How Much Can Taxes Help Selfish Routing?


 Barbara Manning
 1 years ago
 Views:
Transcription
1 How Much Can Taxe Help Selfih Rouing? Tim Roughgarden (Cornell) Join wih Richard Cole (NYU) and Yevgeniy Dodi (NYU)
2 Selfih Rouing a direced graph G = (V,E) a ource and a deinaion one uni of raffic from o for each edge e, a laency funcion l e ( ) aumed coninuou, nondecreaing Example: l(x)=x Flow = ½ l(x)=1 Flow = ½ 2
3 Rouing of Traffic Traffic and Flow: f P = fracion of raffic roued on  pah P flow vecor f rouing of raffic Selfih rouing: wha flow arie a he roue choen by many noncooperaive agen? 3
4 Nah Flow Some aumpion: agen mall relaive o nework wan o minimize peronal laency Def: A flow i a Nah equilibrium (or i a Nah flow) if all flow i roued on minlaency pah [given curren edge congeion] have exience, uniquene [Wardrop, Beckmann e al 50] Example: x 1 Flow =.5 Flow =.5 x 1 Flow = 1 Flow = 0 4
5 Inefficiency of Nah Flow Our objecive funcion: average laency Nah flow need no be opimal oberved informally by [Pigou 1920] x 1 ½ 0 1 ½ Average laency of Nah flow = = 1 of opimal flow = ½ ½ +½ 1 = ¾ 5
6 Brae Paradox Iniial Nework: ½ ½ x 1 ½ ½ 1 x Delay = 1.5 6
7 Brae Paradox Iniial Nework: Augmened Nework: ½ ½ x 1 ½ ½ 1 x ½ ½ x 1 ½ 0 ½ 1 x Delay = 1.5 Now wha? 7
8 Brae Paradox Iniial Nework: Augmened Nework: ½ ½ x 1 ½ ½ 1 x x x Delay = 1.5 Delay = 2 All raffic incur more delay! [Brae 68] 8
9 Marginal Co Taxe Goal: do beer wih axe (one per edge) no addreing implemenaion 9
10 Marginal Co Taxe Goal: do beer wih axe (one per edge) no addreing implemenaion Aume: all raffic minimize ime + money ee STOC 03 paper for relaxing hi Def: he marginal co ax of an edge (w.r.. a flow) i he exra delay o exiing raffic caued by a marginal increae in raffic 10
11 Marginal Co Taxe Goal: do beer wih axe (one per edge) no addreing implemenaion Aume: all raffic minimize ime + money ee STOC 03 paper for relaxing hi Def: he marginal co ax of an edge (w.r.. a flow) i he exra delay o exiing raffic caued by a marginal increae in raffic Thm: [folklore] marginal co axe w.r.. he op flow induce he op flow a a Nah eq. 11
12 Are Taxe a Social Lo? Problem wih MCT: min delay i holy grail; exorbian axe ignored 12
13 Are Taxe a Social Lo? Problem wih MCT: min delay i holy grail; exorbian axe ignored Ever reaonable?: ye, iff axe can be refunded (direcly or indirecly) 13
14 Are Taxe a Social Lo? Problem wih MCT: min delay i holy grail; exorbian axe ignored Ever reaonable?: ye, iff axe can be refunded (direcly or indirecly) New Goal: minimize oal diuiliy wih nonrefundable axe (delay + axe paid) call new objecive fn he co marginal co axe now no a good idea, e.g.: Thm: w/linear laency fn, MCT never help. 14
15 Taxe v. Edge Removal Noe: axe a lea a good a edge removal can effec edge deleion wih large ax are hey ricly more powerful? 15
16 Taxe v. Edge Removal Noe: axe a lea a good a edge removal can effec edge deleion wih large ax are hey ricly more powerful? Thm: axe can improve co by a facor of n/2 (n = V ), bu no more. ame for edge removal [Roughgarden FOCS 01] alo ame a edge removal for rericed clae of laency fn 16
17 Taxe v. Edge Removal Queion: axe no beer han edge removal in be cae, how abou in pecific nework? 17
18 Taxe v. Edge Removal Queion: axe no beer han edge removal in be cae, how abou in pecific nework? Thm: (a) axe can improve he Nah flow co by an n/2 facor more han edge removal ue ep funcionlike laency fn variaion of Brae graph from [Roughgarden FOCS 01] (b) axe are never more powerful han edge removal in nework w/linear laency fn 18
19 Taxe v. Edge Removal General Laency Fn n/2 Nah co afer axe Linear Laency Fn 0 Nah co afer axe Nah co afer edge removal n/2 Nah co afer edge removal 4/3 n/2 4/3 original Nah co original Nah co 19
20 Proof Skech for Linear Cae Fir: aume fale, look a minimal counerexample. Look a counerexample ax on hi nework ha minimize co and ha malle um. Technical Lemma: hi minimum exi (ue minimaliy). Underand how Nah flow change under local perurbaion of he ax (minimaliy, lineariy). Perurbing o a maller ax mu increae co. Oppoie perurbaion lower co (conradicion). 20
21 Taxe Are Powerful bu Eluive Recall: axe can improve co by a facor of n/2 (n = V ), bu no more. powerful, bu can we compue hem? Thm: opimal axe NPhard o approximae wihin facor of o(n/log n). complexiy ca doub on poenial for axe ha minimize co baed on [Roughgarden FOCS 01] 21
22 Some Fuure Direcion Improve model convergence iue, imperfec info oher noion of incenivecompaibiliy e.g., robu o maliciou uer oher objecive fn Beer reul in hi model mulicommodiy flow nework 22
Chapter 13. Network Flow III Applications. 13.1 Edge disjoint paths. 13.1.1 Edgedisjoint 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 Edgedijoin pah in a direced graph 13.1.1.1 Edge dijoin pah queiong: graph (dir/undir)., : verice.
More information2.4 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 informationOn the Connection Between MultipleUnicast Network Coding and SingleSource SingleSink Network Error Correction
On he Connecion Beween MulipleUnica ework Coding and SingleSource SingleSink ework Error Correcion Jörg Kliewer JIT Join work wih Wenao Huang and Michael Langberg ework Error Correcion Problem: Adverary
More informationEconomics Honors Exam 2008 Solutions Question 5
Economics Honors Exam 2008 Soluions Quesion 5 (a) (2 poins) Oupu can be decomposed as Y = C + I + G. And we can solve for i by subsiuing in equaions given in he quesion, Y = C + I + G = c 0 + c Y D + I
More information6.003 Homework #4 Solutions
6.3 Homewk #4 Soluion Problem. Laplace Tranfm Deermine he Laplace ranfm (including he region of convergence) of each of he following ignal: a. x () = e 2(3) u( 3) X = e 3 2 ROC: Re() > 2 X () = x ()e d
More informationOptimal 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 informationTopic: Applications of Network Flow Date: 9/14/2007
CS787: Advanced Algorihm Scribe: Daniel Wong and Priyananda Shenoy Lecurer: Shuchi Chawla Topic: Applicaion of Nework Flow Dae: 9/4/2007 5. Inroducion and Recap In he la lecure, we analyzed he problem
More informationChapter 7. Response of FirstOrder RL and RC Circuits
Chaper 7. esponse of FirsOrder 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 informationChapter 2 Problems. s = d t up. = 40km / hr d t down. 60km / hr. d t total. + t down. = t up. = 40km / hr + d. 60km / hr + 40km / hr
Chaper 2 Problems 2.2 A car ravels up a hill a a consan speed of 40km/h and reurns down he hill a a consan speed of 60 km/h. Calculae he average speed for he rip. This problem is a bi more suble han i
More informationChapter 2 Problems. 3600s = 25m / s d = s t = 25m / s 0.5s = 12.5m. Δx = x(4) x(0) =12m 0m =12m
Chaper 2 Problems 2.1 During a hard sneeze, your eyes migh shu for 0.5s. If you are driving a car a 90km/h during such a sneeze, how far does he car move during ha ime s = 90km 1000m h 1km 1h 3600s = 25m
More information4kq 2. D) south A) F B) 2F C) 4F D) 8F E) 16F
efore you begin: Use black pencil. Wrie and bubble your SU ID Number a boom lef. Fill bubbles fully and erase cleanly if you wish o change! 20 Quesions, each quesion is 10 poins. Each quesion has a mos
More informationBanking, Inside Money and Outside Money
Banking, Inide Mone and Ouide Mone Hongfei Sun Deparmen of Economic Univeri of Torono (Job Marke Paper) Abrac Thi paper preen an inegraed heor of mone and banking. I addre he following queion: when boh
More informationWeek #9  The Integral Section 5.1
Week #9  The Inegral Secion 5.1 From Calculus, Single Variable by HughesHalle, Gleason, McCallum e. al. Copyrigh 005 by John Wiley & Sons, Inc. This maerial is used by permission of John Wiley & Sons,
More informationRC (ResistorCapacitor) Circuits. AP Physics C
(ResisorCapacior Circuis AP Physics C Circui Iniial Condiions An circui is one where you have a capacior and resisor in he same circui. Suppose we have he following circui: Iniially, he capacior is UNCHARGED
More informationOptimal Withdrawal Strategies for Retirees with Multiple Savings Accounts
Opimal Wihdrawal Sraegies for Reirees wih Muliple Savings Accouns 1 May 2008 Sern School of Business New York, New York Sephen M. Horan, Ph.D., CFA Head, Privae Wealh and Invesor Educaion CFA Insiue Overview
More informationPresent 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 information9. 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 informationState Machines: Brief Introduction to Sequencers Prof. Andrew J. Mason, Michigan State University
Inroducion ae Machines: Brief Inroducion o equencers Prof. Andrew J. Mason, Michigan ae Universiy A sae machine models behavior defined by a finie number of saes (unique configuraions), ransiions beween
More informationChapter 9 Bond Prices and Yield
Chaper 9 Bond Prices and Yield Deb Classes: Paymen ype A securiy obligaing issuer o pay ineress and principal o he holder on specified daes, Coupon rae or ineres rae, e.g. 4%, 5 3/4%, ec. Face, par value
More informationTask is a schedulable entity, i.e., a thread
RealTime 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 information1. The graph shows the variation with time t of the velocity v of an object.
1. he graph shows he variaion wih ime of he velociy v of an objec. v Which one of he following graphs bes represens he variaion wih ime of he acceleraion a of he objec? A. a B. a C. a D. a 2. A ball, iniially
More informationAnswer, Key Homework 2 David McIntyre 45123 Mar 25, 2004 1
Answer, Key Homework 2 Daid McInyre 4123 Mar 2, 2004 1 This prinou should hae 1 quesions. Muliplechoice quesions may coninue on he ne column or page find all choices before making your selecion. The
More informationAppendix 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\22348900\4
More information1 The basic circulation problem
2WO08: Graphs and Algorihms Lecure 4 Dae: 26/2/2012 Insrucor: Nikhil Bansal The Circulaion Problem Scribe: Tom Slenders 1 The basic circulaion problem We will consider he maxflow problem again, bu his
More informationRelative velocity in one dimension
Connexions module: m13618 1 Relaive velociy in one dimension Sunil Kumar Singh This work is produced by The Connexions Projec and licensed under he Creaive Commons Aribuion License Absrac All quaniies
More informationSection 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 informationTSGRAN Working Group 1 (Radio Layer 1) meeting #3 Nynashamn, Sweden 22 nd 26 th March 1999
TSGRAN 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 Macrodiversiy for he PRACH Discussion/Decision
More informationChapter 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 informationA Brief Introduction to the Consumption Based Asset Pricing Model (CCAPM)
A Brief Inroducion o he Consumpion Based Asse Pricing Model (CCAPM We have seen ha CAPM idenifies he risk of any securiy as he covariance beween he securiy's rae of reurn and he rae of reurn on he marke
More informationCalculation 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 informationWHAT ARE OPTION CONTRACTS?
WHAT ARE OTION CONTRACTS? By rof. Ashok anekar An oion conrac is a derivaive which gives he righ o he holder of he conrac o do 'Somehing' bu wihou he obligaion o do ha 'Somehing'. The 'Somehing' can be
More informationLenz's Law. Definition from the book:
Lenz's Law Definiion from he book: The induced emf resuling from a changing magneic flux has a polariy ha leads o an induced curren whose direcion is such ha he induced magneic field opposes he original
More informationDuration 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 UVAF38 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 informationBetter Bounds for Online Load Balancing on Unrelated Machines
Beer Bound for Online Load Balancing on Unrelaed Machine Ioanni Caragianni Abrac We udy he roblem of cheduling ermanen ob on unrelaed machine when he obecive i o minimize he L norm of he machine load.
More informationA Mathematical Description of MOSFET Behavior
10/19/004 A Mahemaical Descripion of MOSFET Behavior.doc 1/8 A Mahemaical Descripion of MOSFET Behavior Q: We ve learned an awful lo abou enhancemen MOSFETs, bu we sill have ye o esablished a mahemaical
More informationAP Calculus BC 2010 Scoring Guidelines
AP Calculus BC Scoring Guidelines The College Board The College Board is a noforprofi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in, he College Board
More informationDIFFERENTIAL EQUATIONS with TI89 ABDUL HASSEN and JAY SCHIFFMAN. A. Direction Fields and Graphs of Differential Equations
DIFFERENTIAL EQUATIONS wih TI89 ABDUL HASSEN and JAY SCHIFFMAN We will assume ha he reader is familiar wih he calculaor s keyboard and he basic operaions. In paricular we have assumed ha he reader knows
More informationSolving Equations. PHYSICS Solving Equations. solving equations NOTES. Solving for a Variable. The Rules. The Rules. Grade:«grade»
olving equaion NOTES New Jerey ener for Teaching an Learning Progreive Science Iniiaive Thi maerial i mae freely available a www.njcl.org an i inene for he non commercial ue of uen an eacher. Thee maerial
More informationForecasting Sales: A Model and Some Evidence from the Retail Industry. Russell Lundholm Sarah McVay Taylor Randall
Forecasing Sales: A odel and Some Evidence from he eail Indusry ussell Lundholm Sarah cvay aylor andall Why forecas financial saemens? Seems obvious, bu wo common criicisms: Who cares, can we can look
More information4.8 Exponential Growth and Decay; Newton s Law; Logistic Growth and Decay
324 CHAPTER 4 Exponenial and Logarihmic Funcions 4.8 Exponenial Growh and Decay; Newon s Law; Logisic Growh and Decay OBJECTIVES 1 Find Equaions of Populaions Tha Obey he Law of Uninhibied Growh 2 Find
More informationChapter 6: Business Valuation (Income Approach)
Chaper 6: Business Valuaion (Income Approach) Cash flow deerminaion is one of he mos criical elemens o a business valuaion. Everyhing may be secondary. If cash flow is high, hen he value is high; if he
More informationHow 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 informationCapacity Planning and Performance Benchmark Reference Guide v. 1.8
Environmenal Sysems Research Insiue, Inc., 380 New York S., Redlands, CA 923738100 USA TEL 9097932853 FAX 9093073014 Capaciy Planning and Performance Benchmark Reference Guide v. 1.8 Prepared by:
More informationµ 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 informationStock Trading with Recurrent Reinforcement Learning (RRL) CS229 Application Project Gabriel Molina, SUID 5055783
Sock raing wih Recurren Reinforcemen Learning (RRL) CS9 Applicaion Projec Gabriel Molina, SUID 555783 I. INRODUCION One relaively new approach o financial raing is o use machine learning algorihms o preic
More informationRepresenting Periodic Functions by Fourier Series. (a n cos nt + b n sin nt) n=1
Represening Periodic Funcions by Fourier Series 3. Inroducion In his Secion we show how a periodic funcion can be expressed as a series of sines and cosines. We begin by obaining some sandard inegrals
More informationName: Algebra II Review for Quiz #13 Exponential and Logarithmic Functions including Modeling
Name: Algebra II Review for Quiz #13 Exponenial and Logarihmic Funcions including Modeling TOPICS: Solving Exponenial Equaions (The Mehod of Common Bases) Solving Exponenial Equaions (Using Logarihms)
More informationHeat 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 horerm hea demand forecaing. Foreca of hi hea demand coure i ignifican
More informationAP Calculus AB 2010 Scoring Guidelines
AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a noforprofi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in 1, he College
More information2.6 Limits at Infinity, Horizontal Asymptotes Math 1271, TA: Amy DeCelles. 1. Overview. 2. Examples. Outline: 1. Definition of limits at infinity
.6 Limis a Infiniy, Horizonal Asympoes Mah 7, TA: Amy DeCelles. Overview Ouline:. Definiion of is a infiniy. Definiion of horizonal asympoe 3. Theorem abou raional powers of. Infinie is a infiniy This
More informationDiagnostic Examination
Diagnosic Examinaion TOPIC XV: ENGINEERING ECONOMICS TIME LIMIT: 45 MINUTES 1. Approximaely how many years will i ake o double an invesmen a a 6% effecive annual rae? (A) 10 yr (B) 12 yr (C) 15 yr (D)
More informationPerformance 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 informationGoRA. 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 information4. International Parity Conditions
4. Inernaional ariy ondiions 4.1 urchasing ower ariy he urchasing ower ariy ( heory is one of he early heories of exchange rae deerminaion. his heory is based on he concep ha he demand for a counry's currency
More information17 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 informationLecture III: Finish Discounted Value Formulation
Lecure III: Finish Discouned Value Formulaion I. Inernal Rae of Reurn A. Formally defined: Inernal Rae of Reurn is ha ineres rae which reduces he ne presen value of an invesmen o zero.. Finding he inernal
More informationNewton s Laws of Motion
Newon s Laws of Moion MS4414 Theoreical Mechanics Firs Law velociy. In he absence of exernal forces, a body moves in a sraigh line wih consan F = 0 = v = cons. Khan Academy Newon I. Second Law body. The
More informationCaring 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 informationEstimating TimeVarying Equity Risk Premium The Japanese Stock Market 19802012
Norhfield Asia Research Seminar Hong Kong, November 19, 2013 Esimaing TimeVarying Equiy Risk Premium The Japanese Sock Marke 19802012 Ibboson Associaes Japan Presiden Kasunari Yamaguchi, PhD/CFA/CMA
More informationLaboratory #3 Diode Basics and Applications (I)
Laboraory #3 iode asics and pplicaions (I) I. Objecives 1. Undersand he basic properies of diodes. 2. Undersand he basic properies and operaional principles of some dioderecifier circuis. II. omponens
More informationI. Basic Concepts (Ch. 14)
(Ch. 14) A. Real vs. Financial Asses (Ch 1.2) Real asses (buildings, machinery, ec.) appear on he asse side of he balance shee. Financial asses (bonds, socks) appear on boh sides of he balance shee. Creaing
More informationSc i e n c e a n d t e a c h i n g:
Dikuionpapierreihe Working Paper Serie Sc i e n c e a n d e a c h i n g: Tw o d i m e n i o n a l i g n a l l i n g in he academic job marke Andrea Schneider Nr./ No. 95 Augu 2009 Deparmen of Economic
More informationHow Much Can Taxes Help Selfish Routing?
How Much Can Taxes Help Selfish Routing? Richard Cole Yevgeniy Dodis Tim Roughgarden July 28, 25 Abstract We study economic incentives for influencing selfish behavior in networks. We consider a model
More informationand Decay Functions f (t) = C(1± r) t / K, for t 0, where
MATH 116 Exponenial Growh and Decay Funcions Dr. Neal, Fall 2008 A funcion ha grows or decays exponenially has he form f () = C(1± r) / K, for 0, where C is he iniial amoun a ime 0: f (0) = C r is he rae
More informationMOTION ALONG A STRAIGHT LINE
Chaper 2: MOTION ALONG A STRAIGHT LINE 1 A paricle moes along he ais from i o f Of he following alues of he iniial and final coordinaes, which resuls in he displacemen wih he larges magniude? A i =4m,
More informationPROFIT 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 informationAP Calculus AB 2013 Scoring Guidelines
AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a missiondriven noforprofi organizaion ha connecs sudens o college success and opporuniy. Founded in 19, he College Board was
More informationWorking 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 informationThe Grantor Retained Annuity Trust (GRAT)
WEALTH ADVISORY Esae Planning Sraegies for closelyheld, family businesses The Granor Reained Annuiy Trus (GRAT) An efficien wealh ransfer sraegy, paricularly in a low ineres rae environmen Family business
More informationChapter 6. First Order PDEs. 6.1 Characteristics The Simplest Case. u(x,t) t=1 t=2. t=0. Suppose u(x, t) satisfies the PDE.
Chaper 6 Firs Order PDEs 6.1 Characerisics 6.1.1 The Simples Case Suppose u(, ) saisfies he PDE where b, c are consan. au + bu = 0 If a = 0, he PDE is rivial (i says ha u = 0 and so u = f(). If a = 0,
More information1. y 5y + 6y = 2e t Solution: Characteristic equation is r 2 5r +6 = 0, therefore r 1 = 2, r 2 = 3, and y 1 (t) = e 2t,
Homework6 Soluions.7 In Problem hrough 4 use he mehod of variaion of parameers o find a paricular soluion of he given differenial equaion. Then check your answer by using he mehod of undeermined coeffiens..
More informationOptimal Path Routing in Single and Multiple Clock Domain Systems
IEEE TRANSACTIONS ON COMPUTERAIDED 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 informationDividend taxation, share repurchases and the equity trap
Working Paper 2009:7 Deparmen of Economic Dividend axaion, hare repurchae and he equiy rap Tobia Lindhe and Jan Söderen Deparmen of Economic Working paper 2009:7 Uppala Univeriy May 2009 P.O. Box 53 ISSN
More informationA Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation
A Noe on Using he Svensson procedure o esimae he risk free rae in corporae valuaion By Sven Arnold, Alexander Lahmann and Bernhard Schwezler Ocober 2011 1. The risk free ineres rae in corporae valuaion
More informationPrincipal 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 informationPhysic 231 Lecture 6. Main points of today s lecture: Trajectories of objects in 2 dimensions:
Main poins of oda s lecure: Trajecories of objecs in dimensions: Relaie Veloci Phsic 31 Lecure 6 Main poins of las lecure: Two dimension coordinae ssems Vecors and componens Trajecories of objecs in dimensions:
More informationChabot 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 informationSKF 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 informationInfrastructure and Evolution in Division of Labour
Infrarucure and Evoluion in Diviion of Labour Mei Wen Monah Univery (Thi paper ha been publihed in RDE. (), 906) April 997 Abrac Thi paper udie he relaionhip beween infrarucure ependure and endogenou
More informationThe 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 informationCHARGE 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 informationA 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) 6514065 Abrac: The purpoe of hi paper i
More informationTwo Compartment Body Model and V d Terms by Jeff Stark
Two Comparmen Body Model and V d Terms by Jeff Sark In a onecomparmen model, we make wo imporan assumpions: (1) Linear pharmacokineics  By his, we mean ha eliminaion is firs order and ha pharmacokineic
More informationCLASSIFICATION OF REINSURANCE IN LIFE INSURANCE
CLASSIFICATION OF REINSURANCE IN LIFE INSURANCE Kaarína Sakálová 1. Classificaions of reinsurance There are many differen ways in which reinsurance may be classified or disinguished. We will discuss briefly
More informationWhy Did the Demand for Cash Decrease Recently in Korea?
Why Did he Demand for Cash Decrease Recenly in Korea? Byoung Hark Yoo Bank of Korea 26. 5 Absrac We explores why cash demand have decreased recenly in Korea. The raio of cash o consumpion fell o 4.7% in
More informationImpact of scripless trading on business practices of Subbrokers.
Impac of scripless rading on business pracices of Subbrokers. For furher deails, please conac: Mr. T. Koshy Vice Presiden Naional Securiies Deposiory Ld. Tradeworld, 5 h Floor, Kamala Mills Compound,
More informationMath 201 Lecture 12: CauchyEuler Equations
Mah 20 Lecure 2: CauchyEuler Equaions Feb., 202 Many examples here are aken from he exbook. The firs number in () refers o he problem number in he UA Cusom ediion, he second number in () refers o he problem
More informationSAMPLE LESSON PLAN with Commentary from ReadingQuest.org
Lesson Plan: Energy Resources ubject: Earth cience Grade: 9 Purpose: students will learn about the energy resources, explore the differences between renewable and nonrenewable resources, evaluate the environmental
More information4.2 Trigonometric Functions; The Unit Circle
4. Trigonomeric Funcions; The Uni Circle Secion 4. Noes Page A uni circle is a circle cenered a he origin wih a radius of. Is equaion is as shown in he drawing below. Here he leer represens an angle measure.
More informationDifferential 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 informationAutomatic 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 informationFortified financial forecasting models: nonlinear searching approaches
0 Inernaional Conference on Economic and inance Reearch IPEDR vol.4 (0 (0 IACSIT Pre, Singapore orified financial forecaing model: nonlinear earching approache Mohammad R. Hamidizadeh, Ph.D. Profeor,
More informationDopamine, dobutamine, digitalis, and diuretics during intraaortic balloon support
Dopamine, dobuamine, digialis, and diureics during inraaoric balloon suppor Sephen Slogoff, M.D. n his presenaion, should like o discuss some conceps of drug herapy for inraaoric balloon paiens. Figure
More informationA Curriculum Module for AP Calculus BC Curriculum Module
Vecors: A Curriculum Module for AP Calculus BC 00 Curriculum Module The College Board The College Board is a noforprofi membership associaion whose mission is o connec sudens o college success and opporuniy.
More informationAnalogue 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: 073807 Ifeachor
More informationTrading Strategies for Sliding, Rollinghorizon, and Consol Bonds
Trading Sraegie for Sliding, Rollinghorizon, and Conol Bond MAREK RUTKOWSKI Iniue of Mahemaic, Poliechnika Warzawka, 661 Warzawa, Poland Abrac The ime evoluion of a liding bond i udied in dicree and
More informationPhysics 111 Fall 2007 Electric Currents and DC Circuits
Physics 111 Fall 007 Elecric Currens and DC Circuis 1 Wha is he average curren when all he sodium channels on a 100 µm pach of muscle membrane open ogeher for 1 ms? Assume a densiy of 0 sodium channels
More informationSupply Chain Management Using Simulation Optimization By Miheer Kulkarni
Supply Chain Managemen Using Simulaion Opimizaion By Miheer Kulkarni This problem was inspired by he paper by Jung, Blau, Pekny, Reklaii and Eversdyk which deals wih supply chain managemen for he chemical
More informationENE 104 Electric Circuit Theory
Elecric Circui heory Lecure 0: AC Power Circui Analysis (ENE) Mon, 9 Mar 0 / (EE) Wed, 8 Mar 0 : Dejwoo KHAWPARSUH hp://websaff.ku.ac.h/~dejwoo.kha/ Objecives : Ch Page he insananeous power he average
More informationMA261A Calculus III 2006 Fall Homework 4 Solutions Due 9/29/2006 8:00AM
MA6A Calculus III 006 Fall Homework 4 Soluions Due 9/9/006 00AM 97 #4 Describe in words he surface 3 A halflane in he osiive x and y erriory (See Figure in Page 67) 97 # Idenify he surface cos We see
More information