On the Applicability of Convex Relaxations for Matching Symmetric Shapes
|
|
- Diane Tate
- 5 years ago
- Views:
Transcription
1 On the Applicability of Convex Relaxations for Matching Symmetric Shapes Nadav Dym Weizmann Institute of Science In collaboration with Haggai Maron and Yaron Lipman
2 Shape matching Finding isometries
3 Shape matching-finding isometries aa ii aa jj AA iiii = dd aa ii, aa jj BB kkkk = dd(bb kk, bb ll ) bb kk bb ll Goal: find mapping (permutation) σσ: aa 1,, aa nn bb 1,, bb nn such that AA iiii = BB σσ ii,σσ(jj)
4 Graph isomorphism Input: AA = AA TT, BB = BB TT Goal: find permutation (if exists) σσ such that AA iiii = BB σσ ii,σσ(jj) Goal: find permutation matrix PP Π nn such that AA = PP TT BBBB
5 Graph matching/quadratic assignment Input: AA = AA TT, BB = BB TT Output: PP Π nn such that AA PP TT BBBB: PP = aaaaaaaaaann PP Πnn AA PP TT BBBB FF PP = aaaaaaaaaann PP Πnn PPPP BBBB FF Graph matching
6 DS relaxation Π nn PP = aaaaaaaaaann PP Πnn PPPP BBBB FF NP Hard! conv Π nn SS = aaaaaaaaaann SS cccccccc Πnn SSSS BBBB FF
7 DS relaxation conv Π nn is the Birkhorff polytope: conv Π nn DDDD = SS SS 0, SS1 = 1, SS TT 1 = 1} DDDD relaxation: SS = aaaaaaaaaann SS DDDD SSSS BBBB FF GGMM DDDD (AA, BB)
8 DS relaxation-does it work? PP = aaaaaaaaaann PP Πnn PPPP BBBB FF Part I: exactness? SS PP SS = aaaaaaaaaann SS DDDD SSSS BBBB FF Part II: projection SS
9 Exactness affects projection efficiency Exact case Exact+small noise Very noisy SS SS S SS = aaaaaaaaaann SS DDDD SSSS BBBB FF
10 Π nn Part I: Exactness [Aflalo et al 2015], [Fiori and Sapiro 2015] Assume: (i) AA BB (ii) Unique isomorphism PP min AAAA SSSS FF = 0 SS DDDD PP Usually Usually not SS SS = aaaaaaaaaann SS DDDD SSSS BBBB FF
11 Problem: Unique solution assumption ψψ φφ multiple solutions ψψ, ψψ φφ symmetric
12 Symmetries of natural shapes Bilateral symmetry: [SCAPE, FAUST, TOSCA] [SHREC]
13 Exactness vs. convex exactness Exactness (asymmetric) PP SS Convex exactness (symmetric) PP 1 PP 2
14 Convex exactness-definition IIIIII AA, BB = PP Π nn AAAA = PPPP}, IIIIoo cccccccc AA, BB = SS DDDD AAAA = SSSS} GGMM DDDD (AA, BB) is convex exact if IIIIoo cccccccc (AA, BB) = cccccccc(iiiiii(aa, BB)) PP 1 PP 2
15 A convenient reduction (B=A) (easy) Lemma: GGMM DDDD (A, A) is convex exact For any BB s.t. BB AA, GGMM DDDD (A, B) is convex exact
16 Goal Almost surely Usually Usually not PP SS Almost surely Usually? Usually not? PP 1 PP 2
17 Measure for the space of asymmetric graphs Asymmetric graphs: {AA = AA TT AA has no non-trivial automorphisms} SS nn = AA AA = AA TT } Asymmetric graphs VV GG 1 μμ SS nn = LLLLLLLLLLLLLLLL VV GG 2 GG ii > {II nn } VV GG 3 VV GG = AA SS nn PPPP = AAAA, PP GG}
18 Measure for Graphs with prescribed symmetry group GG 0 Graphs with sym group GG 0 : Graphs whose automorphism group is GG 0 VV GG 0 = AA SS nn PPPP = AAAA, PP GG 0 }
19 Measure for Graphs with prescribed symmetry group GG 0 VV(GG 0 ) Graphs with sym group GG 0 VV GG 2 VV GG 1 μμ GG0 = LLLLLLesgue GG ii > GG 0 VV GG 3 VV GG = AA SS nn PPPP = AAAA, PP GG}
20 Convex exactness for reflective groups Theorem 1: If GG ZZ 2, then for μμ GG almost every AA, GGMM DDDD (AA, AA) is convex exact. Also true for GG = {II nn } PP 1 PP 2
21 In general Theorem 1 holds if GG is reflective (PP 2 = II nn, PP GG ). GG s action on the vertices has a full orbit. PP 0 = II 4 PP 1 PP 2 PP 4
22 ?
23 General groups: 0-1 probability Theorem 2: For any GG Π nn, either (i) For μμ GG a.e. AA, GGMM DDDD (AA, AA) is convex exact. Or (ii) For all AA with sym group GG, GGMM DDDD (AA, AA) is not convex exact. Proof is constructive...
24 2 AA iiii = pp ii pp jj 2 AA iiii = pp ii pp jj 2 AA iiii = pp ii pp jj 1 GGMM DDDD (AA, AA) GGMM DDDD (AA, AA) GGMM DDDD (AA, AA)
25 General groups: 0-1 probability Theorem 2: For any GG Π nn, either (i) For μμ GG a.e. AA, GGMM DDDD (AA, AA) is convex exact. Or (ii) For all AA with sym group GG, GGMM DDDD (AA, AA) is not convex exact.
26 Summary- Part I convex exactness? almost everywhere almost everywhere
27 Part II: Where s my permutation? symmetric seeee oooo mmmmmmmmmmmmmmmmmmmm = SS DDDD AAAA = SSSS} Simplex algorithm
28 Part II: Where s my permutation? symmetric noise SS
29 DS relaxation- LL 2 projection S = aaaaaaaaaann SS DDDD SSSS BBBB FF SS PP LL2 = aaaaaaaaaann PP Π SS PP FF PP LL2
30 DS++: convex2concave projection SS PP LL2 PP ++
31 convex2concave projection [Zaslavskiy, Bach and Vert 2009] Observation: Convex energy EE 0 is equivalent over Π nn to concave energy EE TT. Concave energy: (i) Local/global minima are permutations! (ii) intractable Convex energy: (i) minima may not be permutations (ii) tractable! SS llllll SS SS gggggggggggg = PP
32 convex2concave projection convex concave EE tt0 EE tt1 EE tt2 EE TT SS kk = "aaaaaaaaaannn SS DDDD EE ttkk (SS) Warm start optimization from SS kk 1. SS 0 SS TT
33 DS++: convex2concave projection EE tt SS = SSSS BBBB FF 2 + tt(nn SS FF 2 ) convex concave EE tt0 EE tt1 EE tt2 EE ttff EE 0 = EE EE tt = EE over Π nn EE ttff strictly concave for t F 0 nn SS FF 2 = 0
34 Choosing [tt 0, tt FF ] EE tt SS = SSSS BBBB FF 2 + tt(nn SS FF 2 ) convex concave EE tt0 EE tt1 EE tt2 EE ttff Best choice of tt FF : tt FF = λλ mmmmmm tt FF = λλ mmmmmm over VV DDDD = SS SS1 = 0, SS TT 1 = 0} Best choice of tt 0 : (DS) tt 0 = 0 [Aflalo et al. 15] (DS+) tt 0 = λλ mmmmmm [Fogel et al. 13,15] (DS++) tt 0 = λλ mmmmmm over VV DDDD
35 Relaxation comparison
36 DS++ vs local minimization DS++ vs local minimization with 1000 different initializations:
37 Projection comparison Retrieval ratio LL 2 DS++ Noise (10 xx )
38 Symmetric, no noise EE tt SS = SSSS BBBB FF 2 + tt(nn SS FF 2 ) For tt > 0, PP ii are the only global minima! PP 1 PP 2
39 Symmetric, no noise Theorem 3: If DS(A,B) is convex exact, then (under some conditions) SS 1, SS 2,, SS TT = PP ii SS 0 SS TT PP 1 PP 2
40 Thank you! For more details see: Exact Recovery with Symmetries for the Doubly-Stochastic Relaxation. DS++: A Flexible, Scalable and Provably Tight Relaxation for Matching Problems. Acknowledgments: - European Research Council (ERC Starting Grant) - Israel Science Foundation
Property Testing and Affine Invariance Part II Madhu Sudan Harvard University
Property Testing and Affine Invariance Part II Madhu Sudan Harvard University December 29-30, 2015 IITB: Property Testing & Affine Invariance 1 of 29 Review of last lecture Property testing: Test global
More informationCDI15 6. Haar wavelets (1D) 1027, 1104, , 416, 428 SXD
CDI15 6. Haar wavelets (1D) 1027, 1104, 1110 414, 416, 428 SXD Notations 6.1. The Haar transforms 6.2. Haar wavelets 6.3. Multiresolution analysis 6.4. Compression/decompression James S. Walker A primer
More informationUnit WorkBook 4 Level 4 ENG U13 Fundamentals of Thermodynamics and Heat Engines UniCourse Ltd. All Rights Reserved. Sample
Pearson BTEC Levels 4 Higher Nationals in Engineering (RQF) Unit 13: Fundamentals of Thermodynamics and Heat Engines Unit Workbook 4 in a series of 4 for this unit Learning Outcome 4 Internal Combustion
More informationSimulated Annealing Algorithm for Customer-Centric Location Routing Problem
Simulated Annealing Algorithm for Customer-Centric Location Routing Problem May 22, 2018 Eugene Sohn Advisor: Mohammad Moshref-Javadi, PhD 1 Agenda Why this research? What is this research? Methodology
More informationBRAKE WINCHES B1200B B1200G B2500 B2500G B3500 B1500 B1500G B1500
BRAKE WINCHES B1500 B1200B B1200G B1500 B1500G B2500 B2500G B3500 B1200B, B1200G B1500, B1500G B2500, B2500G B3500 X 6 650 lb/295 kg 1 1200 lb/545 kg 6 728 lb/330 kg 1 1500 lb/680 kg 3 1554 lb/705 kg 1
More informationDevelopment of force feedback in systems for virtual driving simulator
Development of force feedback in systems for virtual driving simulator steering Joga Dharma Setiawan 1,*, Masri B. Baharom 2, and M. Ammar Bin Abdul Wali 2 1 Department of Mechanical Engineering, Faculty
More informationInternal Bracing Design Program Background Information
Internal Bracing Design Program Background Information 2016 by International Masonry Institute All rights reserved. This program is intended as a preliminary design tool for design professionals who are
More informationMPC Z. Song, Z. Liu, and Y. He
MPC 18-359 Z. Song, Z. Liu, and Y. He Optimal Deployment of Wireless Charging Facilities for an Electric Bus System A University Transportation Center sponsored by the U.S. Department of Transportation
More informationPERFORMANCE DATA. The lightweight, durable, low-profile ROD CYLINDER SLIDES
The lightweight, durable, low-profile H-Block design is the most versatile of our rod cylinder slides. It also has one of the highest ratings of load weight vs extension for its kind in the industry. The
More informationManaging Projects Teaching materials to accompany:
Managing Projects Teaching materials to accompany: Product Design and Development Chapter 14 Karl T. Ulrich and Steven D. Eppinger 2nd Edition, Irwin McGraw-Hill, 2000. Product Development Process Planning
More informationEnvironmental Management Chapter
Environmental Management Chapter 335-3-10 ALABAMA DEPARTMENT OF ENVIRONMENTAL MANAGEMENT AIR DIVISION AIR POLLUTION CONTROL PROGRAM ADMINISTRATIVE CODE CHAPTER 335-3-10 STANDARDS OF PERFORMANCE FOR NEW
More informationTECHNICAL SUPPORT MANUAL Fan Coils FSM4X6000AT
Fan Coils FSM4X60 DANGER, WARNING, CAUTION, and NOTE The signal words DANGER, WARNING, CAU- TION, and NOTE are used to identify levels of hazard seriousness. The signal word DANGER is only used on product
More informationWhat makes a good image?
Optical Imaging 1 What makes a good image? A point in the object is mapped (as much as possible) into a point in the image. The image is a scaled version of the object. 2 A flat plane in the object is
More informationWhite Paper. OptiRamp Real-Time Congealing and Pipeline Monitoring. Monitoring Pipelines with Advanced Analytics
OptiRamp Real-Time Congealing and Pipeline Monitoring Monitoring Pipelines with Advanced Analytics Ullas Pathak Dan Theis, Ph.D. John Hooker Statistics & Control, Inc., (S&C) proprietary information. All
More informationModel 5-025, 5-050, &
Model 5-025, 5-050, 5-075 & 5-150 7 Model 5-025, 5-050, 5-075 & 5-150 8 Eductor Block Exploded View Model 5-025, 5-050, 5-075 & 5-150 9 Figure 1 Item Part Name Model Model Model Model 5-025 5-050 5-075
More informationOn The Sensitivity Conjecture. Avishay Tal Institute for Advanced Study ICALP 2016
On The Sensitivity Conjecture Avishay Tal Institute for Advanced Study ICALP 2016 Sensitivity of Boolean Functions Let ff: 0,1 nn {0,1} be a Boolean function. The sensitivity of ff at xx 0,1 nn : ss(ff,
More informationAir Commander Part No , with air Part No , without air
EASYSTREET Air Commander Part No. 27325, with air Part No. 27332, without air www.airliftcompany.com Please read these instructions completely before proceeding with installation. The oil level in the
More informationDesign Development and Comparative Analysis of Spring Mass Flywheel vs Conventional Flywheel for Two-stroke Engine
1 Design Development and Comparative Analysis of Spring Mass vs Conventional for Two-stroke Engine Tejashri Khochare, Mechanical Engineering Department, AISSMS College of Engineering, Pune ABSTRACT In
More informationField Installation of the Joystick Conversion Kit (DUAL CONTROL){1408, 5057, 5059, 5264, 5705}
Media Search - REHS1805 - Field Installation of the 233-5720 Joystick Conversion K Page 1 of 54 Special Instruction Field Installation of the 233-5720 Joystick Conversion Kit (DUAL CONTROL){1408, 5057,
More informationThe reverse order law (ab) # = b (a abb ) a in rings with involution
The reverse order law (ab) # = b (a abb ) a in rings with involution Dijana Mosić and Dragan S. Djordjević Abstract Several equivalent conditions for the reverse order law (ab) # = b (a abb ) a in rings
More informationTECHNICAL SUPPORT MANUAL Fan Coils
Fan Coils FEM4X, WAHM**4, WAHT**4 DANGER, WARNING, CAUTION, and NOTE The signal words DANGER, WARNING, CAUTION, and NOTE are used to identify levels of hazard seriousness. The signal word DANGER is only
More informationMAXIMUM LOAD. 9.1 kg / 20 lb MAXIMUM LOAD. 9.1 kg / 20 lb
TC54-6127 MAXIMUM LOAD 9.1 kg / 20 lb MAXIMUM LOAD 34 kg / 75 lb MAXIMUM LOAD 6.8 kg / 15 lb MAXIMUM LOAD 9.1 kg / 20 lb WARNING: For use with most LCD/Plasma televisions weighing 34 kg / 75 lb or less.
More informationThermal Management of Open and Closed Circuit Hydraulic Hybrids A Comparison Study
Thermal Management of Open and Closed Circuit Hydraulic Hybrids A Comparison Study Hyukjoon Kwon*, Nathan Keller* and Monika Ivantysynova* Maha Fluid Power Research Center, 1500 Kepner Dr., Lafayette,
More informationThe Product Range. Technical Data
The Product Range Section 3.1 - Basic Cylinder Bore sizes (mm): 10, 16, 25, 32, 40, 50 The basic cylinder series satisfies the support and guidance requirements of a great diversity of applications. Various
More informationMultivariable Model Predictive Control Design for Turbocharged Exhaust Gas Recirculation System in Marine Combustion Engines
Multivariable Model Predictive Control Design for Turbocharged Exhaust Gas Recirculation System in Marine Combustion Engines Sergey Samokhin, Kai Zenger Department of Electrical Engineering and Automation
More informationGraphically Characterizing the Equilibrium of the Neoclassical Model
Graphically Characterizing the Equilibrium of the Neoclassical Model ECON 30020: Intermediate Macroeconomics Prof. Eric Sims University of Notre Dame Spring 2018 1 / 28 Readings GLS Ch. 15 GLS Ch. 16 For
More informationReport Addendum. Terry Keller, SDDOT. Noise Study Technical Report I-29 from Tea Interchange to Skunk Creek Sioux Falls, South Dakota
Report Addendum To: Terry Keller, SDDOT From: HDR Project: Noise Study Technical Report I-29 from Tea Interchange to Skunk Creek Sioux Falls, South Dakota cc: file Date: May 28, 2010; rev July 16, July
More informationFOUNDATIONS OF ALGEBRAIC GEOMETRY CLASS 31
FOUNDATIONS OF ALGEBRAIC GEOMETRY CLASS 31 RAVI VAKIL CONTENTS 1. Pushforwards and pullbacks of quasicoherent sheaves 1 2. Pushforwards of quasicoherent sheaves 1 3. Pullback of quasicoherent sheaves 2
More informationSECTION 5: FLOW BATTERIES. ESE 471 Energy Storage Systems
SECTION 5: FLOW BATTERIES ESE 471 Energy Storage Systems 2 Flow Battery Overview Flow Batteries 3 Flow batteries are electrochemical cells, in which the reacting substances are stored in electrolyte solutions
More informationJRPH/JRPL Series. Pressure Reducing Valves. a division of Jordan Valve PRESSURE REDUCING VALVE JRPH & JRPL SERIES FLOW CONFIGURATIONS
a division of Jordan Valve JRPH/JRPL Series Pressure Reducing Valves PRESSURE REDUCING VALVE The LowFlow JRPH Series and JRPL Series are piston operated, balanced trim pressure regulators with high Cv's
More informationFour Shaft Linear Thrusters
Four Shaft Linear Thrusters FOUR SHAFT THRUSTERS Three Models with bores from 2 to 4 Twice the load capacity of comparable two shaft units Reduced deflection and bearing play Compact, light weight robust
More informationDetermination of Arrester Energy Handling Capability - Testing Investigation Surge Protective Devices Committee Spring 2005 Meeting
Determination of Arrester Energy Handling Capability - Testing Investigation Surge Protective Devices Committee Spring 2005 Meeting Raymond C. Hill, PE Introduction Conflicting opinions exist concerning
More informationTwo Shaft Linear Thrusters
Two Shaft Linear Thrusters TWO SHAFT THRUSTERS Seven Models with bores from 9/16 to 4 Compact, light weight robust design Smooth linear motion CYLINDER Several manufacturers to choose from Pneumatic or
More informationTerminal Boxes Series 8252/1
www.stahl.de > Ex d enclosure made of saltwater-resistant, copper-free aluminium cast alloy > Powder coated to RAL 7032 > Available in 3 different sizes > With DIN rail for standard terminals > Enclosure
More informationANALYSIS AND MONITORING OF CAGE DYNAMICS IN BALL BEARINGS FOR SPACE APPLICATIONS
ANALYSIS AND MONITORING OF CAGE DYNAMICS IN BALL BEARINGS FOR SPACE APPLICATIONS Massimo Palladino (1), Silvio Giuseppe Neglia (1), Marcin Wygachiewicz (2) (1) ESA-ESTEC, Keplerlaan 1, 2200 AG Noordwijk
More informationARTICLE SAFETY CODES FOR ELEVATORS, ESCALATORS, MANLIFTS AND HOISTS. Elevator Safety
ARTICLE 21. 3 SAFETY CODES FOR ELEVATORS, ESCALATORS, MANLIFTS AND HOISTS Elevator Safety (The following Indiana Amendments are reprinted here from the Indiana government web site for your convenience.
More informationLinking the Indiana ISTEP+ Assessments to the NWEA MAP Growth Tests. February 2017 Updated November 2017
Linking the Indiana ISTEP+ Assessments to the NWEA MAP Growth Tests February 2017 Updated November 2017 2017 NWEA. All rights reserved. No part of this document may be modified or further distributed without
More informationBoombot: Low Friction Coefficient Stair Climbing Robot Using Rotating Boom and Weight Redistribution
Boombot: Low Friction Coefficient Stair Climbing Robot Using Rotating Boom and Weight Redistribution Sartaj Singh and Ramachandra K Abstract Boombot comprising four wheels and a rotating boom in the middle
More informationCUSTOM ADD-ONS FOR ENGLISH UNITS
Spindles Flange Piloted Slot Collet Jacobs Taper Morse Taper See note on next page for location in the Specification Code No. Description A B C AA Flange 2.625 3.619/3.621 5.313 AB Piloted Slot 2.3125
More informationNPOI Nitrogen Distribution Project Proposal. Wyatt Huling, Amelia Fuller, and Scott Ryan December 11, 2013
NPOI Nitrogen Distribution Project Proposal Wyatt Huling, Amelia Fuller, and Scott Ryan December 11, 2013 1 Presentation Overview About NPOI Needs Identification Needs Statement Goals Objectives Constraints
More informationPredicting Valve Train Dynamics using Simulation with Model Validation
Predicting Valve Train Dynamics using Simulation with Model Validation Brice Willis, Engineer Kevin Ireland, Engineer Computational Engine Research Honda R&D Americas, Inc. Overview 2 Objectives Validation
More informationE-Hub : Solar Powered Electric Vehicle Charging Station
ENERGY E-Hub : Solar Powered Electric Vehicle Charging Station Novy Francis 15 October 2018 DNV GL 15 October 2018 SAFER, SMARTER, GREENER Contents 1. Motivation 2. Research Questions 3. Estimating energy
More informationPlease read these instructions completely before proceeding with installation. Read all maintenance guidelines on page 7 before operating the vehicle.
MN-643 (02511) ECR 5461 Kit No. 39205 Please read these instructions completely before proceeding with installation Item P/N Description Quantity A 26391 Driver-Side Beam Assembly 1 B 26414 Passenger-Side
More informationElectric Vehicles in smart grids: a Hybrid Benders/EPSO Solver for Stochastic Reservoir Optimization
1 Electric Vehicles in smart grids: a Hybrid Benders/EPSO Solver for Stochastic Reservoir Optimization Vladimiro Miranda Fellow IEEE Administration Board INESC TEC President INESC P&D Brasil Hrvoje Keko
More informationDraft for an Appendix G Electrical System
CSPBankability Project Report Draft for an Appendix G Electrical System to the SolarPACES Guideline for Bankable STE Yield Assessment Document prepared by the project CSPBankability funded by the German
More informationAnalysis Contracts for Cyber- Physical Systems
Analysis Contracts for Cyber- Physical Systems Presenter: Dionisio de Niz 1 dionisio@sei.cmu.edu AADL Std Meeting. Sept 30 th, 2014 Team: Ivan Ruchkin 2, Sagar Chaki 1, David Garlan 2 1 Software Engineering
More informationCONTROL DESIGN AND ANALYSIS OF DOUBLY-FED INDUCTION GENERATOR IN WIND POWER APPLICATION SHUKUL MAZARI A THESIS
CONTROL DESIGN AND ANALYSIS OF DOUBLY-FED INDUCTION GENERATOR IN WIND POWER APPLICATION by SHUKUL MAZARI A THESIS Submitted in partial fulfillment of the requirements for the degree of Master of Science
More informationBimba Extruded Linear Thrusters 2X FF X EE DP 2X DD 2X Ø DD X EE DP U V W X Y Z R S Dimensions - ET T B 4X TAP AA THRU Ø BB C BORE X CC DP (OPP.SIDE)
Bimba Extruded Linear Thrusters Engineering Specifications Maximum Operating Pressure 140 psi (10 bar) Temperature Range 15 to 160 degrees F (-10 to 70 degrees C) Expected Service Life 1,500 miles (with
More informationCommon Rail Injection System On-Line Parameter Calibration for Precise Injection Quantity Control
2010 American Control Conference Marriott Waterfront Baltimore MD USA June 30-July 02 2010 WeC19.6 Common Rail Injection System On-Line Parameter Calibration for Precise Injection Quantity Control Fengjun
More informationEC / EB Series Electro Clutches and Brakes
EC / EB Series Electro Clutches and Brakes Shaft Mounted Clutches and Brakes Shaft Mounted Clutches EC Series All the features of an electric clutch in a convenient, preassembled package. Mounts on any
More informationReverse order law for the Moore-Penrose inverse in C*-algebras
Electronic Journal of Linear Algebra Volume 22 Volume 22 (2011) Article 5 2011 Reverse order law for the Moore-Penrose inverse in C*-algebras Dijana Mosic Dragan S. Djordjevic Follow this and additional
More informationSECTION 6: BATTERY BANK SIZING PROCEDURES. ESE 471 Energy Storage Systems
SECTION 6: BATTERY BANK SIZING PROCEDURES ESE 471 Energy Storage Systems Batteries for Stationary Applications 2 Battery energy storage systems are used in a variety of stationary applications Telecom.,
More informationAnalog RF Proof of Performance Testing Methodology
Analog RF Proof of Performance Testing Methodology System Description: Dickey Rural Networks CATV network is a fiber to the home (FTTH) system with an RF overlay. The headend is based in Oakes, ND. This
More informationSeries QP - QPR short-stroke cylinders 1/ Series QP: single and double-acting
CATALOGUE > Release 8.7 > Series QP - QPR cylinders Series QP - QPR short-stroke cylinders Series QP: single and double-acting, magnetic Series QPR: double-acting magnetic, non-rotating ø 2, 6, 20, 25,
More informationWhat Structural Engineers Should Know about Substation Rigid Bus Design
What Structural Engineers Should Know about Substation Rigid Bus Design Minnesota Power Systems Conference November 8, 2017 Paul Somboonyanon, P.E., P.Eng Agenda Substation Rigid Bus System Design Guide
More informationCapacity-Achieving Accumulate-Repeat-Accumulate Codes for the BEC with Bounded Complexity
Capacity-Achieving Accumulate-Repeat-Accumulate Codes for the BEC with Bounded Complexity Igal Sason 1 and Henry D. Pfister 2 Department of Electrical Engineering 1 Techion Institute, Haifa, Israel School
More informationType (12 Inch) Light Units
1-18 Type 98-201 (12 Inch) Light Units 20 28 29 13, 12, 11 17 2 19, 1 23 2 10 1 21 18 27 32 2 16, 30, 31 26 22 7 6 3 1 9 8 Specifications - 12 Inch Flashing Light Unit All castings in the Type 98-201 Light
More informationIntegrating RTN scheduling models with ISA-95 standard. Pedro M. Castro Ignacio E. Grossmann Iiro Harjunkoski
Integrating RTN scheduling models with ISA-95 standard Pedro M. Castro Ignacio E. Grossmann Iiro Harjunkoski Motivation EWO aims to simultaneously account for KPI across multiple business units Integration
More informationDEFECT DISTRIBUTION IN WELDS OF INCOLOY 908
PSFC/RR-10-8 DEFECT DISTRIBUTION IN WELDS OF INCOLOY 908 Jun Feng August 10, 2010 Plasma Science and Fusion Center Massachusetts Institute of Technology Cambridge, MA 02139, USA This work was supported
More informationInfluence of Frame Stiffness and Rider Position on Bicycle Dynamics: An Analytical Study
University of Wisconsin Milwaukee UWM Digital Commons Theses and Dissertations August 2015 Influence of Frame Stiffness and Rider Position on Bicycle Dynamics: An Analytical Study Trevor Alan Williams
More informationGreeting Card Collection
Greeting Card Collection Greeting Cards 1-46 Invitations 47-61 Greeting Cards CLASSIC GREETINGS PRICE CODE M PERSONALIZE YOUR GREETINGS, OPTIONS ON PAGES 62 & 63 MERRY CHRISTMAS! Love The Andersons CGR0001
More informationCapacity-Achieving Accumulate-Repeat-Accumulate Codes for the BEC with Bounded Complexity
Capacity-Achieving Accumulate-Repeat-Accumulate Codes for the BEC with Bounded Complexity Igal Sason 1 and Henry D. Pfister 2 Department of Electrical Engineering 1 Techion Institute, Haifa, Israel Department
More informationGM Duramax Diesel
Please confirm that all parts are present before beginning the factory exhaust system removal and CORSA exhaust system installation. 2001-05 BILL OF MATERIALS: PN 15201, 15203, 15204 & 15210: (1) Muffler,
More informationModels. Save This Manual For Future Reference. International Comfort Products Corporation (USA) Lewisburg, TN USA LP1 5/16/
Models NTC7050BFG / GNL050NG NTC7075BFG / GNL075NG NTC700BHG / GNL00N6G NTC75BKG / GNL5N0G NDC7050BFG / GDL050NG NDC7075BFG / GDL075NG NDC700BHG / GDL00N6G NDC75BKG / GDL5N0G Manufactured by: International
More informationRenaissance Swing. Item# L-GZ542PCO
Renaissance Swing Item# L-GZ542PCO Congratulations on your purchase of our SUNJOY Renaissance Swing. Our clear, easy to follow, step-by-step instructions will guide you through the assembly process from
More informationmemorandum Sasaki Associates, Inc. Coastal Carolina University Master Plan
memorandum date 27 September 2010 to from project name project # 94657.00 subject Coastal Carolina University Master Plan Committee and Steering Committee Sasaki Associates, Inc. Coastal Carolina University
More informationFord Ranger Rear Kit Part No
EASYSTREET Ford Ranger Rear Kit Part No. 75621 www.airliftcompany.com MN-487 (03202) ECN3773 Please read these instructions completely before proceeding with installation Item P/N Description Qty. A 10177
More informationAS/NZS :2010. Water supply Backflow prevention devices AS/NZS :2010. Part 1: Materials, design and performance requirements
Australian/New Zealand Standard Water supply Backflow prevention devices AS/NZS 2845.1:2010 Incorporating Amendment No. 1 Part 1: Materials, design and performance requirements Superseding AS/NZS 2845.1:1998
More informationRecommended Tools: 3/8 drive ratchet 3/8 drive 13mm deep socket 3/8 drive 15mm deep socket 3/8 drive 15mm shallow socket 13mm wrench
Please take time to read and understand these installation instructions. CORSA recommends that the installation of this system be performed by a qualified service center or professional muffler installer
More informationHVTT15: Minimum swept path control for autonomous reversing of long combination vehicles
MINIMUM SWEPT PATH CONTROL FOR AUTONOMOUS REVERSING OF LONG COMBINATION VEHICLES Xuanzuo Liu is a Ph.D. student in the Transport Research Group of the Department of Engineering in Cambridge University,
More informationSECTION 2: ENERGY STORAGE FUNDAMENTALS. ESE 471 Energy Storage Systems
SECTION 2: ENERGY STORAGE FUNDAMENTALS ESE 471 Energy Storage Systems 2 Performance Characteristics Energy Storage Performance Characteristics 3 Defining performance characteristics of energy storage mechanisms
More informationLinear Thrusters/PneuMoment
/PneuMoment Extruded TE Series 3.3-3.10 3.11-3.16 T Series Multiple Position T4 Series Movable Housing 3.17-3.22 3.23-3.24 3.25-3.28 3.29-3.32 Pneu-Moment Checklist PneuMoment Pneumatic Actuators PneuMoment
More informationRESORT MUNICIPALITY OF WHISTLER BYLAW NOTICE ENFORCEMENT AMENDMENT BYLAW NO. 2194, 2018
RESORT MUNICIPALITY OF WHISTLER BYLAW NOTICE ENFORCEMENT AMENDMENT BYLAW NO. 2194, 2018 A BYLAW TO AMEND BYLAW NOTICE ENFORCEMENT BYLAW NO. 2174, 2018. WHEREAS the Council of the Resort Municipality of
More informationSimulation and Visualization of an Innovative Rotary Displacer Stirling Engine Operation
Simulation and Visualization of an Innovative Rotary Displacer Stirling Engine Operation Amirhossein Bagheri, Saikrishna Kondapally, Huseyin Bostanci*, Philip R. Foster, Cheng Yu Department of Engineering
More informationMODELING AND TESTING OF DIGITAL PROTECTION REALY FOR AN INDUCTION MOTOR. Sungmin Cho
MODELING AND TESTING OF DIGITAL PROTECTION REALY FOR AN INDUCTION MOTOR by Sungmin Cho Executive Summary The project details the modelling of the induction motor SEL701 Relay in PowerFactory. In order
More informationPLASMA / LCD DISPLAY SUPPORT MODEL: ADP3/96-PB & ADP3/96-S ASSEMBLY INSTRUCTIONS
AA / C A O OE: A3/96-B & A3/96- AEB CO model shown: A3/96-B OA FOAO! ) Before starting assembly please take time to familiarise yourself with the instructions and the components listed on the back page,
More informationPEC FLY OWNER'S MANUAL SERIAL NO.'S. through. Parts Manual. Maintenance Manual Follows page REVISED: Nov. 07,1998.
TM TM 15,22 16,23 157,159A 28 PEC FLY OWNER'S MANUAL 17,24 30 REVISED: Nov. 07,1998 29 SERIAL NO.'S through 33 33 Contents Parts Manual 1 2 3 4 5 6 7 8 9 FRAME & PAD ASSEMBLY WORKBOX TO FRAME ASSEMBLY
More informationUSDOT Region V Regional University Transportation Center Final Report. NEXTRANS Project No. 107PUY2.1
MN WI MI IL IN OH USDOT Region V Regional University Transportation Center Final Report NEXTRANS Project No. 107PUY2.1 Developing Operational and Policy Insights into Next Generation Vehicle Needs Based
More informationActive and Passive Brakes Series OSP-P
Active and Passive Brakes Series OSP-P Contents Description Page Overview 51-52 Standard cylinder with Active brake 53-56 Plain bearing SLIDELINE with Active brake 33-34 Aluminium roller guide PROLINE
More informationPRONE LEG CURL OWNER'S MANUAL
TM TM 97 105 19 1 1 73 PRONE LEG CURL OWNER'S MANUAL REVISED: May 15,1998 119 51 SERIAL NO.'S through Contents Parts Manual 1 3 4 5 6 7 8 SEAT FRAME ASSEMBLY WORKBOX & CROSSMEMBER ASSEMBLY MOVEMENT ARM
More informationDesign and Application Details
Model 400 OVENPAK Gas Page 2105 Design and Application Details OVENPAK s are nozzle-mixing gas burners for many industrial direct-fired applications where clean combustion and high turndown are required.
More informationTable of Contents. SRS Series...3-6
Table of Contents SRS Series...3-6 Features and Benefits... 3 How to Order.... 4 Technical Specifications... 4 Critical Speed... 4 Dimensions... 5 Load Ratings... 5 Application Request for Belt and Screw
More informationActive and Passive Brakes Series OSP-P
Active and Passive Brakes Series OSP-P Contents Description Data Sheet No. Page Overview P-1.42.001E 69-70 Standard cylinder with Active brake P-1.42.002E 71-74 Plain bearing SLIDELINE with Active brake
More informationSAN FRANCISCO MUNICIPAL TRANSPORTATION AGENCY BOARD OF DIRECTORS. RESOLUTION No
SAN FRANCISCO MUNICIPAL TRANSPORTATION AGENCY BOARD OF DIRECTORS RESOLUTION No. 16-036 WHEREAS, The San Francisco Municipal Transportation Agency has received a request, or identified a need for traffic
More informationPARALLEL PUMP-CONTROLLED MULTI-CHAMBER CYLINDER
Proceedings of the ASME/BATH 2014 Symposium on Fluid Power & Motion Control FPMC2014 September 10-12, Bath, United Kingdom FPMC2014-7820 PARALLEL PUMP-CONTROLLED MULTI-CHAMBER CYLINDER Olli Niemi-Pynttäri
More informationKEY SURGICAL INSTRUMENT PROTECTION
KEY SURGICAL INSTRUMENT PROTECTION Instrument Tip Caps are designed to extend the life of your instruments. Our tip caps protect your valuable instruments from unnecessary wear or damage, helping reduce
More informationGRIPPERS GRIPPERS 178
178 ol-o-matic s line of hardworking grippers are price competitive units, available in both angular and parallel styles and come in a range of six bore sizes (3/8", 5/8", 1", 1-1/2", 2" and 3") for a
More informationJB Series. Gas Back Pressure Reducing Valves BACK PRESSURE REDUCING VALVE
JB Series Gas Back Pressure Reducing Valves BACK PRESSURE REDUCING VALVE The LowFlow JB Series line of back pressure regulators have the ability to handle very high pressures and very low flows. These
More informationEclipse Vortometric Burners Series HI
Version Burner Model Parameter 6V 8V V V V 6V 8V V V 8V 3V 36V Max. Input MM BTU/hr (MW) (.8).5 (3.) 7 (5.0) 3 (6.7) 3 (9.) () (6.) 78 (3) 90 (6) 5 (37) (7) (6) Min. Input MM BTU/hr (MW) (Natural Gas)
More informationNegotiation-Based Task Scheduling and Storage Control Algorithm to Minimize User s Electric Bills under Dynamic Prices
Negotiation-Based Task Scheduling and Storage Control Algorithm to Minimize User s Electric Bills under Dynamic Prices Ji Li, Yanzhi Wang, Xue Lin, Shahin Nazarian, and Massoud Pedram Department of Electrical
More informationReduction in Soil Penetration Resistance for Suction-assisted Installation of Bucket Foundation in Sand
Reduction in Soil Penetration Resistance for Suction-assisted Installation of Bucket Foundation in Sand A.K. Koteras & L.B.Ibsen Department of Civil Engineering, Aalborg University, Denmark Agenda Concept
More informationAE40 CATALOG D38999 CYLINDRICAL CONNECTORS FOR PCB APPLICATIONS
AE40 CATALOG D38999 CYLINDRICAL CONNECTORS FOR PCB APPLICATIONS 9452 De Soto Avenue I Chatsworth, CA 91313-2231 I Voice: 818.407.5400 I Toll Free: 800.458.4412 I Fax: 818.407.5460 I email: sales@airelectro.com
More informationVtg Stencil DIN. fonts by Andreas Seidel ABCDEFGHIJKLM NOPQRSTUVWXYZ
Vtg Stencil DIN apple fonts by Andreas Seidel ABCDEFGHIJKLM NOPQRSTUVWXYZ 987-654-3210 THE GERMAN STANDARD TYPE The Vtg Stencil series of fonts from astype are based on real world stencils. The Vtg Stencil
More informationAssessing Passenger Car Equivalency Factors for High Truck Percentages
Nebraska Transportation Center Report SPR-P1(15) M023 Final Report 26-1121-0020-001 Assessing Passenger Car Equivalency Factors for High Truck Percentages Jianan Zhou Graduate Research Assistant Department
More informationSZENT ISTVÁN UNIVERSITY. Characteristics of the energy balance of agricultural V-belt drives. Theses of doctoral (PhD) dissertation Péter Gárdonyi
SZENT ISTVÁN UNIVERSITY Characteristics of the energy balance of agricultural V-belt drives Theses of doctoral (PhD) dissertation Péter Gárdonyi Gödöllő 2018 Doctoral school denomination: Mechanical Engineering
More informationConcepts of One Dimensional Kinematics Activity Purpose
Concepts of One Dimensional Kinematics Activity Purpose During the activity, students will become familiar with identifying how the position, the velocity, and the acceleration of an object will vary with
More informationPlease confirm that all parts are present before beginning the factory exhaust system removal and db Performance Exhaust system installation.
Please take time to read and understand these installation instructions. We recommend that the installation of this system be performed by a qualified service center or professional muffler installer who
More informationTable 4.10 SELECTED STATE ADMINISTRATIVE OFFICIALS: METHODS OF SELECTION (Key and footnotes listed at end of chart.)
Table 4.10 SELECTED STATE ADMINISTRATIVE OFFICIALS: METHODS OF SELECTION (Key and footnotes listed at end of chart.) State or other Lieutenant Secretary Attorney Adjutant jurisdiction Governor governor
More informationMISCELLANEOUS DESIGN PORTFOLIO
MISCELLANEOUS DESIGN PORTFOLIO 4 WHO I AM 5 RESUME Step Up. Never Step Down. Never Step Aside. Never Make Room. Create Room. -JD Orr 6 16 24 32 36 THE NORTH FACE VISUALS PERSONAL BRANDING INCREDIBLES PLAYSET
More informationOn Using Storage and Genset for Mitigating Power Grid Failures
1 / 27 On Using Storage and Genset for Mitigating Power Grid Failures Sahil Singla ISS4E lab University of Waterloo Collaborators: S. Keshav, Y. Ghiassi-Farrokhfal 1 / 27 Outline Introduction Background
More information