Y 1 /(1+r) The consumer/producer

More information

Cross-sectional and longitudinal weighting in a rotational household panel: applications to EU-SILC. Vijay Verma, Gianni Betti, Giulio Ghellini

Cross-sectional and longitudinal weighting in a rotational household panel: applications to EU-SILC. Vijay Verma, Gianni Betti, Giulio Ghellini Cro-ecional and longiudinal eighing in a roaional houehold panel: applicaion o EU-SILC Viay Verma, Gianni Bei, Giulio Ghellini Working Paper n. 67, December 006 CROSS-SECTIONAL AND LONGITUDINAL WEIGHTING

More information

OPTIMAL BATCH QUANTITY MODELS FOR A LEAN PRODUCTION SYSTEM WITH REWORK AND SCRAP. A Thesis

OPTIMAL BATCH QUANTITY MODELS FOR A LEAN PRODUCTION SYSTEM WITH REWORK AND SCRAP. A Thesis OTIMAL BATH UANTITY MOELS FOR A LEAN ROUTION SYSTEM WITH REWORK AN SRA A Thei Submied o he Graduae Faculy of he Louiiana Sae Univeriy and Agriculural and Mechanical ollege in parial fulfillmen of he requiremen

More information

A Natural Feature-Based 3D Object Tracking Method for Wearable Augmented Reality

A Natural Feature-Based 3D Object Tracking Method for Wearable Augmented Reality A Naural Feaure-Based 3D Objec Tracking Mehod for Wearable Augmened Realiy Takashi Okuma Columbia Universiy / AIST Email: okuma@cs.columbia.edu Takeshi Kuraa Universiy of Washingon / AIST Email: kuraa@ieee.org

More information