Applied Research Laboratory. Decision Theory and Receiver Design


 Allison Blankenship
 3 years ago
 Views:
Transcription
1 Decson Theor and Recever Desgn
2 Sgnal Detecton and Performance Estmaton Sgnal Processor Decde Sgnal s resent or Sgnal s not resent Nose Nose Sgnal? Problem: How should receved sgnals be rocessed n order to detect sgnals n nose? What knd of detecton erformance can be exected? The aroach to soluton: Must be statstcal, snce nose s nvolved Imlement hothess testng
3 Sgnal Detecton Inut to detector s sgnal lus nose. Requrements exressed n terms of robablt of detecton robablt of false alarm Aled Research Laborator Threshold for declarng detecton s set based on models for sgnal and nose Nose background estmaton can be erformed on data to mrove model. Oututs of detector are threshold crossngs Performance defned b recever oeratng characterstc ROC curve robablt of detecton vs. robablt of false alarm for a artcular SNR.
4 Detecton In Nose 3 sgnal nose mean nose nose mean T T sgnal + nose Tme
5 Performance Crtera: Detecton Threshold Probablt of detecton P D Probablt of false alarm P FA These crtera are not ndeendent: a lower threshold ncreases P D, but also ncreases P FA. Theoretcal ROC s used to set thresholds. True test s erformance n water.
6 Recever Oeratng Curve ROC Probablt of Detecton P D T Decreasng threshold T Probablt of False Alarm P FA
7 Possble Hotheses: H : Onl nose s resent Hothess Testng H : Sgnal s resent n addton to nose Stes n formng hotheses: Process arra outut to obtan a detecton statstc x. Calculate the a osteror robabltes PH x and PH x. Pck the hothess whose robablt s the hghest: the maxmum a osteror, or MAP estmate. P H P H x x, <, Choose H Choose H
8 Hothess Testng Cont d Equvalentl, we can use Baes rule to wrte: P H x P x P x H P H P H x P x P x H P H PH and PH are called a ror robabltes Then the test can be wrtten: P H P H x x P x H P x H P H P H, <, Choose H Choose H
9 Hothess Testng Cont d Aled Research Laborator An equvalent test s P x P x H H > P H P H P H P H,, Choose Choose H H P x H λ x s called the lkelhood rato P x H
10 Asde: Baes Rule and Notaton Probablt denst functons are often used to descrbe contnuous random varables: P x Baes Rule as wrtten for robabltes also holds for robablt denst functons df. x A comact notaton s used n what follows: Lkelhood raton test wrtten n terms of r x dx x H x x H x x x > P H P H P H P H,, Choose H Choose H
11 A Frst Examle: Constant Sgnal The ossble nuts are: H H : : x t x t n t μ + n t Nose Sgnal onl lus nose If n t s Gaussan dstrbute d and μ x H x and x H x, then are as shown below : x πσ x πσ / / x ex σ ex x μ σ
12 At tme t, we receve a sgnal xt. Knowng x and x, we can calculate the lkelhood rato λ x x x and comare t to a threshold λ and decde accordngl: λ, λ x < λ, P H P H Choose H Choose H Note that γ s the value of x at whch λx λ n the fgure.
13 Errors and Correct Decsons Aled Research Laborator The ossble errors are: False Alarm: We choose H when H s the rght answer. False Dsmssal: We choose H when H s the rght answer. The ossble correct decsons are: Detecton: We choose H when t s the rght answer. Correct Dsmssal: We choose H when t s the rght answer.
14 Probabltes of Errors and Correct Decsons P FA P FD γ γ x dx x dx Errors P D P CD γ x dx γ x dx Correct Decsons Note : P + P P + P because x dx CD FA FD D 
15 NemanPearson Crteron Aled Research Laborator Usuall we don t know PH and PH and thus cannot calculate λ from ther rato. Instead, we can secf a desred P FA, or false alarm rate, and use t to obtan γ. P FA γ x dx secfed false alarm robablt Then we can calculate λ γ γ or just comare x to γ drectl.
16 Same Examle: Multle Samles, σ μ πσ σ πσ / / x ex x x ex x For each samle x xt, the robabltes are:
17 If we have a set of M multle, ndeendent samles, then ther jont robablt denst functons under H and H are and,... x, x x M / M x ex x σ πσ M / M x ex σ πσ M / M x ex x σ μ πσ Same Examle: Multle Samles Cont d
18 The lkelhood rato becomes: where s the mean value of the samles. Note that each x s Gaussan wth mean under H or μ under H. Also, each x has varance σ under both H and H. Then s also Gaussan, wth the same mean, but wth varance M x M σ μ σ μ σ μ λ M M ex x x ex x x x M M σ Same Examle: Multle Samles Cont d
19 Same Examle: Multle Samles Cont d s a detecton statstc.e. t s a suffcent statstc Usng the NemanPearson crteron, the robablt of a false alarm P FA γ can be used to obtan a threshold γ for. M Note that usng x satsfes our ntuton that the M d recever should counter the effects of nose b averagng the samles.
20 Second Examle: Arbtrar But Known Sgnal Possble recever nuts are: H : xt nt H : xt st + nt Nose onl Sgnal lus nose If the sgnal s resent, we know ts shae exactl. Assume we have M samles s st n the nterval,t. The robabltes are: Under H : x M M / x πσ ex σ Under H : x M / x s πσ ex σ M
21 The lkelhood rato s: The second term can be calculated before recevng the samles. As we samle more fnel n the nterval,t, the summaton becomes the ntegral: where E s the energ n the sgnal. M M M s s x ex x s x ex x x x σ σ σ λ T M dt t s s E
22 The test statstc n ths case s: x M x s T xt st dt Note that the receved sgnal xt s beng correlated wth the sgnal we are trng to detect st. Equvalentl, we can flter xt usng a flter wth mulse resonse functon htstτ as can be seen from ths equaton: T h τ xt τ dτ T st τ xt τ dτ st xt dt A flter whose mulse resonse functon s matched to the sgnal n ths wa s called a matched flter. T
23 We can defne the SNR of to be: Aled Research Laborator Test Statstc SNR The exected values of the test statstc under H and H are E H SNR E H [ E E ] E E var T T xt st dt xt + nt st dt E The varance of under H s usng the shorthand : TT [ ] E st s τ nt n τ dtd E var τ H
24 Let nt be Gaussan whte nose wth sectral level,.e.: R nn τ N δ τ N Then var TT τ δ τ τ N NE st s t dtd And so: SNR E N As long as nt s whte Gaussan nose WGN, there s no other recever,.e. no other test statstc, whch has a hgher SNR. For man other tes of nose, the matched flter s otmal or near otmal as well. Ths s wh the matched flter s used.
25 Thrd Examle: Sgnal Known Excet Amltude and Start Tme Ths s the most common case, n whch we are  Lookng for a target echo  Lstenng for a radated sgnal Aled Research Laborator Exact arrval tme and sgnal amltude are unknown. The hotheses are: H : x t n t Nose onl H : x t a s t t + n t a, t unknown As before, T s the duraton of st
26 We al the sgnal to a matched flter. under H, the outut s t T h τ x t τ dτ T st τ [ a s t τ t + n t τ ] dτ a R s t T t + T st τ n t τ dτ The frst term s the autocorrelaton functon as s at a lag of t T t. It s maxmum when t T+ t, the tme corresondng to the end of the ulse arrval The second term s random due to the nose.
27 Assume st s a tone burst: The autocorrelaton functon s:
28 Autocorrelaton functon s wrtten: R s A a T cos πf t,, T T otherwse Can get the enveloe of Rs b squarng and lowass flterng A a [ R ] T s lf 8 Ths s maxmum when ttt or tt+t. Thus the eak n [ t] lf occurs at t T+t, and snce we know T, can get t
29 Therefore, we defne a new test statstc Zt: The robablt denst functons of Zt under H and H are shown b Burdc to be: Where and s the zeroorder modfed Bessel functon. [ ] lf t Zt S   E  zs z I z ex z N, z ex z σ σ σ σ σ σ S SNR I
30 The robablt denst functons are lotted below Can use the NemanPearson crteron to get γ, then calculate P D P FA γ z dz
31 Fourth Examle: Possble Doler Shft Nonzero radal moton between a transmtter or reflector and recever causes the frequenc of the receved sgnal to be shfted relatve to the transmtted sgnal. Ths s called Doler Shft. Ths comlcaton s usuall met b mlementng a arallel bank of flters or FFT, each matched to a dfferent frequenc. l L
32 Passve Broadband Detecton Want to detect targets wth broadband sgnatures: Aled Research Laborator Assume we know the ambent nose ower sectrum
33 Passve Broadband Detecton Cont d Use the recever shown below, where h t and h t are flters whose mulse functons need to be determned.
34 Passve Broadband Detecton cont. It has been shown that the Eckart Flter s otmal for h t: H f ψ f ψ f s n Eckart Flter Note: when the nose s whte, H f looks lke Ψ s f. Otherwse, H f s mnmzed when Ψ n f s large The ower sectrum of under H and H s then: Ψ Ψ and f Ψ f H f SNR Ψ f + Ψ f n s [ Ψ f Ψ f ] Ψ f n f df Ψ s f Ψ f H n f df Ψ s f Ψ f n Ψ f df Ψ f s n Ψ s f df Ψ f n Ψ s f + Ψ f n
35 Passve Broadband Detecton cont. Burdc shows that the SNR of the outut of the enveloe detector s SNR SNR The commonlused ost detecton flter s an averager whose duraton s as long as ossble, h, T t, T τ otherwse The roduct of Τβ ε s tcall large, where β ε s the effectve nose bandwdth at the outut of the redetecton flter h τ,.e. β ε s the wdth of a rectangular flter whch admts the same nose ower. The frequenc doman exresson for β ε s derved b Burdc n secton 84 to be T β ε [ ] Ψ f H f df Ψ n n f H f 4 df
36 Passve Broadband Detecton cont. Usng the Eckert Flter β ε Ψ s f df Ψ f Ψ f df Ψ f n s n Gven large Tβ ε, Burdc shows that the SNR at the averager outut s SNR z Tβ εsnr Tβε SNR Usng the exressons for SNR and β ε SNR Ψ s f Ψs f df df Ψ n f Ψn f Ψs f T T df Ψs f f n f df Ψ Ψ s Ψ f df n Ψ n f z Note the effect on SNR z of ncreasng T.
37 Passve Narrowband Detecton Aled Research Laborator Want to detect targets that emt ure tone sgnatures: Recever s shown below essentall a sectrum analzer
38 Passve Narrowband Detecton Cont d Tcall mlemented b Fourner transformng the nut sgnal. Second flter s an ntegrator averager. Long averages are usuall emloed, so that Tβ >>. If : Sgnal Sectrum : Ψ f s a δ f f Flter : H f,,  β f f β otherwse Nose Sectrum : Ψ f n Constant around f
39 Passve Narrowband Detecton Cont d Then SNR a ψ f n β As before, the SNR of the test statstc Z s SNR z Tβ SNR Puttng these together SNR z T a β ψ n f
Portfolio Loss Distribution
Portfolo Loss Dstrbuton Rsky assets n loan ortfolo hghly llqud assets holdtomaturty n the bank s balance sheet Outstandngs The orton of the bank asset that has already been extended to borrowers. Commtment
More informationPassive Filters. References: Barbow (pp 265275), Hayes & Horowitz (pp 3260), Rizzoni (Chap. 6)
Passve Flters eferences: Barbow (pp 6575), Hayes & Horowtz (pp 360), zzon (Chap. 6) Frequencyselectve or flter crcuts pass to the output only those nput sgnals that are n a desred range of frequences (called
More informationCommunication Networks II Contents
8 / 1  Communcaton Networs II (Görg)  www.comnets.unbremen.de Communcaton Networs II Contents 1 Fundamentals of probablty theory 2 Traffc n communcaton networs 3 Stochastc & Marovan Processes (SP
More informationQuantization Effects in Digital Filters
Quantzaton Effects n Dgtal Flters Dstrbuton of Truncaton Errors In two's complement representaton an exact number would have nfntely many bts (n general). When we lmt the number of bts to some fnte value
More informationWhat is Candidate Sampling
What s Canddate Samplng Say we have a multclass or mult label problem where each tranng example ( x, T ) conssts of a context x a small (mult)set of target classes T out of a large unverse L of possble
More informationAn Alternative Way to Measure Private Equity Performance
An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate
More informationx f(x) 1 0.25 1 0.75 x 1 0 1 1 0.04 0.01 0.20 1 0.12 0.03 0.60
BIVARIATE DISTRIBUTIONS Let be a varable that assumes the values { 1,,..., n }. Then, a functon that epresses the relatve frequenc of these values s called a unvarate frequenc functon. It must be true
More informationFrequency Selective IQ Phase and IQ Amplitude Imbalance Adjustments for OFDM Direct Conversion Transmitters
Frequency Selectve IQ Phase and IQ Ampltude Imbalance Adjustments for OFDM Drect Converson ransmtters Edmund Coersmeer, Ernst Zelnsk Noka, Meesmannstrasse 103, 44807 Bochum, Germany edmund.coersmeer@noka.com,
More information9.1 The Cumulative Sum Control Chart
Learnng Objectves 9.1 The Cumulatve Sum Control Chart 9.1.1 Basc Prncples: Cusum Control Chart for Montorng the Process Mean If s the target for the process mean, then the cumulatve sum control chart s
More informationPSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 12
14 The Chsquared dstrbuton PSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 1 If a normal varable X, havng mean µ and varance σ, s standardsed, the new varable Z has a mean 0 and varance 1. When ths standardsed
More informationVision Mouse. Saurabh Sarkar a* University of Cincinnati, Cincinnati, USA ABSTRACT 1. INTRODUCTION
Vson Mouse Saurabh Sarkar a* a Unversty of Cncnnat, Cncnnat, USA ABSTRACT The report dscusses a vson based approach towards trackng of eyes and fngers. The report descrbes the process of locatng the possble
More informationThe Analysis of Outliers in Statistical Data
THALES Project No. xxxx The Analyss of Outlers n Statstcal Data Research Team Chrysses Caron, Assocate Professor (P.I.) Vaslk Karot, Doctoral canddate Polychrons Economou, Chrstna Perrakou, Postgraduate
More informationRecurrence. 1 Definitions and main statements
Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.
More informationLoad Balancing of Parallelized Information Filters
IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. XXX, NO. XX, XXXXXXX 2001 1 Load Balancng of Parallelzed Informaton Flters Nel C. Rowe, Member, IEEE Comuter Socety, and Amr Zaky, Member, IEEE
More informationHYPOTHESIS TESTING OF PARAMETERS FOR ORDINARY LINEAR CIRCULAR REGRESSION
HYPOTHESIS TESTING OF PARAMETERS FOR ORDINARY LINEAR CIRCULAR REGRESSION Abdul Ghapor Hussn Centre for Foundaton Studes n Scence Unversty of Malaya 563 KUALA LUMPUR Emal: ghapor@umedumy Abstract Ths paper
More informationModule 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..
More informationCalculation of Sampling Weights
Perre Foy Statstcs Canada 4 Calculaton of Samplng Weghts 4.1 OVERVIEW The basc sample desgn used n TIMSS Populatons 1 and 2 was a twostage stratfed cluster desgn. 1 The frst stage conssted of a sample
More informationNaïve Bayes classifier & Evaluation framework
Lecture aïve Bayes classfer & Evaluaton framework Mlos Hauskrecht mlos@cs.ptt.edu 539 Sennott Square Generatve approach to classfcaton Idea:. Represent and learn the dstrbuton p x, y. Use t to defne probablstc
More informationSection B9: Zener Diodes
Secton B9: Zener Dodes When we frst talked about practcal dodes, t was mentoned that a parameter assocated wth the dode n the reverse bas regon was the breakdown voltage, BR, also known as the peaknverse
More informationTHE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek
HE DISRIBUION OF LOAN PORFOLIO VALUE * Oldrch Alfons Vascek he amount of captal necessary to support a portfolo of debt securtes depends on the probablty dstrbuton of the portfolo loss. Consder a portfolo
More informationbenefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).
REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or
More informationSolutions to First Midterm
rofessor Chrstano Economcs 3, Wnter 2004 Solutons to Frst Mdterm. Multple Choce. 2. (a) v. (b). (c) v. (d) v. (e). (f). (g) v. (a) The goods market s n equlbrum when total demand equals total producton,.e.
More informationChapter 4 ECONOMIC DISPATCH AND UNIT COMMITMENT
Chapter 4 ECOOMIC DISATCH AD UIT COMMITMET ITRODUCTIO A power system has several power plants. Each power plant has several generatng unts. At any pont of tme, the total load n the system s met by the
More informationL10: Linear discriminants analysis
L0: Lnear dscrmnants analyss Lnear dscrmnant analyss, two classes Lnear dscrmnant analyss, C classes LDA vs. PCA Lmtatons of LDA Varants of LDA Other dmensonalty reducton methods CSCE 666 Pattern Analyss
More informationAn RFID Distance Bounding Protocol
An RFID Dstance Boundng Protocol Gerhard P. Hancke and Markus G. Kuhn May 22, 2006 An RFID Dstance Boundng Protocol p. 1 Dstance boundng Verfer d Prover Places an upper bound on physcal dstance Does not
More informationPrinciples of Spread Spectrum and CDMA
Separaton of Overlappng Sgnals Prncples of Spread Spectrum and CDMA Dr Bhasar Ramamurth Professor Department of Electrcal Engneerng Indan Insttute of echnology Madras. Frequency Dvson Multplexng sgnals
More informationSolution: Let i = 10% and d = 5%. By definition, the respective forces of interest on funds A and B are. i 1 + it. S A (t) = d (1 dt) 2 1. = d 1 dt.
Chapter 9 Revew problems 9.1 Interest rate measurement Example 9.1. Fund A accumulates at a smple nterest rate of 10%. Fund B accumulates at a smple dscount rate of 5%. Fnd the pont n tme at whch the forces
More informationLinear Regression Analysis for STARDEX
Lnear Regresson Analss for STARDEX Malcolm Halock, Clmatc Research Unt The followng document s an overvew of lnear regresson methods for reference b members of STARDEX. Whle t ams to cover the most common
More informationINVESTIGATION OF VEHICULAR USERS FAIRNESS IN CDMAHDR NETWORKS
21 22 September 2007, BULGARIA 119 Proceedngs of the Internatonal Conference on Informaton Technologes (InfoTech2007) 21 st 22 nd September 2007, Bulgara vol. 2 INVESTIGATION OF VEHICULAR USERS FAIRNESS
More informationBlind Estimation of Transmit Power in Wireless Networks
Bln Estmaton of Transmt Power n Wreless Networks Murtaza Zafer (IBM Research), Bongjun Ko (IBM Research), Chatschk Bskan (IBM Research) an Ivan Ho (Imperal College, UK) Transmtpower Estmaton: Problem
More informationA Study on Secure Data Storage Strategy in Cloud Computing
Journal of Convergence Informaton Technology Volume 5, Number 7, Setember 00 A Study on Secure Data Storage Strategy n Cloud Comutng Danwe Chen, Yanjun He, Frst Author College of Comuter Technology, Nanjng
More informationAnswer: A). There is a flatter IS curve in the high MPC economy. Original LM LM after increase in M. IS curve for low MPC economy
4.02 Quz Solutons Fall 2004 MultpleChoce Questons (30/00 ponts) Please, crcle the correct answer for each of the followng 0 multplechoce questons. For each queston, only one of the answers s correct.
More informationThe OC Curve of Attribute Acceptance Plans
The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4
More informationOn some special nonlevel annuities and yield rates for annuities
On some specal nonlevel annutes and yeld rates for annutes 1 Annutes wth payments n geometrc progresson 2 Annutes wth payments n Arthmetc Progresson 1 Annutes wth payments n geometrc progresson 2 Annutes
More informationA Comprehensive Analysis of Bandwidth Request Mechanisms in IEEE 802.16 Networks
A Comrehensve Analyss of Bandwdth Reuest Mechansms n IEEE 802.6 Networks Davd Chuck, KuanYu Chen and J. Morrs Chang Deartment of Electrcal and Comuter Engneerng Iowa State Unversty, Ames, Iowa 500, USA
More informationwww.engineerspress.com Neural Network Solutions for Forward Kinematics Problem of Hybrid SerialParallel Manipulator
www.engneersress.com World of Scences Journal ISSN: 307307 Year: 03 Volume: Issue: 8 Pages: 4858 Aahmad Ghanbar,, Arash ahman Deartment of Mechancal Engneerng, Unversty of Tabrz, Tabrz, Iran School of
More informationDEFINING %COMPLETE IN MICROSOFT PROJECT
CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMISP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,
More informationGraph Theory and Cayley s Formula
Graph Theory and Cayley s Formula Chad Casarotto August 10, 2006 Contents 1 Introducton 1 2 Bascs and Defntons 1 Cayley s Formula 4 4 Prüfer Encodng A Forest of Trees 7 1 Introducton In ths paper, I wll
More informationChapter 7. RandomVariate Generation 7.1. Prof. Dr. Mesut Güneş Ch. 7 RandomVariate Generation
Chapter 7 RandomVarate Generaton 7. Contents Inversetransform Technque AcceptanceRejecton Technque Specal Propertes 7. Purpose & Overvew Develop understandng of generatng samples from a specfed dstrbuton
More informationPAS: A Packet Accounting System to Limit the Effects of DoS & DDoS. Debish Fesehaye & Klara Naherstedt University of IllinoisUrbana Champaign
PAS: A Packet Accountng System to Lmt the Effects of DoS & DDoS Debsh Fesehaye & Klara Naherstedt Unversty of IllnosUrbana Champagn DoS and DDoS DDoS attacks are ncreasng threats to our dgtal world. Exstng
More informationAnalysis and Modeling of Buck Converter in DiscontinuousOutputInductorCurrent Mode Operation *
Energy and Power Engneerng, 3, 5, 85856 do:.436/ee.3.54b63 Publshed Onlne July 3 (htt://www.scr.org/journal/ee) Analyss and Modelng of Buck Converter n DscontnuousOututInductorCurrent Mode Oeraton
More informationRealistic Image Synthesis
Realstc Image Synthess  Combned Samplng and Path Tracng  Phlpp Slusallek Karol Myszkowsk Vncent Pegoraro Overvew: Today Combned Samplng (Multple Importance Samplng) Renderng and Measurng Equaton Random
More informationChapter 3: Dualbandwidth Data Path and BOCP Design
Chater 3: Dualbandwdth Data Path and BOCP Desgn 3. Introducton The focus of ths thess s on the 4G wreless moble Internet networks to rovde data servces wthn the overlang areas of CDA2000WLA networks.
More informationAddendum to: Importing SkillBiased Technology
Addendum to: Importng SkllBased Technology Arel Bursten UCLA and NBER Javer Cravno UCLA August 202 Jonathan Vogel Columba and NBER Abstract Ths Addendum derves the results dscussed n secton 3.3 of our
More informationThe Choice of Direct Dealing or Electronic Brokerage in Foreign Exchange Trading
The Choce of Drect Dealng or Electronc Brokerage n Foregn Exchange Tradng Mchael Melvn Arzona State Unversty & Ln Wen Unversty of Redlands MARKET PARTICIPANTS: Customers Endusers Multnatonal frms Central
More informationQUANTUM MECHANICS, BRAS AND KETS
PH575 SPRING QUANTUM MECHANICS, BRAS AND KETS The followng summares the man relatons and defntons from quantum mechancs that we wll be usng. State of a phscal sstem: The state of a phscal sstem s represented
More informationA) 3.1 B) 3.3 C) 3.5 D) 3.7 E) 3.9 Solution.
ACTS 408 Instructor: Natala A. Humphreys SOLUTION TO HOMEWOR 4 Secton 7: Annutes whose payments follow a geometrc progresson. Secton 8: Annutes whose payments follow an arthmetc progresson. Problem Suppose
More informationThe Greedy Method. Introduction. 0/1 Knapsack Problem
The Greedy Method Introducton We have completed data structures. We now are gong to look at algorthm desgn methods. Often we are lookng at optmzaton problems whose performance s exponental. For an optmzaton
More informationEnergybased Design of Steel Structures According to the Predefined Interstory Drift Ratio 1
Dgest 01, December 01, 15731593 Energybased Desgn of Steel Structures Accordng to the Predefned Interstory Drft Rato 1 Onur ERTER* Özgür BOZDAĞ** ustafa DÜZGÜ*** ABSTRACT The methods whch take lace n
More informationChapter 4 Financial Markets
Chapter 4 Fnancal Markets ECON2123 (Sprng 2012) 14 & 15.3.2012 (Tutoral 5) The demand for money Assumptons: There are only two assets n the fnancal market: money and bonds Prce s fxed and s gven, that
More informationNuno Vasconcelos UCSD
Bayesan parameter estmaton Nuno Vasconcelos UCSD 1 Maxmum lkelhood parameter estmaton n three steps: 1 choose a parametrc model for probabltes to make ths clear we denote the vector of parameters by Θ
More informationRisk Model of LongTerm Production Scheduling in Open Pit Gold Mining
Rsk Model of LongTerm Producton Schedulng n Open Pt Gold Mnng R Halatchev 1 and P Lever 2 ABSTRACT Open pt gold mnng s an mportant sector of the Australan mnng ndustry. It uses large amounts of nvestments,
More informationCalculating the high frequency transmission line parameters of power cables
< ' Calculatng the hgh frequency transmsson lne parameters of power cables Authors: Dr. John Dcknson, Laboratory Servces Manager, N 0 RW E B Communcatons Mr. Peter J. Ncholson, Project Assgnment Manager,
More informationBERNSTEIN POLYNOMIALS
OnLne Geometrc Modelng Notes BERNSTEIN POLYNOMIALS Kenneth I. Joy Vsualzaton and Graphcs Research Group Department of Computer Scence Unversty of Calforna, Davs Overvew Polynomals are ncredbly useful
More informationANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING
ANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING Matthew J. Lberatore, Department of Management and Operatons, Vllanova Unversty, Vllanova, PA 19085, 6105194390,
More informationAdaptive Fractal Image Coding in the Frequency Domain
PROCEEDINGS OF INTERNATIONAL WORKSHOP ON IMAGE PROCESSING: THEORY, METHODOLOGY, SYSTEMS AND APPLICATIONS 222 JUNE,1994 BUDAPEST,HUNGARY Adaptve Fractal Image Codng n the Frequency Doman K AI UWE BARTHEL
More informationAn Overview of Financial Mathematics
An Overvew of Fnancal Mathematcs Wllam Benedct McCartney July 2012 Abstract Ths document s meant to be a quck ntroducton to nterest theory. It s wrtten specfcally for actuaral students preparng to take
More informationProbabilities and Probabilistic Models
Probabltes and Probablstc Models Probablstc models A model means a system that smulates an obect under consderaton. A probablstc model s a model that produces dfferent outcomes wth dfferent probabltes
More informationThe Analysis of Covariance. ERSH 8310 Keppel and Wickens Chapter 15
The Analyss of Covarance ERSH 830 Keppel and Wckens Chapter 5 Today s Class Intal Consderatons Covarance and Lnear Regresson The Lnear Regresson Equaton TheAnalyss of Covarance Assumptons Underlyng the
More informationExtending Probabilistic Dynamic Epistemic Logic
Extendng Probablstc Dynamc Epstemc Logc Joshua Sack May 29, 2008 Probablty Space Defnton A probablty space s a tuple (S, A, µ), where 1 S s a set called the sample space. 2 A P(S) s a σalgebra: a set
More informationIntroduction to Regression
Introducton to Regresson Regresson a means of predctng a dependent varable based one or more ndependent varables. Ths s done by fttng a lne or surface to the data ponts that mnmzes the total error. 
More informationState function: eigenfunctions of hermitian operators> normalization, orthogonality completeness
Schroednger equaton Basc postulates of quantum mechancs. Operators: Hermtan operators, commutators State functon: egenfunctons of hermtan operators> normalzaton, orthogonalty completeness egenvalues and
More informationMulticomponent Distillation
Multcomponent Dstllaton need more than one dstllaton tower, for n components, n1 fractonators are requred Specfcaton Lmtatons The followng are establshed at the begnnng 1. Temperature, pressure, composton,
More informationMean Molecular Weight
Mean Molecular Weght The thermodynamc relatons between P, ρ, and T, as well as the calculaton of stellar opacty requres knowledge of the system s mean molecular weght defned as the mass per unt mole of
More informationMOGENS BLADT ABSTRACT
A REVIEW ON PHASETYPE DISTRIBUTIONS AND THEIR USE IN RISK THEORY BY MOGENS BLADT ABSTRACT Phasetye dstrbutons, defned as the dstrbutons of absorton tmes of certan Markov jum rocesses, consttute a class
More informationOnLine Fault Detection in Wind Turbine Transmission System using Adaptive Filter and Robust Statistical Features
OnLne Fault Detecton n Wnd Turbne Transmsson System usng Adaptve Flter and Robust Statstcal Features Ruoyu L Remote Dagnostcs Center SKF USA Inc. 3443 N. Sam Houston Pkwy., Houston TX 77086 Emal: ruoyu.l@skf.com
More informationClassification errors and permanent disability benefits in Spain
1 Classfcaton errors and permanent dsablty benefts n Span Serg JménezMartín José M. Labeaga Crstna Vlaplana Preto 1. Introducton There s a controverted debate about the effects of permanent dsablty benefts
More informationTime Series Analysis in Studies of AGN Variability. Bradley M. Peterson The Ohio State University
Tme Seres Analyss n Studes of AGN Varablty Bradley M. Peterson The Oho State Unversty 1 Lnear Correlaton Degree to whch two parameters are lnearly correlated can be expressed n terms of the lnear correlaton
More informationOptical SignaltoNoise Ratio and the QFactor in FiberOptic Communication Systems
Applcaton ote: FA9.0. Re.; 04/08 Optcal Sgnaltoose Rato and the QFactor n FberOptc Communcaton Systems Functonal Dagrams Pn Confguratons appear at end of data sheet. Functonal Dagrams contnued at
More informationAPPLICATION OF PROBE DATA COLLECTED VIA INFRARED BEACONS TO TRAFFIC MANEGEMENT
APPLICATION OF PROBE DATA COLLECTED VIA INFRARED BEACONS TO TRAFFIC MANEGEMENT Toshhko Oda (1), Kochro Iwaoka (2) (1), (2) Infrastructure Systems Busness Unt, Panasonc System Networks Co., Ltd. Saedocho
More informationOptimal maintenance of a productioninventory system with continuous repair times and idle periods
Proceedngs o the 3 Internatonal Conerence on Aled Mathematcs and Comutatonal Methods Otmal mantenance o a roductonnventory system wth contnuous rear tmes and dle erods T. D. Dmtrakos* Deartment o Mathematcs
More informationOPTIMAL INVESTMENT POLICIES FOR THE HORSE RACE MODEL. Thomas S. Ferguson and C. Zachary Gilstein UCLA and Bell Communications May 1985, revised 2004
OPTIMAL INVESTMENT POLICIES FOR THE HORSE RACE MODEL Thomas S. Ferguson and C. Zachary Glsten UCLA and Bell Communcatons May 985, revsed 2004 Abstract. Optmal nvestment polces for maxmzng the expected
More informationSupport vector domain description
Pattern Recognton Letters 20 (1999) 1191±1199 www.elsever.nl/locate/patrec Support vector doman descrpton Davd M.J. Tax *,1, Robert P.W. Dun Pattern Recognton Group, Faculty of Appled Scence, Delft Unversty
More informationAnalysis of EnergyConserving Access Protocols for Wireless Identification Networks
From the Proceedngs of Internatonal Conference on Telecommuncaton Systems (ITC97), March 223, 1997. 1 Analyss of EnergyConservng Access Protocols for Wreless Identfcaton etworks Imrch Chlamtac a, Chara
More informationThe covariance is the two variable analog to the variance. The formula for the covariance between two variables is
Regresson Lectures So far we have talked only about statstcs that descrbe one varable. What we are gong to be dscussng for much of the remander of the course s relatonshps between two or more varables.
More information+ + +   This circuit than can be reduced to a planar circuit
MeshCurrent Method The meshcurrent s analog of the nodeoltage method. We sole for a new set of arables, mesh currents, that automatcally satsfy KCLs. As such, meshcurrent method reduces crcut soluton to
More informationIDENTIFICATION AND CONTROL OF A FLEXIBLE TRANSMISSION SYSTEM
Abstract IDENTIFICATION AND CONTROL OF A FLEXIBLE TRANSMISSION SYSTEM Alca Esparza Pedro Dept. Sstemas y Automátca, Unversdad Poltécnca de Valenca, Span alespe@sa.upv.es The dentfcaton and control of a
More informationA Prediction System Based on Fuzzy Logic
Proceedngs of the World Congress on Engneerng and Comuter Scence 2008 WCECS 2008, October 2224, 2008, San Francsco, USA A Predcton System Based on Fuzzy Logc Vadeh.V,Monca.S, Mohamed Shek Safeer.S, Deeka.M
More informationInequality and The Accounting Period. Quentin Wodon and Shlomo Yitzhaki. World Bank and Hebrew University. September 2001.
Inequalty and The Accountng Perod Quentn Wodon and Shlomo Ytzha World Ban and Hebrew Unversty September Abstract Income nequalty typcally declnes wth the length of tme taen nto account for measurement.
More information8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by
6 CHAPTER 8 COMPLEX VECTOR SPACES 5. Fnd the kernel of the lnear transformaton gven n Exercse 5. In Exercses 55 and 56, fnd the mage of v, for the ndcated composton, where and are gven by the followng
More informationINVENTORY MANAGEMENT REVISED
Scence & Mltary 2/2011 INVENTORY MANAGEMENT REVISED Analyss of behavoral asects of decson makng wthn Sales & Oeratons Plannng rocess Peter JUREČKA Abstract: The urose of ths artcle s to extend the standard
More informationMonte Carlo Simulation
Chapter 8 Monte Carlo Smulaton Chapter 8 Monte Carlo Smulaton 8. Introducton Monte Carlo smulaton s named ater the cty o Monte Carlo n Monaco, whch s amous or gamblng such as roulette, dce, and slot machnes.
More informationThe Probit Model. Alexander Spermann. SoSe 2009
The Probt Model Aleander Spermann Unversty of Freburg SoSe 009 Course outlne. Notaton and statstcal foundatons. Introducton to the Probt model 3. Applcaton 4. Coeffcents and margnal effects 5. Goodnessofft
More informationCIRCUITS AND ELECTRONICS. Sinusoidal Steady State
6.00 IRUITS AND ELETRONIS Snusodal Steady State te as: Anant Agarwal and Jeffrey Lang, course materals for 6.00 rcuts and Electroncs, Srng 007. MIT OenourseWare (htt://ocw.mt.edu/), Massachusetts Insttute
More informationNPAR TESTS. OneSample ChiSquare Test. Cell Specification. Observed Frequencies 1O i 6. Expected Frequencies 1EXP i 6
PAR TESTS If a WEIGHT varable s specfed, t s used to replcate a case as many tmes as ndcated by the weght value rounded to the nearest nteger. If the workspace requrements are exceeded and samplng has
More informationADAPTIVE WIENERTURBO SYSTEM AND ADAPTIVE WIENERTURBO SYSTEMS WITH JPEG & BIT PLANE COMPRESSIONS
ISTANBUL UNIVERSITY JOURNAL OF ELECTRICAL & ELECTRONICS ENGINEERING YEAR VOLUME NUMBER : 2007 : 7 : 1 (257276) ADAPTIVE WIENERTURBO SYSTEM AND ADAPTIVE WIENERTURBO SYSTEMS WITH JPEG & BIT PLANE COMPRESSIONS
More informationTime Domain simulation of PD Propagation in XLPE Cables Considering Frequency Dependent Parameters
Internatonal Journal of Smart Grd and Clean Energy Tme Doman smulaton of PD Propagaton n XLPE Cables Consderng Frequency Dependent Parameters We Zhang a, Jan He b, Ln Tan b, Xuejun Lv b, HongJe L a *
More informationCHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol
CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK Sample Stablty Protocol Background The Cholesterol Reference Method Laboratory Network (CRMLN) developed certfcaton protocols for total cholesterol, HDL
More informationA Simple Economic Model about the Teamwork Pedagogy
Appled Mathematcal Scences, Vol. 6, 01, no. 1, 130 A Smple Economc Model about the Teamwork Pedagog Gregor L. Lght Department of Management, Provdence College Provdence, Rhode Island 0918, USA glght@provdence.edu
More informationCS 2750 Machine Learning. Lecture 3. Density estimation. CS 2750 Machine Learning. Announcements
Lecture 3 Densty estmaton Mlos Hauskrecht mlos@cs.ptt.edu 5329 Sennott Square Next lecture: Matlab tutoral Announcements Rules for attendng the class: Regstered for credt Regstered for audt (only f there
More informationLinear Circuits Analysis. Superposition, Thevenin /Norton Equivalent circuits
Lnear Crcuts Analyss. Superposton, Theenn /Norton Equalent crcuts So far we hae explored tmendependent (resste) elements that are also lnear. A tmendependent elements s one for whch we can plot an / cure.
More informationCan Auto Liability Insurance Purchases Signal Risk Attitude?
Internatonal Journal of Busness and Economcs, 2011, Vol. 10, No. 2, 159164 Can Auto Lablty Insurance Purchases Sgnal Rsk Atttude? ChuShu L Department of Internatonal Busness, Asa Unversty, Tawan ShengChang
More informationLuby s Alg. for Maximal Independent Sets using Pairwise Independence
Lecture Notes for Randomzed Algorthms Luby s Alg. for Maxmal Independent Sets usng Parwse Independence Last Updated by Erc Vgoda on February, 006 8. Maxmal Independent Sets For a graph G = (V, E), an ndependent
More information2.4 Bivariate distributions
page 28 2.4 Bvarate dstrbutons 2.4.1 Defntons Let X and Y be dscrete r.v.s defned on the same probablty space (S, F, P). Instead of treatng them separately, t s often necessary to thnk of them actng together
More informationCHAPTER 14 MORE ABOUT REGRESSION
CHAPTER 14 MORE ABOUT REGRESSION We learned n Chapter 5 that often a straght lne descrbes the pattern of a relatonshp between two quanttatve varables. For nstance, n Example 5.1 we explored the relatonshp
More informationFeature selection for intrusion detection. Slobodan Petrović NISlab, Gjøvik University College
Feature selecton for ntruson detecton Slobodan Petrovć NISlab, Gjøvk Unversty College Contents The feature selecton problem Intruson detecton Traffc features relevant for IDS The CFS measure The mrmr measure
More informationMAPP. MERIS level 3 cloud and water vapour products. Issue: 1. Revision: 0. Date: 9.12.1998. Function Name Organisation Signature Date
Ttel: Project: Doc. No.: MERIS level 3 cloud and water vapour products MAPP MAPPATBDClWVL3 Issue: 1 Revson: 0 Date: 9.12.1998 Functon Name Organsaton Sgnature Date Author: Bennartz FUB Preusker FUB Schüller
More informationSketching Sampled Data Streams
Sketchng Sampled Data Streams Florn Rusu, Aln Dobra CISE Department Unversty of Florda Ganesvlle, FL, USA frusu@cse.ufl.edu adobra@cse.ufl.edu Abstract Samplng s used as a unversal method to reduce the
More informationDamage detection in composite laminates using cointap method
Damage detecton n composte lamnates usng contap method S.J. Km Korea Aerospace Research Insttute, 45 EoeunDong, YouseongGu, 35333 Daejeon, Republc of Korea yaeln@kar.re.kr 45 The contap test has the
More informationMULTICHROMATIC ANALYSIS OF INSAR DATA: VALIDATION AND POTENTIAL
MULTICHROMATIC AALYSIS OF ISAR DATA: VALIDATIO AD POTETIAL Fabo Bovenga (), Vto Martno Gacovazzo (), Alberto Refce (), cola Venezan (), Raffaele Vtull () () CR ISSIA, Bar, Va Amendola, /d  706 Bar (Italy),
More information