icml10yomikai.key
|
|
|
- みがね はにうだ
- 4 years ago
- Views:
Transcription
1 A Fast Augmented Lagrangian Algorithm for Learning Low- Rank Matrices Ryota Tomioka, Taiji Suzuki, Masashi Sugiyama, Hisashi Kashima 2010/8/18 ICML2010
2
3 1 Matrix completion [Srebro et al. 05; Abernethy et al. 09] (collaborative filtering, link prediction) Y = W Part of Y is observed W = W user W movie 2 Multi-task learning [Argyriou et al., 07] y = W x + b W = w task 1 w task 2. w task R 3 Predicting over matrices (classification/regression) [Tomioka & Aihara, 07] ( time ) y = W, X + b X space W W = W task W feature = W space W time
4 f(x) = W, X + b = Tr ( W X ) + b ( r ) = Tr σ jv j u j X + b j=1 = r σ jtr ( v j u j X ) + b j=1 = r σ jtr ( u ) j Xv j + b j=1 r W = σ j u j v j j=1
5 w 1 = W = n j=1 r j=1 w j σ j (W ) σ j (W ) x 0.01 x 0.5 x x 2
6 minimize L(W )+λ W W R R C
7 W t+1 := argmin W ( W, L(W t ) + λ W + 1 ) W W t 2 fro 2η t = ST ληt ( W t η t L(W t ) ) Spectral Soft-threshold: ST λ (W )=U max(s λi, 0)V W = USV
8 minimize W R R C f l (Avec(W )) + λ W
9 L(W )= m i=1 y i Wx i 2 = Y WX 2 fro = vec(y ) (X I R )vec(w ) ( 2 ) vec(axb) = (B A)vec(X)
10 W t+1 := argmin W ( f l (Avec(W )) + λ W + 1 ) W W t 2 2η t = ST ληt ( W t + η t A α t+1) α t+1 = argmin ϕ t (α)
11 IST 2 2 DAL !0.5!0.5!0!1!1!1!1.5!1.5!1!2!2!2!1.5!1! !2!2!1.5!1! !2!1!1!
12 γ ϕ t (α t+1 ) W t+1 W t fro η t f(w t+1 ) f(w ) σ W t+1 W 2 fro (t =0, 1, 2,...) W t+1 W fro 1 1+2σηt W t W fro
13
14 φ λ (W )=λ K W (k) = λ k=1 ( W (1) W (K) ) φ λ (W )= r g λ(σ j (W )) j=1 ST gλ (σ j ) = argmin (g λ (x)+ 12 ) (x σ j) 2 x R
15 Rank=10 Rank= Time (s) Rank Time (s) Rank Regularization constant! Regularization constant!
16 Rank=10, #observations m=1,200,000 λ time (s) #outer #inner rank S-RMSE (±2.0) 5(±0) 8(±0) 2.8 (±0.4) (±0.0024) (±5.6) 11 (±0) 18 (±0) 5(±0) (±0.0008) (±7.2) 17 (±0) 28 (±0) 6.4 (±0.5) (±0.0015) (±8.0) 23 (±0) 38.4 (±0.84) 8(±0) (± ) (±9.9) 29 (±0) 48.4 (±0.84) 9(±0) (± ) (±9.9) 35 (±0) 58.4 (±0.84) 9(±0) (± ) (±11) 41 (±0) 70 (±0.82) 10 (±0) (± ) #inner iterations is roughly 2 times #outer iterations.
17 Rank=20, #observations m=2,400,000 λ time (s) #outer #inner rank S-RMSE (±19) 6(±0) 15.1 (±1.0) 12.1 (±0.3) (±0.002) (±22) 11 (±0) 24.1 (±1.0) 14 (±0) (±0.001) (±25) 15 (±0) 31.1 (±1.0) 16 (±0) (±0.0008) (±29) 19 (±0) 38.1 (±1.0) 16 (±0) (±0.0007) (±36) 24 (±0) 48.1 (±1.0) 18 (±0) (±0.0004) (±44) 29 (±0) 57.1 (±1.0) 18 (±0) (±0.0003) (±48) 34 (±0) 66.1 (±1.0) 19 (±0) (±0.0002) (±59) 38.5 (±0.5) 74.1 (±1.5) 19 (±0) (±0.0003) (±61) 43.6 (±0.5) 83.9 (±2.3) 20 (±0) (±0.0001) (±78) 48.4 (±0.7) 92.5 (±1.5) 20 (±0) (±0.0002) (±94) 53.4 (±0.7) 102 (±1.5) 20 (±0) (± ) (±105) 57.7 (±0.8) 109 (±2.4) 20 (±0) (± )
18 f l (z) = m log(1 + exp( y iz i )) i=1
19 Relative duality gap CPU time (s) AG IP PG M DAL
20 Relative duality gap Number of iterations Time (s)
21
22 Number of iterations Time (s) Accuracy Regularization constant Regularization constant Regularization constant 50
23 25 1st order 4 2nd order (alpha band) 8 2nd order (beta band) Singular values SV index SV index SV index 1st order component 1:!=24.19 Filter Pattern Time course Time (ms)
24
25
…X…p†[…X’³‚¥›»‡¨‡æ‡Ñ…}…‰…`…J†[…l…‰−w‘K‡Ì‡½‡ß‡Ì“ÅfiK›»…A…‰…S…−…Y…•‡ÆCV†EPR‡Ö‡Ì›žŠp
CV PR 1, 1, 2 1 2 2009-08-31 @ PRMU/CVIM http://www.ibis.t.u-tokyo.ac.jp/ryotat/prmu09/ UT / Tokyo Tech DAL PRMU/CVIM 1 / 58 Outline 1-2 Dual Augmented Lagrangian Proximal minimization Legendre 3 4 UT
: 2 3 2 3 20-0-25 @ RAMP 20 ( ) RAMP20 20-0-25 / 37 - CVX (Grant & Boyd) (80 ) 60-70 ( ) RAMP20 20-0-25 2 / 37 - CVX (Grant & Boyd) (80 ) 60-70 (Accelerated) Proximal gradient methods ( ) RAMP20 20-0-25
,.,. NP,., ,.,,.,.,,, (PCA)...,,. Tipping and Bishop (1999) PCA. (PPCA)., (Ilin and Raiko, 2010). PPCA EM., , tatsukaw
,.,. NP,.,. 1 1.1.,.,,.,.,,,. 2. 1.1.1 (PCA)...,,. Tipping and Bishop (1999) PCA. (PPCA)., (Ilin and Raiko, 2010). PPCA EM., 152-8552 2-12-1, tatsukawa.m.aa@m.titech.ac.jp, 190-8562 10-3, mirai@ism.ac.jp
(2012 rev.1.23) Web DVD 1 1 DVD SF DVD ( ) ( ) ( ) DVD 0.2 ( ) ( ) ( ) amazon.com (MovieLens) (Resnick et al., 1994) 1
(2012 rev.1.23) 0 0.1 Web DVD 1 1 DVD SF DVD ( ) ( ) ( ) DVD 0.2 ( ) ( ) ( ) amazon.com 1600 4000 5 (MovieLens) (Resnick et al., 1994) 1 0.3 optional 1 ( ) ( ) ( ) java java eclipse javadoc api ( ) 0.4
2 Part A B C A > B > C (0) 90, 69, 61, 68, 6, 77, 75, 20, 41, 34 (1) 8, 56, 16, 50, 43, 66, 44, 77, 55, 48 (2) 92, 74, 56, 81, 84, 86, 1, 27,
/ (1) (2) (3) ysawano@tmu.ac.jp (4) (0) (10) 11 (10) (a) (b) (c) (5) - - 11160939-11160939- - 1 2 Part 1. 1. 1. A B C A > B > C (0) 90, 69, 61, 68, 6, 77, 75, 20, 41, 34 (1) 8, 56, 16, 50, 43, 66, 44,
TOP URL 1
TOP URL http://amonphys.web.fc.com/ 3.............................. 3.............................. 4.3 4................... 5.4........................ 6.5........................ 8.6...........................7
201711grade1ouyou.pdf
2017 11 26 1 2 52 3 12 13 22 23 32 33 42 3 5 3 4 90 5 6 A 1 2 Web Web 3 4 1 2... 5 6 7 7 44 8 9 1 2 3 1 p p >2 2 A 1 2 0.6 0.4 0.52... (a) 0.6 0.4...... B 1 2 0.8-0.2 0.52..... (b) 0.6 0.52.... 1 A B 2
‚åŁÎ“·„´Šš‡ðŠp‡¢‡½‹âfi`fiI…A…‰…S…−…Y…•‡ÌMarkovŸA“½fiI›ð’Í
Markov 2009 10 2 Markov 2009 10 2 1 / 25 1 (GA) 2 GA 3 4 Markov 2009 10 2 2 / 25 (GA) (GA) L ( 1) I := {0, 1} L f : I (0, ) M( 2) S := I M GA (GA) f (i) i I Markov 2009 10 2 3 / 25 (GA) ρ(i, j), i, j I
y = x x R = 0. 9, R = σ $ = y x w = x y x x w = x y α ε = + β + x x x y α ε = + β + γ x + x x x x' = / x y' = y/ x y' =
y x = α + β + ε =,, ε V( ε) = E( ε ) = σ α $ $ β w ( 0) σ = w σ σ y α x ε = + β + w w w w ε / w ( w y x α β ) = α$ $ W = yw βwxw $β = W ( W) ( W)( W) w x x w x x y y = = x W y W x y x y xw = y W = w w
untitled
0 ( L CONTENTS 0 . sin(-x-sinx, (-x(x, sin(90-xx,(90-xsinx sin(80-xsinx,(80-x-x ( sin{90-(ωφ}(ωφ. :n :m.0 m.0 n tn. 0 n.0 tn ω m :n.0n tn n.0 tn.0 m c ω sinω c ω c tnω ecω sin ω ω sin c ω c ω tn c tn ω
1. 1 A : l l : (1) l m (m 3) (2) m (3) n (n 3) (4) A α, β γ α β + γ = 2 m l lm n nα nα = lm. α = lm n. m lm 2β 2β = lm β = lm 2. γ l 2. 3
1. 1 A : l l : (1) l m (m 3) (2) m (3) n (n 3) (4) A 2 1 2 1 2 3 α, β γ α β + γ = 2 m l lm n nα nα = lm. α = lm n. m lm 2β 2β = lm β = lm 2. γ l 2. 3 4 P, Q R n = {(x 1, x 2,, x n ) ; x 1, x 2,, x n R}
1: 3.3 1/8000 1/ m m/s v = 2kT/m = 2RT/M k R 8.31 J/(K mole) M 18 g 1 5 a v t πa 2 vt kg (
1905 1 1.1 0.05 mm 1 µm 2 1 1 2004 21 2004 7 21 2005 web 2 [1, 2] 1 1: 3.3 1/8000 1/30 3 10 10 m 3 500 m/s 4 1 10 19 5 6 7 1.2 3 4 v = 2kT/m = 2RT/M k R 8.31 J/(K mole) M 18 g 1 5 a v t πa 2 vt 6 6 10
LLG-R8.Nisus.pdf
d M d t = γ M H + α M d M d t M γ [ 1/ ( Oe sec) ] α γ γ = gµ B h g g µ B h / π γ g = γ = 1.76 10 [ 7 1/ ( Oe sec) ] α α = λ γ λ λ λ α γ α α H α = γ H ω ω H α α H K K H K / M 1 1 > 0 α 1 M > 0 γ α γ =
positron 1930 Dirac 1933 Anderson m 22Na(hl=2.6years), 58Co(hl=71days), 64Cu(hl=12hour) 68Ge(hl=288days) MeV : thermalization m psec 100
positron 1930 Dirac 1933 Anderson m 22Na(hl=2.6years), 58Co(hl=71days), 64Cu(hl=12hour) 68Ge(hl=288days) 0.5 1.5MeV : thermalization 10 100 m psec 100psec nsec E total = 2mc 2 + E e + + E e Ee+ Ee-c mc
Microsoft Word - 01マニュアル・入稿原稿p1-112.doc
4 54 55 56 ( ( 1994 1st stage 2nd stage 2012 57 / 58 365 46.6 120 365 40.4 120 13.0 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 4 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97
2
1 2 3 4 5 6 7 2007 30,870 2008 32,426 2009 34,971 13,000 8 9 http://www.hokkaido-marathon.com/volunteer/ http://www.hokkaido-marathon.com/volunteer/leader.html 2009 / http://www.shonan-kokusai.jp/archives/volunteer/
2005 2006.2.22-1 - 1 Fig. 1 2005 2006.2.22-2 - Element-Free Galerkin Method (EFGM) Meshless Local Petrov-Galerkin Method (MLPGM) 2005 2006.2.22-3 - 2 MLS u h (x) 1 p T (x) = [1, x, y]. (1) φ(x) 0.5 φ(x)
7 π L int = gψ(x)ψ(x)φ(x) + (7.4) [ ] p ψ N = n (7.5) π (π +,π 0,π ) ψ (σ, σ, σ )ψ ( A) σ τ ( L int = gψψφ g N τ ) N π * ) (7.6) π π = (π, π, π ) π ±
![7 π L int = gψ(x)ψ(x)φ(x) + (7.4) [ ] p ψ N = n (7.5) π (π +,π 0,π ) ψ (σ, σ, σ )ψ ( A) σ τ ( L int = gψψφ g N τ ) N π * ) (7.6) π π = (π, π, π ) π ±](/thumbs/91/106462075.jpg "7 π L int = gψ(x)ψ(x)φ(x) + (7.4) [ ] p ψ N = n (7.5) π (π +,π 0,π ) ψ (σ, σ, σ )ψ ( A) σ τ ( L int = gψψφ g N τ ) N π * ) (7.6) π π = (π, π, π ) π ±")
7 7. ( ) SU() SU() 9 ( MeV) p 98.8 π + π 0 n 99.57 9.57 97.4 497.70 δm m 0.4%.% 0.% 0.8% π 9.57 4.96 Σ + Σ 0 Σ 89.6 9.46 K + K 0 49.67 (7.) p p = αp + βn, n n = γp + δn (7.a) [ ] p ψ ψ = Uψ, U = n [ α
20 4 20 i 1 1 1.1............................ 1 1.2............................ 4 2 11 2.1................... 11 2.2......................... 11 2.3....................... 19 3 25 3.1.............................
BayesfiI‡É“ÅfiK‡È−w‘K‡Ì‡½‡ß‡ÌChow-Liu…A…‰…S…−…Y…•
1 / 21 Kruscal V : w i,j R: w i,j = w j,i i j Kruscal (w i,j 0 ) 1 E {{i, j} i, j V, i i} 2 E {} 3 while(e = ϕ) for w i,j {i, j} E 1 E E\{i, j} 2 G = (V, E {i, j}) = E E {i, j} G {i,j} E w i,j 2 / 21 w
SFGÇÃÉXÉyÉNÉgÉãå`.pdf
SFG 1 SFG SFG I SFG (ω) χ SFG (ω). SFG χ χ SFG (ω) = χ NR e iϕ +. ω ω + iγ SFG φ = ±π/, χ φ = ±π 3 χ SFG χ SFG = χ NR + χ (ω ω ) + Γ + χ NR χ (ω ω ) (ω ω ) + Γ cosϕ χ NR χ Γ (ω ω ) + Γ sinϕ. 3 (θ) 180
基礎数学I
I & II ii ii........... 22................. 25 12............... 28.................. 28.................... 31............. 32.................. 34 3 1 9.................... 1....................... 1............
φ 4 Minimal subtraction scheme 2-loop ε 2008 (University of Tokyo) (Atsuo Kuniba) version 21/Apr/ Formulas Γ( n + ɛ) = ( 1)n (1 n! ɛ + ψ(n + 1)
φ 4 Minimal subtraction scheme 2-loop ε 28 University of Tokyo Atsuo Kuniba version 2/Apr/28 Formulas Γ n + ɛ = n n! ɛ + ψn + + Oɛ n =,, 2, ψn + = + 2 + + γ, 2 n ψ = γ =.5772... Euler const, log + ax x
susy.dvi
1 Chapter 1 Why supper symmetry? 2 Chapter 2 Representaions of the supersymmetry algebra SUSY Q a d 3 xj 0 α J x µjµ = 0 µ SUSY ( {Q A α,q βb } = 2σ µ α β P µδ A B (2.1 {Q A α,q βb } = {Q αa,q βb } = 0
知能科学：ニューラルネットワーク
2 3 4 (Neural Network) (Deep Learning) (Deep Learning) ( x x = ax + b x x x ? x x x w σ b = σ(wx + b) x w b w b .2.8.6 σ(x) = + e x.4.2 -.2 - -5 5 x w x2 w2 σ x3 w3 b = σ(w x + w 2 x 2 + w 3 x 3 + b) x,
知能科学：ニューラルネットワーク
2 3 4 (Neural Network) (Deep Learning) (Deep Learning) ( x x = ax + b x x x ? x x x w σ b = σ(wx + b) x w b w b .2.8.6 σ(x) = + e x.4.2 -.2 - -5 5 x w x2 w2 σ x3 w3 b = σ(w x + w 2 x 2 + w 3 x 3 + b) x,
磁性物理学 - 遷移金属化合物磁性のスピンゆらぎ理論
email: takahash@sci.u-hyogo.ac.jp May 14, 2009 Outline 1. 2. 3. 4. 5. 6. 2 / 262 Today s Lecture: Mode-mode Coupling Theory 100 / 262 Part I Effects of Non-linear Mode-Mode Coupling Effects of Non-linear
17 1 25 http://grape.astron.s.u-tokyo.ac.jp/pub/people/makino/kougi/stellar_dynamics/index.html http://grape.astron.s.u-tokyo.ac.jp/pub/people/makino/talks/index-j.html d 2 x i dt 2 = j i Gm j x j x i
*2.5mm ”ŒŠá‡ÆfiÁ™¥‡Ì…Z†[…t…X…N…−†[…j…fi…O
I. Takeuchi, Nagoya Institute of Technology 1/38 f(x) = w 1 x 1 + w 2 x 2 +... + w d x d f(x) = α 1 K(x, x 1 ) + α 2 K(x, x 2 ) +... + α n K(x, x n ) {wj } d j=1 f {αi } n i=1 f I. Takeuchi, Nagoya Institute
QCD 1 QCD GeV 2014 QCD 2015 QCD SU(3) QCD A µ g µν QCD 1
QCD 1 QCD GeV 2014 QCD 2015 QCD SU(3) QCD A µ g µν QCD 1 (vierbein) QCD QCD 1 1: QCD QCD Γ ρ µν A µ R σ µνρ F µν g µν A µ Lagrangian gr TrFµν F µν No. Yes. Yes. No. No! Yes! [1] Nash & Sen [2] Riemann
Hanbury-Brown Twiss (ver. 2.0) van Cittert - Zernike mutual coherence
Hanbury-Brown Twiss (ver. 2.) 25 4 4 1 2 2 2 2.1 van Cittert - Zernike..................................... 2 2.2 mutual coherence................................. 4 3 Hanbury-Brown Twiss ( ) 5 3.1............................................
(1.2) T D = 0 T = D = 30 kn 1.2 (1.4) 2F W = 0 F = W/2 = 300 kn/2 = 150 kn 1.3 (1.9) R = W 1 + W 2 = = 1100 N. (1.9) W 2 b W 1 a = 0
1 1 1.1 1.) T D = T = D = kn 1. 1.4) F W = F = W/ = kn/ = 15 kn 1. 1.9) R = W 1 + W = 6 + 5 = 11 N. 1.9) W b W 1 a = a = W /W 1 )b = 5/6) = 5 cm 1.4 AB AC P 1, P x, y x, y y x 1.4.) P sin 6 + P 1 sin 45
一般演題（ポスター）
6 5 13 : 00 14 : 00 A μ 13 : 00 14 : 00 A β β β 13 : 00 14 : 00 A 13 : 00 14 : 00 A 13 : 00 14 : 00 A β 13 : 00 14 : 00 A β 13 : 00 14 : 00 A 13 : 00 14 : 00 A β 13 : 00 14 : 00 A 13 : 00 14 : 00 A
2 1 κ c(t) = (x(t), y(t)) ( ) det(c (t), c x (t)) = det (t) x (t) y (t) y = x (t)y (t) x (t)y (t), (t) c (t) = (x (t)) 2 + (y (t)) 2. c (t) =
1 1 1.1 I R 1.1.1 c : I R 2 (i) c C (ii) t I c (t) (0, 0) c (t) c(i) c c(t) 1.1.2 (1) (2) (3) (1) r > 0 c : R R 2 : t (r cos t, r sin t) (2) C f : I R c : I R 2 : t (t, f(t)) (3) y = x c : R R 2 : t (t,
q quark L left-handed lepton. λ Gell-Mann SU(3), a = 8 σ Pauli, i =, 2, 3 U() T a T i 2 Ỹ = 60 traceless tr Ỹ 2 = 2 notation. 2 off-diagonal matrices
Grand Unification M.Dine, Supersymmetry And String Theory: Beyond the Standard Model 6 2009 2 24 by Standard Model Coupling constant θ-parameter 8 Charge quantization. hypercharge charge Gauge group. simple
Mｏｔｔ散乱によるParity対称性の破れを検証
Mott Parity P2 Mott target Mott Parity Parity Γ = 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 t P P ),,, ( 3 2 1 0 1 γ γ γ γ γ γ ν ν µ µ = = Γ 1 : : : Γ P P P P x x P ν ν µ µ vector axial vector ν ν µ µ γ γ Γ ν γ
untitled
GeoFem 1 1.1 1 1.2 1 1.3 1 2 2.1 2 2.2 3 2.3 FEM 5 (1) 5 (2) 5 (3) 6 2.4 GeoFem 7 2.5 FEM 16 2.6 19 2.7 26 3.1 33 3.2 35 3.3 GeoFem 36 3.4 48 3.5 49 A A1 A2 A3 A4 A5 A6 A7 GeoFem GeoFem CRS GeoFem GeoFem
#2 (IISEC)
#2 (IISEC) 2007 10 6 E Y 2 = F (X) E(F p ) E : Y 2 = F (X) = X 3 + AX + B, A, B F p E(F p ) = {(x, y) F 2 p y2 = F (x)} {P } P : E(F p ) E F p - Given: E/F p : EC, P E(F p ), Q P Find: x Z/NZ s.t. Q =
Gravothermal Catastrophe & Quasi-equilibrium Structure in N-body Systems
2004/3/1 3 N 1 Antonov Problem & Quasi-equilibrium State in N-body N Systems A. Taruya (RESCEU, Univ.Tokyo) M. Sakagami (Kyoto Univ.) 2 Antonov problem N-body study of quasi-attractivity M15 T Antonov
untitled
1 n m (ICA = independent component analysis) BSS (= blind source separation) : s(t) =(s 1 (t),...,s n (t)) R n : x(t) =(x 1 (t),...,x n (t)) R m 1 i s i (t) a ji R j 2 (A =(a ji )) x(t) =As(t) (1) n =
P1-1 P1-2 P1-3 P1-4 P1-5 P1-6 P3-1 P3-2 P3-3 P3-4 P3-5 P3-6 P5-1 P5-2 P5-3 P5-4 P5-5 P5-6 P7-1 P7-2 P7-3 P7-4 P7-5 P7-6 P9-1 P9-2 P9-3 P9-4 P9-5 P9-6 P11-1 P11-2 P11-3 P11-4 P13-1 P13-2 P13-3 P13-4 P13-5
untitled
BELLE TOP 12 1 3 2 BELLE 4 2.1 BELLE........................... 4 2.1.1......................... 4 2.1.2 B B........................ 7 2.1.3 B CP............... 8 2.2 BELLE...................... 9 2.3
高次元データ スパース正則化学習法 最適化手法 proximal point algorithm 確率最適化手法 2
正則化学習法における最適化手法 鈴木大慈東京大学情報理工学系研究科数理情報学専攻 2013/2/18@ 九州大学伊都キャンパス文部科学省委託事業数学協働プログラム 最適化ワークショップ : 拡がっていく最適化 1 高次元データ スパース正則化学習法 最適化手法 proximal point algorithm 確率最適化手法 2 問題設定スパース正則化学習 3 高次元線形判別 物体認識 音声認識 自然言語処理
001 No.3/12 1 1 2 3 4 5 6 4 8 13 27 33 39 001 No.3/12 4 001 No.3/12 5 001 No.3/12 6 001 No.3/12 7 001 8 No.3/12 001 No.3/12 9 001 10 No.3/12 001 No.3/12 11 Index 1 2 3 14 18 21 001 No.3/12 14 001 No.3/12
1 913 10301200 A B C D E F G H J K L M 1A1030 10 : 45 1A1045 11 : 00 1A1100 11 : 15 1A1115 11 : 30 1A1130 11 : 45 1A1145 12 : 00 1B1030 1B1045 1C1030
1 913 9001030 A B C D E F G H J K L M 9:00 1A0900 9:15 1A0915 9:30 1A0930 9:45 1A0945 10 : 00 1A1000 10 : 15 1B0900 1B0915 1B0930 1B0945 1B1000 1C0900 1C0915 1D0915 1C0930 1C0945 1C1000 1D0930 1D0945 1D1000
untitled
MRR Physical Basis( 1.8.4) METEK MRR 1 MRR 1.1 MRR 24GHz FM-CW(frequency module continuous wave) 30 r+ r f+ f 1.2 1 4 MRR 24GHz 1.3 50mW 1 rf- (waveguide) (horn) 60cm ( monostatic radar) (continuous wave)
P-12 P-13 3 4 28 16 00 17 30 P-14 P-15 P-16 4 14 29 17 00 18 30 P-17 P-18 P-19 P-20 P-21 P-22
1 14 28 16 00 17 30 P-1 P-2 P-3 P-4 P-5 2 24 29 17 00 18 30 P-6 P-7 P-8 P-9 P-10 P-11 P-12 P-13 3 4 28 16 00 17 30 P-14 P-15 P-16 4 14 29 17 00 18 30 P-17 P-18 P-19 P-20 P-21 P-22 5 24 28 16 00 17 30 P-23
医系の統計入門第 2 版 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 第 2 版 1 刷発行時のものです.
医系の統計入門第 2 版 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. http://www.morikita.co.jp/books/mid/009192 このサンプルページの内容は, 第 2 版 1 刷発行時のものです. i 2 t 1. 2. 3 2 3. 6 4. 7 5. n 2 ν 6. 2 7. 2003 ii 2 2013 10 iii 1987
FX ) 2
(FX) 1 1 2009 12 12 13 2009 1 FX ) 2 1 (FX) 2 1 2 1 2 3 2010 8 FX 1998 1 FX FX 4 1 1 (FX) () () 1998 4 1 100 120 1 100 120 120 100 20 FX 100 100 100 1 100 100 100 1 100 1 100 100 1 100 101 101 100 100
平成20年5月 協会創立50年の歩み 海の安全と環境保全を目指して 友國八郎 海上保安庁 長官 岩崎貞二 日本船主協会 会長 前川弘幸 JF全国漁業協同組合連合会 代表理事会長 服部郁弘 日本船長協会 会長 森本靖之 日本船舶機関士協会 会長 大内博文 航海訓練所 練習船船長 竹本孝弘 第二管区海上保安本部長 梅田宜弘
![Œ{Ł¶/1ŒÊ −ªfiª„¾ [ 1…y†[…W ]](/thumbs/50/26134150.jpg "Œ{Ł¶/1ŒÊ −ªfiª„¾ [ 1…y†[…W ]")
,, Andrej Gendiar (Density Matrix Renormalization Group, DMRG) 1 10 S.R. White [1, 2] 2 DMRG ( ) [3, 2] DMRG Baxter [4, 5] 2 Ising 2 1 Ising 1 1 Ising
![,, Andrej Gendiar (Density Matrix Renormalization Group, DMRG) 1 10 S.R. White [1, 2] 2 DMRG ( ) [3, 2] DMRG Baxter [4, 5] 2 Ising 2 1 Ising 1 1 Ising](/thumbs/94/118770363.jpg ",, Andrej Gendiar (Density Matrix Renormalization Group, DMRG) 1 10 S.R. White [1, 2] 2 DMRG ( ) [3, 2] DMRG Baxter [4, 5] 2 Ising 2 1 Ising 1 1 Ising")
,, Andrej Gendiar (Density Matrix Renormalization Group, DMRG) 1 10 S.R. White [1, 2] 2 DMRG ( ) [3, 2] DMRG Baxter [4, 5] 2 Ising 2 1 Ising 1 1 Ising Model 1 Ising 1 Ising Model N Ising (σ i = ±1) (Free
廃棄物処理施設生活環境影響調査指針
- - 0.04ppm 0.1ppm 10ppm 0ppm 0.10mg/m 3 0.0 mg/m 3 0.06ppm 0.04ppm 0.06ppm 0.003 mg/m 3 0. mg/m 3 0. mg/m 3 0.15 mg/m 3 - -1 - 0.6pg-TEQ/m 3 53 3 1 0.10.ppm 0.0ppm 5 6 16 136 0.0ppm 7 15 7 31 0.04g-Hg/m
τ τ
1 1 1.1 1.1.1 τ τ 2 1 1.1.2 1.1 1.1 µ ν M φ ν end ξ µ ν end ψ ψ = µ + ν end φ ν = 1 2 (µφ + ν end) ξ = ν (µ + ν end ) + 1 1.1 3 6.18 a b 1.2 a b 1.1.3 1.1.3.1 f R{A f } A f 1 B R{AB f 1 } COOH A OH B 1.3
05避難シミュレーション編.PDF
1....5-2 1.1...5-2 1.2...5-2 1.3...5-4 1.4...5-5 1.5...5-8 1.6...5-8 1.7...5-9 1.8...5-19 2....5-21 5-1 5-2 ) ( ) / ( ) / ( ) ( 2 ( ) ( ) 5-3 1-1 5-4 ( 17 3 ) 1 ( 1) 1-2 ( )2 3 ( 5 ) 5 1 5 ( ) ( ) 1-2