Transient Stimulation of Distinct Subpopulations of Striatal Neurons Mimics Changes in the Value of Competing Actions
|
|
- Calvin Franklin
- 5 years ago
- Views:
Transcription
1 Supplementl mterils for: Trnsient Stimultion of Distinct Supopultions of Stritl Neurons Mimics Chnges in the Vlue of Competing Actions Lung-Ho Ti, A. Moses Lee,2, Nor Benvidez 3, Antonello Bonci 4,,6, Lind Wilrecht,4 Ernest Gllo Clinic nd Reserch Center, Emeryville, CA 2 Medicl Scientist Trining Progrm, Neuroscience Grdute Progrm, University of Cliforni, Sn Frncisco 3 Deprtment of Cognitive Science, University of Cliforni, Berkeley 4 Deprtment of Neurology, University of Cliforni, Sn Frncisco Intrmurl Progrm, Ntionl Institute of Drug Ause, Bltimore, MD 6 Solomon H. Snyder Deprtment of Neuroscience, Johns Hopkins School of Medicine These uthors mde equl contriutions. Nture Neuroscience: doi:.38/nn.388
2 Supplementry Figure. Chosen port: Left Right Frction left choice Withdrwl time (ms) Frction rewrd trils t left port Reltive ction vlue for left choice c Frction of totl trils. 2 2 Go-Cue to nose-out (ms) d Movement time (ms) Chosen port: Left Right Reltive ction vlue for left choice e. f... Reltive ction vlue. Predicted. Supplementry Figure. Chrcteriztion of responses within the tsk () The reltionship of frction of left choices nd frction of rewrd trils t left port for ll 6 possile rewrd histories in the previous two trils verged cross ll sujects. The frequency of trils of given rewrd history is indicted y the reltive size of the circle. () Averge medin withdrwl time from gosignl to nose-withdrwl t center port (n=28). Withdrwl time is shorter when the ction vlue for the chosen port is higher. (c) Cumultive distriution of rection time from Go-Cue to nose-withdrwl from center port for ll sujects (men ±s.d., n=28). The dotted line indictes the onset of opticl ultion t ms ltency. (d) Averge movement time from nose-withdrwl t center port to rewrd port (n=28). Movement time is shorter when the ction vlue for the chosen port is higher. All error rs represent s.e.m. (e) The frction of choices for the left port from 3% of dt given the reltive ction vlue eted from the other 7% of dt. Dt from ech suject were grouped in ins nd represented in distinct color. (f) The frction of choices for the left port from 3% of dt given the frction of left choices predicted y the regression model using the other 7% of dt. Nture Neuroscience: doi:.38/nn.388
3 Supplementry Figure 2 D-ChR2-eYFP D-eYFP +.3±.2 mm +.7±.2 mm +.±.2 mm eyfp control c D2-ChR2-eYFP ChR2-eYFP D2-eYFP d +.3±.2 mm +.7±.2 mm +.±.2 mm Supplementry Figure 2. Antomy of ultion sites () Coronl series demonstrting the extent of infection (grey) nd plcements of fier optic tips (dots) for D-Cre injected with AAV2/-EF-DIO-ChR2-eYFP (left series) or AAV2/-EF-DIO-eYFP (right) series. Light grey represents the extent of the lrgest injection while drk grey represents the smllest extent. () Coronl (top pnel) nd sgittl histologicl sections (ottom pnel) from two representtive D-Cre nimls expressing ChR2-eYFP. (c) Coronl series demonstrting the extent of infection (grey) nd plcements of fier optic tips (dots) for D2-Cre injected with AAV2/-EF-DIO-ChR2-eYFP (left series) or AAV2/-EF-DIO-eYFP (right) series. (d) Coronl (top pnel) nd sgittl histologicl sections (ottom pnel) from two representtive D2-Cre nimls expressing ChR2eYFP. Nture Neuroscience: doi:.38/nn.388
4 Supplementry Figure 3 D-Cre c D2-Cre D-Cre d Supplementry Figure 3. Expression of ChR2 in Stritl MSNs nd ChAT+ Interneuons () Single plne confocl imges of medium spiny neurons nd cholinergic interneurons in the dorsomedil stritum from D-Cre mouse injected with AAV-EFα-DIO-ChR2-eYFP (ChR2-eYFP, green in merged imge). Histologicl slices were leled using immunohistochemistry for the intrcellulr C-terminus of Kv2. chnnel, mrker of MSNs 2 (red in merged imge), nd choline cetyltrnsferse (ChAT, lue in merged imge) respectively. ChR2-eYFP expression in D-Cre nimls ws found to coloclize with Kv2. expression s indicted y the red rrows in (), ut never with ChAT positive neurons (/68 neurons). () Single plne confocl imges of medium spiny neurons nd cholinergic interneurons in the dorsomedil stritum from D2-Cre mouse injected with AAV- EFα-DIO-ChR2-eYFP. ChR2-eYFP expression in D2-Cre nimls ws found to coloclize with Kv2. expression (43/4 neurons) s indicted y the red rrows in mny cells ( nd c). In D2-Cre nimls, ChR2-eYFP expression ws found to coloclize with suset of ChAT immunostined neurons (29/7) (lue dot in ()), ut not ll ChAT immunostined neurons (lue dot in (c)) despite the presence of ChR2-eYFP expression in nery cells s seen y 3D-reconstruction (d). Scle r in (c): μm. Scle r in (d): 2 μm Nture Neuroscience: doi:.38/nn.388
5 Supplementry Figure 4 Light ultion Tril # Normlized spike mplitude D-ChR n= Time (ms) Tril # Tril # Tril # Time (sec) Time (sec) Normlized spike mplitude Normlized Spike Amplitude Normlized spike mplitude D-ChR n= Time (ms) D2-ChR2 - n= Time (ms) D2-ChR n= Time (ms) Supplementry Figure 4. Opticl ultion induces spiking in ChR2-trnsduced stritum () Spike rster of two representtive single units for light-evoked ctivity in the stritum of D-ChR2 mice. Stimultion ws delivered with ms pulses t 2 Hz for ms. The wveforms of the units re shown in the right pnels. () Spike rster of two representtive single units for light-evoked ctivity in the stritum of D2-ChR2 mice. Right: recorded spike wveforms. Nture Neuroscience: doi:.38/nn.388
6 Supplementry Figure Hz (3 pulses) Hz ( pulses) 2 Hz ( pulses) Hz (3 pulses) Hz ( pulses) 2 Hz ( pulses) D D D D D Reltive ction vlue.. - D Reltive ction vlue Supplementry Figure. Gllery of individul D-ChR2 nimls dt Frction of choices for the left port on trils with different reltive ction vlue etes in D-cre nimls in the presence (red) or sence (lue) of opticl ultion (protocol in Fig. 3). All sujects were trnsduced with AAV-EFα-DIO-ChR2-eYFP. Opticl ultion in the right nd left hemisphere re shown seprtely. Some mice only demonstrted ChR2 expression unilterlly nd ultion sessions were only used from the trnsduced side. Logistic regression ws used to fit the dt from trils with (red curve) nd without ultion (lue curve). All error rs represent s.e.m. Nture Neuroscience: doi:.38/nn.388
7 Supplementry Figure 6 Hz (3 pulses) Hz ( pulses) 2 Hz ( pulses) Hz (3 pulses) Hz ( pulses) 2 Hz ( pulses).. - D D D D D D D D Reltive ction vlue Reltive ction vlue Supplementry Figure 6. Gllery of individul D2-ChR2 nimls dt Frction of choices for the left port on trils with different reltive ction vlue etes in D2-cre nimls in the presence (red) or sence (lue) of opticl ultion (protocol in Fig. 3). Dt from ll sujects trnsduced with AAV-EFα-DIO-ChR2-eYFP with opticl ultion in the right nd left hemisphere. Logistic regression ws used to fit the dt from trils with (red curve) nd without ultion (lue curve). All error rs represent s.e.m. Nture Neuroscience: doi:.38/nn.388
8 Supplementry Figure 7 Prev. choice: contrlterl Current Choice: contrlterl Withdrwl time (ms) D DMS (ChR2-ChR2-eYFP summry dt, n= ultion sites, 6 nimls) Prev. choice: ipsilterl Current Choice: ipsilterl Prev. choice: contrlterl Current Choice: contrlterl Withdrwl time (ms) Withdrwl time (ms) D2 DMS (ChR2-ChR2-eYFP summry dt, n=3 ultion sites, 8 nimls) Reltive ction vlue for ipsilterl choice Prev. choice: ipsilterl Current Choice: ipsilterl Withdrwl time (ms) Reltive ction vlue for ipsilterl choice Supplementry Figure 7. Opticl ultion ltered withdrwl time on trils when nimls did not switch sides On trils when nimls did not switch sides reltive to the previous tril (sty trils) we plot time to withdrw from center port fter the go signl (withdrwl time) ginst port choice on trils with different reltive ction vlue etes. Two different lines reflect the presence (red) or sence (lue) of opticl ultion (protocol in Fig. 3). () shows tht ultion speeds contrlterl choice nd slows ipsilterl choice withdrwl time in D-cre mice. () Shows ultion speeds ipsilterl choice nd slows contrlterl choice withdrwl time in D2-cre mice. Note we plot only dt points where more thn % of sujects hve or more trils. All dt is from sujects trnsduced with AAV-EFα- DIO-ChR2-eYFP. All error rs represent s.e.m. : p<.; : p<., Wilcoxon signed-rnk test. Nture Neuroscience: doi:.38/nn.388
9 Supplementry Figure 8 D-9, left DMS. D-22, left DMS. D-22, right DMS.... p< 3 p< 29 Reltive ction vlue Reltive ction vlue p< 3 Reltive ction vlue D2-3, left DMS. D2-4, left DMS. D2-, left DMS. D2-6, left DMS..... p< 47 p< 3 p< 8 p< 2 Reltive ction vlue Reltive ction vlue Reltive ction vlue Reltive ction vlue c Withdrwl time (ms) 2 D-ChR2 DMS (n=3 sites, 2 nimls) Reltive ction vlue for ipsilterl choice d 2 D2-ChR2 DMS (n=4 sites, 4 nimls) Reltive ction vlue for ipsilterl choice Supplementl Figure 8. Individul nimls dt for pre go-signl ultion experiment (-) Frction of choices for the left port on trils with different reltive ction vlue etes in () D- cre or () D2-cre nimls in the presence (red) or sence (lue) of opticl ultion efore gosound (protocol shown in Fig 7). Logistic regression ws used to fit the dt from trils with (red curve) nd without ultion (lue curve). P vlues reported for t-tests: H :ß = (distnce etween red nd lue lines). (c-d) The medin time tken to withdrw from the center port verged cross individul D-Cre sujects (c) nd D2-Cre sujects (d) in trils without ultion (lue) or with ultion (red) nd cross different reltive ction vlues for choosing the port ipsilterl versus contrlterl to the site of ultion. Positive reltive ction vlues correspond to trils in which the vlue of the port ipsilterl to the site of ultion is greter thn the contrlterl port. All dt is from sujects trnsduced with AAV-EFα-DIO-ChR2-eYFP. : p<., Wilcoxon signed-rnk test. All error rs represent s.e.m. Nture Neuroscience: doi:.38/nn.388
10 Supplementry Figure 9 Center-port-in Go signl In proilistic switching tsk Frme: Frme: Frme: (/3 sec) (/6 sec) Rewrd port in Frme: Frme: (/2 sec) Red: initil ody orienttion Frme: 9 (3/ sec) Frme: 3 (3/3 sec) Frme: (/2 sec) Yellow: turning degree clockwise Blue: turning 7 degree clockwise c Frme: (ultion onset) Outside tsk context trnsient ultion d Frme: (/2 sec) Normlized ody turning (degree) - D-ChR2 (n=8 sites,4 mice) D2-ChR2 (n=2 sites,7 mice). sec sec. sec sec fter trnsient ultion (2 Hz ms) Ipsilterl is Contrlterl is Outside tsk context prolonged ultion e D-ChR2 (n=9 sites, mice) f D2-ChR2 (n= sites, 7 mice) Bseline (6 s) Stimultion (6 s) Recovery (6 s) Bseline (6 s) Stimultion (6 s) Recovery (6 s) # of contrlterl rottion per minute - ^ ^^^ ^^^ Hz, 6 sec Hz, 6 sec 2 Hz, 6 sec # of contrlterl rottion per minute - - ^^ Bseline vs. ultion : p<. : p<. : p<. Wilcoxon rnk sum test ^^^ ^^ Stimultion vs. recovery ^: p<. ^^: p<. ^^^ p<. Wilcoxon rnk sum test Nture Neuroscience: doi:.38/nn.388
11 Supplementry Figure 9. Effect of ultion on ody orienttion nd rottion outside of the tsk context () A series of video frmes showing the time course of typicl tril. () Two top-view video frmes showing the typicl ody orienttion t center-port-in nd. sec lter. (c) Two top-view video frmes showing the typicl ody orienttion t ultion onset nd. sec lter. Red dot: eted center of ody. (d) Normlized ody turning in. sec or sec fter rief ms 2 Hz stritl ultion in D-ChR2 (p=.46 nd p=.74, n=8) nd D2-ChR2 nimls (p=.79 nd p=.9, n=2) outside the ehvior tsk. P vlues reported for Wilcoxon sign rnk test. (e) The numer of contrlterl nd ipsilterl rottions in the seline, prolonged ultion nd recovery periods from D-ChR2 nimls. The durtion of ech period ws 6 seconds. (f) The numer of contrlterl nd ipsilterl rottions in the seline, prolonged ultion nd recovery periods from D2-ChR2 nimls. Reported n refers to numer of ultion sites. All error rs represent s.e.m. Nture Neuroscience: doi:.38/nn.388
12 Supplementry Figure log( P Models: ) = Z + β X Akike Informtion Criterion (AIC) : L AIC = ± 3.2 PL log( P L ) = β Signed-rnk Test P-Vlue 2: AIC 2 = 69.6 ± 3.23 H : P AIC = AIC 2.26 L Z + β 3 PL Re wrd 3: log( ) = β j ( YL ( i j) YR ( i j)) + AIC 3 = 7.84 ± 3.67 H : PL j = AIC = AIC 3.3 n j = β No Re wrd j ( N L ( i j) N R 4: P AIC 4 = ± 3.7 L = ( Z + β X ( i )) + e : AIC = 7.69 ± 4.4 H : ( Z + β X ( i )) AIC 4 = AIC.9 + e 6: L AIC 6 = ± 2.3 H : ( Z + β X ( i )) AIC 4 = AIC : L AIC 7 = 7.7 ± 2.9 H : ( Z + β X ( i )) / AIC 4 = AIC Z is the eted reltive ction vlue for no-ultion trils with the sme pst rewrd nd choice history. :AIC clculted with correction 2k(k+)/(n-k-) for finite smple size. AIC vlue reported: medin ± stndrd error of medin clculted using ootstrp smpling ( i X j)) + Z + β P L i = ( ) / P = + + e P = + + n j = e y n Re wrd No Re wrd j ( YL ( i j) YR ( i j)) + β j ( N L ( i j) N R ( i j)) β j = Z = β + y X D D2 c D D2 Chnge in reltive ction vlue D-ChR2 (n=) D-eYFP (n=7) Hz Hz 2Hz Hz Hz 2Hz D2-ChR2 (n=3) D2-eYFP (n=7) Slope et coefficient.4 Hz Hz 2 Hz Hz Hz 2 Hz.2.8 p=.4 p=.383 p=.28 p= p= p=.3 D-ChR2 (n=) D2-ChR2 (n=3) D-eYFP (n=7) D2-eYFP (n=7) Nture Neuroscience: doi:.38/nn.388
13 Supplementry Figure. Comprison of lterntive models in descriing the nimls ehvior () In order to rule out whether other lterntive models could e used to descrie the nimls ehvior, we generted fmily of more complex models. In these models, we compre our simple generlized liner model (model ) with: Model 2: A model tht llows for ultion to chnge the generl sensitivity to the ction vlue. Model 3: A model tht llows for ultion to chnge the sensitivity to the pst rewrd history in the lst three trils. Model 4: A nonliner fit model similr to our generlized liner model tht llows for shift. Model : A nonliner fit model tht llows for ultion to chnge the generl sensitivity to the ction vlue. Model 6: A nonliner fit model tht llows for chnge in the upper nd lower ound symptotes. Model 7: A nonliner fit model tht llows for chnge in the symptotes s well s generl chnge in sensitivity to the ction vlue. This model ws sed upon method used y Erlich, Bilek, nd Brody. Neuron. 2. We then compred ll of these models to our generlized liner model to determine whether ny of these models could more ccurtely descrie our dt given the dditionl free prmeters tht they require using the Akike Informtion Criterion (AIC). Bsed upon this model selection criterion, we found tht these clsses of more complex models were not significntly different or performed worse thn our simple generlized liner model in terms of their goodness-of-fit. Given its simplicity, we elieve tht descriing the effect of ultion s shift in the ction vlue is vlid nd ccurte mesure for descriing our dt. P vlues reported for Wilcoxon signed-rnk test. Exmple nlysis from Model 2. We nlyzed the effect of opticl ultion using model 2 which llows the ultion to cuse shift in reltive ction vlue (ß ) s well s chnges in nimls sensitivity to rewrd (slope, ß ). () Eted chnge in the reltive ction vlue (shift, ß ) for choosing the port ipsilterl versus contrlterl to the side of ultion verged cross individuls within group. Positive chnges in reltive ction vlues correspond with n ipsilterl is while negtive chnges correspond to contrlterl is. (c) Eted chnge in rewrd sensitivity (slope, ß ) verged cross individuls within group. No significnt chnge in rewrd sensitivity ws oserved. Reported n refers to numer of ultion sites. : p<., P vlues reported for Wilcoxon rnk-sum test. All error rs represent s.e.m. Nture Neuroscience: doi:.38/nn.388
SUPPLEMENTARY INFORMATION
doi:.38/nture8499 doi:.38/nture8499 5 6 5 4.5 Firing rte (Hz) -67-65 -66-6 -58 V m (mv) -7-67 -68-66 -64 c Thet power (mv ) -73-69 -7-7 -7.5.8 3....9.9.4.6.6. 9 8 9 8 9 8 9 8 9 8 Supplementry Figure Firing
More informationSupplementary Figure 1
Supplementry Figure (nesthetized) (wke) Normlized mplitude.5 Pek width (ms).6.4.2 4 2 2 x 3 Wveform slope Normlized mplitude.5 Pek width (ms).6.4.2 x 3 3 2 Wveform slope c (nesthetized) d (wke) Normlized
More informationSUPPLEMENTARY FIGURES
A m ultory distnce (cm ) % C enter distnce C e n te r tim e (s ) A m ultory distnce (cm ) % C enter distnce C e n te r tim e (s ) N o v e l c g e % h o m e c g e c o n s u m p tio n % M ic e fe e d in
More informationSUPPLEMENTARY INFORMATION
doi:1.138/nture11444 CMKIIN Gold prticles/ mitochondril re ( m ) 4 3 1 CMKIIN mtcmkiin mtcmkiin SERCA ATP synthse HA mitoplsts mtcmkiin CMKIIN cytosolic mtcmkiin CMKIIN 97 kdl 64 kdl 51 kdl 14 kdl 6 kdl
More informationa cacnb1 ts25/ts25 Supplemental Figure 1
ccn1 ts/ts α -ungrotoxin prlyzed 0.6 ΔF/F 0.0 2 ΔF/F 2 s stimulus α -ungrotoxin ccn1 ts/ts Supplementl Figure 1 CSF-cNs recorded from lrv prlyzed with α-ungrotoxin nd ccn1 mutnt lrv show no difference
More informationSupplementary material
10.1071/FP11237_AC CSIRO 2012 Accessory Puliction: Functionl Plnt Biology 2012, 39(5), 379 393. Supplementry mteril Tle S1. Effect of wter regime nd genotype on different growth prmeters: spike dry mtter
More informationInformation processing via physical soft body. Supplementary Information
Informtion processing vi physicl soft body Supplementry Informtion Kohei Nkjim 1, Helmut Huser 2, o Li 3, Rolf Pfeifer 4,5 1 he Hkubi Center for Advnced Reserch & Grdute School of Informtics, Kyoto University,
More informationSUPPLEMENTARY INFORMATION
doi:.38/nture896 c Resting stte Resting stte Resting stte Supplementry Figure Illustrtion of pttern clssifiction nd its effects on neuronl representtions. Dynmic ctivity ptterns evoked y different stimuli
More informationNon-Linear & Logistic Regression
Non-Liner & Logistic Regression If the sttistics re boring, then you've got the wrong numbers. Edwrd R. Tufte (Sttistics Professor, Yle University) Regression Anlyses When do we use these? PART 1: find
More informationTremor-rich shallow dyke formation followed by silent magma flow at Bárðarbunga in Iceland
In the formt provided y the uthors nd unedited. SUPPLEMENTARY INFORMATION DOI: 1.138/NGEO9 Tremor-rich shllow dyke formtion followed y silent mgm flow t Bárðrung in Icelnd 1,, 1, 3 1, 1 1, NATURE GEOSCIENCE
More informationAcceptance Sampling by Attributes
Introduction Acceptnce Smpling by Attributes Acceptnce smpling is concerned with inspection nd decision mking regrding products. Three spects of smpling re importnt: o Involves rndom smpling of n entire
More informationDOI:.8/nc5 Cpilities of MCAK Sidesliding, endctching on microtuules MCAKdecorted ed Functions in mitotic spindle Prometphse Slides on the microtuule surfce + Redily slides long the microtuule surfce Strongly
More information3.94 ± 0.50 (95% CI) Correlative inhibition index (slope)
Supplementl Tle S. Selected rchitecturl prmeters of phy nd phyphy grown under. Vlues re mens ± SE, except for predicted primry rosette rnches where the vlues re the men with the ssocited 9% confidence
More informationLAMEPS Limited area ensemble forecasting in Norway, using targeted EPS
Limited re ensemle forecsting in Norwy, using trgeted Mrit H. Jensen, Inger-Lise Frogner* nd Ole Vignes, Norwegin Meteorologicl Institute, (*held the presenttion) At the Norwegin Meteorologicl Institute
More information7.1 Integral as Net Change and 7.2 Areas in the Plane Calculus
7.1 Integrl s Net Chnge nd 7. Ares in the Plne Clculus 7.1 INTEGRAL AS NET CHANGE Notecrds from 7.1: Displcement vs Totl Distnce, Integrl s Net Chnge We hve lredy seen how the position of n oject cn e
More informationDerivations for maximum likelihood estimation of particle size distribution using in situ video imaging
2 TWMCC Texs-Wisconsin Modeling nd Control Consortium 1 Technicl report numer 27-1 Derivtions for mximum likelihood estimtion of prticle size distriution using in situ video imging Pul A. Lrsen nd Jmes
More informationDriving Cycle Construction of City Road for Hybrid Bus Based on Markov Process Deng Pan1, a, Fengchun Sun1,b*, Hongwen He1, c, Jiankun Peng1, d
Interntionl Industril Informtics nd Computer Engineering Conference (IIICEC 15) Driving Cycle Construction of City Rod for Hybrid Bus Bsed on Mrkov Process Deng Pn1,, Fengchun Sun1,b*, Hongwen He1, c,
More informationSupplementary Figure 1 Supplementary Figure 2
Supplementry Figure 1 Comprtive illustrtion of the steps required to decorte n oxide support AO with ctlyst prticles M through chemicl infiltrtion or in situ redox exsolution. () chemicl infiltrtion usully
More informationp-adic Egyptian Fractions
p-adic Egyptin Frctions Contents 1 Introduction 1 2 Trditionl Egyptin Frctions nd Greedy Algorithm 2 3 Set-up 3 4 p-greedy Algorithm 5 5 p-egyptin Trditionl 10 6 Conclusion 1 Introduction An Egyptin frction
More informationHaplotype Frequencies and Linkage Disequilibrium. Biostatistics 666
Hlotye Frequencies nd Linkge isequilirium iosttistics 666 Lst Lecture Genotye Frequencies llele Frequencies Phenotyes nd Penetrnces Hrdy-Weinerg Equilirium Simle demonstrtion Exercise: NO2 nd owel isese
More informationFORM FIVE ADDITIONAL MATHEMATIC NOTE. ar 3 = (1) ar 5 = = (2) (2) (1) a = T 8 = 81
FORM FIVE ADDITIONAL MATHEMATIC NOTE CHAPTER : PROGRESSION Arithmetic Progression T n = + (n ) d S n = n [ + (n )d] = n [ + Tn ] S = T = T = S S Emple : The th term of n A.P. is 86 nd the sum of the first
More informationSupplementary Information
Supplementry Informtion Coopertion of locl motions in the Hsp90 moleculr chperone ATPse mechnism Andre Schulze 1, Gerti Beliu 1, Dominic A. Helmerich 1, Jonthn Schubert 1, Lurence H. Perl 2, Chrisostomos
More informationDiscrete Mathematics and Probability Theory Summer 2014 James Cook Note 17
CS 70 Discrete Mthemtics nd Proility Theory Summer 2014 Jmes Cook Note 17 I.I.D. Rndom Vriles Estimting the is of coin Question: We wnt to estimte the proportion p of Democrts in the US popultion, y tking
More informationDiscrete Mathematics and Probability Theory Spring 2013 Anant Sahai Lecture 17
EECS 70 Discrete Mthemtics nd Proility Theory Spring 2013 Annt Shi Lecture 17 I.I.D. Rndom Vriles Estimting the is of coin Question: We wnt to estimte the proportion p of Democrts in the US popultion,
More informationProperties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives
Block #6: Properties of Integrls, Indefinite Integrls Gols: Definition of the Definite Integrl Integrl Clcultions using Antiderivtives Properties of Integrls The Indefinite Integrl 1 Riemnn Sums - 1 Riemnn
More informationSUPPLEMENTARY INFORMATION
SUPPLEMENTARY INFORMATION doi: 1.138/nnno.29.451 Aove-ndgp voltges from ferroelectric photovoltic devices S. Y. Yng, 1 J. Seidel 2,3, S. J. Byrnes, 2,3 P. Shfer, 1 C.-H. Yng, 3 M. D. Rossell, 4 P. Yu,
More information4.1. Probability Density Functions
STT 1 4.1-4. 4.1. Proility Density Functions Ojectives. Continuous rndom vrile - vers - discrete rndom vrile. Proility density function. Uniform distriution nd its properties. Expected vlue nd vrince of
More informationTests for the Ratio of Two Poisson Rates
Chpter 437 Tests for the Rtio of Two Poisson Rtes Introduction The Poisson probbility lw gives the probbility distribution of the number of events occurring in specified intervl of time or spce. The Poisson
More informationTemperature influence compensation in microbolometer detector for image quality enhancement
.26/qirt.26.68 Temperture influence compenstion in microolometer detector for imge qulity enhncement More info out this rticle: http://www.ndt.net/?id=2647 Astrct y M. Krupiński*, T. Sosnowski*, H. Mdur*
More informationPrecalculus Spring 2017
Preclculus Spring 2017 Exm 3 Summry (Section 4.1 through 5.2, nd 9.4) Section P.5 Find domins of lgebric expressions Simplify rtionl expressions Add, subtrct, multiply, & divide rtionl expressions Simplify
More informationSUPPLEMENTARY INFORMATION
DOI: 1.138/NMAT3984 Supplementry Informtion for Improved performnce nd stility in quntum dot solr cells through nd lignment engineering Chi- Ho M. Chung 1, Ptrick R. Brown 2, Vldimir Bulović 3 & Moungi
More informationStudent Activity 3: Single Factor ANOVA
MATH 40 Student Activity 3: Single Fctor ANOVA Some Bsic Concepts In designed experiment, two or more tretments, or combintions of tretments, is pplied to experimentl units The number of tretments, whether
More informationChapter 6 Continuous Random Variables and Distributions
Chpter 6 Continuous Rndom Vriles nd Distriutions Mny economic nd usiness mesures such s sles investment consumption nd cost cn hve the continuous numericl vlues so tht they cn not e represented y discrete
More informationReview of Probability Distributions. CS1538: Introduction to Simulations
Review of Proility Distriutions CS1538: Introduction to Simultions Some Well-Known Proility Distriutions Bernoulli Binomil Geometric Negtive Binomil Poisson Uniform Exponentil Gmm Erlng Gussin/Norml Relevnce
More informationGenetic Programming. Outline. Evolutionary Strategies. Evolutionary strategies Genetic programming Summary
Outline Genetic Progrmming Evolutionry strtegies Genetic progrmming Summry Bsed on the mteril provided y Professor Michel Negnevitsky Evolutionry Strtegies An pproch simulting nturl evolution ws proposed
More information14.3 comparing two populations: based on independent samples
Chpter4 Nonprmetric Sttistics Introduction: : methods for mking inferences bout popultion prmeters (confidence intervl nd hypothesis testing) rely on the ssumptions bout probbility distribution of smpled
More informationList all of the possible rational roots of each equation. Then find all solutions (both real and imaginary) of the equation. 1.
Mth Anlysis CP WS 4.X- Section 4.-4.4 Review Complete ech question without the use of grphing clcultor.. Compre the mening of the words: roots, zeros nd fctors.. Determine whether - is root of 0. Show
More informationSatellite Retrieval Data Assimilation
tellite etrievl Dt Assimiltion odgers C. D. Inverse Methods for Atmospheric ounding: Theor nd Prctice World cientific Pu. Co. Hckensck N.J. 2000 Chpter 3 nd Chpter 8 Dve uhl Artist depiction of NAA terr
More informationBridging the gap: GCSE AS Level
Bridging the gp: GCSE AS Level CONTENTS Chpter Removing rckets pge Chpter Liner equtions Chpter Simultneous equtions 8 Chpter Fctors 0 Chpter Chnge the suject of the formul Chpter 6 Solving qudrtic equtions
More informationQuantum Nonlocality Pt. 2: No-Signaling and Local Hidden Variables May 1, / 16
Quntum Nonloclity Pt. 2: No-Signling nd Locl Hidden Vriles My 1, 2018 Quntum Nonloclity Pt. 2: No-Signling nd Locl Hidden Vriles My 1, 2018 1 / 16 Non-Signling Boxes The primry lesson from lst lecture
More informationContinuous Random Variables Class 5, Jeremy Orloff and Jonathan Bloom
Lerning Gols Continuous Rndom Vriles Clss 5, 8.05 Jeremy Orloff nd Jonthn Bloom. Know the definition of continuous rndom vrile. 2. Know the definition of the proility density function (pdf) nd cumultive
More informationDesigning Information Devices and Systems I Anant Sahai, Ali Niknejad. This homework is due October 19, 2015, at Noon.
EECS 16A Designing Informtion Devices nd Systems I Fll 2015 Annt Shi, Ali Niknejd Homework 7 This homework is due Octoer 19, 2015, t Noon. 1. Circuits with cpcitors nd resistors () Find the voltges cross
More informationa * a (2,1) 1,1 0,1 1,1 2,1 hkl 1,0 1,0 2,0 O 2,1 0,1 1,1 0,2 1,2 2,2
18 34.3 The Reciprocl Lttice The inverse of the intersections of plne with the unit cell xes is used to find the Miller indices of the plne. The inverse of the d-spcing etween plnes ppers in expressions
More informationThe Properties of Stars
10/11/010 The Properties of Strs sses Using Newton s Lw of Grvity to Determine the ss of Celestil ody ny two prticles in the universe ttrct ech other with force tht is directly proportionl to the product
More informationChapter 4 Contravariance, Covariance, and Spacetime Diagrams
Chpter 4 Contrvrince, Covrince, nd Spcetime Digrms 4. The Components of Vector in Skewed Coordintes We hve seen in Chpter 3; figure 3.9, tht in order to show inertil motion tht is consistent with the Lorentz
More informationThe Minimum Label Spanning Tree Problem: Illustrating the Utility of Genetic Algorithms
The Minimum Lel Spnning Tree Prolem: Illustrting the Utility of Genetic Algorithms Yupei Xiong, Univ. of Mrylnd Bruce Golden, Univ. of Mrylnd Edwrd Wsil, Americn Univ. Presented t BAE Systems Distinguished
More informationpolyimide Spray-coated ZrP/epoxy film Spray-coated ZrP/epoxy film glass
c d e polyimide Spry-coted ZrP/epoxy film glss Spry-coted ZrP/epoxy film f g Supplementry Figure 1. Opticl microscopy of smectic ( = 0.044) α-zrp/epoxy films., Trnsmission opticl microscopy (TOM) of smectic
More informationI1 = I2 I1 = I2 + I3 I1 + I2 = I3 + I4 I 3
2 The Prllel Circuit Electric Circuits: Figure 2- elow show ttery nd multiple resistors rrnged in prllel. Ech resistor receives portion of the current from the ttery sed on its resistnce. The split is
More informationSUPPLEMENTARY INFORMATION
SUPPLEMENTARY INFORMATION Synthesis of metl oxide with roomtemperture photoreversile phse trnsition Shin-ichi Ohkoshi 1 *, Yoshihide Tsunouchi, 1 Tomoyuki Mtsud, 1 Kzuhito Hshimoto, 2 Asuk Nmi, 1 Fumiyoshi
More informationHow do we solve these things, especially when they get complicated? How do we know when a system has a solution, and when is it unique?
XII. LINEAR ALGEBRA: SOLVING SYSTEMS OF EQUATIONS Tody we re going to tlk out solving systems of liner equtions. These re prolems tht give couple of equtions with couple of unknowns, like: 6= x + x 7=
More informationSection 6: Area, Volume, and Average Value
Chpter The Integrl Applied Clculus Section 6: Are, Volume, nd Averge Vlue Are We hve lredy used integrls to find the re etween the grph of function nd the horizontl xis. Integrls cn lso e used to find
More informationMath 259 Winter Solutions to Homework #9
Mth 59 Winter 9 Solutions to Homework #9 Prolems from Pges 658-659 (Section.8). Given f(, y, z) = + y + z nd the constrint g(, y, z) = + y + z =, the three equtions tht we get y setting up the Lgrnge multiplier
More informationTitle of file for HTML: Supplementary Information Description: Supplementary Figures. Title of file for HTML: Peer Review File Description:
Title of file for HTML: Supplementry Informtion Description: Supplementry Figures Title of file for HTML: Peer Review File Description: WTP SST IPO PDO WTP leds IPO PDO Supplementry Figure 1 IPO (or PDO)
More informationThe area under the graph of f and above the x-axis between a and b is denoted by. f(x) dx. π O
1 Section 5. The Definite Integrl Suppose tht function f is continuous nd positive over n intervl [, ]. y = f(x) x The re under the grph of f nd ove the x-xis etween nd is denoted y f(x) dx nd clled the
More information5: The Definite Integral
5: The Definite Integrl 5.: Estimting with Finite Sums Consider moving oject its velocity (meters per second) t ny time (seconds) is given y v t = t+. Cn we use this informtion to determine the distnce
More informationCh AP Problems
Ch. 7.-7. AP Prolems. Willy nd his friends decided to rce ech other one fternoon. Willy volunteered to rce first. His position is descried y the function f(t). Joe, his friend from school, rced ginst him,
More informationThermal Diffusivity. Paul Hughes. Department of Physics and Astronomy The University of Manchester Manchester M13 9PL. Second Year Laboratory Report
Therml iffusivity Pul Hughes eprtment of Physics nd Astronomy The University of nchester nchester 3 9PL Second Yer Lbortory Report Nov 4 Abstrct We investigted the therml diffusivity of cylindricl block
More information( dg. ) 2 dt. + dt. dt j + dh. + dt. r(t) dt. Comparing this equation with the one listed above for the length of see that
Arc Length of Curves in Three Dimensionl Spce If the vector function r(t) f(t) i + g(t) j + h(t) k trces out the curve C s t vries, we cn mesure distnces long C using formul nerly identicl to one tht we
More informationEnergy (kcal mol -1 ) Force (kcal mol -1 Å -1 ) Pore axis (Å) Mixed Mo-only S-only Graphene
Force (kcl mol -1 Å -1 ) Energy (kcl mol -1 ) 3 1-1 - -3 Mixed Mo-only S-only Grphene 6 5 3 1 Mixed Mo-only S-only Grphene - -1-1 1 Pore xis (Å) -1 1 Pore xis (Å) Supplementry Figure 1 Energy Brriers.
More informationMultiscale Fourier Descriptor for Shape Classification
Multiscle Fourier Descriptor for Shpe Clssifiction Iivri Kunttu, een epistö, Juhni Ruhm 2, nd Ari Vis Tmpere University of Technology Institute of Signl Processing P. O. Box 553, FI-330 Tmpere, Finlnd
More informationDepartment of Physical Pharmacy and Pharmacokinetics Poznań University of Medical Sciences Pharmacokinetics laboratory
Deprtment of Physicl Phrmcy nd Phrmcoinetics Poznń University of Medicl Sciences Phrmcoinetics lbortory Experiment 1 Phrmcoinetics of ibuprofen s n exmple of the first-order inetics in n open one-comprtment
More information8Similarity ONLINE PAGE PROOFS. 8.1 Kick off with CAS 8.2 Similar objects 8.3 Linear scale factors. 8.4 Area and volume scale factors 8.
8.1 Kick off with S 8. Similr ojects 8. Liner scle fctors 8Similrity 8.4 re nd volume scle fctors 8. Review Plese refer to the Resources t in the Prelims section of your eookplus for comprehensive step-y-step
More informationSUMMER KNOWHOW STUDY AND LEARNING CENTRE
SUMMER KNOWHOW STUDY AND LEARNING CENTRE Indices & Logrithms 2 Contents Indices.2 Frctionl Indices.4 Logrithms 6 Exponentil equtions. Simplifying Surds 13 Opertions on Surds..16 Scientific Nottion..18
More informationDesigning Information Devices and Systems I Spring 2018 Homework 7
EECS 16A Designing Informtion Devices nd Systems I Spring 2018 omework 7 This homework is due Mrch 12, 2018, t 23:59. Self-grdes re due Mrch 15, 2018, t 23:59. Sumission Formt Your homework sumission should
More information8Similarity UNCORRECTED PAGE PROOFS. 8.1 Kick off with CAS 8.2 Similar objects 8.3 Linear scale factors. 8.4 Area and volume scale factors 8.
8.1 Kick off with S 8. Similr ojects 8. Liner scle fctors 8Similrity 8. re nd volume scle fctors 8. Review U N O R R E TE D P G E PR O O FS 8.1 Kick off with S Plese refer to the Resources t in the Prelims
More informationChapter 1: Logarithmic functions and indices
Chpter : Logrithmic functions nd indices. You cn simplify epressions y using rules of indices m n m n m n m n ( m ) n mn m m m m n m m n Emple Simplify these epressions: 5 r r c 4 4 d 6 5 e ( ) f ( ) 4
More information2. VECTORS AND MATRICES IN 3 DIMENSIONS
2 VECTORS AND MATRICES IN 3 DIMENSIONS 21 Extending the Theory of 2-dimensionl Vectors x A point in 3-dimensionl spce cn e represented y column vector of the form y z z-xis y-xis z x y x-xis Most of the
More informationSupplementary Information to The role of endogenous and exogenous mechanisms in the formation of R&D networks
Supplementry Informtion to The role of endogenous nd exogenous mechnisms in the formtion of R&D networks Mrio V. Tomsello 1, Nicol Perr 2, Cludio J. Tessone 1, Márton Krsi 3, nd Frnk Schweitzer 1 1 Chir
More informationChapter 9: Inferences based on Two samples: Confidence intervals and tests of hypotheses
Chpter 9: Inferences bsed on Two smples: Confidence intervls nd tests of hypotheses 9.1 The trget prmeter : difference between two popultion mens : difference between two popultion proportions : rtio of
More informationLinear Inequalities. Work Sheet 1
Work Sheet 1 Liner Inequlities Rent--Hep, cr rentl compny,chrges $ 15 per week plus $ 0.0 per mile to rent one of their crs. Suppose you re limited y how much money you cn spend for the week : You cn spend
More informationFarey Fractions. Rickard Fernström. U.U.D.M. Project Report 2017:24. Department of Mathematics Uppsala University
U.U.D.M. Project Report 07:4 Frey Frctions Rickrd Fernström Exmensrete i mtemtik, 5 hp Hledre: Andres Strömergsson Exmintor: Jörgen Östensson Juni 07 Deprtment of Mthemtics Uppsl University Frey Frctions
More information( ) as a fraction. Determine location of the highest
AB Clculus Exm Review Sheet - Solutions A. Preclculus Type prolems A1 A2 A3 A4 A5 A6 A7 This is wht you think of doing Find the zeros of f ( x). Set function equl to 0. Fctor or use qudrtic eqution if
More informationIdentify graphs of linear inequalities on a number line.
COMPETENCY 1.0 KNOWLEDGE OF ALGEBRA SKILL 1.1 Identify grphs of liner inequlities on number line. - When grphing first-degree eqution, solve for the vrible. The grph of this solution will be single point
More information5.1 How do we Measure Distance Traveled given Velocity? Student Notes
. How do we Mesure Distnce Trveled given Velocity? Student Notes EX ) The tle contins velocities of moving cr in ft/sec for time t in seconds: time (sec) 3 velocity (ft/sec) 3 A) Lel the x-xis & y-xis
More informationDesigning Information Devices and Systems I Spring 2018 Homework 8
EECS 16A Designing Informtion Devices nd Systems I Spring 2018 Homework 8 This homework is due Mrch 19, 2018, t 23:59. Self-grdes re due Mrch 22, 2018, t 23:59. Sumission Formt Your homework sumission
More informationLecture INF4350 October 12008
Biosttistics ti ti Lecture INF4350 October 12008 Anj Bråthen Kristoffersen Biomedicl Reserch Group Deprtment of informtics, UiO Gol Presenttion of dt descriptive tbles nd grphs Sensitivity, specificity,
More informationAB Calculus Review Sheet
AB Clculus Review Sheet Legend: A Preclculus, B Limits, C Differentil Clculus, D Applictions of Differentil Clculus, E Integrl Clculus, F Applictions of Integrl Clculus, G Prticle Motion nd Rtes This is
More informationMath 8 Winter 2015 Applications of Integration
Mth 8 Winter 205 Applictions of Integrtion Here re few importnt pplictions of integrtion. The pplictions you my see on n exm in this course include only the Net Chnge Theorem (which is relly just the Fundmentl
More informationBayesian Networks: Approximate Inference
pproches to inference yesin Networks: pproximte Inference xct inference Vrillimintion Join tree lgorithm pproximte inference Simplify the structure of the network to mkxct inferencfficient (vritionl methods,
More informationSupporting Information. Cytosolic Irradiation of Femtosecond Laser Induces Mitochondria-dependent Apoptosis-like
Supporting Informtion Cytosolic Irrdition of Femtosecond Lser Induces Mitochondri-dependent Apoptosis-like Cell Deth vi Intrinsic Rective Oxygen Cscdes Jonghee Yoon 1,2, Seung-wook Ryu 1,3, Seunghee Lee
More informationExercise 5.5: Large-scale log-normal fading
Exercise 5.5: Lrge-scle log-norml fding Since the system is designed to hndle propgtion loss of 135 db, outge will hppen when the propgtion loss is 8 db higher thn the deterministic loss of 17 db 135 17
More information( ) where f ( x ) is a. AB Calculus Exam Review Sheet. A. Precalculus Type problems. Find the zeros of f ( x).
AB Clculus Exm Review Sheet A. Preclculus Type prolems A1 Find the zeros of f ( x). This is wht you think of doing A2 A3 Find the intersection of f ( x) nd g( x). Show tht f ( x) is even. A4 Show tht f
More informationContinuous Random Variables
CPSC 53 Systems Modeling nd Simultion Continuous Rndom Vriles Dr. Anirn Mhnti Deprtment of Computer Science University of Clgry mhnti@cpsc.uclgry.c Definitions A rndom vrile is sid to e continuous if there
More informationSupplementary Figures
Electronic Supplementry Mteril (ESI) for Integrtie Biology. This journl is The Royl Society of Chemistry 214 Supplementry Figures CWound Are µm2 A EGTA Low Clcium 8 1 min. fter wounding Wound + 1 min.
More informationSection 1.3 Triangles
Se 1.3 Tringles 21 Setion 1.3 Tringles LELING TRINGLE The line segments tht form tringle re lled the sides of the tringle. Eh pir of sides forms n ngle, lled n interior ngle, nd eh tringle hs three interior
More informationsupplementary information
DOI: 1.138/nc8 Top-GFP!-ctenin GFP Intensity 3 1 1 3 5 6 7 8 Nucler Bet-Ctenin c MUC FABP KRT 8 5 3 6 15 1 5 LGR5 ASCL AXIN 15 5 15 5 Figure S1 TOP-GFP expression nd reltion with nucler β-ctenin, wnt trgets
More informationDiverse modes of eco-evolutionary dynamics in communities of antibiotic-producing microorganisms
In the formt provided y the uthors nd unedited. ULEMENTAY INFOMATION VOLUME: 1 ATICLE NUMBE: 0189 iverse modes of eco-evolutionry dynmics in communities of ntiiotic-producing microorgnisms Klin Vetsigin
More informationNote 12. Introduction to Digital Control Systems
Note Introduction to Digitl Control Systems Deprtment of Mechnicl Engineering, University Of Ssktchewn, 57 Cmpus Drive, Ssktoon, SK S7N 5A9, Cnd . Introduction A digitl control system is one in which the
More informationPolynomials and Division Theory
Higher Checklist (Unit ) Higher Checklist (Unit ) Polynomils nd Division Theory Skill Achieved? Know tht polynomil (expression) is of the form: n x + n x n + n x n + + n x + x + 0 where the i R re the
More informationMath 1B, lecture 4: Error bounds for numerical methods
Mth B, lecture 4: Error bounds for numericl methods Nthn Pflueger 4 September 0 Introduction The five numericl methods descried in the previous lecture ll operte by the sme principle: they pproximte the
More informationz TRANSFORMS z Transform Basics z Transform Basics Transfer Functions Back to the Time Domain Transfer Function and Stability
TRASFORS Trnsform Bsics Trnsfer Functions Bck to the Time Domin Trnsfer Function nd Stility DSP-G 6. Trnsform Bsics The definition of the trnsform for digitl signl is: -n X x[ n is complex vrile The trnsform
More informationSUPPLEMENTARY INFORMATION
DOI: 1.138/nc2975 GM13 / DNA F-ctin α shrna CLASP1 shrna shrna shrna CLASP1 shrna shrna e Tuulin CLASP1 CLASP1 shrna #32 shrna #33 #55 #58 Tuulin c Tuulin ppmlc E-Cdherin shrna CLASP1 shrna shrna f Golgi
More informationWe partition C into n small arcs by forming a partition of [a, b] by picking s i as follows: a = s 0 < s 1 < < s n = b.
Mth 255 - Vector lculus II Notes 4.2 Pth nd Line Integrls We begin with discussion of pth integrls (the book clls them sclr line integrls). We will do this for function of two vribles, but these ides cn
More informationChapter 9 Definite Integrals
Chpter 9 Definite Integrls In the previous chpter we found how to tke n ntiderivtive nd investigted the indefinite integrl. In this chpter the connection etween ntiderivtives nd definite integrls is estlished
More informationSTRAND J: TRANSFORMATIONS, VECTORS and MATRICES
Mthemtics SKE: STRN J STRN J: TRNSFORMTIONS, VETORS nd MTRIES J3 Vectors Text ontents Section J3.1 Vectors nd Sclrs * J3. Vectors nd Geometry Mthemtics SKE: STRN J J3 Vectors J3.1 Vectors nd Sclrs Vectors
More informationSimple Harmonic Motion I Sem
Simple Hrmonic Motion I Sem Sllus: Differentil eqution of liner SHM. Energ of prticle, potentil energ nd kinetic energ (derivtion), Composition of two rectngulr SHM s hving sme periods, Lissjous figures.
More informationInterpreting Integrals and the Fundamental Theorem
Interpreting Integrls nd the Fundmentl Theorem Tody, we go further in interpreting the mening of the definite integrl. Using Units to Aid Interprettion We lredy know tht if f(t) is the rte of chnge of
More informationCHM Physical Chemistry I Chapter 1 - Supplementary Material
CHM 3410 - Physicl Chemistry I Chpter 1 - Supplementry Mteril For review of some bsic concepts in mth, see Atkins "Mthemticl Bckground 1 (pp 59-6), nd "Mthemticl Bckground " (pp 109-111). 1. Derivtion
More information6. Photoionization of acridine through singlet and triplet channels
Chpter 6: Photoioniztion of cridine through singlet nd triplet chnnels 59 6. Photoioniztion of cridine through singlet nd triplet chnnels Photoioinztion of cridine (Ac) in queous micelles hs not yet een
More informationRandom subgroups of a free group
Rndom sugroups of free group Frédérique Bssino LIPN - Lortoire d Informtique de Pris Nord, Université Pris 13 - CNRS Joint work with Armndo Mrtino, Cyril Nicud, Enric Ventur et Pscl Weil LIX My, 2015 Introduction
More information