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i 1 · · · m x 1 i fi1(x 1 i ) · · · fim(x 1 i ) xK i fi1(xK i ) · · · fim(xK i ) x l1 1 x ln n 1 · · · m f11(x l1 1 ) · · · f1m(x l1 1 ) fn1(xln n ) · · · fnm(xln n ) min mini fi1(x li i ) · · · mini fim(x li i ) i K K ≤ mi i ∈ {1, . . . , n} i ∈ {1, . . . , n} K x 1 i , · · · , x K i x 1 i , · · · , x K i i fij(x l i) l ∈ {1, . . . , K} j ∈ {1, . . . , m} i ∈ {1, . . . , n} j i fij(x l i) = ∞ l ∈ {1, . . . , K} i fij x l1 1 , · · · , xln n m j=1 mini fij(x li i )) F
W λ2(W ) W λ2(W ) λ2(LW ) λn(LW ) LW λ2(LW ) W λ2(LW ) LW = I − W λ2(W ) = 1−λ2(LW ) n ∈ N i ∈ {1, . . . , n} G = (V, E) V = {1, . . . , n} E (i, j) ∈ E i j n × n C G Cij = 0 (i, j) /∈ E j = i Cii A ∈ {0, 1} n×n
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R. Aragüés (1980, Zaragoza) recei
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n n
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n n
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y 1000 500 −500 2000 1000 0 z
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• •
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• •
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k−
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•
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•
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(x, y)
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ρi = 0
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j xr zj
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xri i = 1, 2 zij j
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• (xr, yr,
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% final divergence number of steps
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14 12 10 8 6 4 2 0 −2 −4 FINAL
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14 12 10 8 6 4 2 0 −2 −4 FINAL
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i mi ∈ N i
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i Hi Hi
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Lchild i Li Lchild j
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i Li(0) = Li, I i G(0) = Σ
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ˆ Σi G (t)−Qi G (t)
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10 8 6 4 2 0 −2 −4 −6 −8
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10 8 6 4 2 0 −2 −4 −6 −8
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10 8 6 4 2 0 −2 −4 −6 −8
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n i, j r, s G
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i [I k j ]r,s [i k j ]r
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LW = diag(W 1) − W
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Y = P T ZP r S2 . . . Sn 0 P = 0
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exw(t) exw(t + 1) = A exw(t), exw(
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k1a k2b |k1a−k2b| ≤ max{k
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k x k ∗ = rr T u k = 1x k avg, w
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k − 1 k β k λ t
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i ∈ V
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A(t + kl) t k Ψ (t1 +
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15 10 5 0 −5 −10 −15 −5 0 5
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15 10 5 0 −5 −10 −15 −5 0 5
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i th f i r A, Ar,s [A]r,s
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msum |Fdis| = n i=1 mi = msum
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i, ti t, Xij(t) ∼ Xij(t
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i ∈ Vcom, r ∈ Si.
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3 < df = 7 f A 1 f A 2
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[ji]s,r (d) i f i r Cq
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f i r ∈ ˜ Si Xij ¯r ∈
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f i r ∈ ˜ Si i f i r
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, s ∈ C [C]r,s ≥ 0, C,
Page 111 and 112: 1, . . . , rℓ, Cℓ.
Page 113 and 114: 0 6 1 9 7 8 8 3 1 0 7 9 8 8 3 6 1 6
Page 115 and 116: 10 8 6 4 2 0 −2 −4 −6 −8
Page 117 and 118: Gdis
Page 120 and 121: Gdis
Page 122 and 123: i, j e, e ′ e i
Page 124 and 125: 0 < θi < π i ∈ V
Page 126 and 127: lim t→∞ T i G(t) = (R i ) T T
Page 128 and 129: zθ ∈ Rm Σzθ ∈ Rm×m
Page 130 and 131: ˆx a Va ˆ θa Va Υw = Σ
Page 132 and 133: tmax ¯ θ a i tmax ¯
Page 134 and 135: i ˆp a i = Υˆp a Va ˆpaV a =
Page 136 and 137: ˆx a V
Page 138 and 139: G a ∈ Ni i ∈ Va J
Page 140 and 141: i ∈ V ˆx cen i (t)
Page 142 and 143: ρ(J) = λeff(W) ||ecen(t)||2
Page 144 and 145: 3 m G
Page 146 and 147: 3.38 ◦ 1.87 ◦ x cm cm y
Page 148 and 149: −2 −2.5 −3 −3.5 −4 Centr.
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Page 152 and 153: 35 30 25 20 15 10 5 0 0 200 400 600
Page 154 and 155: k k
Page 156 and 157: P(k + 1|k) = I Si Si = 1 +
Page 158 and 159: ¯x(k + 1) = ((¯xr(k + 1)) T , ¯x
Page 160 and 161: 8 6 4 2 0 −2 F1 Initial map −4
Page 164 and 165: G n k k ∈ N i, j t
Page 166 and 167: i xi(t) xj(t) (i)
Page 168 and 169: i ˜ Cij(k) ˜ Cij(k) = 0
Page 170 and 171: T = diam(G) βi(T ) i ∈ V
Page 172 and 173: L V T L LVL = λL = diag(0, λ2(
Page 174 and 175: ˙x(t) = −Lˆx(t) = u(t), ei(t) =
Page 176 and 177: F 16 r1
Page 178 and 179: 14 12 10 8 6 4 2 0 −2 λ * (L) Es
Page 180 and 181: 60m × 45m
Page 182 and 183: 15 10 5 0 −5 −10 −15 F23 −5
Page 184 and 185: 4 2 0 3000 2000 1000 x 10 4 0 20 40
Page 186 and 187: 23 22.5 22 0.5 −0.5 0 20 40 23 22
Page 188 and 189: 1 7 16
Page 190 and 191: 6 4 2 0 −2 k=1 k=2 k=3 k=4 k=5
Page 192 and 193: 9 9 9
Page 194 and 195: (C) msum
Page 196 and 197: (c) msum
Page 198 and 199: y −1000 500 2000 x
Page 200 and 201: −200 200 400 0 R9 R7 R5 R2 R6 −
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2000 1000 0 −1000 −1000 0 1000
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2000 1000 0 −1000 −1000 0 1000
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O(n)
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p
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p
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60×45m
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