Adaptive Algorithms for Blind Separation of Dependent Sources. George V. Moustakides INRIA, Sigma 2
|
|
- Gregers Thomsen
- 4 år siden
- Visninger:
Transkript
1 Adaptive Algorithms for Blind Separation of Dependent Sources George V. Moustakides INRIA, Sigma 2
2 Problem definition-motivation Existing adaptive scheme-independence General adaptive scheme-dependence Imposing the desired limits Imposing symmetric behavior Non-separable sources Performance measure Optimum algorithms Conclusion Outline 2
3 Problem Definition-Motivation x1() n a11 a12 L a1 L s1() n x2() n a21 a22 a 2L s2() n L = M M M M M M x () n a a L a s () n L L1 L2 LL L Xn () = ASn () If the observation sequence X(n) is available, estimate the source sequence S(n). Equivalently estimate B = A -1. Interested in adaptive techniques. At every time n, available X(n) and form an estimate B(n) of A -1. 3
4 Why Dependent Sources? Because it is analytically challenging. Here is a practical reason to motivate such an analysis L f( s1, K, s ) = 0.99 f ( s) L i i i= 1 ε-contamination model L i= 1 g( s) i i f(s 1,,s L ) no longer corresponds to independent sources!! Question: Do BSS algorithms still work under such mild divergence from the independence assumption? 4
5 Existing adaptive technique Consider L = 2 sources and let B(n) denote the estimate of A -1 at time n. At time n available: B(n-1), X(n) Sn ˆ( ) = B ( n 1) Xn ( ) B( n) = B( n 1) Sˆ µ H ( n) B( n 1), B(0) = I ( ) µ is a constant (step size) with 0 < µ << 1. 2 z1 1 zz gzz 1( 1) 2 gzz 2( 2) 1 H() Z = 2 + zz 12 z2 1 gzz 1( 2) 1 gzz 2( 1) 2 0 g i (z) are odd univariate nonlinear function (i.e. g i (-z) = - g i (z)). 5
6 Acceptable solution(s) Sn ˆ( ) = B( n 1) Xn ( ) = B( n 1) ASn ( ) = C( n 1) Sn ( ) ± c1 0 ˆ ± cs 1 1( n) C( n) S( n) 0 ± c ± c s ( n) c c s n 0 ± 2 ± 2 2( ), ± c1 0 ± cs 1 1( n) 6
7 Does C(n) = B(n)A converge to one of the eight matrices? ± c1 0 0 ± c2 or? 0 ± c ± c Theorem 1: If the sources s i (n) are independent random variables, with symmetric probability density functions; and at most one is Gaussian, then ± c { } ± c2 lim E C( n) = or n 0 ± c 2 ± c1 0 lim n E{(C(n)-E{C( )}) 2 }= O(µ) 7
8 Observations No knowledge of the exact pdfs is required; only symmetry (and independence (?)). 2 z1 1 zz 1 2 H( z1, z2) = 2 zz 1 2 z2 1 0 g( z) z g ( z ) z g() z = α z i g1( z1) z2+ g2( z2) z1 0 i 3 common choice Two or more Gaussian sources are NOT separable, in the sense that for ANY adaptive algorithm there is a continuum of limits instead of the 8 desirable ones. 8
9 Dependent Source Statistics If sources are dependent and the joint pdf is known, in principle we can construct adaptive algorithms that solve the source separation problem. We are interested in dependent sources for which it is not required knowledge of the pdfs. All bivariate densities must satisfy the following quadratal symmetry s j f ( s, s ) = f ( s, s ) = f ( s, s ) ij i j ij i j ij i j s i L f( s1, K, s ) = 0.99 f ( s) L i i i= 1 L i= 1 g( s) i i 9
10 General adaptive scheme Sn ˆ( ) = B ( n 1) Xn ( ), Xn ( ) = ASn ( ) ( ˆ ) B( n) = B( n 1) µ H S( n) B( n 1), B(0) = I H( z, z ) 1 2 hz ( ) qz (, z) = qz (, z) hz ( ) Sn ˆ( ) = C ( n 1) Sn ( ), C ( n ) = B ( n ) A ( ˆ ) C( n) = C( n 1) µ H S( n) C( n 1), C(0) = A C( n) = C( n 1) µ H C( n 1) S( n) C( n 1) ( ) 10
11 Imposing the desired limits From the theory of adaptive algorithms we know that an algorithm of the form C( n) = C( n 1) µ H C( n 1) S( n) C( n 1) ( ) converges in the mean lim n E{C(n)}= C, where C is an equilibrium matrix satisfying the equation { ( ( ))} C= C µe H CS n C or equivalently { H( C )} E S( n ) = 0 11
12 Since H( z, z ) 1 2 hz ( ) qz (, z) = q( z1, z2) h( z2) relation { H( C )} E S( n ) = 0 is equivalent to a system of four (in general nonlinear) equations { ( C )} ( C ) { } E h S( n) = E q S( n) = 0 in four unknowns (the four elements of matrix C) that can be solved to identify the equilibrium matrices. 12
13 If we want a specific matrix C 0 to become an equilibrium, then the elements of H(Z) must satisfy { ( C )} ( C ) If in particular we like the following eight matrices C 0 ± c 0 0 ± c 1 2 =, 0 ± c 2 ± c1 0 to become equilibriums, then { } E h S( n) = E q S( n) = { } { ( )} ( ) i i i i j j E h ± cs = E q ± cs, ± c s = 0 13
14 Imposing symmetric behavior For every trajectory converging to one limit we require existence of symmetric trajectories converging to the other seven limits with the same probability. hz ( 1) qz ( 2, z1) H( z1, z2) = qz ( 1, z2) hz ( 2) h( z) = h( z) q( z, z ) = q( z, z ) = q( z, z ) E h( c s ) = E h( c s ) = 0 { } { } E qcs (, cs) = E qcs (, cs) = 0 (for free) { } { }
15 Necessary conditions 1. H( z1, z2) 2. h( z) = h( z) hz ( ) qz (, z) = qz ( 1, z2) hz ( 2) 3. q( z, z ) = q( z, z ) = q( z, z ) E h( c s ) = E h( c s ) = 0 (existenceof c, c ) { } { } z1 1 zz 1 2+ g( z1) z2 g( z2) z 1 H( z1, z2) = 2 zz 1 2 g( z1) z2+ g( z2) z1 z2 1 15
16 Theorem 2: If the sources s i (n) are random variables, with symmetric bivariate densities and no bivariate density is of the form f s s β Ks K s 2 2 ij( i, j) = ( i i + j j ) that is, no bivariate density exhibits either elliptical or hyperbolic symmetry (with respect to the two axis), then the generalized algorithm has exactly the same convergence properties for the dependent class, as the existing algorithm for the independent class. 16
17 Quadrantally symmetric bivariate pdfs 17
18 Example Existing scheme H( z, z ) z1 1 zz 1 2+ g( z1) z2 g( z2) z 1 = 2 zz 1 2 gz ( 1) z2+ gz ( 2) z1 z2 1 Select H z 1 zzsgn( z ) = z2 2 z2z1sgn( z1) z2 1 ( z, ) There is no whitening involved!!! 18
19 /2 2/2 σ 1 /2 σ 2/2 s s s a s a e e e e f( s1, s2) = π 2πσ 2πaσ 2πa If σ 1 the two sources are separable If σ = 1 the two sources are not separable a=1.5, σ =0.8 19
20 2 1.5 a=1.5, σ = x
21 2 1.5 a=1.5, σ = x
22 Performance measure Define a performance measure for the algorithmic class C( n) = C( n 1) µ H C( n 1) S( n) C( n 1) ( ) with H(z 1, z 2 ) satisfying the five necessary conditions. For performance there are two important quantities: Rate of convergence Steady state estimation error power Both quantities depend on µ. Combine the two quantities to define a fair performance measure. 22
23 5 2 ( ) 2 C( n) E C( ) = C ( n) E C ( ) { } { } ij ij i, j 0 Estimation Error Power in db Time n 23
24 2 ( ) 2 C( n) E C( ) = C ( n) E C ( ) { } { } ij ij i, j Estimation Error Power in db Adjust the step sizes µ so Classical that the algorithms Optimum have the same steady state error power, then compare their convergence rates n x
25 It is possible to define an analytic performance measure that can characterize an adaptive algorithm. ( hz qz ) 1 z2 fij si sj Efficacy = function ( ), (, ), (, ) The important properties of the Efficacy are the following When comparing Efficacies of two algorithms, it is equivalent to comparing the two algorithms fairly!! The optimum algorithm is the one that maximizes the Efficacy over h(z), q(z 1,z 2 ). 25
26 Optimum adaptive algorithms When the bivariate pdfs are different the optimization problem is still open. When the sources are independent with the same pdf f (z), then hz ( ) = a zlz ( ) 1 ( ) qz (, z) = bzlz ( ) + czlz ( ) where a, b, c, proper constants l ' f ( z ) ( z ) =, f ( z ) Existing scheme ( ) h( z) = z 1, q( z, z) = zz + zg( z) zg( z) Maximize Efficacy with respect to g(z) qz (, z) = zz + d zlz ( ) zlz ( ) ( )
27 Conclusion We have presented a rich class of adaptive algorithms that can solve the blind source separation problem for dependent sources with symmetries. We have identified the sources that cannot be separated with the specific combination of source statistics and algorithmic model. We have proposed an analytic performance measure that can be optimized to yield the fastest converging algorithm in the equidistributed source case. 27
28 Questions please? F i N 28
Generalized Probit Model in Design of Dose Finding Experiments. Yuehui Wu Valerii V. Fedorov RSU, GlaxoSmithKline, US
Generalized Probit Model in Design of Dose Finding Experiments Yuehui Wu Valerii V. Fedorov RSU, GlaxoSmithKline, US Outline Motivation Generalized probit model Utility function Locally optimal designs
Læs mereMultivariate Extremes and Dependence in Elliptical Distributions
Multivariate Extremes and Dependence in Elliptical Distributions Filip Lindskog, RiskLab, ETH Zürich joint work with Henrik Hult, KTH Stockholm I II III IV V Motivation Elliptical distributions A class
Læs mereBasic statistics for experimental medical researchers
Basic statistics for experimental medical researchers Sample size calculations September 15th 2016 Christian Pipper Department of public health (IFSV) Faculty of Health and Medicinal Science (SUND) E-mail:
Læs mereExercise 6.14 Linearly independent vectors are also affinely independent.
Affine sets Linear Inequality Systems Definition 6.12 The vectors v 1, v 2,..., v k are affinely independent if v 2 v 1,..., v k v 1 is linearly independent; affinely dependent, otherwise. We first check
Læs mereSkriftlig Eksamen Kombinatorik, Sandsynlighed og Randomiserede Algoritmer (DM528)
Skriftlig Eksamen Kombinatorik, Sandsynlighed og Randomiserede Algoritmer (DM58) Institut for Matematik og Datalogi Syddansk Universitet, Odense Torsdag den 1. januar 01 kl. 9 13 Alle sædvanlige hjælpemidler
Læs mereLinear Programming ١ C H A P T E R 2
Linear Programming ١ C H A P T E R 2 Problem Formulation Problem formulation or modeling is the process of translating a verbal statement of a problem into a mathematical statement. The Guidelines of formulation
Læs mereStatistik for MPH: oktober Attributable risk, bestemmelse af stikprøvestørrelse (Silva: , )
Statistik for MPH: 7 29. oktober 2015 www.biostat.ku.dk/~pka/mph15 Attributable risk, bestemmelse af stikprøvestørrelse (Silva: 333-365, 381-383) Per Kragh Andersen 1 Fra den 6. uges statistikundervisning:
Læs mereStatistik for MPH: 7
Statistik for MPH: 7 3. november 2011 www.biostat.ku.dk/~pka/mph11 Attributable risk, bestemmelse af stikprøvestørrelse (Silva: 333-365, 381-383) Per Kragh Andersen 1 Fra den 6. uges statistikundervisning:
Læs mereThe X Factor. Målgruppe. Læringsmål. Introduktion til læreren klasse & ungdomsuddannelser Engelskundervisningen
The X Factor Målgruppe 7-10 klasse & ungdomsuddannelser Engelskundervisningen Læringsmål Eleven kan give sammenhængende fremstillinger på basis af indhentede informationer Eleven har viden om at søge og
Læs mereSign variation, the Grassmannian, and total positivity
Sign variation, the Grassmannian, and total positivity arxiv:1503.05622 Slides available at math.berkeley.edu/~skarp Steven N. Karp, UC Berkeley FPSAC 2015 KAIST, Daejeon Steven N. Karp (UC Berkeley) Sign
Læs mereVina Nguyen HSSP July 13, 2008
Vina Nguyen HSSP July 13, 2008 1 What does it mean if sets A, B, C are a partition of set D? 2 How do you calculate P(A B) using the formula for conditional probability? 3 What is the difference between
Læs mereBesvarelser til Lineær Algebra Reeksamen Februar 2017
Besvarelser til Lineær Algebra Reeksamen - 7. Februar 207 Mikkel Findinge Bemærk, at der kan være sneget sig fejl ind. Kontakt mig endelig, hvis du skulle falde over en sådan. Dette dokument har udelukkende
Læs mereEric Nordenstam 1 Benjamin Young 2. FPSAC 12, Nagoya, Japan
Eric 1 Benjamin 2 1 Fakultät für Matematik Universität Wien 2 Institutionen för Matematik Royal Institute of Technology (KTH) Stockholm FPSAC 12, Nagoya, Japan The Aztec Diamond Aztec diamonds of orders
Læs mereDepartment of Public Health. Case-control design. Katrine Strandberg-Larsen Department of Public Health, Section of Social Medicine
Department of Public Health Case-control design Katrine Strandberg-Larsen Department of Public Health, Section of Social Medicine Case-control design Brief summary: Comparison of cases vs. controls with
Læs mereDoodleBUGS (Hands-on)
DoodleBUGS (Hands-on) Simple example: Program: bino_ave_sim_doodle.odc A simulation example Generate a sample from F=(r1+r2)/2 where r1~bin(0.5,200) and r2~bin(0.25,100) Note that E(F)=(100+25)/2=62.5
Læs mereProbabilistic properties of modular addition. Victoria Vysotskaya
Probabilistic properties of modular addition Victoria Vysotskaya JSC InfoTeCS, NPK Kryptonite CTCrypt 19 / June 4, 2019 vysotskaya.victory@gmail.com Victoria Vysotskaya (Infotecs, Kryptonite) Probabilistic
Læs merePARALLELIZATION OF ATTILA SIMULATOR WITH OPENMP MIGUEL ÁNGEL MARTÍNEZ DEL AMOR MINIPROJECT OF TDT24 NTNU
PARALLELIZATION OF ATTILA SIMULATOR WITH OPENMP MIGUEL ÁNGEL MARTÍNEZ DEL AMOR MINIPROJECT OF TDT24 NTNU OUTLINE INEFFICIENCY OF ATTILA WAYS TO PARALLELIZE LOW COMPATIBILITY IN THE COMPILATION A SOLUTION
Læs mereUniversity of Copenhagen Faculty of Science Written Exam April Algebra 3
University of Copenhagen Faculty of Science Written Exam - 16. April 2010 Algebra This exam contains 5 exercises which are to be solved in hours. The exercises are posed in an English and in a Danish version.
Læs merePontryagin Approximations for Optimal Design of Elastic Structures
Pontryagin Approximations for Optimal Design of Elastic Structures Jesper Carlsson NADA, KTH jesperc@nada.kth.se Collaborators: Anders Szepessy, Mattias Sandberg October 5, 2005 A typical optimal design
Læs mereSkriftlig Eksamen Beregnelighed (DM517)
Skriftlig Eksamen Beregnelighed (DM517) Institut for Matematik & Datalogi Syddansk Universitet Mandag den 31 Oktober 2011, kl. 9 13 Alle sædvanlige hjælpemidler (lærebøger, notater etc.) samt brug af lommeregner
Læs mereComputing the constant in Friedrichs inequality
Computing the constant in Friedrichs inequality Tomáš Vejchodský vejchod@math.cas.cz Institute of Mathematics, Žitná 25, 115 67 Praha 1 February 8, 212, SIGA 212, Prague Motivation Classical formulation:
Læs mereVores mange brugere på musskema.dk er rigtig gode til at komme med kvalificerede ønsker og behov.
På dansk/in Danish: Aarhus d. 10. januar 2013/ the 10 th of January 2013 Kære alle Chefer i MUS-regi! Vores mange brugere på musskema.dk er rigtig gode til at komme med kvalificerede ønsker og behov. Og
Læs mereResource types R 1 1, R 2 2,..., R m CPU cycles, memory space, files, I/O devices Each resource type R i has W i instances.
System Model Resource types R 1 1, R 2 2,..., R m CPU cycles, memory space, files, I/O devices Each resource type R i has W i instances. Each process utilizes a resource as follows: request use e.g., request
Læs mereSKRIFTLIG EKSAMEN I NUMERISK DYNAMIK Bygge- og Anlægskonstruktion, 7. semester Torsdag den 19. juni 2003 kl Alle hjælpemidler er tilladt
SKRIFTLIG EKSAMEN I NUMERISK DYNAMIK Bygge- og Anlægskonstruktion, 7. semester Torsdag den 9. juni 23 kl. 9.-3. Alle hjælpemidler er tilladt OPGAVE f(x) x Givet funktionen f(x) x, x [, ] Spørgsmål (%)
Læs mereCurve Modeling B-Spline Curves. Dr. S.M. Malaek. Assistant: M. Younesi
Curve Modeling B-Spline Curves Dr. S.M. Malaek Assistant: M. Younesi Motivation B-Spline Basis: Motivation Consider designing the profile of a vase. The left figure below is a Bézier curve of degree 11;
Læs merePrivat-, statslig- eller regional institution m.v. Andet Added Bekaempelsesudfoerende: string No Label: Bekæmpelsesudførende
Changes for Rottedatabasen Web Service The coming version of Rottedatabasen Web Service will have several changes some of them breaking for the exposed methods. These changes and the business logic behind
Læs mereUniversity of Copenhagen Faculty of Science Written Exam - 3. April Algebra 3
University of Copenhagen Faculty of Science Written Exam - 3. April 2009 Algebra 3 This exam contains 5 exercises which are to be solved in 3 hours. The exercises are posed in an English and in a Danish
Læs mereProject Step 7. Behavioral modeling of a dual ported register set. 1/8/ L11 Project Step 5 Copyright Joanne DeGroat, ECE, OSU 1
Project Step 7 Behavioral modeling of a dual ported register set. Copyright 2006 - Joanne DeGroat, ECE, OSU 1 The register set Register set specifications 16 dual ported registers each with 16- bit words
Læs merePortal Registration. Check Junk Mail for activation . 1 Click the hyperlink to take you back to the portal to confirm your registration
Portal Registration Step 1 Provide the necessary information to create your user. Note: First Name, Last Name and Email have to match exactly to your profile in the Membership system. Step 2 Click on the
Læs mereUser Manual for LTC IGNOU
User Manual for LTC IGNOU 1 LTC (Leave Travel Concession) Navigation: Portal Launch HCM Application Self Service LTC Self Service 1. LTC Advance/Intimation Navigation: Launch HCM Application Self Service
Læs mereSkriftlig Eksamen Beregnelighed (DM517)
Skriftlig Eksamen Beregnelighed (DM517) Institut for Matematik & Datalogi Syddansk Universitet Mandag den 7 Januar 2008, kl. 9 13 Alle sædvanlige hjælpemidler (lærebøger, notater etc.) samt brug af lommeregner
Læs mereKurver og flader Aktivitet 15 Geodætiske kurver, Isometri, Mainardi-Codazzi, Teorema Egregium
Kurver og flader Aktivitet 15 Geodætiske kurver, Isometri, Mainardi-Codazzi, Teorema Egregium Lisbeth Fajstrup Institut for Matematiske Fag Aalborg Universitet Kurver og Flader 2013 Lisbeth Fajstrup (AAU)
Læs mereCHAPTER 8: USING OBJECTS
Ruby: Philosophy & Implementation CHAPTER 8: USING OBJECTS Introduction to Computer Science Using Ruby Ruby is the latest in the family of Object Oriented Programming Languages As such, its designer studied
Læs mereMeasuring Evolution of Populations
Measuring Evolution of Populations 2007-2008 5 Agents of evolutionary change Mutation Gene Flow Non-random mating Genetic Drift Selection Populations & gene pools Concepts a population is a localized group
Læs mereSkriftlig Eksamen Diskret matematik med anvendelser (DM72)
Skriftlig Eksamen Diskret matematik med anvendelser (DM72) Institut for Matematik & Datalogi Syddansk Universitet, Odense Onsdag den 18. januar 2006 Alle sædvanlige hjælpemidler (lærebøger, notater etc.),
Læs mereModtageklasser i Tønder Kommune
Modtageklasser i Tønder Kommune - et tilbud i Toftlund og Tønder til børn, der har behov for at blive bedre til dansk TOFTLUND TØNDER Hvad er en modtageklasse? En modtageklasse er en klasse med særligt
Læs mereFejlbeskeder i SMDB. Business Rules Fejlbesked Kommentar. Validate Business Rules. Request- ValidateRequestRegist ration (Rules :1)
Fejlbeskeder i SMDB Validate Business Rules Request- ValidateRequestRegist ration (Rules :1) Business Rules Fejlbesked Kommentar the municipality must have no more than one Kontaktforløb at a time Fejl
Læs mereVLSI Design. DC & Transient Response. EE 447 VLSI Design 4: DC and Transient Response 1
VLSI Design DC & Transient Response 4: DC and Transient Response 1 Outline DC Response Logic Levels and Noise Margins Transient Response Delay Estimation 4: DC and Transient Response DC Response DC Response:
Læs mereStrings and Sets: set complement, union, intersection, etc. set concatenation AB, power of set A n, A, A +
Strings and Sets: A string over Σ is any nite-length sequence of elements of Σ The set of all strings over alphabet Σ is denoted as Σ Operators over set: set complement, union, intersection, etc. set concatenation
Læs mereNyhedsmail, december 2013 (scroll down for English version)
Nyhedsmail, december 2013 (scroll down for English version) Kære Omdeler Julen venter rundt om hjørnet. Og netop julen er årsagen til, at NORDJYSKE Distributions mange omdelere har ekstra travlt med at
Læs mereSatisability of Boolean Formulas
SAT exercises 1 March, 2016 slide 1 Satisability of Boolean Formulas Combinatorics and Algorithms Prof. Emo Welzl Assistant: (CAB G36.1, cannamalai@inf.ethz.ch) URL: http://www.ti.inf.ethz.ch/ew/courses/sat16/
Læs mereOXFORD. Botley Road. Key Details: Oxford has an extensive primary catchment of 494,000 people
OXFORD Key Details: Oxford has an extensive primary catchment of 494,000 people Prominent, modern scheme situated in prime retail area Let to PC World & Carpetright and close to Dreams, Currys, Land of
Læs mereLarge Scale Sequencing By Hybridization. Tel Aviv University
Large Scale Sequencing By Hybridization Ron Shamir Dekel Tsur Tel Aviv University Outline Background: SBH Shotgun SBH Analysis of the errorless case Analysis of error-prone Sequencing By Hybridization
Læs mereSouth Baileygate Retail Park Pontefract
Key Details : available June 2016 has a primary shopping catchment of 77,000 (source: PMA), extending to 186,000 within 10km (source: FOCUS) 86,000 sq ft of retail including Aldi, B&M, Poundstretcher,
Læs mereIntroduction Ronny Bismark
Introduction 1 Outline Motivation / Problem Statement Tool holder Sensor calibration Motion primitive Concatenation of clouds Segmentation Next possible pose Problems and Challenges Future Work 2 Motivation
Læs mereCS 4390/5387 SOFTWARE V&V LECTURE 5 BLACK-BOX TESTING - 2
1 CS 4390/5387 SOFTWARE V&V LECTURE 5 BLACK-BOX TESTING - 2 Outline 2 HW Solution Exercise (Equivalence Class Testing) Exercise (Decision Table Testing) Pairwise Testing Exercise (Pairwise Testing) 1 Homework
Læs mereBarnets navn: Børnehave: Kommune: Barnets modersmål (kan være mere end et)
Forældreskema Barnets navn: Børnehave: Kommune: Barnets modersmål (kan være mere end et) Barnets alder: år og måneder Barnet begyndte at lære dansk da det var år Søg at besvare disse spørgsmål så godt
Læs mereBusiness Rules Fejlbesked Kommentar
Fejlbeskeder i SMDB Validate Business Request- ValidateRequestRegi stration ( :1) Business Fejlbesked Kommentar the municipality must have no more than one Kontaktforløb at a time Fejl 1: Anmodning En
Læs mereEngelsk. Niveau D. De Merkantile Erhvervsuddannelser September Casebaseret eksamen. og
052431_EngelskD 08/09/05 13:29 Side 1 De Merkantile Erhvervsuddannelser September 2005 Side 1 af 4 sider Casebaseret eksamen Engelsk Niveau D www.jysk.dk og www.jysk.com Indhold: Opgave 1 Presentation
Læs mereFejlbeskeder i Stofmisbrugsdatabasen (SMDB)
Fejlbeskeder i Stofmisbrugsdatabasen (SMDB) Oversigt over fejlbeskeder (efter fejlnummer) ved indberetning til SMDB via webløsning og via webservices (hvor der dog kan være yderligere typer fejlbeskeder).
Læs mereKursus 02323: Introducerende Statistik. Forelæsning 12: Forsøgsplanlægning. Peder Bacher
Kursus 02323: Introducerende Statistik Forelæsning 12: Forsøgsplanlægning Peder Bacher DTU Compute, Dynamiske Systemer Bygning 303B, Rum 009 Danmarks Tekniske Universitet 2800 Lyngby Danmark e-mail: pbac@dtu.dk
Læs merePattern formation Turing instability
Pattern formation Turing instability Tomáš Vejchodský Centre for Mathematical Biology Mathematical Institute Summer school, Prague, 6 8 August, 213 Outline Motivation Turing instability general conditions
Læs mereIBM Network Station Manager. esuite 1.5 / NSM Integration. IBM Network Computer Division. tdc - 02/08/99 lotusnsm.prz Page 1
IBM Network Station Manager esuite 1.5 / NSM Integration IBM Network Computer Division tdc - 02/08/99 lotusnsm.prz Page 1 New esuite Settings in NSM The Lotus esuite Workplace administration option is
Læs mereHvor er mine runde hjørner?
Hvor er mine runde hjørner? Ofte møder vi fortvivlelse blandt kunder, når de ser deres nye flotte site i deres browser og indser, at det ser anderledes ud, i forhold til det design, de godkendte i starten
Læs mereEngelsk. Niveau C. De Merkantile Erhvervsuddannelser September 2005. Casebaseret eksamen. www.jysk.dk og www.jysk.com.
052430_EngelskC 08/09/05 13:29 Side 1 De Merkantile Erhvervsuddannelser September 2005 Side 1 af 4 sider Casebaseret eksamen Engelsk Niveau C www.jysk.dk og www.jysk.com Indhold: Opgave 1 Presentation
Læs mereSpecial VFR. - ved flyvning til mindre flyveplads uden tårnkontrol som ligger indenfor en kontrolzone
Special VFR - ved flyvning til mindre flyveplads uden tårnkontrol som ligger indenfor en kontrolzone SERA.5005 Visual flight rules (a) Except when operating as a special VFR flight, VFR flights shall be
Læs mereOn the complexity of drawing trees nicely: corrigendum
Acta Informatica 40, 603 607 (2004) Digital Object Identifier (DOI) 10.1007/s00236-004-0138-y On the complexity of drawing trees nicely: corrigendum Thorsten Akkerman, Christoph Buchheim, Michael Jünger,
Læs mereArbejsskadeAnmeldelse
ArbejsskadeAnmeldelse OpretAnmeldelse 001 All Klassifikations: KlassifikationKode is an unknown value in the current Klassifikation 002 All Klassifikations: KlassifikationKode does not correspond to KlassifikationTekst
Læs mereHeuristics for Improving
Heuristics for Improving Model Learning Based Testing Muhammad Naeem Irfan VASCO-LIG LIG, Computer Science Lab, Grenoble Universities, 38402 Saint Martin d Hères France Introduction Component Based Software
Læs mereParticle-based T-Spline Level Set Evolution for 3D Object Reconstruction with Range and Volume Constraints
Particle-based T-Spline Level Set for 3D Object Reconstruction with Range and Volume Constraints Robert Feichtinger (joint work with Huaiping Yang, Bert Jüttler) Institute of Applied Geometry, JKU Linz
Læs mereTimetable will be aviable after sep. 5. when the sing up ends. Provicius timetable on the next sites.
English Information about the race. Practise Friday oct. 9 from 12.00 to 23.00 Saturday oct. 10. door open at 8.00 to breakfast/coffee Both days it will be possible to buy food and drinks in the racecenter.
Læs mereSport for the elderly
Sport for the elderly - Teenagers of the future Play the Game 2013 Aarhus, 29 October 2013 Ditte Toft Danish Institute for Sports Studies +45 3266 1037 ditte.toft@idan.dk A growing group in the population
Læs mereFrequency Dispersion: Dielectrics, Conductors, and Plasmas
1/23 Frequency Dispersion: Dielectrics, Conductors, and Plasmas Carlos Felipe Espinoza Hernández Professor: Jorge Alfaro Instituto de Física Pontificia Universidad Católica de Chile 2/23 Contents 1 Simple
Læs mereNoter til kursusgang 9, IMAT og IMATØ
Noter til kursusgang 9, IMAT og IMATØ matematik og matematik-økonomi studierne 1. basissemester Esben Høg 4. november 013 Institut for Matematiske Fag Aalborg Universitet Esben Høg Noter til kursusgang
Læs mereTrolling Master Bornholm 2016 Nyhedsbrev nr. 5
Trolling Master Bornholm 2016 Nyhedsbrev nr. 5 English version further down Kim Finne med 11 kg laks Laksen blev fanget i denne uge øst for Bornholm ud for Nexø. Et andet eksempel er her to laks taget
Læs mereDen nye Eurocode EC Geotenikerdagen Morten S. Rasmussen
Den nye Eurocode EC1997-1 Geotenikerdagen Morten S. Rasmussen UDFORDRINGER VED EC 1997-1 HVAD SKAL VI RUNDE - OPBYGNINGEN AF DE NYE EUROCODES - DE STØRSTE UDFORDRINGER - ER DER NOGET POSITIVT? 2 OPBYGNING
Læs mereBilag. Resume. Side 1 af 12
Bilag Resume I denne opgave, lægges der fokus på unge og ensomhed gennem sociale medier. Vi har i denne opgave valgt at benytte Facebook som det sociale medie vi ligger fokus på, da det er det største
Læs mereCirculating Beams Søren Pape Møller ISA / DANFYSIK A/S Chapter 4 i Wilson - 1 hour
Circulating Beams Søren Pape Møller ISA / DANFYSIK A/S Chapter 4 i Wilson - 1 hour Particles in space En partikel har to transversale koordinater og en longitudinal og tilsvarende hastigheder. Ofte er
Læs mereInstructor: Jessica Wu Harvey Mudd College
Kernels Instructor: Jessica Wu Harvey Mudd College The instructor gratefully acknowledges Andrew Ng (Stanford), Eric Eaton (UPenn), Tommi Jaakola (MIT) and the many others who made their course materials
Læs mereTrolling Master Bornholm 2012
Trolling Master Bornholm 1 (English version further down) Tak for denne gang Det var en fornøjelse især jo også fordi vejret var med os. Så heldig har vi aldrig været før. Vi skal evaluere 1, og I må meget
Læs mereECE 551: Digital System * Design & Synthesis Lecture Set 5
ECE 551: Digital System * Design & Synthesis Lecture Set 5 5.1: Verilog Behavioral Model for Finite State Machines (FSMs) 5.2: Verilog Simulation I/O and 2001 Standard (In Separate File) 3/4/2003 1 ECE
Læs mereDM549 Diskrete Metoder til Datalogi
DM549 Diskrete Metoder til Datalogi Spørgsmål 1 (8%) Hvilke udsagn er sande? Husk, at symbolet betyder går op i. Which propositions are true? Recall that the symbol means divides. Svar 1.a: n Z: 2n > n
Læs mereATEX direktivet. Vedligeholdelse af ATEX certifikater mv. Steen Christensen stec@teknologisk.dk www.atexdirektivet.
ATEX direktivet Vedligeholdelse af ATEX certifikater mv. Steen Christensen stec@teknologisk.dk www.atexdirektivet.dk tlf: 7220 2693 Vedligeholdelse af Certifikater / tekniske dossier / overensstemmelseserklæringen.
Læs mereA multimodel data assimilation framework for hydrology
A multimodel data assimilation framework for hydrology Antoine Thiboult, François Anctil Université Laval June 27 th 2017 What is Data Assimilation? Use observations to improve simulation 2 of 8 What is
Læs mereRotational Properties of Bose - Einstein Condensates
Rotational Properties of Bose - Einstein Condensates Stefan Baumgärtner April 30, 2013 1 / 27 Stefan Baumgärtner Rotational Properties of Bose - Einstein Condensates Outline 2 / 27 Stefan Baumgärtner Rotational
Læs mereBrug sømbrættet til at lave sjove figurer. Lav fx: Få de andre til at gætte, hvad du har lavet. Use the nail board to make funny shapes.
Brug sømbrættet til at lave sjove figurer. Lav f: Et dannebrogsflag Et hus med tag, vinduer og dør En fugl En bil En blomst Få de andre til at gætte, hvad du har lavet. Use the nail board to make funn
Læs mereImproving Interdisciplinary Education of Anatomy, Practical Sports using Non-Profit Software
Improving Interdisciplinary Education of Anatomy, Biomechanics and Practical Sports using Non-Profit Software Interdeciplinary Sports Biomechanics Anatomy How to improve interdeciplinary? Examples in biomechanics
Læs mereBasic Design Flow. Logic Design Logic synthesis Logic optimization Technology mapping Physical design. Floorplanning Placement Fabrication
Basic Design Flow System design System/Architectural Design Instruction set for processor Hardware/software partition Memory, cache Logic design Logic Design Logic synthesis Logic optimization Technology
Læs mereE-PAD Bluetooth hængelås E-PAD Bluetooth padlock E-PAD Bluetooth Vorhängeschloss
E-PAD Bluetooth hængelås E-PAD Bluetooth padlock E-PAD Bluetooth Vorhängeschloss Brugervejledning (side 2-6) Userguide (page 7-11) Bedienungsanleitung 1 - Hvordan forbinder du din E-PAD hængelås med din
Læs mereOversigt. 1 Motiverende eksempel - energiforbrug. 2 Hypotesetest (Repetition) 3 Two-sample t-test og p-værdi. 4 Konfidensinterval for forskellen
Kursus 02402/02323 Introducerende Statistik Forelæsning 6: Sammenligning af to grupper Oversigt 1 Motiverende eksempel - energiforbrug 2 Hypotesetest (Repetition) 3 Klaus K. Andersen og Per Bruun Brockhoff
Læs mere28 April 2003 Retrospective: Semicore Visit
28 April 2003 Retrospective: Semicore Visit What is highest growth Industry? Rebuild versus remanufacture Importance of Documentation, blueprinting, spares What are barriers to high uptime? Review Homeworks
Læs mereCross-Sectorial Collaboration between the Primary Sector, the Secondary Sector and the Research Communities
Cross-Sectorial Collaboration between the Primary Sector, the Secondary Sector and the Research Communities B I R G I T T E M A D S E N, P S Y C H O L O G I S T Agenda Early Discovery How? Skills, framework,
Læs mereIntro to: Symposium on Syntactic Islands in Scandinavian and English
Intro to: Symposium on Syntactic Islands in Scandinavian and English Ken Ramshøj Christensen Dept. of English, AU Symposium on Syntactic Islands in Scandinavian and English Aarhus University, June 11-12,
Læs mereMolio specifications, development and challenges. ICIS DA 2019 Portland, Kim Streuli, Molio,
Molio specifications, development and challenges ICIS DA 2019 Portland, Kim Streuli, Molio, 2019-06-04 Introduction The current structure is challenged by different factors. These are for example : Complex
Læs mereSampling real algebraic varieties for topological data analysis
Sampling real algebraic varieties for topological data analysis Joint with: Emilie Dufresne (U. York) Heather Harrington (U. Oxford) Jonathan Hauenstein (U. Notre Dame) AG19, July 2019 Sampling real varieties
Læs mereSKRIFTLIG EKSAMEN I NUMERISK DYNAMIK Bygge- og Anlægskonstruktion, 8. semester Fredag den 30. juni 2005, kl Alle hjælpemidler er tilladt
SKRIFTLIG EKSAMEN I NUMERISK DYNAMIK Bygge- og Anlægskonstruktion, 8. semester Fredag den 3. juni 5, kl. 8.3-.3 Alle hjælpemidler er tilladt OPGAVE u = y B u = u C A x c u = D u = Figuren viser en homogen
Læs mereUnitel EDI MT940 June 2010. Based on: SWIFT Standards - Category 9 MT940 Customer Statement Message (January 2004)
Unitel EDI MT940 June 2010 Based on: SWIFT Standards - Category 9 MT940 Customer Statement Message (January 2004) Contents 1. Introduction...3 2. General...3 3. Description of the MT940 message...3 3.1.
Læs mereSammenligning af adresser til folkeregistrering (CPR) og de autoritative adresser
Sammenligning af adresser til folkeregistrering (CPR) og de autoritative adresser Comparison of addresses used in the population register and the authentic addresses Side 1 Formål Purpose Undersøge omfanget
Læs mereMeget formel, modtager har en meget speciel titel som skal bruges i stedet for deres navne
- Åbning Engelsk Dansk Dear Mr. President, Kære Hr. Direktør, Meget formel, modtager har en meget speciel titel som skal bruges i stedet for deres navne Dear Sir, Formel, mandelig modtager, navn ukendt
Læs mereMeget formel, modtager har en meget speciel titel som skal bruges i stedet for deres navne
- Åbning Dansk Engelsk Kære Hr. Direktør, Dear Mr. President, Meget formel, modtager har en meget speciel titel som skal bruges i stedet for deres navne Kære Hr., Formel, mandelig modtager, navn ukendt
Læs mereTrolling Master Bornholm 2014?
Trolling Master Bornholm 214? (English version further down) Trolling Master Bornholm 214? Den endelige beslutning er ikke taget endnu, men meget tyder på at vi kan gennemføre TMB i 214. Det ser nemlig
Læs mereAktivering af Survey funktionalitet
Surveys i REDCap REDCap gør det muligt at eksponere ét eller flere instrumenter som et survey (spørgeskema) som derefter kan udfyldes direkte af patienten eller forsøgspersonen over internettet. Dette
Læs mereEksamen i Signalbehandling og matematik
Opgave. (%).a. Figur og afbilleder et diskret tid signal [n ] og dets DTFT. [n] bruges som input til et LTI filter med en frekvens amplitude respons som vist på figur. Hvilket af de 4 output signaler (y
Læs mereSortering fra A-Z. Henrik Dorf Chefkonsulent SAS Institute
Sortering fra A-Z Henrik Dorf Chefkonsulent SAS Institute Hvorfor ikke sortering fra A-Å? Det er for svært Hvorfor ikke sortering fra A-Å? Hvorfor ikke sortering fra A-Å? Hvorfor ikke sortering fra A-Å?
Læs merek normalfordelte observationsrækker (ensidet variansanalyse)
k normalfordelte observationsrækker (ensidet variansanalyse) Lad x ij, i = 1,...,k, j = 1,..., n i, være udfald af stokastiske variable X ij og betragt modellen M 1 : X ij N(µ i, σ 2 ). Estimaterne er
Læs mereTM4 Central Station. User Manual / brugervejledning K2070-EU. Tel Fax
TM4 Central Station User Manual / brugervejledning K2070-EU STT Condigi A/S Niels Bohrs Vej 42, Stilling 8660 Skanderborg Denmark Tel. +45 87 93 50 00 Fax. +45 87 93 50 10 info@sttcondigi.com www.sttcondigi.com
Læs merehow to save excel as pdf
1 how to save excel as pdf This guide will show you how to save your Excel workbook as PDF files. Before you do so, you may want to copy several sheets from several documents into one document. To do so,
Læs mereTrolling Master Bornholm 2014
Trolling Master Bornholm 2014 (English version further down) Den ny havn i Tejn Havn Bornholms Regionskommune er gået i gang med at udvide Tejn Havn, og det er med til at gøre det muligt, at vi kan være
Læs mereAsking whether there are commission fees when you withdraw money in a certain country
- General Can I withdraw money in [country] without paying fees? Kan jeg hæve penge i [land] uden at betale gebyrer? Asking whether there are commission fees when you withdraw money in a certain country
Læs mereAsking whether there are commission fees when you withdraw money in a certain country
- General Kan jeg hæve penge i [land] uden at betale gebyrer? Can I withdraw money in [country] without paying fees? Asking whether there are commission fees when you withdraw money in a certain country
Læs mere