David HORN and Irit OPHER. School of Physics and Astronomy. Raymond and Beverly Sackler Faculty of Exact Sciences


 Maud Hunter
 2 years ago
 Views:
Transcription
1 Cmplex Dynamics f Neurnal Threshlds David HORN and Irit OPHER Schl f Physics and Astrnmy Raymnd and Beverly Sackler Faculty f Exact Sciences Tel Aviv University, Tel Aviv 69978, Israel Abstract We study an integrate and re mdel f an adapting neurn. Using tw dynamic threshlds we accunt fr cmplex lng term behavir f single neurns under peridic pulsed inputs. We nd that the pattern f tempral respnse is that f a staircase f interspike interval values. The characteristic time scales f transitins between these ISI values are f the rder f tens f secnds. The tempral behavir f ur system can be described as a path thrugh the 2dimensinal phase space f dynamic threshlds. 1 Intrductin Single neurns display interesting cmplex behavir fr dierent inputs. When driven by a cnstant suprathreshld current, a neurn will usually re regularly with sme frequency. After a while, this frequency will decrease t a steady state value manifesting adaptatin f the neurn t the cnstantly applied stimulus. A ttally dierent tempral behavir is seen when the neurn is driven by a peridic stimulus. In a recent experiment, Tal et al: [7] studied the eect f 2 minutes applicatin f 2ms current pulses, using dierent frequencies. The current amplitude was just abve threshld, sucient fr making the neurn re at 1 Hz when stimulated with 1 Hz pulsed inputs. This behavir we call a "1:1 respnse". When the input frequency was higher, abut 1/2 f the neurns respnded with cmplex ring patterns, and did nt display this simple 1:1 respnse. Examples f ISI series recrded in respnse t stimulatin f 3 and 30 Hz are shwn in Fig. 1. It is evident that a high frequency input causes the neurn t respnd with a staircase f ISI values. The time Crrespnding authr. Phne Fax Submitted fr ral presentatin at CNS99. 1
2 Input Frequency=3 Hz Input Frequency=30 Hz Figure 1: ISI recrded in respnse t stimulatins f 3 Hz (upper frame) and 30 Hz (lwer frame). All ISI values are integer multiples f the input perid. intervals between successive spikes grw, but the ring rate des nt necessarily reach a steady state value. In this paper we present a minimal mdel that describes such cmplex and variable behavir. It is based n dynamic threshlds assciated with an I&F neurn. 2 Dynamical Threshlds in an IntegrateandFire Neurn An Integrateandre (I&F ) neurn [3] can be dened by the frmula C dv dt =?g L(V? V rest ) + I (1) where V is the membrane ptential, C is the capacitance, g L is the leak cnductance and I is the external input current. When V reaches threshld a spike is emitted and V is reset t V reset such that V rest < V reset < V threshld V reset + : (2) Refractriness may be added as a shrt deadtime after ring. 2
3 When the external current has a cnstant cmpnent that is much larger than statistical uctuatins, ne can apprximate the interspikeinterval by ISI =? C g L lg(1? g L I ef f ): (3) where I ef f = I? g L (V reset? V rest ). It fllws then that the ring rate will be I ef f =C fr large input currents. MacGregr[5, 6] discusses the use f dynamical changes f the threshld parameter as suggested by varius authrs since the early 30s. One natural extensin [2] is using the threshld t describe adaptatin, r fatigue, accunting fr the fact that the ring rate decreases in time fr a given cnstant input. This can be dne by hypthesizing a behavir f d dt =?(? 0) (4) with an updating prescriptin such that after every a spike is emitted! + : (5) A typical value fr is in the range f msec, which is the range in which dierent types f neurns display adaptatin. Alternatively ne can intrduce a `current threshld', a term which appears naturally if we try t accunt fr afterhyperplarizatin eects by mdifying the I&F equatin: C dv dt =?g L(V? V rest ) + I? g x x(v? V x ) (6) x dentes a variable like the cncentratin f Ca ++ in the cell. In that case g x = g AHP and V x = V K, the K + reversal ptential. This current threshld is linearly dependent n x and has als fatigue type eects n the ring rate f the neurn. x is increased after every spike and is endwed with decay dynamics f the type x! x + x (7) x dx dt where nw x determines the tempral scale f adaptatin. =?x; (8) This prblem was recently investigated in detail by Liu and Wang [4] whse ntatin we have adpted in the descriptin s far. They pint ut that the AHP current leads t adaptatin, and can therefre act as the equivalent f the vltagethreshld. They cmpare the tw in light f experimental ndings by Ahmed et al: [1] and cnclude that the currentthreshld serves as a better descriptin. 3
4 3 Mdel f Tw Dynamical Threshlds The mdel we prpse fr qualitative descriptin f the data[7] discussed in the Intrductin relies n using bth types f threshlds tgether. In ding s we assume that there is a new behavir assciated with time scales f tens f secnds, that has t perate in additin t the cnventinal adaptatin represented by either the vltagethreshld r the currentthreshld terms. Our descriptin is therefre represented by the set f equatins 48, where 6 describes the membrane ptential and all the ther the behavir f bth dynamical threshlds. The interplay f bth threshlds gives us the richness f many dierent ISI patterns fr a given highfrequency input. We have run simulatins with the 2ms pulse prtcl, using dierent input frequencies. The structures we btain can be characterized as a staircase f ISI values. This is because the dynamics f the threshlds change slwly and the system stays fr lng times at metastable values f the m : n rati between input and utput frequencies, as can be seen in Fig. 2a. Such a staircase is the backbne f the ISI structure bserved experimentally, as seen in Fig. 1. Once nise is added t the system, as in Fig. 2b, the results can be made t t the data bserved experimentally. 4
5 150 (a) (b) Figure 2: Examples f staircase f ISI values fr a 30 Hz stimulus in ur mdel: a. In the absence f nise, the system stays fr rather lng times in xed m : n ratis f input t utput frequencies. The ratis 1:1, 2:1, 3:1 and 4:1 are metastable. At later times we bserve mre cmplex behavir f scillatins between the ratis f 4:1 and 5:1. b. When little nise is added t the input, we get time series that resemble experimental results. The basic staircase structure can still be seen, but the pattern is less regular. Using ur simple mdel we were able t mimic the behavir f many neurns. In each case, the distributin f ISI as well as the tempral behavir f the neurn were successfully recnstructed. An example is shwn in Fig. 3, resembling the tempral pattern f the neurn shwn in the tp frame f Fig Phase Space Analysis The dynamics f ur cmbined mdel can be separated int fast and slw cmpnents. The tempral integratin that the neurn perfrms during the 2 ms current pulse is the fast cmpnent. The dynamics f the threshlds, whse values vary cnsiderably nly after a large number f spikes have been emitted, is the slw cmpnent. This separatin allws us t calculate, fr each pint (; x), the expected m : n rati 5
6 Figure 3: Simulatin results that resemble the experimental example f 3 Hz shwn in Fig. 1. The similarity between the tw time series is evident. Furthermre, statistical prperties f these tw series are the same. between input and utput frequencies. It fllws that we can cnstruct a twdimensinal phase space where the tempral develpment f the system is represented as a trajectry. An example that crrespnds t the ISI staircase f Fig. 2a is shwn in Fig. 4. X cmplex behavir 5:1 4:1 3:1 2:1 Figure 4: A tw dimensinal phase space f ur system. Different areas in this phase space crrespnd t dierent m : n ratis between input and utput frequencies. The circles represent the trajectry crrespnding t the ISI time series f Fig. 2a. 1:1 θ This representatin pens the pssibility fr an investigatin f the behavir f the same neurn under input currents f dierent frequencies. S far we have allwed urselves the freedm f chsing apprpriate parameters fr dierent runs even fr the same neurn. We hpe t btain a cnsistent descriptin that will allw us t t the dierent runs n the same phase space, and nd the crrect dynamics that will cnsistently accunt fr all f the behavir displayed by the same neurn. 6
7 Acknwledgment It is a pleasure t thank Shimn Marm fr sharing his data with us and fr many helpful cnversatins. References [1] B. Ahmed, J.C. Andersn, R.J. Duglas, K.A.C. Martin and D. Whitteridge, Estimates f the net excitatry currents evked by visual stimulatin f identied neurns in cat visual crtex. Cerebral Crtex submitted. [2] D. Hrn and M. Usher, Neural Netwrks with Dynamical Threshlds. Phys. Rev. A40, [3] B. W. Knight, Dynamics f encding in a ppulatin f neurns. J. f Gen. Physil. 59, [4] Y.H. Liu and X.J. Wang, Adaptatin and decrrelatin in crtical pyramidal neurns: A generalized integrateandre mdel with stchastic inputs. t be published in Behaviral/Systems Neurscience. [5] R. J. MacGregr, Neural Mdeling, Plenum Press. [6] R. J. MacGregr, Neural and Brain Mdeling, Academic Press. [7] D. Tal, E. Jacbsn, V. Lyakhv and S. Marm, Frequencytuning f a single neurn transfer functin. Preprint. 7
Determining the Accuracy of Modal Parameter Estimation Methods
Determining the Accuracy f Mdal Parameter Estimatin Methds by Michael Lee Ph.D., P.E. & Mar Richardsn Ph.D. Structural Measurement Systems Milpitas, CA Abstract The mst cmmn type f mdal testing system
More informationBuilding to Transformations on Coordinate Axis Grade 5: Geometry Graph points on the coordinate plane to solve realworld and mathematical problems.
Building t Transfrmatins n Crdinate Axis Grade 5: Gemetry Graph pints n the crdinate plane t slve realwrld and mathematical prblems. 5.G.1. Use a pair f perpendicular number lines, called axes, t define
More information, which yields. where z1. and z2
The Gaussian r Nrmal PDF, Page 1 The Gaussian r Nrmal Prbability Density Functin Authr: Jhn M Cimbala, Penn State University Latest revisin: 11 September 13 The Gaussian r Nrmal Prbability Density Functin
More informationModule 4: General Formulation of Electric Circuit Theory
Mdule 4: General Frmulatin f Electric Circuit Thery 4. General Frmulatin f Electric Circuit Thery All electrmagnetic phenmena are described at a fundamental level by Maxwell's equatins and the assciated
More informationSections 15.1 to 15.12, 16.1 and 16.2 of the textbook (RobbinsMiller) cover the materials required for this topic.
Tpic : AC Fundamentals, Sinusidal Wavefrm, and Phasrs Sectins 5. t 5., 6. and 6. f the textbk (RbbinsMiller) cver the materials required fr this tpic.. Wavefrms in electrical systems are current r vltage
More informationComputational modeling techniques
Cmputatinal mdeling techniques Lecture 4: Mdel checing fr ODE mdels In Petre Department f IT, Åb Aademi http://www.users.ab.fi/ipetre/cmpmd/ Cntent Stichimetric matrix Calculating the mass cnservatin relatins
More informationComputational modeling techniques
Cmputatinal mdeling techniques Lecture 2: Mdeling change. In Petre Department f IT, Åb Akademi http://users.ab.fi/ipetre/cmpmd/ Cntent f the lecture Basic paradigm f mdeling change Examples Linear dynamical
More informationDeadbeat controller design
J. Hetthéssy, A. Barta, R. Bars: Dead beat cntrller design Nvember, 4 Deadbeat cntrller design In sampled data cntrl systems the cntrller is realised by an intelligent device, typically by a PLC (Prgrammable
More informationLecture 13: Electrochemical Equilibria
3.012 Fundamentals f Materials Science Fall 2005 Lecture 13: 10.21.05 Electrchemical Equilibria Tday: LAST TIME...2 An example calculatin...3 THE ELECTROCHEMICAL POTENTIAL...4 Electrstatic energy cntributins
More informationRevision: August 19, E Main Suite D Pullman, WA (509) Voice and Fax
.7.4: Direct frequency dmain circuit analysis Revisin: August 9, 00 5 E Main Suite D Pullman, WA 9963 (509) 334 6306 ice and Fax Overview n chapter.7., we determined the steadystate respnse f electrical
More informationVerification of Quality Parameters of a Solar Panel and Modification in Formulae of its Series Resistance
Verificatin f Quality Parameters f a Slar Panel and Mdificatin in Frmulae f its Series Resistance Sanika Gawhane Pune411037India Onkar Hule Pune411037 India Chinmy Kulkarni Pune411037India Ojas Pandav
More informationModeling the Nonlinear Rheological Behavior of Materials with a HyperExponential Type Function
www.ccsenet.rg/mer Mechanical Engineering Research Vl. 1, N. 1; December 011 Mdeling the Nnlinear Rhelgical Behavir f Materials with a HyperExpnential Type Functin Marc Delphin Mnsia Département de Physique,
More informationDifferentiation Applications 1: Related Rates
Differentiatin Applicatins 1: Related Rates 151 Differentiatin Applicatins 1: Related Rates Mdel 1: Sliding Ladder 10 ladder y 10 ladder 10 ladder A 10 ft ladder is leaning against a wall when the bttm
More informationECE 2100 Circuit Analysis
ECE 2100 Circuit Analysis Lessn 25 Chapter 9 & App B: Passive circuit elements in the phasr representatin Daniel M. Litynski, Ph.D. http://hmepages.wmich.edu/~dlitynsk/ ECE 2100 Circuit Analysis Lessn
More informationInterference is when two (or more) sets of waves meet and combine to produce a new pattern.
Interference Interference is when tw (r mre) sets f waves meet and cmbine t prduce a new pattern. This pattern can vary depending n the riginal wave directin, wavelength, amplitude, etc. The tw mst extreme
More informationOn Huntsberger Type Shrinkage Estimator for the Mean of Normal Distribution ABSTRACT INTRODUCTION
Malaysian Jurnal f Mathematical Sciences 4(): 74 () On Huntsberger Type Shrinkage Estimatr fr the Mean f Nrmal Distributin Department f Mathematical and Physical Sciences, University f Nizwa, Sultanate
More informationIntroduction to Smith Charts
Intrductin t Smith Charts Dr. Russell P. Jedlicka Klipsch Schl f Electrical and Cmputer Engineering New Mexic State University as Cruces, NM 88003 September 2002 EE521 ecture 3 08/22/02 Smith Chart Summary
More informationDepartment of Electrical Engineering, University of Waterloo. Introduction
Sectin 4: Sequential Circuits Majr Tpics Types f sequential circuits Flipflps Analysis f clcked sequential circuits Mre and Mealy machines Design f clcked sequential circuits State transitin design methd
More informationBootstrap Method > # Purpose: understand how bootstrap method works > obs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(obs) >
Btstrap Methd > # Purpse: understand hw btstrap methd wrks > bs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(bs) > mean(bs) [1] 21.64625 > # estimate f lambda > lambda = 1/mean(bs);
More informationIntroduction: A Generalized approach for computing the trajectories associated with the Newtonian N Body Problem
A Generalized apprach fr cmputing the trajectries assciated with the Newtnian N Bdy Prblem AbuBar Mehmd, Syed Umer Abbas Shah and Ghulam Shabbir Faculty f Engineering Sciences, GIK Institute f Engineering
More informationINTRODUCTION TO THE PHYSIOLOGY OF PERCEPTION Chapter 2
Intr t the Physilgy f Perceptin 1 Perceptin (PSY 4204) Christine L. Ruva, Ph.D. INTRODUCTION TO THE PHYSIOLOGY OF PERCEPTION Chapter 2 RECEPTORS & NEURAL PROCESSING Theme f Chapter: We d nt just perceive
More informationA Few Basic Facts About Isothermal Mass Transfer in a Binary Mixture
Few asic Facts but Isthermal Mass Transfer in a inary Miture David Keffer Department f Chemical Engineering University f Tennessee first begun: pril 22, 2004 last updated: January 13, 2006 dkeffer@utk.edu
More information2.161 Signal Processing: Continuous and Discrete Fall 2008
MIT OpenCurseWare http://cw.mit.edu 2.161 Signal Prcessing: Cntinuus and Discrete Fall 2008 Fr infrmatin abut citing these materials r ur Terms f Use, visit: http://cw.mit.edu/terms. Massachusetts Institute
More informationCopyright Paul Tobin 63
DT, Kevin t. lectric Circuit Thery DT87/ TwPrt netwrk parameters ummary We have seen previusly that a twprt netwrk has a pair f input terminals and a pair f utput terminals figure. These circuits were
More informationENG2410 Digital Design Sequential Circuits: Part A
ENG2410 Digital Design Sequential Circuits: Part A Fall 2017 S. Areibi Schl f Engineering University f Guelph Week #6 Tpics Sequential Circuit Definitins Latches FlipFlps Delays in Sequential Circuits
More informationENSC Discrete Time Systems. Project Outline. Semester
ENSC 49  iscrete Time Systems Prject Outline Semester 0061. Objectives The gal f the prject is t design a channel fading simulatr. Upn successful cmpletin f the prject, yu will reinfrce yur understanding
More informationAerodynamic Separability in Tip Speed Ratio and Separability in Wind Speed a Comparison
Jurnal f Physics: Cnference Series OPEN ACCESS Aerdynamic Separability in Tip Speed Rati and Separability in Wind Speed a Cmparisn T cite this article: M L Gala Sants et al 14 J. Phys.: Cnf. Ser. 555
More informationLeast Squares Optimal Filtering with Multirate Observations
Prc. 36th Asilmar Cnf. n Signals, Systems, and Cmputers, Pacific Grve, CA, Nvember 2002 Least Squares Optimal Filtering with Multirate Observatins Charles W. herrien and Anthny H. Hawes Department f Electrical
More informationReview Problems 3. Four FIR Filter Types
Review Prblems 3 Fur FIR Filter Types Fur types f FIR linear phase digital filters have cefficients h(n fr 0 n M. They are defined as fllws: Type I: h(n = h(mn and M even. Type II: h(n = h(mn and M dd.
More information8 th Grade Math: PreAlgebra
Hardin Cunty Middle Schl (20132014) 1 8 th Grade Math: PreAlgebra Curse Descriptin The purpse f this curse is t enhance student understanding, participatin, and reallife applicatin f middleschl mathematics
More informationNUMBERS, MATHEMATICS AND EQUATIONS
AUSTRALIAN CURRICULUM PHYSICS GETTING STARTED WITH PHYSICS NUMBERS, MATHEMATICS AND EQUATIONS An integral part t the understanding f ur physical wrld is the use f mathematical mdels which can be used t
More informationSPH3U1 Lesson 06 Kinematics
PROJECTILE MOTION LEARNING GOALS Students will: Describe the mtin f an bject thrwn at arbitrary angles thrugh the air. Describe the hrizntal and vertical mtins f a prjectile. Slve prjectile mtin prblems.
More informationinitially lcated away frm the data set never win the cmpetitin, resulting in a nnptimal nal cdebk, [2] [3] [4] and [5]. Khnen's Self Organizing Featur
Cdewrd Distributin fr Frequency Sensitive Cmpetitive Learning with One Dimensinal Input Data Aristides S. Galanpuls and Stanley C. Ahalt Department f Electrical Engineering The Ohi State University Abstract
More informationLecture 6: Phase Space and Damped Oscillations
Lecture 6: Phase Space and Damped Oscillatins Oscillatins in Multiple Dimensins The preius discussin was fine fr scillatin in a single dimensin In general, thugh, we want t deal with the situatin where:
More informationSection 5.8 Notes Page Exponential Growth and Decay Models; Newton s Law
Sectin 5.8 Ntes Page 1 5.8 Expnential Grwth and Decay Mdels; Newtn s Law There are many applicatins t expnential functins that we will fcus n in this sectin. First let s lk at the expnential mdel. Expnential
More informationthe results to larger systems due to prop'erties of the projection algorithm. First, the number of hidden nodes must
M.E. Aggune, M.J. Dambrg, M.A. ElSharkawi, R.J. Marks II and L.E. Atlas, "Dynamic and static security assessment f pwer systems using artificial neural netwrks", Prceedings f the NSF Wrkshp n Applicatins
More information3D FE Modeling Simulation of Cold Rotary Forging with Double Symmetry Rolls X. H. Han 1, a, L. Hua 1, b, Y. M. Zhao 1, c
Materials Science Frum Online: 20090831 ISSN: 16629752, Vls. 628629, pp 623628 di:10.4028/www.scientific.net/msf.628629.623 2009 Trans Tech Publicatins, Switzerland 3D FE Mdeling Simulatin f Cld
More informationDesign and Simulation of DcDc Voltage Converters Using Matlab/Simulink
American Jurnal f Engineering Research (AJER) 016 American Jurnal f Engineering Research (AJER) eissn: 300847 pissn : 300936 Vlume5, Issue, pp936 www.ajer.rg Research Paper Open Access Design and
More informationPhys. 344 Ch 7 Lecture 8 Fri., April. 10 th,
Phys. 344 Ch 7 Lecture 8 Fri., April. 0 th, 009 Fri. 4/0 8. Ising Mdel f Ferrmagnets HW30 66, 74 Mn. 4/3 Review Sat. 4/8 3pm Exam 3 HW Mnday: Review fr est 3. See nline practice test lectureprep is t
More informationBASIC DIRECTCURRENT MEASUREMENTS
Brwn University Physics 0040 Intrductin BASIC DIRECTCURRENT MEASUREMENTS The measurements described here illustrate the peratin f resistrs and capacitrs in electric circuits, and the use f sme standard
More informationChapter 4. Unsteady State Conduction
Chapter 4 Unsteady State Cnductin Chapter 5 Steady State Cnductin Chee 318 1 41 Intrductin ransient Cnductin Many heat transfer prblems are time dependent Changes in perating cnditins in a system cause
More informationROUNDING ERRORS IN BEAMTRACKING CALCULATIONS
Particle Acceleratrs, 1986, Vl. 19, pp. 99105 00312460/86/19040099/$15.00/0 1986 Grdn and Breach, Science Publishers, S.A. Printed in the United States f America ROUNDING ERRORS IN BEAMTRACKING CALCULATIONS
More informationLCAO APPROXIMATIONS OF ORGANIC Pi MO SYSTEMS The allyl system (cation, anion or radical).
Principles f Organic Chemistry lecture 5, page LCAO APPROIMATIONS OF ORGANIC Pi MO SYSTEMS The allyl system (catin, anin r radical).. Draw mlecule and set up determinant. 2 3 0 3 C C 2 = 0 C 2 3 0 = 
More informationLead/Lag Compensator Frequency Domain Properties and Design Methods
Lectures 6 and 7 Lead/Lag Cmpensatr Frequency Dmain Prperties and Design Methds Definitin Cnsider the cmpensatr (ie cntrller Fr, it is called a lag cmpensatr s K Fr s, it is called a lead cmpensatr Ntatin
More informationHomology groups of disks with holes
Hmlgy grups f disks with hles THEOREM. Let p 1,, p k } be a sequence f distinct pints in the interir unit disk D n where n 2, and suppse that fr all j the sets E j Int D n are clsed, pairwise disjint subdisks.
More informationInternal vs. external validity. External validity. This section is based on Stock and Watson s Chapter 9.
Sectin 7 Mdel Assessment This sectin is based n Stck and Watsn s Chapter 9. Internal vs. external validity Internal validity refers t whether the analysis is valid fr the ppulatin and sample being studied.
More informationFlipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal MassSpring System
Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal MassSpring System A Hrizntal MassSpring System is where a mass is attached t a spring, riented hrizntally, and then placed
More informationBiocomputers. [edit]scientific Background
Bicmputers Frm Wikipedia, the free encyclpedia Bicmputers use systems f bilgically derived mlecules, such as DNA and prteins, t perfrm cmputatinal calculatins invlving string, retrieving, and prcessing
More informationLecture 17: Free Energy of Multiphase Solutions at Equilibrium
Lecture 17: 11.07.05 Free Energy f Multiphase Slutins at Equilibrium Tday: LAST TIME...2 FREE ENERGY DIAGRAMS OF MULTIPHASE SOLUTIONS 1...3 The cmmn tangent cnstructin and the lever rule...3 Practical
More informationACCELEROGRAPH RECORDINGS OF THE M USA EARTHQUAKE 16 SEPTEMBER, 1972
115 ACCELEROGRAPH RECORDINGS OF THE M USA EARTHQUAKE 16 SEPTEMBER, 1972 B.Gauir SUMMARY On 16 September, 1972 at 04 15 09.8 UT an earthquake f magnitude ML 5.0 ccurred in sutheast Papua within abut 20
More informationEnhancing Performance of MLP/RBF Neural Classifiers via an Multivariate Data Distribution Scheme
Enhancing Perfrmance f / Neural Classifiers via an Multivariate Data Distributin Scheme Halis Altun, Gökhan Gelen Nigde University, Electrical and Electrnics Engineering Department Nigde, Turkey haltun@nigde.edu.tr
More informationMethods for Determination of Mean Speckle Size in Simulated Speckle Pattern
0.478/msr04004 MEASUREMENT SCENCE REVEW, Vlume 4, N. 3, 04 Methds fr Determinatin f Mean Speckle Size in Simulated Speckle Pattern. Hamarvá, P. Šmíd, P. Hrváth, M. Hrabvský nstitute f Physics f the Academy
More informationBOUNDED UNCERTAINTY AND CLIMATE CHANGE ECONOMICS. Christopher Costello, Andrew Solow, Michael Neubert, and Stephen Polasky
BOUNDED UNCERTAINTY AND CLIMATE CHANGE ECONOMICS Christpher Cstell, Andrew Slw, Michael Neubert, and Stephen Plasky Intrductin The central questin in the ecnmic analysis f climate change plicy cncerns
More informationThermodynamics and Equilibrium
Thermdynamics and Equilibrium Thermdynamics Thermdynamics is the study f the relatinship between heat and ther frms f energy in a chemical r physical prcess. We intrduced the thermdynamic prperty f enthalpy,
More informationSolution to HW14 Fall2002
Slutin t HW14 Fall2002 CJ5 10.CQ.003. REASONING AND SOLUTION Figures 10.11 and 10.14 shw the velcity and the acceleratin, respectively, the shadw a ball that underges unirm circular mtin. The shadw underges
More informationPhysics 2010 Motion with Constant Acceleration Experiment 1
. Physics 00 Mtin with Cnstant Acceleratin Experiment In this lab, we will study the mtin f a glider as it accelerates dwnhill n a tilted air track. The glider is supprted ver the air track by a cushin
More informationNUROP CONGRESS PAPER CHINESE PINYIN TO CHINESE CHARACTER CONVERSION
NUROP Chinese Pinyin T Chinese Character Cnversin NUROP CONGRESS PAPER CHINESE PINYIN TO CHINESE CHARACTER CONVERSION CHIA LI SHI 1 AND LUA KIM TENG 2 Schl f Cmputing, Natinal University f Singapre 3 Science
More information( ) + θ θ. ω rotation rate. θ g geographic latitude   θ geocentric latitude   Reference Earth Model  WGS84 (Copyright 2002, David T.
1 Reference Earth Mdel  WGS84 (Cpyright, David T. Sandwell) ω spherid c θ θ g a parameter descriptin frmula value/unit GM e (WGS84) 3.9864418 x 1 14 m 3 s M e mass f earth  5.98 x 1 4 kg G gravitatinal
More informationThermodynamics Partial Outline of Topics
Thermdynamics Partial Outline f Tpics I. The secnd law f thermdynamics addresses the issue f spntaneity and invlves a functin called entrpy (S): If a prcess is spntaneus, then Suniverse > 0 (2 nd Law!)
More informationCambridge Assessment International Education Cambridge Ordinary Level. Published
Cambridge Assessment Internatinal Educatin Cambridge Ordinary Level ADDITIONAL MATHEMATICS 4037/1 Paper 1 Octber/Nvember 017 MARK SCHEME Maximum Mark: 80 Published This mark scheme is published as an aid
More informationA.H. Helou Ph.D.~P.E.
1 EVALUATION OF THE STIFFNESS MATRIX OF AN INDETERMINATE TRUSS USING MINIMIZATION TECHNIQUES A.H. Helu Ph.D.~P.E. :\.!.\STRAC'l' Fr an existing structure the evaluatin f the Sti"ffness matrix may be hampered
More information1. Transformer A transformer is used to obtain the approximate output voltage of the power supply. The output of the transformer is still AC.
PHYSIS 536 Experiment 4: D Pwer Supply I. Intrductin The prcess f changing A t D is investigated in this experiment. An integrated circuit regulatr makes it easy t cnstruct a highperfrmance vltage surce
More informationSupporting information
Electrnic Supplementary Material (ESI) fr Physical Chemistry Chemical Physics This jurnal is The wner Scieties 01 ydrgen perxide electrchemistry n platinum: twards understanding the xygen reductin reactin
More informationRigid Body Dynamics (continued)
Last time: Rigid dy Dynamics (cntinued) Discussin f pint mass, rigid bdy as useful abstractins f reality Manyparticle apprach t rigid bdy mdeling: Newtn s Secnd Law, Euler s Law Cntinuus bdy apprach t
More informationSection I5: Feedback in Operational Amplifiers
Sectin I5: eedback in Operatinal mplifiers s discussed earlier, practical pamps hae a high gain under dc (zer frequency) cnditins and the gain decreases as frequency increases. This frequency dependence
More information13. PO TREATMENT OF DEPT (DISTORTIONLESS ENHANCEMENT POLARIZATION TRANSFER)
94 Prduct Operatr Treatment 3. PO TREATMENT OF DEPT (DISTORTIONLESS ENHANCEMENT POLARIZATION TRANSFER) DEPT is a nedimensinal sequence used as a tl fr unambiguus identificatin f the CH, CH, and CH 3 peaks
More informationA Novel Electrothermal Simulation Approach to Power IGBT Modules for Automotive Traction Applications
Special Issue Recent R&D Activities f Pwer Devices fr Hybrid Electric Vehicles 27 Research Reprt A Nvel Electrthermal Simulatin Apprach t Pwer IGBT Mdules fr Autmtive Tractin Applicatins Takashi Kjima,
More informationFlipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal MassSpring System
Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal MassSpring System A Hrizntal MassSpring System is where a mass is attached t a spring, riented hrizntally, and then placed
More informationOptimization Programming Problems For Control And Management Of Bacterial Disease With Two Stage Growth/Spread Among Plants
Internatinal Jurnal f Engineering Science Inventin ISSN (Online): 9 67, ISSN (Print): 9 676 www.ijesi.rg Vlume 5 Issue 8 ugust 06 PP.007 Optimizatin Prgramming Prblems Fr Cntrl nd Management Of Bacterial
More informationAnalysis of Curved Bridges Crossing Fault Rupture Zones
Analysis f Curved Bridges Crssing Fault Rupture Znes R.K.Gel, B.Qu & O.Rdriguez Dept. f Civil and Envirnmental Engineering, Califrnia Plytechnic State University, San Luis Obisp, CA 93407, USA SUMMARY:
More informationOn Boussinesq's problem
Internatinal Jurnal f Engineering Science 39 (2001) 317±322 www.elsevier.cm/lcate/ijengsci On Bussinesq's prblem A.P.S. Selvadurai * Department f Civil Engineering and Applied Mechanics, McGill University,
More informationMedium Scale Integrated (MSI) devices [Sections 2.9 and 2.10]
EECS 270, Winter 2017, Lecture 3 Page 1 f 6 Medium Scale Integrated (MSI) devices [Sectins 2.9 and 2.10] As we ve seen, it s smetimes nt reasnable t d all the design wrk at the gatelevel smetimes we just
More information3D KMC simulation on the precipitation in the annealed ternary alloy system
3D KM simulatin n the precipitatin in the annealed ternary ally system Xuan Zhang, Mengqi Huang Abstract Kinetic Mnte arl methd is used t study the precipitatin phenmenn in binary and ternary ally system,
More informationFall 2013 Physics 172 Recitation 3 Momentum and Springs
Fall 03 Physics 7 Recitatin 3 Mmentum and Springs Purpse: The purpse f this recitatin is t give yu experience wrking with mmentum and the mmentum update frmula. Readings: Chapter.3.5 Learning Objectives:.3.
More informationSAMPLING DYNAMICAL SYSTEMS
SAMPLING DYNAMICAL SYSTEMS Melvin J. Hinich Applied Research Labratries The University f Texas at Austin Austin, TX 787138029, USA (512) 8353278 (Vice) 8353259 (Fax) hinich@mail.la.utexas.edu ABSTRACT
More informationWe can see from the graph above that the intersection is, i.e., [ ).
MTH 111 Cllege Algebra Lecture Ntes July 2, 2014 Functin Arithmetic: With nt t much difficulty, we ntice that inputs f functins are numbers, and utputs f functins are numbers. S whatever we can d with
More informationInferring and quantifying the role of an intrinsic current in a mechanism for a halfcenter bursting oscillation
Jurnal f Bilgical Physics (preprint versin, see www.springerlink.cm fr final versin) Rbert Clewley Inferring and quantifying the rle f an intrinsic current in a mechanism fr a halfcenter bursting scillatin
More informationChapter 2 GAUSS LAW Recommended Problems:
Chapter GAUSS LAW Recmmended Prblems: 1,4,5,6,7,9,11,13,15,18,19,1,7,9,31,35,37,39,41,43,45,47,49,51,55,57,61,6,69. LCTRIC FLUX lectric flux is a measure f the number f electric filed lines penetrating
More informationComparing Several Means: ANOVA. Group Means and Grand Mean
STAT 511 ANOVA and Regressin 1 Cmparing Several Means: ANOVA Slide 1 Blue Lake snap beans were grwn in 12 pentp chambers which are subject t 4 treatments 3 each with O 3 and SO 2 present/absent. The ttal
More informationCurrent/voltagemode third order quadrature oscillator employing two multiple outputs CCIIs and grounded capacitors
Indian Jurnal f Pure & Applied Physics Vl. 49 July 20 pp. 494498 Current/vltagemde third rder quadrature scillatr emplying tw multiple utputs CCIIs and grunded capacitrs JiunWei Hrng Department f Electrnic
More information22.54 Neutron Interactions and Applications (Spring 2004) Chapter 11 (3/11/04) Neutron Diffusion
.54 Neutrn Interactins and Applicatins (Spring 004) Chapter (3//04) Neutrn Diffusin References  J. R. Lamarsh, Intrductin t Nuclear Reactr Thery (AddisnWesley, Reading, 966) T study neutrn diffusin
More informationModelling of Clock Behaviour. Don Percival. Applied Physics Laboratory University of Washington Seattle, Washington, USA
Mdelling f Clck Behaviur Dn Percival Applied Physics Labratry University f Washingtn Seattle, Washingtn, USA verheads and paper fr talk available at http://faculty.washingtn.edu/dbp/talks.html 1 Overview
More informationarxiv:hepph/ v1 2 Jun 1995
WIS95//MayPH The rati F n /F p frm the analysis f data using a new scaling variable S. A. Gurvitz arxiv:hepph/95063v1 Jun 1995 Department f Particle Physics, Weizmann Institute f Science, Rehvt 76100,
More informationMODULE 1. e x + c. [You can t separate a demominator, but you can divide a single denominator into each numerator term] a + b a(a + b)+1 = a + b
. REVIEW OF SOME BASIC ALGEBRA MODULE () Slving Equatins Yu shuld be able t slve fr x: a + b = c a d + e x + c and get x = e(ba +) b(c a) d(ba +) c Cmmn mistakes and strategies:. a b + c a b + a c, but
More informationSupplementary Course Notes Adding and Subtracting AC Voltages and Currents
Supplementary Curse Ntes Adding and Subtracting AC Vltages and Currents As mentined previusly, when cmbining DC vltages r currents, we nly need t knw the plarity (vltage) and directin (current). In the
More informationUNIT 6 DETERMINATION OF FLASH AND FIRE POINT OF A LUBRICATING OIL BY OPEN CUP AND CLOSED CUP METHODS
UNIT 6 DETERMINATION OF FLASH AND FIRE POINT OF A LUBRICATING OIL BY OPEN CUP AND CLOSED CUP METHODS Determinatin f Flash and Fire Pint f a Cup and Clsed Cup Structure 6. Intrductin Objectives 6. Experiment
More informationSTIMULUS ENCODING BY MUL TIDIMENSIONAL RECEPTIVE FIELDS IN SINGLE CELLS AND CELL POPULATIONS IN VI OF A WAKE MONKEY
STIMULUS ENCODING BY MUL TIDIMENSIONAL RECEPTIVE FIELDS IN SINGLE CELLS AND CELL POPULATIONS IN VI OF A WAKE MONKEY Edward Stern Center fr Neural Cmputatin and Department f Neurbilgy Life Sciences Institute
More informationANALYTICAL SOLUTIONS TO THE PROBLEM OF EDDY CURRENT PROBES
ANALYTICAL SOLUTIONS TO THE PROBLEM OF EDDY CURRENT PROBES CONSISTING OF LONG PARALLEL CONDUCTORS B. de Halleux, O. Lesage, C. Mertes and A. Ptchelintsev Mechanical Engineering Department Cathlic University
More informationCHAPTER 24: INFERENCE IN REGRESSION. Chapter 24: Make inferences about the population from which the sample data came.
MATH 1342 Ch. 24 April 25 and 27, 2013 Page 1 f 5 CHAPTER 24: INFERENCE IN REGRESSION Chapters 4 and 5: Relatinships between tw quantitative variables. Be able t Make a graph (scatterplt) Summarize the
More informationChurn Prediction using Dynamic RFMAugmented node2vec
Churn Predictin using Dynamic RFMAugmented nde2vec Sandra Mitrvić, Jchen de Weerdt, Bart Baesens & Wilfried Lemahieu Department f Decisin Sciences and Infrmatin Management, KU Leuven 18 September 2017,
More informationFebruary 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA
February 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA Mental Experiment regarding 1D randm walk Cnsider a cntainer f gas in thermal
More informationChE 471: LECTURE 4 Fall 2003
ChE 47: LECTURE 4 Fall 003 IDEL RECTORS One f the key gals f chemical reactin engineering is t quantify the relatinship between prductin rate, reactr size, reactin kinetics and selected perating cnditins.
More informationChapter 23 Electromagnetic Waves Lecture 14
Chapter 23 Electrmagnetic Waves Lecture 14 23.1 The Discvery f Electrmagnetic Waves 23.2 Prperties f Electrmagnetic Waves 23.3 Electrmagnetic Waves Carry Energy and Mmentum 23.4 Types f Electrmagnetic
More informationLecture 2: Supervised vs. unsupervised learning, biasvariance tradeoff
Lecture 2: Supervised vs. unsupervised learning, biasvariance tradeff Reading: Chapter 2 STATS 202: Data mining and analysis September 27, 2017 1 / 20 Supervised vs. unsupervised learning In unsupervised
More informationAdmissibility Conditions and Asymptotic Behavior of Strongly Regular Graphs
Admissibility Cnditins and Asympttic Behavir f Strngly Regular Graphs VASCO MOÇO MANO Department f Mathematics University f Prt Oprt PORTUGAL vascmcman@gmailcm LUÍS ANTÓNIO DE ALMEIDA VIEIRA Department
More informationPattern Recognition 2014 Support Vector Machines
Pattern Recgnitin 2014 Supprt Vectr Machines Ad Feelders Universiteit Utrecht Ad Feelders ( Universiteit Utrecht ) Pattern Recgnitin 1 / 55 Overview 1 Separable Case 2 Kernel Functins 3 Allwing Errrs (Sft
More informationSodium Dline doublet. Lectures 56: Magnetic dipole moments. Orbital magnetic dipole moments. Orbital magnetic dipole moments
Lectures 56: Magnetic diple mments Sdium Dline dublet Orbital diple mments. Orbital precessin. Grtrian diagram fr dublet states f neutral sdium shwing permitted transitins, including Na Dline transitin
More information2004 AP CHEMISTRY FREERESPONSE QUESTIONS
2004 AP CHEMISTRY FREERESPONSE QUESTIONS 6. An electrchemical cell is cnstructed with an pen switch, as shwn in the diagram abve. A strip f Sn and a strip f an unknwn metal, X, are used as electrdes.
More informationAP Statistics Notes Unit Two: The Normal Distributions
AP Statistics Ntes Unit Tw: The Nrmal Distributins Syllabus Objectives: 1.5 The student will summarize distributins f data measuring the psitin using quartiles, percentiles, and standardized scres (zscres).
More information