Topic: Applications of Network Flow Date: 9/14/2007

Size: px
Start display at page:

Download "Topic: Applications of Network Flow Date: 9/14/2007"

Transcription

1 CS787: Advanced Algorihm Scribe: Daniel Wong and Priyananda Shenoy Lecurer: Shuchi Chawla Topic: Applicaion of Nework Flow Dae: 9/4/ Inroducion and Recap In he la lecure, we analyzed he problem of finding he maximum flow in a graph, and how i can be efficienly olved uing he Ford-Fulkeron algorihm. We alo came acro he Min Cu-Max Flow Theorem which relae he ize of he maximum flow o he ize of he minimal cu in he graph. In hi lecure, we will be eeing how variou differen problem can be olved by reducing he problem o an inance of he nework flow problem. The fir applicaion we will be eeing i he Biparie Maching problem. 5.2 Biparie Maching A Biparie Graph G(V, E) i a graph in which he verex e V can be divided ino wo dijoin ube X and Y uch ha every edge e ɛ E ha one end in X and he oher end in Y. A maching M i a ube of edge uch ha each node in V appear in a mo one edge in M. A Maximum Maching i a maching of he large ize. X Y Fig : Biparie Graph A clarificaion abou he erminology: Definiion 5.2. (Maximal Maching) A maximal maching i a maching o which no more edge can be added wihou increaing he degree of one of he node o wo; i i a local maximum. Definiion (Maximum Maching) A maximum maching i one which i he large poible; i i globally opimal.

2 I can be hown ha for any maximal maching M i, M i 2 M where M i he maximum maching. Given hi, i i raighforward o obain a 2-approximaion o he maximum maching. The problem of finding he maximum maching can be reduced o maximum flow in he following manner. Le G(V, E) be he biparie graph where V i divided ino X, Y. We will conruc a direced graph G (V, E ), in which V which conain all he node of V along wih a ource node and a ink node. For every edge in E, we add a direced edge in E from X o Y. Finally we add a direced edge from o all node in X and from all node of Y o. Each edge i given uni weigh. X Y Fig 2: The Biparie Graph convered ino a flow graph Le f be he maximum inegral flow of G, of value k. Then we can make he following obervaion:. There i no node in X which ha more han one ougoing edge where here i a flow. 2. There i no node in Y which ha more han one incoming edge where here i a flow. 3. The number of edge beween X and Y which carry flow i k. By hee obervaion, i i raighforward o conclude ha he e of edge carrying flow in f form he maximum maching for he graph G. The running ime for he Ford-Fulkeron algorihm i O(mF ) where m i he number of edge in E and F = e δ() (c e). In cae of biparie maching problem, F V ince here can be only V poible edge coming ou from ource node. So he running ime i O(mn) where n i he number of node. An inereing hing o noe i ha any pah in he reidual graph of he problem will have alernaing mached and unmached edge. Such pah are called alernaing pah. Thi propery can be ued o find maching even in general graph Perfec Maching A perfec maching i a maching in which each node ha exacly one edge inciden on i. One poible way of finding ou if a given biparie graph ha a perfec maching i o ue he above 2

3 algorihm o find he maximum maching and checking if he ize of he maching equal he number of node in each pariion. There i anoher way of deermining hi, uing Hall Theorem. Theorem A Biparie graph G(V,E) ha a Perfec Maching iff for every ube S XorS Y, he ize of he neighbor of S i a lea a large a S, i.e Γ(S) S We will no dicu he proof of hi heorem in he cla. 5.3 Scheduling Problem We will now ee how he Max Flow algorihm can be ued o olve cerain kind of cheduling problem. The fir example we will ake will be of cheduling job on a machine. Le J = {J, J 2,..., J n } be he e of job, and T = {T, T 2,.., T k } be lo available on a machine where hee job can be performed. Each job J ha a e of valid lo S j T when i can be cheduled. The conrain i ha no wo job can be cheduled a he ame ime. The problem i o find he large e of job which can be cheduled. Thi problem can be olved by reducing i o a biparie maching problem. For every job, creae a node in X, and for every imelo creae a node in Y. For every imelo T in S j, creae an edge beween J and T. The maximum maching of hi biparie graph i he maximum e of job ha can be cheduled. We can alo olve cheduling problem wih more conrain by having inermediae node in he graph. Le u conider a more complex problem: There are k vacaion period each panning muliple coniguou day. Le D j be he e of day included in he j h vacaion period. There are n docor in he hopial, each wih a e of vacaion day when he or he i available. We need o maximize he aignmen of docor o day under he following conrain:. Each docor ha a capaciy c i which i he maximum oal number of day he or he can be cheduled. 2. For every vacaion period, any given docor i cheduled a mo once. We will olve hi problem by nework flow. A wa done earlier, for every docor i we creae a node u i and for every vacaion day j we creae a node v j. We add a direced edge wih uni capaciy from ar node o u i and from v j o ink. To include he conrain, he way he graph i conruced in he following way: The docor capaciie are modeled a capaciie of he edge from he ource o he verex correponding o he docor. To preven he docor o be cheduled more han once in a vacaion period, we inroduce inermediae node. For any docor i and a vacaion period j, we creae an inermediae node w ij. We creae an edge wih uni capaciy from u i o w ij. For every day in he vacaion period ha he docor i available, we creae an edge from w ij o he node correponding o ha day wih uni capaciy. 3

4 docor inermediae node vacaion period ci Fig 3: Scheduling Problem wih conrain Le u ee if he an inegral flow hrough he graph produce a valid chedule. Since he edge connecing o he node correponding o he docor ha he capaciy equal o he oal availabiliy of he docor, he flow hrough he docor node canno exceed i. So he fir conrain i aified. From any docor o any vacaion period he flow i amo one, ince he inermediae node ha only one incoming edge of uni capaciy. Thi make ure ha he econd crieria i me. So he flow produced aifie all he conrain. If k i he ize of an inegral flow hrough he graph, hen he oal number of vacaion day which have been aigned i alo k, ince he edge which connec he node correponding o he vacaion day o he ink node have uni capaciy each. So he ize of he cheduling i equal o he ize of he flow. From hi we can conclude ha he large valid cheduling i produced by he maximum flow. 5.4 Pariioning Problem Now we will ee how cerain kind of pariioning problem can be olved uing he nework flow algorihm. The general idea i o reduce i o min-cu raher han max-flow problem. The fir example we will ee i he Image egmenaion problem Image Segmenaion Conider he following implificaion of he image egmenaion problem. Aume every pixel in an image belong o eiher he foreground of an image or he background. Uing image analyi echnique baed on he value of he pixel i poible o aign probabilie ha an individual pixel belong o he foreground or he background. Thee probabilie can hen be ranlaed o co for aigning a pixel o eiher foreground or background. In addiion, here are co for egmening pixel uch ha pixel from differan region are adjacen. The goal hen i o find an aignmen of all pixel uch ha he co are minimized. Le f i be he co of aigning pixel i o he foreground. Le b i be he co of aigning pixel i o he background. 4

5 Le ij be he co of eparaing neighboring pixel i and j ino differen region. Problem: Find a pariion of pixel ino, p S, he e of foreground pixel and S, he e of background pixel,uch ha he global co of hi aignmen i minimized. Le (S, S) be he pariion of pixel ino foreground and background repecively. Then he co of hi pariion i defined a: co(s) = i S b i + i/ S f i + i S,j / S i and j are neighbour ij (5.4.) We need o find an S which minimize co. Thi problem can be reduced o a min-cu max-flow problem. The naural reducion i o a min-cu problem. Le each pixel be a node, wih neighboring pixel conneced o each oher by undireced edge wih capaciy ij. Creae addiional ource and ink node, and, repecively which have edge o every pixel. The edge from o each pixel have capaciy b i. The edge from each pixel o have capaciy f i. background vi foreground fi bi ij Fig 3: Image egmenaion flow graph Any cu in he graph will hen naurally eparae he pixel ino wo group. Wih he arrangemen he capaciy of he cu i he co aociaed wih ha pariion. The min-cu max-flow algorihm will find uch a pariion of minimum co Image Segmenaion con. Conider a modificaion of he original problem. Replace f i and b i wih value repreening he benefi/value for aigning he pixel i o eiher he foreground or background. Problem: Find an aigmen uch ha for all pixel, p S, he e of foreground pixel, or S, he e of background pixel,uch ha he global value i maximized. Where value i: 5

6 val(s) = i S f i + i/ S b i i S,j / S i and j are neighbour ij (5.4.2) Since he min-cu approach i a minimizaion problem, we need o conver i ino a minimizaion problem in order o reduce i o min-co. Le (S, S) be he pariion of pixel ino foreground and background repecively. We can relae co (defined a per 5.4.) and val by auming co o mean lo benefi : co(s) = i (b i + f i ) val(s) (5.4.3) Since i (b i + f i ) i a conan for any given inance, he problem of maximiing val reduce o minimizing he co. We can reformulae co a co(s) = i S b i + i/ S f i + i S,j / S i and j are neighbour ij (5.4.4) Comparing hi o he previou problem, we ee ha hi i he ame a inerchanging b i and f i in he graph we ued o olve he fir problem; i.e. he weigh of he node from o v i i e a f i and weigh of v i o i e a b i. Solving hi uing min-cu will give u he pariion which maximize he benefi. background vi foreground bi fi ij Fig 4: Flow graph for maximizing benefi 5.5 Max-Flow wih Co Le u conider an exenion of he perfec maching problem where differen edge have differen co. The naurally lead o he min-co max-flow problem. In hi cae, no only do we have o find a max flow hrough he graph, bu alo have o find one wih he lea co. 6

7 Likewie, in he min-co perfec maching problem, he co of a perfec maching M i eɛm c(e)f(e) where f(e) i he co of including he edge e in he maching. I can be hown ha by direcing he flow hrough he minimum co augemening pah fir,we will find he maximum flow wih he lea co. Reference [] Eva Tardo, Jon Kleinberg Algorihm Deign. Pearon Educaion,

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

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

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

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

5.1 Bipartite Matching

5.1 Bipartite Matching CS787: Advanced Algorithms Lecture 5: Applications of Network Flow In the last lecture, we looked at the problem of finding the maximum flow in a graph, and how it can be efficiently solved using the Ford-Fulkerson

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

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

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

Circle Geometry (Part 3)

Circle Geometry (Part 3) Eam aer 3 ircle Geomery (ar 3) emen andard:.4.(c) yclic uadrilaeral La week we covered u otheorem 3, he idea of a convere and we alied our heory o ome roblem called IE. Okay, o now ono he ne chunk of heory

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

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

STABILITY OF LOAD BALANCING ALGORITHMS IN DYNAMIC ADVERSARIAL SYSTEMS

STABILITY OF LOAD BALANCING ALGORITHMS IN DYNAMIC ADVERSARIAL SYSTEMS STABILITY OF LOAD BALANCING ALGORITHMS IN DYNAMIC ADVERSARIAL SYSTEMS ELLIOT ANSHELEVICH, DAVID KEMPE, AND JON KLEINBERG Absrac. In he dynamic load balancing problem, we seek o keep he job load roughly

More information

AP Calculus AB 2013 Scoring Guidelines

AP Calculus AB 2013 Scoring Guidelines AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a mission-driven no-for-profi organizaion ha connecs sudens o college success and opporuniy. Founded in 19, he College Board was

More information

WHAT ARE OPTION CONTRACTS?

WHAT 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 information

What is a swap? A swap is a contract between two counter-parties who agree to exchange a stream of payments over an agreed period of several years.

What is a swap? A swap is a contract between two counter-parties who agree to exchange a stream of payments over an agreed period of several years. Currency swaps Wha is a swap? A swap is a conrac beween wo couner-paries who agree o exchange a sream of paymens over an agreed period of several years. Types of swap equiy swaps (or equiy-index-linked

More information

Imagine a Source (S) of sound waves that emits waves having frequency f and therefore

Imagine a Source (S) of sound waves that emits waves having frequency f and therefore heoreical Noes: he oppler Eec wih ound Imagine a ource () o sound waes ha emis waes haing requency and hereore period as measured in he res rame o he ource (). his means ha any eecor () ha is no moing

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

Distributed Broadcasting and Mapping Protocols in Directed Anonymous Networks

Distributed Broadcasting and Mapping Protocols in Directed Anonymous Networks Disribued Broadcasing and Mapping Proocols in Direced Anonymous Neworks Michael Langberg Moshe Schwarz Jehoshua Bruck Absrac We iniiae he sudy of disribued proocols over direced anonymous neworks ha are

More information

STABILITY OF LOAD BALANCING ALGORITHMS IN DYNAMIC ADVERSARIAL SYSTEMS

STABILITY OF LOAD BALANCING ALGORITHMS IN DYNAMIC ADVERSARIAL SYSTEMS SIAM J. COMPUT. Vol. 37, No. 5, pp. 1656 1673 c 2008 Sociey for Indusrial and Applied Mahemaics STABILITY OF LOAD BALANCING ALGORITHMS IN DYNAMIC ADVERSARIAL SYSTEMS ELLIOT ANSHELEVICH, DAVID KEMPE, AND

More information

RC (Resistor-Capacitor) Circuits. AP Physics C

RC (Resistor-Capacitor) Circuits. AP Physics C (Resisor-Capacior 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 information

Better Bounds for Online Load Balancing on Unrelated Machines

Better 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 information

THE PRESSURE DERIVATIVE

THE PRESSURE DERIVATIVE Tom Aage Jelmer NTNU Dearmen of Peroleum Engineering and Alied Geohysics THE PRESSURE DERIVATIVE The ressure derivaive has imoran diagnosic roeries. I is also imoran for making ye curve analysis more reliable.

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

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

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

Module 4. Single-phase AC circuits. Version 2 EE IIT, Kharagpur

Module 4. Single-phase AC circuits. Version 2 EE IIT, Kharagpur Module 4 Single-phase A circuis ersion EE T, Kharagpur esson 5 Soluion of urren in A Series and Parallel ircuis ersion EE T, Kharagpur n he las lesson, wo poins were described:. How o solve for he impedance,

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

Permutations and Combinations

Permutations and Combinations Permuaions and Combinaions Combinaorics Copyrigh Sandards 006, Tes - ANSWERS Barry Mabillard. 0 www.mah0s.com 1. Deermine he middle erm in he expansion of ( a b) To ge he k-value for he middle erm, divide

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

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

CLASSIFICATION OF REINSURANCE IN LIFE INSURANCE

CLASSIFICATION 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 information

Using RCtime to Measure Resistance

Using RCtime to Measure Resistance Basic Express Applicaion Noe Using RCime o Measure Resisance Inroducion One common use for I/O pins is o measure he analog value of a variable resisance. Alhough a buil-in ADC (Analog o Digial Converer)

More information

ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS

ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS R. Caballero, E. Cerdá, M. M. Muñoz and L. Rey () Deparmen of Applied Economics (Mahemaics), Universiy of Málaga,

More information

Lecture 15 Isolated DC-DC converters

Lecture 15 Isolated DC-DC converters ELEC440/940 Lecure 15 olae C-C converer Ofen, he oupu C volage fro a C-C converer u be iolae fro he inpu AC upply. C power upplie for appliance an equipen are goo exaple. i avanageou o have he iolaion

More information

Formulating Cyber-Security as Convex Optimization Problems

Formulating Cyber-Security as Convex Optimization Problems Formulaing Cyber-Securiy a Convex Opimizaion Problem Kyriako G. Vamvoudaki, João P. Hepanha, Richard A. Kemmerer, and Giovanni Vigna Univeriy of California, Sana Barbara Abrac. Miion-cenric cyber-ecuriy

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

Globally-Optimal Greedy Algorithms for Tracking a Variable Number of Objects

Globally-Optimal Greedy Algorithms for Tracking a Variable Number of Objects Globally-Opimal Greedy Algorihm for Tracking a Variable Number of Objec Hamed Piriavah Deva Ramanan Charle C. Fowlke Deparmen of Compuer Science, Univeriy of California, Irvine {hpiriav,dramanan,fowlke}@ic.uci.edu

More information

Newton s Laws of Motion

Newton 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 information

Multi-resource Allocation Scheduling in Dynamic Environments

Multi-resource Allocation Scheduling in Dynamic Environments MANUFACTURING & SERVICE OPERATIONS MANAGEMENT Vol. 00, No. 0, Xxxxx 0000, pp. 000 000 in 1523-4614 ein 1526-5498 00 0000 0001 INFORMS doi 10.1287/xxxx.0000.0000 c 0000 INFORMS Muli-reource Allocaion Scheduling

More information

Policies & Procedures. I.D. Number: 1071

Policies & Procedures. I.D. Number: 1071 Policie & Procedure Tile: Licened Pracical Nure (LPN ) ADDED SKILLS (Aigned Funcion) Auhorizaion: [x] SHR Nuring Pracice Commiee I.D. Number: 1071 Source: Nuring Dae Revied: Sepember 2004 Dae Effecive:

More information

Module 8. Three-phase Induction Motor. Version 2 EE IIT, Kharagpur

Module 8. Three-phase Induction Motor. Version 2 EE IIT, Kharagpur Module 8 Three-phae Induction Motor Verion EE IIT, Kharagpur Leon 33 Different Type of Starter for Induction Motor (IM Verion EE IIT, Kharagpur Inructional Objective Need of uing arter for Induction motor

More information

Full-wave rectification, bulk capacitor calculations Chris Basso January 2009

Full-wave rectification, bulk capacitor calculations Chris Basso January 2009 ull-wave recificaion, bulk capacior calculaions Chris Basso January 9 This shor paper shows how o calculae he bulk capacior value based on ripple specificaions and evaluae he rms curren ha crosses i. oal

More information

A Probability Density Function for Google s stocks

A Probability Density Function for Google s stocks A Probabiliy Densiy Funcion for Google s socks V.Dorobanu Physics Deparmen, Poliehnica Universiy of Timisoara, Romania Absrac. I is an approach o inroduce he Fokker Planck equaion as an ineresing naural

More information

Chapter 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

Chapter 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 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

E0 370 Statistical Learning Theory Lecture 20 (Nov 17, 2011)

E0 370 Statistical Learning Theory Lecture 20 (Nov 17, 2011) E0 370 Saisical Learning Theory Lecure 0 (ov 7, 0 Online Learning from Expers: Weighed Majoriy and Hedge Lecurer: Shivani Agarwal Scribe: Saradha R Inroducion In his lecure, we will look a he problem of

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

s-domain Circuit Analysis

s-domain Circuit Analysis Domain ircui Analyi Operae direcly in he domain wih capacior, inducor and reior Key feaure lineariy i preered c decribed by ODE and heir Order equal number of plu number of Elemenbyelemen and ource ranformaion

More information

MTH6121 Introduction to Mathematical Finance Lesson 5

MTH6121 Introduction to Mathematical Finance Lesson 5 26 MTH6121 Inroducion o Mahemaical Finance Lesson 5 Conens 2.3 Brownian moion wih drif........................... 27 2.4 Geomeric Brownian moion........................... 28 2.5 Convergence of random

More information

Nanocubes for Real-Time Exploration of Spatiotemporal Datasets

Nanocubes for Real-Time Exploration of Spatiotemporal Datasets Nanocube for RealTime Exploraion of Spaioemporal Daae Lauro Lin, Jame T Kloowki, and arlo Scheidegger Fig 1 Example viualizaion of 210 million public geolocaed Twier po over he coure of a year The daa

More information

Trading Strategies for Sliding, Rolling-horizon, and Consol Bonds

Trading Strategies for Sliding, Rolling-horizon, and Consol Bonds Trading Sraegie for Sliding, Rolling-horizon, 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 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

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

Dividend taxation, share repurchases and the equity trap

Dividend 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 information

Real-time Particle Filters

Real-time Particle Filters Real-ime Paricle Filers Cody Kwok Dieer Fox Marina Meilă Dep. of Compuer Science & Engineering, Dep. of Saisics Universiy of Washingon Seale, WA 9895 ckwok,fox @cs.washingon.edu, mmp@sa.washingon.edu Absrac

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

4. International Parity Conditions

4. 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 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

Lecture 2: Telegrapher Equations For Transmission Lines. Power Flow.

Lecture 2: Telegrapher Equations For Transmission Lines. Power Flow. Whies, EE 481 Lecure 2 Page 1 of 13 Lecure 2: Telegraher Equaions For Transmission Lines. Power Flow. Microsri is one mehod for making elecrical connecions in a microwae circui. I is consruced wih a ground

More information

Two Compartment Body Model and V d Terms by Jeff Stark

Two Compartment Body Model and V d Terms by Jeff Stark Two Comparmen Body Model and V d Terms by Jeff Sark In a one-comparmen model, we make wo imporan assumpions: (1) Linear pharmacokineics - By his, we mean ha eliminaion is firs order and ha pharmacokineic

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

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

Return Calculation of U.S. Treasury Constant Maturity Indices

Return Calculation of U.S. Treasury Constant Maturity Indices Reurn Calculaion of US Treasur Consan Mauri Indices Morningsar Mehodolog Paper Sepeber 30 008 008 Morningsar Inc All righs reserved The inforaion in his docuen is he proper of Morningsar Inc Reproducion

More information

Formulating Cyber-Security as Convex Optimization Problems Æ

Formulating Cyber-Security as Convex Optimization Problems Æ Formulaing Cyber-Securiy a Convex Opimizaion Problem Æ Kyriako G. Vamvoudaki,João P. Hepanha, Richard A. Kemmerer 2, and Giovanni Vigna 2 Cener for Conrol, Dynamical-yem and Compuaion (CCDC), Univeriy

More information

Signal Rectification

Signal Rectification 9/3/25 Signal Recificaion.doc / Signal Recificaion n imporan applicaion of juncion diodes is signal recificaion. here are wo ypes of signal recifiers, half-wae and fullwae. Le s firs consider he ideal

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

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

Chapter 6: Business Valuation (Income Approach)

Chapter 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 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

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

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

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

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

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

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

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

Chapter 4: Exponential and Logarithmic Functions

Chapter 4: Exponential and Logarithmic Functions Chaper 4: Eponenial and Logarihmic Funcions Secion 4.1 Eponenial Funcions... 15 Secion 4. Graphs of Eponenial Funcions... 3 Secion 4.3 Logarihmic Funcions... 4 Secion 4.4 Logarihmic Properies... 53 Secion

More information

Forecasting and Information Sharing in Supply Chains Under Quasi-ARMA Demand

Forecasting and Information Sharing in Supply Chains Under Quasi-ARMA Demand Forecasing and Informaion Sharing in Supply Chains Under Quasi-ARMA Demand Avi Giloni, Clifford Hurvich, Sridhar Seshadri July 9, 2009 Absrac In his paper, we revisi he problem of demand propagaion in

More information

Circuit Types. () i( t) ( )

Circuit Types. () i( t) ( ) Circui Types DC Circuis Idenifying feaures: o Consan inpus: he volages of independen volage sources and currens of independen curren sources are all consan. o The circui does no conain any swiches. All

More information

Cooperation with Network Monitoring

Cooperation with Network Monitoring Cooperaion wih Nework Monioring Alexander Wolizky Microsof Research and Sanford Universiy November 2011 Absrac This paper sudies he maximum level of cooperaion ha can be susained in perfec Bayesian equilibrium

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

Behavior Analysis of a Biscuit Making Plant using Markov Regenerative Modeling

Behavior Analysis of a Biscuit Making Plant using Markov Regenerative Modeling Behavior Analysis of a Biscui Making lan using Markov Regeneraive Modeling arvinder Singh & Aul oyal Deparmen of Mechanical Engineering, Lala Lajpa Rai Insiue of Engineering & Technology, Moga -, India

More information

Infrastructure and Evolution in Division of Labour

Infrastructure and Evolution in Division of Labour Infrarucure and Evoluion in Diviion of Labour Mei Wen Monah Univery (Thi paper ha been publihed in RDE. (), 9-06) April 997 Abrac Thi paper udie he relaionhip beween infrarucure ependure and endogenou

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

Multiple Structural Breaks in the Nominal Interest Rate and Inflation in Canada and the United States

Multiple Structural Breaks in the Nominal Interest Rate and Inflation in Canada and the United States Deparmen of Economics Discussion Paper 00-07 Muliple Srucural Breaks in he Nominal Ineres Rae and Inflaion in Canada and he Unied Saes Frank J. Akins, Universiy of Calgary Preliminary Draf February, 00

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

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

AP Calculus AB 2007 Scoring Guidelines

AP Calculus AB 2007 Scoring Guidelines AP Calculus AB 7 Scoring Guidelines The College Board: Connecing Sudens o College Success The College Board is a no-for-profi membership associaion whose mission is o connec sudens o college success and

More information

Cooperation with Network Monitoring

Cooperation with Network Monitoring Cooperaion wih Nework Monioring Alexander Wolizky Microsof Research and Sanford Universiy February 2012 Absrac This paper sudies he maximum level of cooperaion ha can be susained in perfec Bayesian equilibrium

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

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

Two Dimensional FEM Simulation of Ultrasonic Wave Propagation in Isotropic Solid Media using COMSOL

Two Dimensional FEM Simulation of Ultrasonic Wave Propagation in Isotropic Solid Media using COMSOL Excerpt from the Proceeding of the COMSO Conference 0 India Two Dimenional FEM Simulation of Ultraonic Wave Propagation in Iotropic Solid Media uing COMSO Bikah Ghoe *, Krihnan Balaubramaniam *, C V Krihnamurthy

More information

Mathematics in Pharmacokinetics What and Why (A second attempt to make it clearer)

Mathematics in Pharmacokinetics What and Why (A second attempt to make it clearer) Mahemaics in Pharmacokineics Wha and Why (A second aemp o make i clearer) We have used equaions for concenraion () as a funcion of ime (). We will coninue o use hese equaions since he plasma concenraions

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

Chapter 2 Problems. 3600s = 25m / s d = s t = 25m / s 0.5s = 12.5m. Δx = x(4) x(0) =12m 0m =12m

Chapter 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 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

A Load Balancing Method in Downlink LTE Network based on Load Vector Minimization

A Load Balancing Method in Downlink LTE Network based on Load Vector Minimization A Load Balancing Mehod in Downlink LTE Nework based on Load Vecor Minimizaion Fanqin Zhou, Lei Feng, Peng Yu, and Wenjing Li Sae Key Laboraory of Neworking and Swiching Technology, Beijing Universiy of

More information

1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z 1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z

1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z 1 A B C D E F G H I J K L M N O P Q R S { U V W X Y Z o ffix uden abel ere uden ame chool ame isric ame/ ender emale ale onh ay ear ae of irh an eb ar pr ay un ul ug ep c ov ec as ame irs ame lace he uden abel ere ae uden denifier chool se nly rined in he

More information

Voltage level shifting

Voltage level shifting rek Applicaion Noe Number 1 r. Maciej A. Noras Absrac A brief descripion of volage shifing circuis. 1 Inroducion In applicaions requiring a unipolar A volage signal, he signal may be delivered from a bi-polar

More information

Density Dependence. births are a decreasing function of density b(n) and deaths are an increasing function of density d(n).

Density Dependence. births are a decreasing function of density b(n) and deaths are an increasing function of density d(n). FW 662 Densiy-dependen populaion models In he previous lecure we considered densiy independen populaion models ha assumed ha birh and deah raes were consan and no a funcion of populaion size. Long-erm

More information