1 9 - - PowerPoint PPT Presentation

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1 9 - - PowerPoint PPT Presentation

Aug 22, 2023 184 likes •947 views

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SLIDE 1
  • 1 9
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SLIDE 2
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SLIDE 3
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SLIDE 4
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SLIDE 5
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SLIDE 6

≥ /

  • 3¥

c d-e)

I

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SLIDE 7

≥ /

  • O
slide-8
SLIDE 8

≥ /

  • [()] ()

|{ : = }|

slide-9
SLIDE 9

[()] () [()] ≥ ()

  • ()
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SLIDE 10

[()] () [()] ≥ ()

[()]

() = ()

  • ()
slide-11
SLIDE 11

[()] () [()] ≥ ()

[()]

() = ()

[()] = () +

̸=:()=() () ()
  • ⇐

I

ACHIDI>f k )

slide-12
SLIDE 12

[()] = () +

  • ̸=:()=()

()

  • .
  • ()
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SLIDE 13

[()] = () +

  • ̸=:()=()

()

  • .

E ⎡ ⎣

  • ̸=:()=()

() ⎤ ⎦ =

  • ()
  • f t fly)

P r(Ky): h1×7)i'm

slide-14
SLIDE 14

[()] = () +

  • ̸=:()=()

()

  • .

E ⎡ ⎣

  • ̸=:()=()

() ⎤ ⎦ =

  • ̸=

(() = ()) · ()

  • ()
slide-15
SLIDE 15

[()] = () +

  • ̸=:()=()

()

  • .

E ⎡ ⎣

  • ̸=:()=()

() ⎤ ⎦ =

  • ̸=

(() = ()) · () =

  • ̸=
  • · ()
  • ()
slide-16
SLIDE 16

[()] = () +

  • ̸=:()=()

()

  • .

E ⎡ ⎣

  • ̸=:()=()

() ⎤ ⎦ =

  • ̸=

(() = ()) · () =

  • ̸=
  • · () =

· ( − ()) ≤

  • ()
  • Iffy.rs/ftnifly)Htn)0
  • =

E#fly):{ftp.gty.fly));§×$I''

#

If'Isshly)

nudity)

s§×tnI)

slide-17
SLIDE 17

[()] = () +

  • ̸=:()=()

()

  • .

E ⎡ ⎣

  • ̸=:()=()

() ⎤ ⎦ =

  • ̸=

(() = ()) · () =

  • ̸=
  • · () =

· ( − ()) ≤

  • ≥
  • ()
  • markers' inequality
slide-18
SLIDE 18

[()] = () +

  • ̸=:()=()

()

  • .

E ⎡ ⎣

  • ̸=:()=()

() ⎤ ⎦ =

  • ̸=

(() = ()) · () =

  • ̸=
  • · () =

· ( − ()) ≤

  • ≥
  • ̸=:()=() () ≥
  • ≤
  • ()
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SLIDE 19

[()] = () +

  • ̸=:()=()

()

  • .

E ⎡ ⎣

  • ̸=:()=()

() ⎤ ⎦ =

  • ̸=

(() = ()) · () =

  • ̸=
  • · () =

· ( − ()) ≤

  • ≥
  • ̸=:()=() () ≥
  • ≤
  • ()
  • O
  • z ,

universal

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SLIDE 20

[()] = () +

  • ̸=:()=()

()

  • .

E ⎡ ⎣

  • ̸=:()=()

() ⎤ ⎦ =

  • ̸=

(() = ()) · () =

  • ̸=
  • · () =

· ( − ()) ≤

  • ≥
  • ̸=:()=() () ≥
  • ≤
  • ()
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SLIDE 21

/ () ≤ [()] ≤ () + .

  • ()
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SLIDE 22

/ () ≤ [()] ≤ () + . (, ) =

  • ()
  • speeds,[

k¥2,21

want: E D K

G

3£:

42

31ms 33¥:9£ spot:O

(Kailyn)

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SLIDE 23

/ () ≤ [()] ≤ () + . (, ) =

  • ()
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SLIDE 24

/ () ≤ [()] ≤ () + . (, ) =

  • ()
slide-25
SLIDE 25

/ () ≤ [()] ≤ () + . (, ) =

()
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SLIDE 26
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SLIDE 27
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SLIDE 28
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SLIDE 29
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SLIDE 30

() ˜ () = ∈[] [()]

  • OO

O

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SLIDE 31

() ˜ () = ∈[] [()]

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SLIDE 32

() ˜ () = ∈[] [()]

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SLIDE 33

() ˜ () = ∈[] [()]

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SLIDE 34

() ˜ () = ∈[] [()] ∈ [] = (/) ≥ / () ≤ [()] ≤ () + .

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SLIDE 35

() ˜ () = ∈[] [()] ∈ [] = (/) ≥ / () ≤ [()] ≤ () + . [() ≤ ˜ () ≤ () +

]
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SLIDE 36

() ˜ () = ∈[] [()] ∈ [] = (/) ≥ / () ≤ [()] ≤ () + . [() ≤ ˜ () ≤ () +

] − /
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SLIDE 37

() ˜ () = ∈[] [()] ∈ [] = (/) ≥ / () ≤ [()] ≤ () + . [() ≤ ˜ () ≤ () +

] − /

≥ − δ = ((/δ))

  • bsdls)

+51¥)

& I

lost)

1-Yzts, l - s d ?

1/3+1%18)?

b )

(113%1-1>1113)

bj(g)

I t . -b)

13)

O

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SLIDE 38

() ˜ () = ∈[] [()] ∈ [] = (/) ≥ / () ≤ [()] ≤ () + . [() ≤ ˜ () ≤ () +

] − /

≥ − δ = ((/δ))

slide-39
SLIDE 39 ≥ − δ

((/δ) · /)

  • losch)
slide-40
SLIDE 40 ≥ − δ

((/δ) · /)

(, )

slide-41
SLIDE 41 ≥ − δ

((/δ) · /)

(, )

  • ≥ /

() ≥ /

  • 10001.0,

I

10,000

[

01000]

  • I

Ef

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SLIDE 42
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SLIDE 43
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SLIDE 44
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SLIDE 45

× ≥ × ,

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SLIDE 46

× ≥ × ,

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SLIDE 47
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SLIDE 48
  • ↳

2 8

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SLIDE 49

⟨, ⟩ ∥ − ∥

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SLIDE 50

⃗ ,⃗ , . . . ,⃗ ∈ R ∈ R× ⃗

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SLIDE 51

⃗ ,⃗ , . . . ,⃗ ∈ R ∈ R× ⃗

  • E

T}did

points

  • deities
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SLIDE 52

⃗ ,⃗ , . . . ,⃗ ∈ R ∈ R× ⃗

  • =

⇒ = ⇒

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SLIDE 53
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SLIDE 54

⃗ , . . . ,⃗ ∈ R → ˜ , . . . ,˜ ∈ R .

  • .
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SLIDE 55

⃗ , . . . ,⃗ ∈ R → ˜ , . . . ,˜ ∈ R . ⃗ , . . . ,⃗

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SLIDE 56

⃗ , . . . ,⃗ ∈ R → ˜ , . . . ,˜ ∈ R . ⃗ , . . . ,⃗

  • ˜

⃗

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SLIDE 57
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SLIDE 58
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SLIDE 59
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SLIDE 60
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SLIDE 61
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SLIDE 62
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SLIDE 63

⃗ , . . . ,⃗ ∈ R ≥ ˜ , . . . ,˜ ∈ R ) ˜ , ∈ [] ( − )(⃗ ,⃗ ) ≤ ˜ (˜ ,˜ ) ≤ ( + )(⃗ ,⃗ ).

  • O
slide-64
SLIDE 64

⃗ , . . . ,⃗ ∈ R ≥ ˜ , . . . ,˜ ∈ R ) ˜ , ∈ [] ( − )(⃗ ,⃗ ) ≤ ˜ (˜ ,˜ ) ≤ ( + )(⃗ ,⃗ ).

  • JIA,B)

s

Hawkppin g

total

Helots

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SLIDE 65

⃗ , . . . ,⃗ ∈ R ≥ ˜ , . . . ,˜ ∈ R ) ˜ , ∈ [] ( − )(⃗ ,⃗ ) ≤ ˜ (˜ ,˜ ) ≤ ( + )(⃗ ,⃗ ).

  • =
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SLIDE 66

⃗ , . . . ,⃗ ∈ R ≥ ˜ , . . . ,˜ ∈ R ) ˜ , ∈ [] ( − )(⃗ ,⃗ ) ≤ ˜ (˜ ,˜ ) ≤ ( + )(⃗ ,⃗ ).

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SLIDE 67

⃗ , . . . ,⃗ ∈ R ≥ ˜ , . . . ,˜ ∈ R ) ˜ , ∈ [] ( − )(⃗ ,⃗ ) ≤ ˜ (˜ ,˜ ) ≤ ( + )(⃗ ,⃗ ). # ˜

, ˜
  • ≈ (⃗

,⃗ )

  • C

I D

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SLIDE 68

⃗ , . . . ,⃗ ∈ R ≥ ˜ , . . . ,˜ ∈ R ) ˜ , ∈ [] ( − )(⃗ ,⃗ ) ≤ ˜ (˜ ,˜ ) ≤ ( + )(⃗ ,⃗ ). # ˜

, ˜
  • ≈ (⃗

,⃗ ) = || (⃗ ,⃗ )

  • C

]

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SLIDE 69

⃗ , . . . ,⃗ ∈ R ≥ ˜ , . . . ,˜ ∈ R ) , ∈ [] ( − )∥⃗ −⃗ ∥ ≤ ∥˜ − ˜ ∥ ≤ ( + )∥⃗ −⃗ ∥. ⃗ ∈ R ∥⃗ ∥ =

  • =⃗

()

  • D,

D a r e

← d i

Lem

d i dace

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SLIDE 70

⃗ , . . . ,⃗ ∈ R ≥ ˜ , . . . ,˜ ∈ R ) , ∈ [] ( − )∥⃗ −⃗ ∥ ≤ ∥˜ − ˜ ∥ ≤ ( + )∥⃗ −⃗ ∥. ⃗ ∈ R ∥⃗ ∥ =

  • =⃗

()

  • I
slide-71
SLIDE 71

⃗ , . . . ,⃗ ∈ R ≥ ˜ , . . . ,˜ ∈ R ) , ∈ [] ( − )∥⃗ −⃗ ∥ ≤ ∥˜ − ˜ ∥ ≤ ( + )∥⃗ −⃗ ∥.

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SLIDE 72

⃗ , . . . ,⃗ ∈ R ≥ ˜ , . . . ,˜ ∈ R ) , ∈ [] ( − )∥⃗ −⃗ ∥ ≤ ∥˜ − ˜ ∥ ≤ ( + )∥⃗ −⃗ ∥. ˜ , . . . ,˜ ⃗ , . . . ,⃗

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SLIDE 73

⃗ , . . . ,⃗ R

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SLIDE 74

⃗ , . . . ,⃗ R = ˜ = ⃗ () ˜ ∥˜ − ˜ ∥ =

  • [⃗

() −⃗ ()] = |⃗ () −⃗ ()| = ∥⃗ −⃗ ∥

  • Gill) o o
  • o ]

t e

Xi:[xi(i))

  • r
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SLIDE 75

⃗ , . . . ,⃗ R = ˜ = ⃗ () ˜ ∥˜ − ˜ ∥ =

  • [⃗

() −⃗ ()] = |⃗ () −⃗ ()| = ∥⃗ −⃗ ∥ =

  • ✓ lowd i

Horton

°

  • embedding

O O

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Effidi.it? tan?0

°.!

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