NR3A-containing NMDA receptors promote neurotransmitter release and spike timing-dependent plasticity

Size: px
Start display at page:

Download "NR3A-containing NMDA receptors promote neurotransmitter release and spike timing-dependent plasticity"

Transcription

1 NR3A-ontaining NMDA rptors promot nurotransmittr rlas an spik timing-pnnt plastiity Rylan S. Larsn, Rkah J. Corlw, Mail A. Hnson, Aam C. Rorts, Masayoshi Mishina, Masahiko Watana, Stuart A. Lipton, Nouki Nakanishi, Isal Pérz-Otaño, Rihar J. Winrg, & Bnjamin D. Philpot SUPPLEMENTARY FIGURES Natur Nurosin: oi:.3/nn.7

2 a MW (kd) Antioy NRA (#-9) 7 7 NRA (#AB) NRB NRD (#3) NRD (#s-7) NR3A NR Protin lvls (% rainstm) Protin lvls (% WT) BS VC BS VC NR3A NRD WT / WT / WT / WT / WT / WT / NR NR3A NRD 37 β-atin Supplmntary Figur : NRD lvls ar omparativly low in visual ortx (VC), an ths lvls ar unhang in NR3A / mi. (a) Largr rprsntativ lots show antioy spifiity for th targt antigns with molular wight markrs. () Rprsntativ lots an quantifi protin lvls of NR3A an NRD in P P V (n = ) an rainstm (BS) (n = ). NR3A lvls wr omparal in rainstm an visual ortx, ut NRD lvls wr minimal in visual ortx ompar to rainstm. Protin lvls wr stanariz to an atin loaing ontrol an normaliz to rainstm valus. () Rprsntativ lots an quantifiation of NR (n = pr gnotyp), NR3A (n = 3 pr gnotyp), an NRD (n = 3 pr gnotyp) protin lvls in visual ortx. NR an NRD lvls wr unhang in P NR3A / mi ompar to WT ontrols (P =. an P =., rsptivly) whil NR3A was not tt in NR3A / mi (P <<.). Protin lvls in NR3A / an WT animals wr stanariz to a β-atin loaing ontrol an xprss as a prntag of WT lvls. Error ars rprsnt s..m. P <.. Natur Nurosin: oi:.3/nn.7

3 a P3 WT NRA / pa ms pa ms WT NRA / WT f NRA / 3 3 Supplmntary Figur : Th NRA suunit os not signifiantly ontriut to th aility of prnmdars to nhan spontanous nurotransmittr rlas onto L/3 pyramial nurons in juvnil V. (a,) Sampl voltag-lamp rorings of AMPAR-miat mepscs from L/3 pyramial lls uring as an D- appliation prios in (a) WT an () NRA / mi. mepscs ar iniat y. (, ) Amplitu an (, ) intr-vnt intrval umulativ proaility histograms from th sam lls shown in a an uring as an D- ( µm) appliation rval a hang in mepsc frquny, ut not amplitu, for oth ( ) WT ontrol an ( ) NRA / mi. (,f) Sattr plots of amplitu an frquny, for an aftr D- appliation, in () WT an (f) NRA / mi. L/3 pyramial lls xhiit a signifiant rution in mepsc frquny y D- in oth WT (n = 7, P <.3) an NRA / mi (n = 7, P <.), ut no hangs in amplitu. Th D- fft on mepsc frquny was similar twn WT an NRA / mi. P <.. Natur Nurosin: oi:.3/nn.7

4 P3 a UBP pa ms pa ms UBP f EPSC amp. (%as) mepsc (% as) UBP Amplitu 3 UBP UBP 3 3 UBP Frquny g EPSC amp. (%as) UBP 7 pa ms UBP / UBP 7 pa ms UBP Supplmntary Figur 3: Th NMDAR antagonist UBP affts th amplitu of AMPAR-miat urrnts whn all NMDARs ar lok, suggsting that this rug laks spifiity. (a,) Sampl voltag-lamp rorings of AMPAR-miat mepscs from L/3 pyramial lls from P3 P WT mi uring (a) vhil (ACSF) ontrol or () UBP (3 µm) appliation. mepsc vnts ar iniat y. (,) Sattr plots of mepsc amplitu an frquny for an aftr () vhil ontrol or () UBP appliation. UBP signifiantly ras oth amplitu (n =, P <.3) an frquny (P <.) of AMPAR-miat mepscs, whil thr wr no hangs in amplitu an frquny in vhil ontrol xprimnts (n = ). Baus postsynapti NMDARs wr lok, this ras in amplitu suggsts that UBP might afft AMPAR-miat urrnts y an NMDAR-inpnnt pathway. () mepsc amplitu aftr vhil ACSF vhil ontrol or UBP appliation, avrag an normaliz to as ontrols (ar graph of ata prsnt in an ). (f) UBP appliation ras th amplitu of vok AMPAR urrnts in L /3 synapss ror in voltag-lamp from P P WT mi (n = ), whil thr wr no hangs with vhil ontrol (n = ). All NMDARs wr lok uring this xprimnt y D,L- ( µm) in th xtrnal roring solution. (g) Quantifiation an sampl tras from ata takn from th last fiv minuts of rug tratmnt in f, monstrating that UBP signifiantly ru AMPAR EPSC amplitus ompar to vhil ontrols (P <.). Baus UBP afft our postsynapti raout of glutamat rlas (AMPAR urrnts), w wr unal to us this rug to assss th rol of UBP-targt prnmdar suunits on nurotransmittr rlas. Natur Nurosin: Error ars rprsnt oi:.3/nn.7 s..m. P <., P <., P <..

5 P3 WT a NRD / pa ms NRD / WT pa ms NRD / f s AP s AP 3 WT 3 s AP s AP Supplmntary Figur : Th NRD suunit is not rquir for prnmdars to nhan spontanous nurotransmittr rlas onto L/3 pyramial nurons in juvnil V. (a,) Sampl voltag-lamp rorings of AMPAR-miat mepscs from L/3 pyramial lls uring as an D- appliation prios in (a) WT an () NRD / mi. mepscs ar iniat y. (,) Amplitu an (,) intr-vnt intrval umulativ proaility histograms from th sam lls shown in a an uring as an D- appliation rval a hang in mepsc frquny ut not amplitu for oth () WT ontrol an () NRD / mi. (,f) Sattr plots of amplitu an frquny, for an aftr D- appliation, in () WT an (f) NRD / mi. L/3 pyramial lls xhiit a signifiant rution in mepsc frquny y D- in oth WT (n =, P =.) an NRD / mi (n =, P <.7), ut no hangs in amplitu. Th fft on mepsc frquny was similar twn WT an NRD / mi. P <.. Natur Nurosin: oi:.3/nn.7

6 P3 a Ro -9 Ro -9 pa ms pa ms Ro Ro f Ro -9 s C on tro l s C on tro l 3 3 Ro -9 3 B R as o - 9 B R as o l in - 9 Supplmntary Figur : NRB-ontaining prnmdars nhan spontanous nurotransmittr rlas onto L/3 pyramial nurons in juvnil V. (a-) Sampl voltag-lamp rorings of AMPAR-miat mepscs from WT L/3 pyramial lls in (a) ontrol xprimnts with vhil (ACSF) appliation or () with. µm Ro -9 appliation. mepscs ar iniat y. (,) Amplitu an (,) intr-vnt intrval umulativ proaility histograms from th sam lls shown in a an uring as an () vhil ontrol or () Ro -9 appliation. Thr was no hang in ithr mepsc amplitu or frquny in th ontrol xprimnt with vhil appliation, whil Ro -9 appliation ras mepsc frquny without hanging amplitu. (,f) Sattr plots of amplitu an frquny for an aftr () vhil (ACSF) ontrol or (f) Ro -9 appliation. Thr wr no signifiant hangs in amplitu or frquny in ontrol xprimnts (n = ). Ro -9 aus a signifiant rution in mepsc frquny (n = 7, P <.7), ut i not altr mepsc amplitu. P <.. Natur Nurosin: oi:.3/nn.7

7 P3 a Ifnproil pa ms pa ms Ifnproil.. Ifnproil Ifnproil Ifnproil.. 3 f 3 Ifnproil Ifnproil Ifnproil Supplmntary Figur : Bloka of NRB-ontaining prnmdars y ifnproil rus spontanous nurotransmittr rlas onto L/3 pyramial nurons. (a-) Sampl voltag-lamp rorings of AMPAR-miat mepscs from WT L/3 pyramial lls in (a) ontrol xprimnts with vhil (ACSF) appliation or () with 3 µm ifnproil appliation. mepscs ar iniat y. (, ) Amplitu an (, ) intr-vnt intrval umulativ proaility histograms from th sam lls shown in a an uring as an () vhil ontrol or () ifnproil appliation. (,f) Sattr plots of amplitu an frquny for an aftr () vhil (ACSF) ontrol or (f) ifnproil appliation. Thr wr no signifiant hangs in amplitu or frquny in ontrol xprimnts (n = 7). Ifnproil aus a signifiant rution in mepsc frquny (n =, P <.), ut i not altr mepsc amplitu. P <.. Natur Nurosin: oi:.3/nn.7

8 a pa ms WT NR3A / P3 pa ms WT NR3A / Prntag Prntag Prntag.. Prntag.. 3 WT f NR3A / Supplmntary Figur 7: Th NR3A suunit is rquir for th aility of prnmdars to nhan spontanous nurotransmittr rlas in juvnil V. (a,) Sampl voltag-lamp rorings of AMPAR-miat mepscs from L/3 pyramial lls uring as an D- appliation prios in (a) WT an () NR3A / mi. mepscs ar iniat y. (, ) Amplitu an (, ) intr-vnt intrval umulativ proaility histograms from th sam lls shown in a an. D- ras mepsc frquny ut not amplitu in L/3 nurons in WT mi, whil thr was no hang in ithr amplitu or frquny in NR3A / mi. (,f) Sattr plots of amplitu an frquny for an aftr D- appliation in () WT an (f) NR3A / mi. mepsc frquny (n =, P <.7), ut not amplitu, was signifiantly ru in L/3 pyramial nurons from WT mi. Thr wr no hangs in mepsc frquny an amplitu osrv in L/3 pyramial nurons from NR3A / mi (n = ). P <.. Natur Nurosin: oi:.3/nn.7

9 a P P P3 GFP-NR3A µm P3 STg NR3A OE pa ms pa ms f STg STg g.. NR3A OE NR3A OE Supplmntary Figur : Ovrxprssion of th NR3A suunit in xitatory nurons nows prnmdars with a gratr aility to nhan spontanous nurotransmittr rlas in L/3 pyramial lls of mor matur V. (a) Dvlopmntal timours of GFP-NR3A ovrxprssion in V monstrating minimal xprssion of th transgn for P. (,) Sampl voltag-lamp rorings of AMPAR-miat mepscs from L/3 pyramial lls uring as an D- appliation prios in () singl-transgni (STg) mi an () oul-transgni mi ovrxprssing (OE) NR3A. mepscs ar iniat y. (, ) Amplitu an (, ) intr-vnt intrval umulativ proaility histograms from th sam lls shown in an uring as an D- appliation. (f,g) Sattr plots of amplitu an frquny for an aftr D- appliation in (f) STg an (g) NR3A OE mi. Thr was no hang in amplitu with D- appliation in ithr STg or NR3A OE mi. Th ras in mepsc frquny with D- appliation was muh largr in OE mi (n =, P <.) ompar to thir STg littrmats (n = 7, P <.3). frquny prior to D- was also highr in OE mi as ompar to STg mi, although this fft i not rah statistial signifian (OE = 7. Hz, STg =.3 Hz, P <.7). P <. an Natur Nurosin: P <.. oi:.3/nn.7

10 P3, Low Mg +,NR3A / a pa ms pa ms f Supplmntary Figur 9: In low Mg + onitions, prnmdars laking NR3A ar al to nhan spontanous nurotransmittr rlas in juvnil V. (a,) Sampl voltag-lamp rorings in low Mg + ACSF from L/3 pyramial lls in NR3A / mi for or aftr (a) vhil (ACSF) or () D- appliation. mepscs ar iniat y. (, ) Amplitu an (, ) intr-vnt intrval umulativ proaility histograms from lls shown in a an uring as an D- appliation prios. Not that D- ru mepsc frquny. (,f) Sattr plots of amplitu an frquny for an aftr () vhil or (f) D- appliation in NR3A / mi. In low Mg + ACSF, mepsc amplitu an frquny wr onstant in ontrol xprimnts (n = 3), ut D- appliation ru mepsc frquny (n =, P <.) without affting amplitu. P <.. Natur Nurosin: oi:.3/nn.7

11 P Low Mg + Normal Mg + f Ro -9 pa ms Low Mg g + 3 f 3 j 3 Low Mg+ h k Low Mg+ h Low Mg + 3 Ro -9 Ro s AP s AP s AP Normal Mg + + s AP.. 3. i g Low Mg pa ms pa ms l Low Mg + 3 R o s - 9 pa ms Low Mg+ Low Mg + R s o - 9 s C on tro l Normal Mg + s C on tro l a Supplmntary Figur : In low Mg+, NRB-ontaining prnmdars nhan nurotransmittr rlas in P WT mi. (a) Sampl voltag-lamp roring in normal Mg+ ( mm) ACSF from L/3 pyramial lls in a P mous uring as an D- appliation prios. (,,) Rorings in low Mg+ ACSF from WT L/3 pyramial lls in P mi uring () vhil (ACSF) ontrol, () D-, or () Ro -9 appliation prios. mepscs ar iniat y. (-h) Amplitu an intr-vnt intrval umulativ proaility histograms from th sam lls shown in a-. Thr is no hang in mepsc amplitu in any onition, ut mepsc frquny ras with D- or Ro -9 appliation in th low Mg+ onition. (i-l) Sattr plots of mepsc amplitu an frquny monstrating rsponss to ontrol or NMDAR antagonist appliation whn rorings wr ma in (i) normal Mg+ (n = 9), or (j,k,l) low Mg+ (n = for ontrol xprimnts, n = 9 for xprimnts, n = 7 for Ro -9 xprimnts). A signifiant rution in mepsc frquny was osrv only in th low magnsium onition with D- appliation (P <.) or with Ro -9 appliation (P <.). P <.. Natur Nurosin: oi:.3/nn.7

12 Slop (% as) P3 AP-EPSP NRD / (n = ) 3 3 Supplmntary Figur : NRD-ontaining NMDARs ar not rquir for spik timing-pnnt long-trm prssion (tltd) in juvnil V. tltd was inu in L/3 V synapss in rspons to ation potntials pair with L-gnrat EPSPs whil postsynapti NMDARs wr lok in P3 P NRD / mi (n =, quantifiation of th last minuts = ± % of as EPSP slop, P <.). Natur Nurosin: oi:.3/nn.7

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION SUPPLEMENTRY INFORMTION Olfatory ortial nurons ra out a rlativ tim o in th olfatory ul Rafi Haa, nn Lanjuin, Lina Maisn, Hongkui Zng, Vnkatsh N. Murthy an Naoshig Uhia. ntr for rain Sin, Dartmnt of Molular

More information

8 U2OS 6. Aph HU IR UV Aph HU IR UV +HU. Caff UCN01 Caff UCN01 S C S C S C S C S C S C PrimPol. d

8 U2OS 6. Aph HU IR UV Aph HU IR UV +HU. Caff UCN01 Caff UCN01 S C S C S C S C S C S C PrimPol. d Rlativ mr RNA lvls 1..75 5.5.25. 4 Chr / S ol 3 2 1 A G1-S S G2-M A G1-S S G2-M HLa Chr / S ol 8 U2OS 6 4 2 Aph HU IR UV Aph HU IR UV +HU Caff UCN1 Caff UCN1 S C S C S C S C S C S C CCF 1 2 3 4 5 6 7 8

More information

d Lamp1-GFP Starvation 2h Starvation 2h Starvation 2h + ML-SI3

d Lamp1-GFP Starvation 2h Starvation 2h Starvation 2h + ML-SI3 DOI: 10.1038/ncb3324 a b c Lamp1-GFP Lamp1-GFP Lamp1-GFP Lamp1-GFP WT ibroblast Lysotrackr WT ibroblast xtran Starvation 2h WT ibroblast γ-tubulin Starvation 2h γ-tubulin GFP-LC3 HLa LC3-GFP LC3-RFP g

More information

Case Study Vancomycin Answers Provided by Jeffrey Stark, Graduate Student

Case Study Vancomycin Answers Provided by Jeffrey Stark, Graduate Student Cas Stuy Vancomycin Answrs Provi by Jffry Stark, Grauat Stunt h antibiotic Vancomycin is liminat almost ntirly by glomrular filtration. For a patint with normal rnal function, th half-lif is about 6 hours.

More information

Multiple Short Term Infusion Homework # 5 PHA 5127

Multiple Short Term Infusion Homework # 5 PHA 5127 Multipl Short rm Infusion Homwork # 5 PHA 527 A rug is aministr as a short trm infusion. h avrag pharmacokintic paramtrs for this rug ar: k 0.40 hr - V 28 L his rug follows a on-compartmnt boy mol. A 300

More information

Above. Below H&E. Above CD4. CD11b. Fluoromyelin BDA BDA BDA. Cerebral cortex. Focal lesion. Thoracic cord. Lumbar cord. Hindlimb placing score

Above. Below H&E. Above CD4. CD11b. Fluoromyelin BDA BDA BDA. Cerebral cortex. Focal lesion. Thoracic cord. Lumbar cord. Hindlimb placing score 1. 1. 1 1 3 Tim tr lsion inution () wks wks 3 1 1 1 3 Tim tr lsion inution () i Ltrl sor. Mil Aov Blow.. 1 wk On sgmnt ov g 3. Lsion Fluoromylin Fluoromylin h CD11 Hinlim pling sor CD Aov Blow Fol lsion

More information

Problem 22: Journey to the Center of the Earth

Problem 22: Journey to the Center of the Earth Problm : Journy to th Cntr of th Earth Imagin that on drilld a hol with smooth sids straight through th ntr of th arth If th air is rmod from this tub (and it dosn t fill up with watr, liquid rok, or iron

More information

N1.1 Homework Answers

N1.1 Homework Answers Camrig Essntials Mathmatis Cor 8 N. Homwork Answrs N. Homwork Answrs a i 6 ii i 0 ii 3 2 Any pairs of numrs whih satisfy th alulation. For xampl a 4 = 3 3 6 3 = 3 4 6 2 2 8 2 3 3 2 8 5 5 20 30 4 a 5 a

More information

Handout 28. Ballistic Quantum Transport in Semiconductor Nanostructures

Handout 28. Ballistic Quantum Transport in Semiconductor Nanostructures Hanout 8 Ballisti Quantum Transport in Smionutor Nanostruturs In this ltur you will larn: ltron transport without sattring (ballisti transport) Th quantum o onutan an th quantum o rsistan Quanti onutan

More information

3) Use the average steady-state equation to determine the dose. Note that only 100 mg tablets of aminophylline are available here.

3) Use the average steady-state equation to determine the dose. Note that only 100 mg tablets of aminophylline are available here. PHA 5127 Dsigning A Dosing Rgimn Answrs provi by Jry Stark Mr. JM is to b start on aminophyllin or th tratmnt o asthma. H is a non-smokr an wighs 60 kg. Dsign an oral osing rgimn or this patint such that

More information

General Notes About 2007 AP Physics Scoring Guidelines

General Notes About 2007 AP Physics Scoring Guidelines AP PHYSICS C: ELECTRICITY AND MAGNETISM 2007 SCORING GUIDELINES Gnral Nots About 2007 AP Physics Scoring Guidlins 1. Th solutions contain th most common mthod of solving th fr-rspons qustions and th allocation

More information

Present state Next state Q + M N

Present state Next state Q + M N Qustion 1. An M-N lip-lop works s ollows: I MN=00, th nxt stt o th lip lop is 0. I MN=01, th nxt stt o th lip-lop is th sm s th prsnt stt I MN=10, th nxt stt o th lip-lop is th omplmnt o th prsnt stt I

More information

CS553 Lecture Register Allocation I 3

CS553 Lecture Register Allocation I 3 Low-Lvl Issus Last ltur Intrproural analysis Toay Start low-lvl issus Rgistr alloation Latr Mor rgistr alloation Instrution shuling CS553 Ltur Rgistr Alloation I 2 Rgistr Alloation Prolm Assign an unoun

More information

TP A.31 The physics of squirt

TP A.31 The physics of squirt thnial proof TP A. Th physis of squirt supporting: Th Illustratd Prinipls of Pool and Billiards http://illiards.olostat.du y David G. Aliator, PhD, PE ("Dr. Dav") thnial proof originally postd: 8//7 last

More information

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION Figure S1 Multiplicative scaling of the granule cell input-output relation is not dependent on input rate. Input-output relations with short-term depression (STD) from Fig. 1d after normalizing by the

More information

MA1506 Tutorial 2 Solutions. Question 1. (1a) 1 ) y x. e x. 1 exp (in general, Integrating factor is. ye dx. So ) (1b) e e. e c.

MA1506 Tutorial 2 Solutions. Question 1. (1a) 1 ) y x. e x. 1 exp (in general, Integrating factor is. ye dx. So ) (1b) e e. e c. MA56 utorial Solutions Qustion a Intgrating fator is ln p p in gnral, multipl b p So b ln p p sin his kin is all a Brnoulli quation -- st Sin w fin Y, Y Y, Y Y p Qustion Dfin v / hn our quation is v μ

More information

MCB137: Physical Biology of the Cell Spring 2017 Homework 6: Ligand binding and the MWC model of allostery (Due 3/23/17)

MCB137: Physical Biology of the Cell Spring 2017 Homework 6: Ligand binding and the MWC model of allostery (Due 3/23/17) MCB37: Physical Biology of th Cll Spring 207 Homwork 6: Ligand binding and th MWC modl of allostry (Du 3/23/7) Hrnan G. Garcia March 2, 207 Simpl rprssion In class, w drivd a mathmatical modl of how simpl

More information

ECE 3600 Lumped-Parameter Transmission Line Models b

ECE 3600 Lumped-Parameter Transmission Line Models b Lumpd-Paramtr Transmission Lin Modls b Lon-th Lins: ovr 40 (50 mils) (ovr 00 mi in som tts) Nd: Units lin th:, d stik to th sam unit th for all paramtrs mils ma also b usd Rsistan pr unit th: r Units ndutan

More information

Magnetic vector potential. Antonio Jose Saraiva ; -- Electric current; -- Magnetic momentum; R Radius.

Magnetic vector potential. Antonio Jose Saraiva ; -- Electric current; -- Magnetic momentum; R Radius. Magnti vtor potntial Antonio Jos araiva ajps@hotail.o ; ajps137@gail.o A I.R A Magnti vtor potntial; -- auu prability; I -- ltri urrnt; -- Magnti ontu; R Radius. un agnti ronntion un tru surfa tpratur

More information

PHA 5127 Answers Homework 2 Fall 2001

PHA 5127 Answers Homework 2 Fall 2001 PH 5127 nswrs Homwork 2 Fall 2001 OK, bfor you rad th answrs, many of you spnt a lot of tim on this homwork. Plas, nxt tim if you hav qustions plas com talk/ask us. Thr is no nd to suffr (wll a littl suffring

More information

Additional Math (4047) Paper 2 (100 marks) y x. 2 d. d d

Additional Math (4047) Paper 2 (100 marks) y x. 2 d. d d Aitional Math (07) Prpar b Mr Ang, Nov 07 Fin th valu of th constant k for which is a solution of th quation k. [7] Givn that, Givn that k, Thrfor, k Topic : Papr (00 marks) Tim : hours 0 mins Nam : Aitional

More information

Mor Tutorial at www.dumblittldoctor.com Work th problms without a calculator, but us a calculator to chck rsults. And try diffrntiating your answrs in part III as a usful chck. I. Applications of Intgration

More information

Activity-dependent decrease of excitability in rat hippocampal neurons through increases in I h

Activity-dependent decrease of excitability in rat hippocampal neurons through increases in I h Ntur Pulishing Group http://www.ntur.om/nturnurosin Ativity-pnnt rs o xitility in rt hippompl nurons through inrss in I h Yun Fn 1,, Dsmon Frikr,, Drrin H Brgr 1, Xixi Chn 1, Hui-Chn Lu 3, Rymon A Chitwoo

More information

Observer Bias and Reliability By Xunchi Pu

Observer Bias and Reliability By Xunchi Pu Obsrvr Bias and Rliability By Xunchi Pu Introduction Clarly all masurmnts or obsrvations nd to b mad as accuratly as possibl and invstigators nd to pay carful attntion to chcking th rliability of thir

More information

22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches.

22/ Breakdown of the Born-Oppenheimer approximation. Selection rules for rotational-vibrational transitions. P, R branches. Subjct Chmistry Papr No and Titl Modul No and Titl Modul Tag 8/ Physical Spctroscopy / Brakdown of th Born-Oppnhimr approximation. Slction ruls for rotational-vibrational transitions. P, R branchs. CHE_P8_M

More information

Nature Neuroscience: doi: /nn Supplementary Figure 1. Amygdaloid complex and evoked synaptic currents recorded in CeM amygdala neurons.

Nature Neuroscience: doi: /nn Supplementary Figure 1. Amygdaloid complex and evoked synaptic currents recorded in CeM amygdala neurons. Supplementary Figure 1 Amygdaloid complex and evoked synaptic currents recorded in CeM amygdala neurons. (a) Left: Schematic representation (modified from: Allen Brain Atlas) of coronal sections containing

More information

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION SUPPLEMENTARY INFORMATION oi:.38/ntur58 istn trvll (m) 4 3 Slin multory tim (s) 6 Slin multory ounts 8 6 Slin tim strotypi (s) 5 5 Slin strotypi ounts 6 4 Slin f rsting tim (s) 5 5 Slin g 3 Slin h 8 Slin

More information

3 a b c km m m 8 a 3.4 m b 2.4 m

3 a b c km m m 8 a 3.4 m b 2.4 m Chaptr Exris A a 9. m. m. m 9. km. mm. m Purpl lag hapr y 8p 8m. km. m Th triangl on th right 8. m 9 a. m. m. m Exris B a m. m mm. km. mm m a. 9 8...8 m. m 8. 9 m Ativity p. 9 Pupil s own answrs Ara =

More information

2008 AP Calculus BC Multiple Choice Exam

2008 AP Calculus BC Multiple Choice Exam 008 AP Multipl Choic Eam Nam 008 AP Calculus BC Multipl Choic Eam Sction No Calculator Activ AP Calculus 008 BC Multipl Choic. At tim t 0, a particl moving in th -plan is th acclration vctor of th particl

More information

Digital Signal Processing, Fall 2006

Digital Signal Processing, Fall 2006 Digital Signal Prossing, Fall 006 Ltur 7: Filtr Dsign Zhng-ua an Dpartmnt of Eltroni Systms Aalborg Univrsity, Dnmar t@om.aau. Cours at a glan MM Disrt-tim signals an systms Systm MM Fourir-omain rprsntation

More information

DUET WITH DIAMONDS COLOR SHIFTING BRACELET By Leslie Rogalski

DUET WITH DIAMONDS COLOR SHIFTING BRACELET By Leslie Rogalski Dut with Dimons Brlt DUET WITH DIAMONDS COLOR SHIFTING BRACELET By Lsli Roglski Photo y Anrw Wirth Supruo DUETS TM from BSmith rt olor shifting fft tht mks your work tk on lif of its own s you mov! This

More information

Junction Tree Algorithm 1. David Barber

Junction Tree Algorithm 1. David Barber Juntion Tr Algorithm 1 David Barbr Univrsity Collg London 1 Ths slids aompany th book Baysian Rasoning and Mahin Larning. Th book and dmos an b downloadd from www.s.ul.a.uk/staff/d.barbr/brml. Fdbak and

More information

Numerical methods, Mixed exercise 10

Numerical methods, Mixed exercise 10 Numrial mthos, Mi ris a f ( ) 6 f ( ) 6 6 6 a = 6, b = f ( ) So. 6 b n a n 6 7.67... 6.99....67... 6.68....99... 6.667....68... To.p., th valus ar =.68, =.99, =.68, =.67. f (.6).6 6.6... f (.6).6 6.6.7...

More information

AP Chemistry Multiple Choice Questions - Chapter a. Updated July 3, 2015 Boyceville High School, Mr. Hamm Page 1 of 7

AP Chemistry Multiple Choice Questions - Chapter a. Updated July 3, 2015 Boyceville High School, Mr. Hamm Page 1 of 7 18.2a Upat July 3, 2015 Boycvill High School, Mr. Hamm Pag 1 of 7 407 A solution is prpar y aing 100 ml of 1.0 M HC 2 H 3 O 2 (aq) to 100 ml of 1.0 M NaC 2 H 3 O 2 (aq). Th a solution is stirr an th ph

More information

Chapter 9. There are 7 out of 50 measurements that are greater than or equal to 5.1; therefore, the fraction of the

Chapter 9. There are 7 out of 50 measurements that are greater than or equal to 5.1; therefore, the fraction of the Pratie questions 6 1 a y i = 6 µ = = 1 i = 1 y i µ i = 1 ( ) = 95 = s n 95 555. x i f i 1 1+ + 5+ n + 5 5 + n µ = = = f 11+ n 11+ n i 7 + n = 5 + n = 6n n = a Time (minutes) 1.6.1.6.1.6.1.6 5.1 5.6 6.1

More information

are given in the table below. t (hours)

are given in the table below. t (hours) CALCULUS WORKSHEET ON INTEGRATION WITH DATA Work th following on notbook papr. Giv dcimal answrs corrct to thr dcimal placs.. A tank contains gallons of oil at tim t = hours. Oil is bing pumpd into th

More information

u r du = ur+1 r + 1 du = ln u + C u sin u du = cos u + C cos u du = sin u + C sec u tan u du = sec u + C e u du = e u + C

u r du = ur+1 r + 1 du = ln u + C u sin u du = cos u + C cos u du = sin u + C sec u tan u du = sec u + C e u du = e u + C Tchniqus of Intgration c Donald Kridr and Dwight Lahr In this sction w ar going to introduc th first approachs to valuating an indfinit intgral whos intgrand dos not hav an immdiat antidrivativ. W bgin

More information

Leucine-Rich Repeat Transmembrane Proteins Instruct Discrete Dendrite Targeting in an Olfactory Map

Leucine-Rich Repeat Transmembrane Proteins Instruct Discrete Dendrite Targeting in an Olfactory Map 12 hrs APF N/n82 Hon t l, 2009 Luin-Rih Rpt Trnsmmrn Protins Instrut isrt nrit Trtin in n Oltory Mp Wizh Hon 1, Hito Zhu 1, Christophr J. Pottr 1, Grill Brsh 1, Mitsuhiko Kurusu 2,3, Ki Zinn 2, Liqun Luo

More information

The function y loge. Vertical Asymptote x 0.

The function y loge. Vertical Asymptote x 0. Grad 1 (MCV4UE) AP Calculus Pa 1 of 6 Drivativs of Eponntial & Loarithmic Functions Dat: Dfinition of (Natural Eponntial Numr) 0 1 lim( 1 ). 7188188459... 5 1 5 5 Proprtis of and ln Rcall th loarithmic

More information

Elements of Statistical Thermodynamics

Elements of Statistical Thermodynamics 24 Elmnts of Statistical Thrmodynamics Statistical thrmodynamics is a branch of knowldg that has its own postulats and tchniqus. W do not attmpt to giv hr vn an introduction to th fild. In this chaptr,

More information

Errata. Items with asterisks will still be in the Second Printing

Errata. Items with asterisks will still be in the Second Printing rrata Itms with astrisks will still b in th Scond Printing Author wbsit URL: http://chs.unl.du/dpsych/rjsit/hom. P7. Th squar root of rfrrd to (i.., is rfrrd to not Th squar root of (i.., P8. A narrow

More information

Solutions to Homework 5

Solutions to Homework 5 Solutions to Homwork 5 Pro. Silvia Frnánz Disrt Mathmatis Math 53A, Fall 2008. [3.4 #] (a) Thr ar x olor hois or vrtx an x or ah o th othr thr vrtis. So th hromati polynomial is P (G, x) =x (x ) 3. ()

More information

Kernels. ffl A kernel K is a function of two objects, for example, two sentence/tree pairs (x1; y1) and (x2; y2)

Kernels. ffl A kernel K is a function of two objects, for example, two sentence/tree pairs (x1; y1) and (x2; y2) Krnls krnl K is a function of two ojcts, for xampl, two sntnc/tr pairs (x1; y1) an (x2; y2) K((x1; y1); (x2; y2)) Intuition: K((x1; y1); (x2; y2)) is a masur of th similarity (x1; y1) twn (x2; y2) an ormally:

More information

CSI35 Chapter 11 Review

CSI35 Chapter 11 Review 1. Which of th grphs r trs? c f c g f c x y f z p q r 1 1. Which of th grphs r trs? c f c g f c x y f z p q r . Answr th qustions out th following tr 1) Which vrtx is th root of c th tr? ) wht is th hight

More information

Case Study 4 PHA 5127 Aminoglycosides Answers provided by Jeffrey Stark Graduate Student

Case Study 4 PHA 5127 Aminoglycosides Answers provided by Jeffrey Stark Graduate Student Cas Stuy 4 PHA 527 Aminoglycosis Answrs provi by Jffry Stark Grauat Stunt Backgroun Gntamicin is us to trat a wi varity of infctions. Howvr, u to its toxicity, its us must b rstrict to th thrapy of lif-thratning

More information

Determination of Vibrational and Electronic Parameters From an Electronic Spectrum of I 2 and a Birge-Sponer Plot

Determination of Vibrational and Electronic Parameters From an Electronic Spectrum of I 2 and a Birge-Sponer Plot 5 J. Phys. Chm G Dtrmination of Vibrational and Elctronic Paramtrs From an Elctronic Spctrum of I 2 and a Birg-Sponr Plot 1 15 2 25 3 35 4 45 Dpartmnt of Chmistry, Gustavus Adolphus Collg. 8 Wst Collg

More information

... Endogenous cannabinoids mediate retrograde signalling at hippocampal synapses

... Endogenous cannabinoids mediate retrograde signalling at hippocampal synapses ... Enognous nninois mit rtrogr signlling t hippompl synpss Rhl I. Wilson & Rogr A. Nioll Dprtmnts of Cllulr n Molulr Phrmology n Physiology, Univrsity of Cliforni, Sn Frniso, Cliforni 94143, USA... Mrijun

More information

PHA Final Exam Fall 2001

PHA Final Exam Fall 2001 PHA 5127 Final Exam Fall 2001 On my honor, I hav nithr givn nor rcivd unauthorizd aid in doing this assignmnt. Nam Qustion/Points 1. /12 pts 2. /8 pts 3. /12 pts 4. /20 pts 5. /27 pts 6. /15 pts 7. /20

More information

1997 AP Calculus AB: Section I, Part A

1997 AP Calculus AB: Section I, Part A 997 AP Calculus AB: Sction I, Part A 50 Minuts No Calculator Not: Unlss othrwis spcifid, th domain of a function f is assumd to b th st of all ral numbrs x for which f (x) is a ral numbr.. (4x 6 x) dx=

More information

CSE 373: More on graphs; DFS and BFS. Michael Lee Wednesday, Feb 14, 2018

CSE 373: More on graphs; DFS and BFS. Michael Lee Wednesday, Feb 14, 2018 CSE 373: Mor on grphs; DFS n BFS Mihl L Wnsy, F 14, 2018 1 Wrmup Wrmup: Disuss with your nighor: Rmin your nighor: wht is simpl grph? Suppos w hv simpl, irt grph with x nos. Wht is th mximum numr of gs

More information

Y 0. Standing Wave Interference between the incident & reflected waves Standing wave. A string with one end fixed on a wall

Y 0. Standing Wave Interference between the incident & reflected waves Standing wave. A string with one end fixed on a wall Staning Wav Intrfrnc btwn th incint & rflct wavs Staning wav A string with on n fix on a wall Incint: y, t) Y cos( t ) 1( Y 1 ( ) Y (St th incint wav s phas to b, i.., Y + ral & positiv.) Rflct: y, t)

More information

AP Calculus BC Problem Drill 16: Indeterminate Forms, L Hopital s Rule, & Improper Intergals

AP Calculus BC Problem Drill 16: Indeterminate Forms, L Hopital s Rule, & Improper Intergals AP Calulus BC Problm Drill 6: Indtrminat Forms, L Hopital s Rul, & Impropr Intrgals Qustion No. of Instrutions: () Rad th problm and answr hois arfully () Work th problms on papr as ndd () Pik th answr

More information

That is, we start with a general matrix: And end with a simpler matrix:

That is, we start with a general matrix: And end with a simpler matrix: DIAGON ALIZATION OF THE STR ESS TEN SOR INTRO DUCTIO N By th us of Cauchy s thorm w ar abl to rduc th numbr of strss componnts in th strss tnsor to only nin valus. An additional simplification of th strss

More information

A Simple Method of Tuning PI Controllers for Interval Plant of Cold Rolling Mill

A Simple Method of Tuning PI Controllers for Interval Plant of Cold Rolling Mill ntrnational Journal of Rnt Trns in Enginring, Vol. 1, No. 4, May 009 A Simpl Mtho of Tuning P Controllrs for ntrval Plant of Col Rolling Mill S.Umamahswari 1, V.Palanisamy, M.Chiambaram 3, 1 Dpartmnt of

More information

Why the Junction Tree Algorithm? The Junction Tree Algorithm. Clique Potential Representation. Overview. Chris Williams 1.

Why the Junction Tree Algorithm? The Junction Tree Algorithm. Clique Potential Representation. Overview. Chris Williams 1. Why th Juntion Tr lgorithm? Th Juntion Tr lgorithm hris Willims 1 Shool of Informtis, Univrsity of Einurgh Otor 2009 Th JT is gnrl-purpos lgorithm for omputing (onitionl) mrginls on grphs. It os this y

More information

A. Limits and Horizontal Asymptotes ( ) f x f x. f x. x "±# ( ).

A. Limits and Horizontal Asymptotes ( ) f x f x. f x. x ±# ( ). A. Limits and Horizontal Asymptots What you ar finding: You can b askd to find lim x "a H.A.) problm is asking you find lim x "# and lim x "$#. or lim x "±#. Typically, a horizontal asymptot algbraically,

More information

PHA 5128 Answer CASE STUDY 3 Question #1: Model

PHA 5128 Answer CASE STUDY 3 Question #1: Model PHA 5128 Answr CASE STUDY 3 Spring 2008 Qustion #1: Aminoglycosids hav a triphasic disposition, but tobramycin concntration-tim profil hr is dscribd via a 2-compartmnt modl sinc th alpha phas could not

More information

Evaluation of Polycyclic Aromatic Hydrocarbons in the Activation of Early Growth Response-1 and Peroxisome Proliferator Activated Receptors

Evaluation of Polycyclic Aromatic Hydrocarbons in the Activation of Early Growth Response-1 and Peroxisome Proliferator Activated Receptors TOXIOLOGIAL SIENES 85, 585 59 (5) oi:.9/toxsi/kfi8 Avan Ass puliation Fruary 6, 5 Evaluation of Polyyli Aromati Hyroarons in th Ativation of Early Growth Rspons- an Proxisom Prolifrator Ativat Rptors Jong-Ho

More information

Math 34A. Final Review

Math 34A. Final Review Math A Final Rviw 1) Us th graph of y10 to find approimat valus: a) 50 0. b) y (0.65) solution for part a) first writ an quation: 50 0. now tak th logarithm of both sids: log() log(50 0. ) pand th right

More information

Lecture 14 (Oct. 30, 2017)

Lecture 14 (Oct. 30, 2017) Ltur 14 8.31 Quantum Thory I, Fall 017 69 Ltur 14 (Ot. 30, 017) 14.1 Magnti Monopols Last tim, w onsidrd a magnti fild with a magnti monopol onfiguration, and bgan to approah dsribing th quantum mhanis

More information

Edge-Triggered D Flip-flop. Formal Analysis. Fundamental-Mode Sequential Circuits. D latch: How do flip-flops work?

Edge-Triggered D Flip-flop. Formal Analysis. Fundamental-Mode Sequential Circuits. D latch: How do flip-flops work? E-Trir D Flip-Flop Funamntal-Mo Squntial Ciruits PR A How o lip-lops work? How to analys aviour o lip-lops? R How to sin unamntal-mo iruits? Funamntal mo rstrition - only on input an an at a tim; iruit

More information

Math 61 : Discrete Structures Final Exam Instructor: Ciprian Manolescu. You have 180 minutes.

Math 61 : Discrete Structures Final Exam Instructor: Ciprian Manolescu. You have 180 minutes. Nm: UCA ID Numr: Stion lttr: th 61 : Disrt Struturs Finl Exm Instrutor: Ciprin nolsu You hv 180 minuts. No ooks, nots or lultors r llow. Do not us your own srth ppr. 1. (2 points h) Tru/Fls: Cirl th right

More information

Causes of deadlocks. Four necessary conditions for deadlock to occur are: The first three properties are generally desirable

Causes of deadlocks. Four necessary conditions for deadlock to occur are: The first three properties are generally desirable auss of dadloks Four ssary oditios for dadlok to our ar: Exlusiv ass: prosss rquir xlusiv ass to a rsour Wait whil hold: prosss hold o prviously aquird rsours whil waitig for additioal rsours No prmptio:

More information

A Prey-Predator Model with an Alternative Food for the Predator, Harvesting of Both the Species and with A Gestation Period for Interaction

A Prey-Predator Model with an Alternative Food for the Predator, Harvesting of Both the Species and with A Gestation Period for Interaction Int. J. Opn Problms Compt. Math., Vol., o., Jun 008 A Pry-Prdator Modl with an Altrnativ Food for th Prdator, Harvsting of Both th Spcis and with A Gstation Priod for Intraction K. L. arayan and. CH. P.

More information

September 23, Honors Chem Atomic structure.notebook. Atomic Structure

September 23, Honors Chem Atomic structure.notebook. Atomic Structure Atomic Structur Topics covrd Atomic structur Subatomic particls Atomic numbr Mass numbr Charg Cations Anions Isotops Avrag atomic mass Practic qustions atomic structur Sp 27 8:16 PM 1 Powr Standards/ Larning

More information

Errata. Items with asterisks will still be in the Second Printing

Errata. Items with asterisks will still be in the Second Printing Errata Itms with astrisks will still b in th Scond Printing Author wbsit URL: http://chs.unl.du/edpsych/rjsit/hom. P7. Th squar root of rfrrd to σ E (i.., σ E is rfrrd to not Th squar root of σ E (i..,

More information

Steinberg s Conjecture is false

Steinberg s Conjecture is false Stinrg s Conjtur is als arxiv:1604.05108v2 [math.co] 19 Apr 2016 Vinnt Cohn-Aa Mihal Hig Danil Král Zhntao Li Estan Salgao Astrat Stinrg onjtur in 1976 that vry planar graph with no yls o lngth our or

More information

Chapter 1. Analysis of a M/G/1/K Queue without Vacations

Chapter 1. Analysis of a M/G/1/K Queue without Vacations Chatr nalysis of a M/G// Quu without Vaations W onsir th singl srvr finit aaity quu with Poisson arrivals an gnrally istriut srvi tims. Th M/G// systm may analys using an im Marov Chain aroah vry similar

More information

Lecture 16: Bipolar Junction Transistors. Large Signal Models.

Lecture 16: Bipolar Junction Transistors. Large Signal Models. Whits, EE 322 Ltur 16 Pag 1 of 8 Ltur 16: Bipolar Juntion Transistors. Larg Signal Modls. Transistors prform ky funtions in most ltroni iruits. This is rtainly tru in RF iruits, inluding th NorCal 40A.

More information

Linked-List Implementation. Linked-lists for two sets. Multiple Operations. UNION Implementation. An Application of Disjoint-Set 1/9/2014

Linked-List Implementation. Linked-lists for two sets. Multiple Operations. UNION Implementation. An Application of Disjoint-Set 1/9/2014 Disjoint Sts Data Strutur (Chap. 21) A disjoint-st is a olltion ={S 1, S 2,, S k } o distint dynami sts. Eah st is idntiid by a mmbr o th st, alld rprsntativ. Disjoint st oprations: MAKE-SET(x): rat a

More information

Homework #3. 1 x. dx. It therefore follows that a sum of the

Homework #3. 1 x. dx. It therefore follows that a sum of the Danil Cannon CS 62 / Luan March 5, 2009 Homwork # 1. Th natural logarithm is dfind by ln n = n 1 dx. It thrfor follows that a sum of th 1 x sam addnd ovr th sam intrval should b both asymptotically uppr-

More information

Answer Homework 5 PHA5127 Fall 1999 Jeff Stark

Answer Homework 5 PHA5127 Fall 1999 Jeff Stark Answr omwork 5 PA527 Fall 999 Jff Stark A patint is bing tratd with Drug X in a clinical stting. Upon admiion, an IV bolus dos of 000mg was givn which yildd an initial concntration of 5.56 µg/ml. A fw

More information

Why is a E&M nature of light not sufficient to explain experiments?

Why is a E&M nature of light not sufficient to explain experiments? 1 Th wird world of photons Why is a E&M natur of light not sufficint to xplain xprimnts? Do photons xist? Som quantum proprtis of photons 2 Black body radiation Stfan s law: Enrgy/ ara/ tim = Win s displacmnt

More information

1. (25pts) Answer the following questions. Justify your answers. (Use the space provided below and the next page)

1. (25pts) Answer the following questions. Justify your answers. (Use the space provided below and the next page) Phyi 6 xam#3 1. (pt) Anwr th foowing qution. Jutify your anwr. (U th pa providd bow and th nxt pag) a). Two inrtia obrvr ar in rativ motion. Whih of th foowing quantiti wi thy agr or diagr on? i) thir

More information

a 1and x is any real number.

a 1and x is any real number. Calcls Nots Eponnts an Logarithms Eponntial Fnction: Has th form y a, whr a 0, a an is any ral nmbr. Graph y, Graph y ln y y Th Natral Bas (Elr s nmbr): An irrational nmbr, symboliz by th lttr, appars

More information

Search sequence databases 3 10/25/2016

Search sequence databases 3 10/25/2016 Sarch squnc databass 3 10/25/2016 Etrm valu distribution Ø Suppos X is a random variabl with probability dnsity function p(, w sampl a larg numbr S of indpndnt valus of X from this distribution for an

More information

2. Finite Impulse Response Filters (FIR)

2. Finite Impulse Response Filters (FIR) .. Mthos for FIR filtrs implmntation. Finit Impuls Rspons Filtrs (FIR. Th winow mtho.. Frquncy charactristic uniform sampling. 3. Maximum rror minimizing. 4. Last-squars rror minimizing.. Mthos for FIR

More information

1973 AP Calculus AB: Section I

1973 AP Calculus AB: Section I 97 AP Calculus AB: Sction I 9 Minuts No Calculator Not: In this amination, ln dnots th natural logarithm of (that is, logarithm to th bas ).. ( ) d= + C 6 + C + C + C + C. If f ( ) = + + + and ( ), g=

More information

In which direction do compass needles always align? Why?

In which direction do compass needles always align? Why? AQA Trloy Unt 6.7 Mntsm n Eltromntsm - Hr 1 Complt t p ll: Mnt or s typ o or n t s stronst t t o t mnt. Tr r two typs o mnt pol: n. Wrt wt woul ppn twn t pols n o t mnt ntrtons low: Drw t mnt l lns on

More information

Chemical Physics II. More Stat. Thermo Kinetics Protein Folding...

Chemical Physics II. More Stat. Thermo Kinetics Protein Folding... Chmical Physics II Mor Stat. Thrmo Kintics Protin Folding... http://www.nmc.ctc.com/imags/projct/proj15thumb.jpg http://nuclarwaponarchiv.org/usa/tsts/ukgrabl2.jpg http://www.photolib.noaa.gov/corps/imags/big/corp1417.jpg

More information

Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers Roy D. Yates and David J.

Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers Roy D. Yates and David J. Probability and Stochastic Procsss: A Frindly Introduction for Elctrical and Computr Enginrs Roy D. Yats and David J. Goodman Problm Solutions : Yats and Goodman,4.3. 4.3.4 4.3. 4.4. 4.4.4 4.4.6 4.. 4..7

More information

Classical Magnetic Dipole

Classical Magnetic Dipole Lctur 18 1 Classical Magntic Dipol In gnral, a particl of mass m and charg q (not ncssarily a point charg), w hav q g L m whr g is calld th gyromagntic ratio, which accounts for th ffcts of non-point charg

More information

12. Traffic engineering

12. Traffic engineering lt2.ppt S-38. Introution to Tltrffi Thory Spring 200 2 Topology Pths A tlommunition ntwork onsists of nos n links Lt N not th st of nos in with n Lt J not th st of nos in with j N = {,,,,} J = {,2,3,,2}

More information

BETA DECAY VISUAL PHYSICS ONLINE

BETA DECAY VISUAL PHYSICS ONLINE VISUAL PHYSICS ONLINE BETA DECAY Suppos now that a nuclus xists which has ithr too many or too fw nutrons rlativ to th numbr of protons prsnt for stability. Stability can b achivd by th convrsion insid

More information

Mathematics 1110H Calculus I: Limits, derivatives, and Integrals Trent University, Summer 2018 Solutions to the Actual Final Examination

Mathematics 1110H Calculus I: Limits, derivatives, and Integrals Trent University, Summer 2018 Solutions to the Actual Final Examination Mathmatics H Calculus I: Limits, rivativs, an Intgrals Trnt Univrsity, Summr 8 Solutions to th Actual Final Eamination Tim-spac: 9:-: in FPHL 7. Brought to you by Stfan B lan k. Instructions: Do parts

More information

Need to understand interaction of macroscopic measures

Need to understand interaction of macroscopic measures CE 322 Transportation Enginring Dr. Ahmd Abdl-Rahim, h. D.,.E. Nd to undrstand intraction o macroscopic masurs Spd vs Dnsity Flow vs Dnsity Spd vs Flow Equation 5.14 hlps gnraliz Thr ar svral dirnt orms

More information

GEOMETRICAL PHENOMENA IN THE PHYSICS OF SUBATOMIC PARTICLES. Eduard N. Klenov* Rostov-on-Don, Russia

GEOMETRICAL PHENOMENA IN THE PHYSICS OF SUBATOMIC PARTICLES. Eduard N. Klenov* Rostov-on-Don, Russia GEOMETRICAL PHENOMENA IN THE PHYSICS OF SUBATOMIC PARTICLES Eduard N. Klnov* Rostov-on-Don, Russia Th articl considrs phnomnal gomtry figurs bing th carrirs of valu spctra for th pairs of th rmaining additiv

More information

SUMMER 17 EXAMINATION

SUMMER 17 EXAMINATION (ISO/IEC - 7-5 Crtifid) SUMMER 7 EXAMINATION Modl wr jct Cod: Important Instructions to aminrs: ) Th answrs should b amind by ky words and not as word-to-word as givn in th modl answr schm. ) Th modl answr

More information

Metabolic control of type 1 regulatory (Tr1) cell differentiation by AHR and HIF1-α. Francisco J. Quintana 1

Metabolic control of type 1 regulatory (Tr1) cell differentiation by AHR and HIF1-α. Francisco J. Quintana 1 Metaoli ontrol of type regulatory () ell ifferentiation y AHR an HIF-α Ivan D. Masanfroni, Maisa C. Takenaka, Aa Yeste, Bonny Patel, Yan Wu, Jessia E. Kenison, Shafiuin Siiqui, Alexanre S. Basso, Leo E.

More information

XV Exponential and Logarithmic Functions

XV Exponential and Logarithmic Functions MATHEMATICS 0-0-RE Dirnial Calculus Marin Huard Winr 08 XV Eponnial and Logarihmic Funcions. Skch h graph o h givn uncions and sa h domain and rang. d) ) ) log. Whn Sarah was born, hr parns placd $000

More information

Title: Vibrational structure of electronic transition

Title: Vibrational structure of electronic transition Titl: Vibrational structur of lctronic transition Pag- Th band spctrum sn in th Ultra-Violt (UV) and visibl (VIS) rgions of th lctromagntic spctrum can not intrprtd as vibrational and rotational spctrum

More information

TURFGRASS DISEASE RESEARCH REPORT J. M. Vargas, Jr. and R. Detweiler Department of Botany and Plant Pathology Michigan State University

TURFGRASS DISEASE RESEARCH REPORT J. M. Vargas, Jr. and R. Detweiler Department of Botany and Plant Pathology Michigan State University I TURFGRASS DISEASE RESEARCH REPORT 9 J. M. Vrgs, Jr. n R. Dtwilr Dprtmnt f Btny n Plnt Pthlgy Mihign Stt Univrsity. Snw Ml Th 9 snw ml fungii vlutin trils wr nut t th Byn Highln Rsrt, Hrr Springs, Mihign

More information

, each of which is a tree, and whose roots r 1. , respectively, are children of r. Data Structures & File Management

, each of which is a tree, and whose roots r 1. , respectively, are children of r. Data Structures & File Management nrl tr T is init st o on or mor nos suh tht thr is on sint no r, ll th root o T, n th rminin nos r prtition into n isjoint susts T, T,, T n, h o whih is tr, n whos roots r, r,, r n, rsptivly, r hilrn o

More information

SOLVED EXAMPLES. be the foci of an ellipse with eccentricity e. For any point P on the ellipse, prove that. tan

SOLVED EXAMPLES. be the foci of an ellipse with eccentricity e. For any point P on the ellipse, prove that. tan LOCUS 58 SOLVED EXAMPLES Empl Lt F n F th foci of n llips with ccntricit. For n point P on th llips, prov tht tn PF F tn PF F Assum th llips to, n lt P th point (, sin ). P(, sin ) F F F = (-, 0) F = (,

More information

5.80 Small-Molecule Spectroscopy and Dynamics

5.80 Small-Molecule Spectroscopy and Dynamics MIT OpnCoursWar http://ocw.mit.du 5.80 Small-Molcul Spctroscopy and Dynamics Fall 008 For information about citing ths matrials or our Trms of Us, visit: http://ocw.mit.du/trms. Lctur # 3 Supplmnt Contnts

More information

Learning Spherical Convolution for Fast Features from 360 Imagery

Learning Spherical Convolution for Fast Features from 360 Imagery Larning Sphrical Convolution for Fast Faturs from 36 Imagry Anonymous Author(s) 3 4 5 6 7 8 9 3 4 5 6 7 8 9 3 4 5 6 7 8 9 3 3 3 33 34 35 In this fil w provid additional dtails to supplmnt th main papr

More information

What are those βs anyway? Understanding Design Matrix & Odds ratios

What are those βs anyway? Understanding Design Matrix & Odds ratios Ral paramtr stimat WILD 750 - Wildlif Population Analysis of 6 What ar thos βs anyway? Undrsting Dsign Matrix & Odds ratios Rfrncs Hosmr D.W.. Lmshow. 000. Applid logistic rgrssion. John Wily & ons Inc.

More information

Final Exam Solutions

Final Exam Solutions CS 2 Advancd Data Structurs and Algorithms Final Exam Solutions Jonathan Turnr /8/20. (0 points) Suppos that r is a root of som tr in a Fionacci hap. Assum that just for a dltmin opration, r has no childrn

More information

Acoustic Analysis with Consideration of Damping Effects of Air Viscosity in Sound Pathway

Acoustic Analysis with Consideration of Damping Effects of Air Viscosity in Sound Pathway Aousti Analysis with Consiration of Damping Effts of Air Visosity in Soun Pathway M. Sasajima, M. Watana, T. Yamaguhi, Y. Kurosawa, an Y. Koi Astrat Soun pathways in th nlosurs of small arphons ar vry

More information