merges.txt

#version: 0.2
_ {
^ {
} \
m a
t h
ma th
} ^{
} (
\ [
r a
i g
} )
, \
i n
l e
} _{
t a
Ġ \
{ \
a l
m e
f ra
} }
\ ]
fra c
\[ \
math b
a r
_{ \
f t
t i
( \
ig h
d e
r igh
= \
} {
e ta
p h
a m
le ft
righ t
) \
} }\
^{ \
- \
}( \
c al
math cal
+ \
s i
r i
} ,\
. \]
l o
mathb b
s u
| \
o t
d ot
}^{ \
r m
p ri
pri me
p si
mathb f
}\ ]
le q
} ,
ph a
al pha
t o
d a
am b
amb da
math rm
v ar
n a
lo n
l a
}) \
b ig
su m
l ta
l ambda
}_{ \
psi lon
am ma
e psilon
e x
} +
g a
me ga
n g
b o
ph i
in t
ti l
til de
ig ma
q u
} -
c dot
ng le
ex t
t ext
m u
a d
o p
p ar
qu ad
bo l
ti al
par tial
b m
b eta
ti me
time s
^{ -
e r
th eta
l l
e q
a t
g amma
s igma
} =
h at
| _{
{ (
} +\
h o
} =\
ft y
in fty
ta u
to r
l in
e ra
Ġ &
lin e
era tor
op erator
na me
operator name
de lta
var epsilon
r ho
w i
,\ ]
} {\
b ar
n d
p i
wi de
) \]
) ^{
x i
} .\]
}} {
s e
} -\
b la
) }\
na bla
B ig
e ll
} |
a p
d s
} }(
v er
e g
O mega
o mega
r o
math s
s q
Ġ 0
) =\
e nd
b eg
beg in
o ver
dot s
g eq
r t
sq rt
h i
) =
}) \]
} }^{
| ^{
[ \
ra ngle
var phi
n u
over line
y m
Ġ \[
la ngle
l i
D e
math fra
mathfra k
ym bol
bol ds
bolds ymbol
De lta
^{ *
Ġ 1
Ġ \[\
l dots
se t
{ )
},\ ]
& \
o times
ta r
c o
wide tilde
} ]
}^{ (
Ġ {
\ |
t ri
maths f
G amma
lo g
} :
ra y
p a
}^{ -
\ |_{
Ġ x
Ġ C
}^{ *
ma tri
matri x
Ġ 2
ro w
) )
}}\ ]
wide hat
m in
q quad
\ \
}\ ,
{( }\
}} {\
k ap
kap pa
} }(\
Ġ i
}) ^{
) .\]
; \
P hi
cdot s
r c
\ {
Ġ f
li m
Ġ }
u s
o r
) -
tar row
\ ,
Ġ t
z eta
} }_{
c i
c ap
} })
^{ (
Ġ a
ci rc
Ġ }\
u n
L ambda
{ |
) ,\
}\ |
) +
c hi
) ,
big g
si m
Ġ =\
Ġ n
) }
righ tarrow
v e
de r
Ġ u
un der
}) =
\ |\
Ġ =
{( }
n t
s la
c u
}\ |_{
} |\
ar ray
}) =\
] \
su p
S igma
p ro
} [
Ġ d
) (
) }{
ma x
su b
cu p
r e
c a
Ġ _{
}\ \
: =\
}\ ,\
sub set
Ġ\ \
sla nt
) +\
\[ (
c r
) -\
e d
\ {\
ca se
case s
} /
maths cr
s p
under line
) ,\]
Ġ L
{ )}\
d x
) ^{\
p matrix
Ġ k
g e
c k
Ġ (
pro d
i j
li t
i d
} &
to p
Ġ A
Ġ B
< \
Ġ c
}} ,\
sp lit
^{ -\
d i
p m
} }^{\
P si
s s
Ġ s
i t
Ġ S
! \
Ġ T
Ġ\ (
_{ *
Ġ e
Ġ H
. \
Ġ\[ =
b f
1 2
) )\
Ġ v
bo x
}} .\]
Ġ p
) }(
leq slant
ed ge
f o
}) }\
w edge
\ ,\
co lon
ra ll
fo rall
}) .\]
ex p
{ [
n eq
Ġ\[ =\
l us
_{ -
}) -
. .
}} +\
s tar
) |
ve c
le ss
Ġ N
}} =\
less sim
op lus
o m
min us
}} }\
}| ^{
su bar
subar ray
Ġ X
Ġ I
}) ,\
set minus
m id
0 0
_{ (
}\ |\
{ ]
Ġ M
u l
( -
b matrix
}^{ +
)\ ,
Ġ y
}: =\
d t
}) _{
Ġ {\
s in
b ul
} [\
) _{
/ \
Ġ r
P i
\ }\]
Ġ m
Ġ V
}} =
s t
T h
Ġ j
} &\
Ġ E
Ġ R
: \
}) +
h line
Ġ D
\[ (\
Th eta
Ġ F
\[\ |
}} ,
1 1
co s
lim it
] \]
}} +
}) (
limit s
} })\
Ġ -
}) -\
1 0
}) ^{\
}) ,
m box
) }{\
Ġ P
_{ +
Ġ h
i f
}) +\
\ )
Ġ b
\| _{\
) ^{-
{\ |
Ġ g
^{ +
} ;
Ġ K
\[ |
Ġ w
c c
Ġ ^{
\ }\
t frac
o n
Ġ G
f lo
flo or
Ġ z
) :=\
} }_{\
p t
}} ,\]
p s
: =
}) ,\]
Ġ 3
) }\]
lon g
s h
}} -
}} |
ma ps
le t
maps to
subset eq
}} -\
{| }\
Ġa nd
Ġ q
}} }{
bul let
}\ )
\[\ |\
l n
co ng
c e
s ta
re l
p er
) |\
i v
g g
{\ {
}: \
Ġ U
Ġ $
| _{\
}= (
}] \
{) }\]
b in
^{* }\
} ;\
bin om
o d
sta ck
stack rel
) )\]
long rightarrow
}) }{
per p
,\ \
} >
Ġ\ (\
gg er
da gger
Ġ W
f or
}\ }\]
{ -
{[ }\
\[ |\
Ġf or
a nd
,\ ,
}) )\
e qu
t r
i o
\ |^{
( -\
} ^
equ iv
ve e
io ta
Ġ& \
{) }
in f
Ġ (\
}\ |^{
}( -
\ }.\]
Ġ 4
)\ |_{
eq q
1 6
colon eqq
var theta
b ra
) ]
c h
}_{ +
}) ^{-
}) }
t t
, -
1 3
i l
.. .
}\| _{\
) |^{
d y
}}\ ,
}^{* }\
( (
Ġ Q
R e
)\ ,\
} })\]
di m
Ġ J
}+ (
} <
Ġ Y
Big g
) /
) (\
Ġ -\
}{ (
) }(\
}} }
) }_{
^{* }
}: =
de t
2 2
}) |
var rho
x rightarrow
}) )\]
{) }^{
+ |
}{ |
me q
si meq
)\ \
^{* }(
* *
Ġ al
) }^{
}/ \
) },\
] }\
tri a
- (
}^{ (\
}} {(
{ {\
+ (
math ds
},\ \
a b
\[\ {
Ġ l
big cup
Ġ in
Ġal l
Ġ }(
}} |\
}_{ (
})\ ,
geq slant
}}^{ (
l floor
Ġ o
Ġ Z
= (
) }=\
r floor
2 1
T r
}}\ |
Ġ\[ +\
} _
] _{
b le
n ot
)= (
} <\
v dots
}) }{\
] ^{
o l
) }.\]
> \
Ġ +
, (
2 3
e t
}=\ {
}) }\]
] .\]
2 4
Ġ _{\
1 4
& -
di v
,\ ,\
}( (
math tt
_{ [
}] \]
ar p
e m
} .\
1 5
\[ [
bul ar
ta bular
Ġ ^{\
} |_{
big r
b a
big l
}) (\
2 0
H om
ta ble
Ġ }^{
{[ }
) }=
Ġi f
}\ }\
( |
{ (\
}}\ ,\
) _{\
}}^{ -
in g
}\, .\]
}) _{\
Ġ +\
{) }.\]
}^{* }
}= -\
) },
}( [
X i
Ġi s
_{ -\
) :=
\[ =\
) )^{
\ !\
) }+\
| ^{\
Ġ 5
pro x
^{ (\
\[ =
{ {
}_{ -
| \]
), (
) &
}^{ -\
\ },\]
tria ngle
}^{* }(
... ,
d z
k er
de g
}) }^{
}= (\
sla sh
}- (
}} [
h bar
}}\ |\
| }\
m p
ba ck
Ġ }_{
] =
}}^{ *
back slash
{\{ }\
Ġ1 0
}) )
] =\
{ }_{
\[ {\
pt y
_{ |
{| }
big oplus
e c
u t
em pty
Ġ |\
I m
bra ce
{ |\
\[ -\
) }}\
empty set
}} }{\
Ġ 6
}_{ *
ap prox
| |
) !
) )=
bra ck
3 2
brack et
}) |\
Ġ O
x y
Ġ )\
}}{ {\
/ (
}\ !\
Ġo f
under brace
re f
i st
{ }^{\
}} }(
sh arp
Ġ th
}}\ \
{] }\
ti on
}= -
},\ ,
}\ {
Ġ }{
2 5
] ,
})\ |_{
ho o
var pi
) :
0 1
ch e
a st
p re
over set
\ !
{\| }\
Ġ |
} *
) )=\
= -\
s ma
}} }\]
S p
) }-
che ck
) }+
d u
] ,\]
e n
ar row
{\{ }
a s
})\ \
sma ll
j k
{ =
] ,\
a g
\[\ {\
1 8
}( {\
ar g
}\, ,\]
}^{ [
\, .\]
U psilon
}\ }_{
ex ist
|\ ,
i k
}) :=\
er t
( [
Ġ\[ +
}) }(
_{* }\
d r
s c
) })\
under set
r r
exist s
) }-\
9 9
) >
+ |\
_{ (\
^{* }_{
| =
}\ !
pre c
})\ ,\
V ert
lim sup
wi th
) &\
o th
ig n
) },\]
o w
)) .\]
}+\ |
e s
\ ;
, &\
})= (
m od
Ġ :=\
i p
} })^{
1 7
)\ |
)= -\
x x
{\| }_{
\ },\
\ }}\
Ġ }}\
] }
}\ ;
- |
= -
d frac
m n
rc e
Ġ }(\
[ -
{) },\]
rce il
{) }^{\
3 4
ce il
2 7
}) ]
l ceil
ver t
} $
( (\
Ġ 8
co n
ow n
}+\ |\
Ġ\ ,\
}] _{
! }\
Ġ\ |
) <
1 9
\[ [\
{] }\]
ar e
Ġ [
3 3
i i
}\ ;\
d own
^{* }(\
o dot
R igh
Big r
ta n
}( |
Righ tarrow
small matrix
Big l
}) }.\]
{( }(
I d
er e
)+ (
},\ ,\
}] =
}} &
)\ )
}}\ |_{
di ag
text bf
Ġ& =\
[ (
6 4
Ġ **
i s
}+ |
wi se
di st
Ġ\ ,
big cap
; \]
}| _{\
a n
sup p
ra l
}}{ |
t in
le f
)^{ -\
tin y
}+ (\
}, ...,
bol d
not in
bold math
mu l
er wise
^{- (
4 5
Ġ 7
}\ }.\]
Ġ on
li min
sq cup
limin f
) })
{| }_{
)^{ *
_{\ {
Ġd x
| }
k l
) }_{\
I I
lef tarrow
s f
}}) =\
2 8
P r
* {
}{ |\
}\ {\
d dots
),\ \
}, (
}| }\
) }}{
| (
d v
Ġ\ |\
u p
\, ,\]
3 0
3 6
L o
di am
left rightarrow
\ {(
p r
i int
G L
}} [\
_{* }(
}^{+ }\
}} &\
s qu
C o
down arrow
t e
}) /
)\ |_{\
( |\
c d
5 6
\[ -
)\ }\]
Ġ 9
f f
Ġ\[ -\
}^{* }(\
}} :=\
r l
!\ !\
}_{ [
) }|
hoo k
Ġ$ \
tria ng
00 0
)}\ ,
}}) =
|\ ,\
hook rightarrow
( {\
triang leq
^{ [
}> \
] (
4 8
h ere
}^{+ }(
}} }(\
}( -\
}| =
| }{
4 0
{) }=\
) <\
i m
x t
)\ |\
] +
{ }^{
3 5
(\ |
lo r
)\, .\]
n k
_{ |\
a c
mul ti
var sigma
cc cc
bigg r
ll bracket
)= -
Ġ de
if f
| +
) }}
{) }=
}) |^{
ign ed
$ \
lo c
. }\
, |
i c
int er
squ are
pa n
V ar
}| |
al igned
}] =\
\ }
bigg l
}=\ {\
}^{ +\
A B
h box
] _{\
Ġ= -\
)= (\
s k
)}{ (
sin h
) ]\
rr bracket
L e
}| \]
0 2
^{* },
cos h
) :\
}, &\
0 5
_{* }
, &
Ġth e
{\ }}\]
v ol
] +\
* \
{\ }}.\]
Ġ }^{\
) })\]
= (\
}}}{ {\
\ ;\
}}) .\]
da sh
{\| }
) )}\
3 1
| ^{-
, [
3 7
oth erwise
] ^{\
}) :
par row
}, -
box times
)) -
, *
u parrow
}) &
| -
)) ,\]
}} }^{
{)}\ ,
eq ref
# \
) .\
Ġ with
n i
1 00
la t
| +\
] }(
{( -
{) }+\
+ }\
Sp ec
})\ |^{
}) )^{
) }^{\
2 6
}) )=
) [
inter cal
&\ \
\ }}
_{ {}_{
\ %
{] }
) /\
Ġa n
}( (\
{\ }}\
7 5
)=\ {
}) }(\
}\, ,\
{| }^{
0 4
{= }}\
}_{\ {
Ġ co
)- (
}}( -
s g
}) ).\]
Ġ= (
}| ^{\
Ġ{ -
}] ^{
}) )=\
le l
cu rl
}+ |\
ral lel
=\ {
9 6
pa rallel
& &
Lo ng
^{* })\
, -\
D u
sup set
) ;
}} }.\]
Ġ or
\[ +\
su cc
}), (
Ġ to
}) }=\
Ġ }{\
c t
i x
f lat
math op
c l
r ing
(\ |\
pm od
ra d
| |\
}- (\
Ġ :=
}} :
p q
)) ,\
, +
- (\
\ }^{
+\ |
0 3
l Vert
)\ |^{
Ġ },\
Le ft
l y
] )\
_{+ }(
Left rightarrow
r Vert
Ġ\ {
}:=\ {
)\, ,\]
^{* }}\
Ġ )
^{+ }(
5 0
Ġ\ |_{
}, {\
_{ {\
2 9
}) >
i mp
u psilon
+ (\
}{ }^{
, (\
d dot
math ring
o nd
}_{ (\
, ...,
B o
: \,
E xt
li es
) |_{
| .\]
^{ {}^{\
arp o
hoo se
u v
)) -\
c hoose
}& =
b re
l u
}}) ^{\
n o
A d
}= [
}) },\]
}}) _{
}| |_{
. }\]
s pan
| =\
n e
)) +
4 4
}} :\
3 8
o ut
ve n
Ġ ^{-
{( }-\
9 8
sk ip
}] .\]
}) &\
}) <
S ym
m o
Ġ })\
{) }+
od d
}} ]
{) }_{
imp lies
{\ |\
ra nk
ker n
o me
_{* }^{
\, ,\
})= (\
| |_{
M od
}] }\
\ }_{
Bo x
A ut
sg n
}, &
^{* }_{\
] {
l vert
}| |\
)) +\
})+ (
j i
G r
}) :=
}(\ {
6 0
[ -\
}_{+ }^{
bre ve
] -\
, {\
}{ (\
t u
}( |\
r vert
Ġ }_{\
- |\
* }\
or d
& -\
Ġ },
}^{* },\
}; \]
)) ^{\
{( }(\
)\ ;
}] (
}\ },\
}^{- }(
}& =\
})\ }\]
i r
}) ]\
] \\
}}^{ +
big wedge
h skip
}^{- }\
}}\, .\]
o int
b c
) ^
_{+ }\
) }}{\
{ -\
}* \
w here
}) :\
h e
Ġ }}
=\ ,\
{ $
{) }(
var kappa
b b
g r
K L
Ġ\[= -\
Ġ }+\
S L
0 6
(\ {
})\ |
Ġ }-
} .
over rightarrow
{] }.\]
re s
z e
Re s
}} <\
de f
}^{* },
_{* }(\
)^{ (
7 8
}/ (
Ġa s
7 9
)| \]
}) }=
0 8
7 6
}{ }_{
)}\ \
ec t
Ġ {(
Ġ\( (
)) (
}} /
)) _{
+\ |\
dx dt
}\ },\]
{| }_{\
}\, (
prec eq
lu mn
^{* }-
Ġs ome
e v
E nd
)} |\
}}) (
v dash
;\ ;\
}} |^{
Ġ\[ -
Ġ }+
d V
}) }+\
5 5
{) }-\
^{+ }_{
| <
Ġth at
{ }_{\
! }
}}{ (\
n eg
math it
t s
! [
Ġ& +\
in d
r u
})\ |\
diam ond
co lumn
}} },\
\ }=\
^{+ }\
] -
r times
multi column
] ;
}) /\
T V
4 9
) ;\
}^{* })\
long mapsto
I nd
^{- }(
l g
}) <\
}) },\
{) },\
Ġ& =
e l
}| +
... ,\
k j
_{- }(
}& -
}| +|
) ]\]
\| \]
}] ,
}}) }\
}, (\
text tt
3 9
Ġ /
}} <
p th
| (\
ar c
e ss
))\ ,
)}\ ,\
.. .\
}) ^{*
Ġ= -
| )\
Ġ :\
Ġ }|
d W
})= -\
Ġan y
oth ing
g cd
{\ }},\]
\, (
] }\]
}}) ,\]
4 6
}^{+ }
var n
varn othing
Ġ con
8 8
})\, .\]
}] +
}=\ {(
Ġ )^{
_{+ }^{
^{+ }}\
{) }^{-
) })^{
, |\
r k
]\ !
n p
}] ,\
Ġ *
}}+\ |
}\ .\]
{| }\]
dx dy
}),\ \
Ġd t
Ġ\[= (
}}) ,\
{= }}
}[ (
!\ !
a x
ge n
}} >
tan h
^{* })
] }{
}} }=\
\| (
,\ ;
ij k
}} }^{\
}}\ }\]
}}\ )
0 7
)) }{
{)}\ \
pro j
^{* },\
Ġ su
{)}\ ,\
| +|
V ol
}^{* }\]
)| =
ym p
S O
}} ^
}}^{ (\
[ (\
A x
d w
bb k
B bbk
\ },
)}\ |_{
\[\ {(
: \,\
ho m
triangle right
| }{\
L ip
L i
Ġ }-\
}] _{\
)}{ |
8 0
}}= (
}}{ |\
4 2
\[ +
r eg
}} ]\
ver y
| )^{
r s
}, -\
}) ),\]
) >\
Ġ re
)}\ |
)^{ |
), &
| >
R ic
] )\]
text sc
})\ )
Ġ{ *
})=\ {
Ġ\[ (
cc c
mathb in
}:= (
7 2
_{- }\
g tr
i math
_{ [\
}}^{* }\
d m
Ġe very
})\ |_{\
9 5
Ġ odd
4 3
}} },\]
}) [
})- (
}_{+ }\
p e
}^{* }}\
}| }{
de l
as ymp
th arpo
, +\
}} }+\
\},\ {
-\ !
}^{ {}^{\
}) ]\]
gtr sim
h d
})}{ (
}| -
{- }\
}) }+
=\ ,
4 1
\ }=
s ign
)\ }\
big vee
}] ^{\
{) }-
}}) -
}}) ^{-
Ġe ven
K er
h en
d f
}^{* }=\
) }}\]
n m
}}}{ {=}}\
}}) +\
}{\ |
}- |
w p
^{* }}
}}) -\
d R
e igh
}{ }^{\
)& =
q ed
bm od
r n
_{+ }
i se
v box
)] ^{
D i
}, [
}}) +
}\ }}\
)\ !
no limits
4 7
y y
}}+\ |\
t w
}\| \]
), &\
Ġ )}\
s ym
o nu
Long rightarrow
6 6
}} ;\
tharpo onu
tharpoonu p
}] ,\]
n n
)\ }.\]
)) ,
; \\
0 9
{( }|
\{ |
Co v
\, |\,
}) .\
H S
}\ ,\]
s o
X Y
}}\, ,\]
w t
| <\
{\| }_{\
ti ve
}] +\
Ġ ds
5 8
big otimes
)! }\
] }(\
}) )}\
^{* }}(
S h
)_{ +
{ ,
}| .\]
d p
re d
}(\ |
d om
},\ ;
{( }-
)& =\
^{ |
}| =\
}}{\ |
Ġ1 2
})= -
v al
}} :=
})^{ -\
}} }_{
g rad
c line
}) }^{\
c tion
Ġ= (\
12 3
Long leftrightarrow
Ġde f
righ tharpoonup
}^{* }_{
}= [\
\{ -
}^{+ }(\
m k
}{ *
s m
] (\
C S
} !
;\ ;
\ .\]
\ })\
7 7
Ġ\( -
}& -\
}| +\
d g
Ġ â
})\, ,\]
P ro
Ġ }}{
)) }{\
d S
)} [
multi row
m b
Ġw here
a v
t y
}} .\
}| (
}\ }
+\ !
S E
t x
& (
ru le
: (
i a
Ġ1 6
( [\
t ra
}\, |\,
^{+ }
\[| |
k i
g h
) }}(
O p
eigh t
}}\ |_{\
e nt
{] },\]
}) |_{
5 4
)) ^{-
}}{ {
}) )_{
Ġsu ch
6 8
,\ {
e a
}_{ >
e ff
|^{ -\
}] )\
)} &
5 7
B C
00 00
= [
{(}\ |
Ġ })
}} }=
{- }
{ {(
\ (\
})| \]
succ eq
lo w
)/ (
}^{* }-
}}( (
arg min
op t
supset eq
}}= -\
) }:=\
}) }_{
_{\ {\
A lg
Ġ ^{(
}) ^{*}\
}| }
big sqcup
}] -
}} ;
| -\
9 7
p o
}}+ (
)}\ |\
}=\ |
}} /\
)^{ +
})\ }_{
k n
}( [\
\[\| (
}) )-
j j
^{\ #
wi d
re e
^{* }+
pr op
d d
$ ,
i b
d A
^{- }\
\[( -
)} &\
})^{ (
\| (\
)+ (\
}: (
C on
triangle left
}} }}\
Ġ }\,
{| }\,\
Pi c
mo del
}= {\
wid th
c y
}} ]\]
}, ...,\
}}\ {
C P
6 7
}_{\ {\
}), (\
u b
[\ ![
& =
)^{* }\
),\ ,
}^{* }-\
5 9
{(}\ |\
Ġ( -
d X
}}\ !\
na tu
|\ !
_{- }
ra ise
i z
) {\
}:=\ {\
| ,\]
{] }^{
^{- (\
& &\
^{* }=\
y z
! (
B M
Co h
)) )\
[ [
Ġ [\
}}= (\
Ġ1 1
}= (-
}| +|\
natu ral
Ġde pth
}) }}\
Ġ |^{
\{ -\
)) )\]
5 2
}} }+
S t
))\ ,\
C h
}\, (\
e rm
{\| }^{
)) }
b y
}) )+
Ġd y
}} |_{
Ġ1 4
\| _
}) ),\
- $
S S
T M
}^{ |
\ (
):=\ {
model s
_{- }^{
con v
}}_{ (
; .\]
}^{( -
}},\ \
}}}{ (
ĠR e
{[ }(
{(} |\
)\, ,\
Ġ }}(
ge ts
)=\ {\
v rule
Ġ2 0
^{- }_{
}^{* }=
) [\
|\ !\
M ap
}] }
{| }\,
^{ |\
}) ^
}{ }{
], [
}(\ |\
u e
| ,\
A C
\ #
l k
a u
}:= (\
Ġo th
}) }\|
= |
}_{ {\
12 8
)| _{\
rc l
6 3
}) )+\
})+ (\
Ġ\ {\
6 5
}) )^{\
}) )-\
/ (\
) *
Ġ width
9 0
}}) _{\
_{* },
{\ }}
Ġh eight
)\ ;\
}] )\]
small setminus
,\ ;\
Ġ at
}) }-\
d n
), (\
Ġ se
}}{ {=}}\
{$ -$
}) }-
}] -\
}}{\ |\
}\| (
d B
prop to
5 1
^{* }\]
}) )(
Ġ2 8
n s
k k
}}) ,
}[\ |\
i y
b s
] ,\\
| )
}, |
^{+ }_{\
u r
}- {\
) $
}= |
ĠC h
-\ !\
\{ (\
}^{- }
6 9
] \,
Ġd i
+ }
x z
{] }=\
\ })\]
)- (\
t er
,\ |
I n
{\{ }(
},\ {
\ ,\]
\ }\\
}\, {\
] ;\
^{* })\]
N R
8 4
Ġt r
}) ;\
}+ {\
s l
}}) )\]
) }^{(
}} }-\
7 0
=\ {\
c op
ol y
}^{* })^{
H H
; (
Ġ= &\
Ġ} |\
}\,\ ,\
}| <
ca le
\, (\
}{ }_{\
u u
_{* }^{\
C H
er f
}}) )\
8 1
& =\
\[( (
}| ^{-
}[\ |
}} },
}{* }{
G al
}^{* }+
u ph
on right
arpo onright
uph arpoonright
d k
5 3
8 9
)= (-
}| >
Ġoth erwise
{ }
}^{* })\]
j l
$ }\
)) }\]
in it
}\;\ ;
F ro
}[ |
}}=\ {
+\ !\
Ġ=\ {
8 6
) })=\
k m
| +|\
}[ (\
}=\ |\
u nd
] }{\
rn er
k h
},\ ;\
)] =
}\, |
}) >\
b ot
Ġd iv
E x
^{* *
}_{+ }(
raise box
co rner
] ^{-
Ġ <
}_{ -\
)] =\
}[ -
Re p
& *
2 00
\[| |\
& &\\
}}\ |^{
}} }-
\ }}\]
. \\
a ch
) })_{
in v
| }\]
)\ .\]
}_{ |
N N
Bigg r
}}^{* }
$ }.\]
}; \\
pa ce
w hen
Ġ& -\
}] (\
\ _
c ot
),\ ,\
)= [
}}\ !
P S
d h
f g
) })=
m i
})- (\
R S
}}) (\
}) [\
Ġ\[= (\
a ngle
}\!\ !\
b d
)) (\
)| =\
^{* })^{
}]\ !
ĠC e
Ġ un
Ġ\[= -
_{+ }(\
7 4
a cu
ta b
)| }\
8 5
}^{+ }}\
Ġi j
{] }=
\| =\
=\ !\
r hd
# \{
[\ |\
+ (-
}^{+ },\
}}^{* }(
acu te
}^{* })
Bigg l
g l
^{* }-\
d q
d le
}\, |\,\
}} })\
arc tan
bla ck
F un
) ;\]
\ }}(
Ġ ma
\[ {}_{
Ġ} [
}- |\
^{* }=
me nt
he ad
$ }_{
}+ (-
II I
r d
s cale
}^{ |\
}}}{ {=}}
ro d
}^{* }+\
})\ }\
Ġb y
)] _{
tw o
* }
] }^{
\, {\
ĠT r
Ġ1 3
) })^{\
D f
_{* }}\
}) }+\|
] {\
- }\
8 7
Ġ me
Ġ}\ ,\
}^{+ }_{
gen frac
Ġ\[ (\
Ġ ra
co lim
\[\| (\
f in
Ġ1 00
ro r
}| }{\
y x
Ġ& +
) }}{{\
cop rod
D iff
)( -
a y
Ġ }}^{
{] }+\
):= (
] :
)| }{
S A
\| .\]
si ze
Ġ }=\
}_{* }\
mid dle
] }|
S T
| >\
F il
C A
{ $\
+\ ,\
S U
}-\ |
two head
twohead rightarrow
\, ,
{(} [
subset neq
}) },
_{+ }^{\
}) ;
[\ |
)}+\ |
}) }\\
ar d
_{+ },
^{( -
)| ^{\
}= |\
mb er
A A
6 1
)\ }_{
=\ !
^{*}\ |^{
a le
b i
Ġ <\
A v
si on
scale box
_{\ |
) }}.\]
ma l
7 3
}\ })\]
$ -
}} _
}) }|
}^{+ },
))\ \
a top
in j
M L
) }).\]
}| )\
al g
^{* }\|_{
^{+ }}
}^{\ #
}) ^{*}
Ġ\ |_{\
co mp
}\ }=\
9 4
)|\ ,
L S
)) }^{
Ġ }}{\
ti c
}\,\ ,
_{ <
ra n
I J
Ġe ach
}+ \]
C C
P T
}^{- }(\
^{+ }(\
}}\ }\
}}\ ;
}\ },
Ġ& &
}\, :\,
up p
s n
[ |
4 99
Ġ }^{(
Ġ1 5
:=\ {
_{* })\
})}\ |\
}_{+ }}\
B K
]= [
I nt
}\| (\
}}) }{
_{\ #
l m
}}( [
Ġ\ |^{
}}) }
}^{ [\
}\ }}
Ġ )-
}\ }=
Ġi d
)} <\
! [\
b e
y s
}) }}{
\ }^{\
)\ },\]
{)}\, .\]
9 2
=\ {(
Ġ }=
dot eq
C l
\| =
}: |
se arrow
}}= -
Li e
] }=\
}\;\ ;\
)^{ |\
l times
: ,
n h
}^{* }}
Ġm od
= |\
\{ |\
}\; .\]
d P
45 27
p p
}})\ ,
}(\ {\
\! -\!
i h
}} })\]
}{ $\
a a
\| +\
! }{
{) }_{\
)| .\]
37 8
Ġ are
)) |\
})\ ;
^{* }}{
j ect
}^{+ }\]
C F
}| <\
S tab
\ }+\
}}) }{\
_{ {}_{\
Ġ ad
) !\
Ġn o
sin g
a tion
Ġ )-\
}}( {\
Ġ op
6 2
}\| =\
| |^{
}\ })\
Ġ min
7 1
C at
}|= |
=\ ;\
de pth
}}\ {\
+\ ,
A P
| }{|
] },\
}} }|
= }\
\, |\,\
c n
}\ #
{) }(\
Ġ pa
C R
}{\ |\
Ġ}\ \
}_{* }(
S D
}| |^{
c s
)] .\]
^{* }+\
}}}{ {
) }=(
_{ ,
| ^
9 3
}) }\,\
] [
)^{* }
)= |
}^{* }_{\
22 6
} ...
}_{ [\
Ġ int
c m
]\ )
Ġ{ +
) })-
})^{ +
}& (
Ġâ Ģ
< +\
M N
^{* }}^{
T or
})\ }.\]
})_{ +
D R
| /
}}) }\]
\[( -\
u ll
}^{* }\|_{
}|\ ,
\{\ |
_{+ }-
)\ ,\]
_{+ }}\
{ /
a q
\ }&\
] }_{
. ,
l r
) }}^{
{) }}{\
Ġ :
to m
i e
}\| _
12 0
00 1
) .
) )=(
}) _{(
^{- }
proj lim
)}{ (\
^{+ },
var projlim
* {\
< |
25 6
8 3
M C
})=\ {\
k t
|\ \
en s
Ġ ),\
v matrix
}) ]^{
)}\, .\]
$ }\\
) }}(\
Ġ bo
Ġ time
{) }}{
s r
$ },\\
)} [\
C N
S pan
)| |_{
;\ ,
)! }
* _{
o minus
}}( -\
}\,\ |
P D
)| |
y pe
}}^{ [
)\ !\
* }(
) }:
p n
}}, &\
init e
}| }{|
Ġd z
}^{\ ,
Ġ1 8
,\, -
triangle down
}\, |\
ab c
},\ {\
}^{- (
n r
}| ,\]
B B
H F
Ġ& &&
curl y
S upp
k x
Ġ >
,\ |\
z z
}) })\]
D G
Ġâ ľ
p le
\[ {}^{
}}- (
D F
n x
}| }\]
|\ {
}| ,\
m m
Ġ )+\
\!\ !
Ġ De
}]= [
}\, ,
re a
| |_{\
I S
M M
11 1
b j
p lus
]\ ,\
Ġ }\]
d F
_{- }(\
l d
}}( |
B S
] )
T x
A u
op y
}} }_{\
}:=\ {(
{ :
Ġ loc
curly eq
}\, =\,\
Ġ le
:= (
}\},\ {
e ven
)| }{|
)) _{\
Ġ ;\
i ze
}) })\
) })-\
k r
tion s
R T
)| +|
e p
Ġs t
) }]
c x
it y
Ġn ot
t v
Ġ }^{-
j math
\[\ #
9 1
}) }_{\
}) ]_{
}, [\
a ve
_{ {
Ġ pro
ca n
}| (\
]\ }\]
cccc c
Ġ })^{
)}{ |\
fo rm
\, |
long leftrightarrow
c b
}} }\|
{] }\\
}\ }_{\
}}\ ;\
}/ (\
i u
}\!\ !
}[ |\
}] }(
4527 56
] )=\
}] \\
}}\, ,\
C D
}), &\
Ġ{ -\
}_{ {}_{
A D
C B
ac t
I C
{ }\
| ,
] },
| }.\]
\[| (
S P
Ġ }}(\
T C
}) ),
sub ject
t A
. }
)}+\ |\
Ġ\[ +(
a k
) }),\
H ess
\| ^{\
}\| .\]
}} }}
ng e
}^{+ }}
D v
B V
}) }|\
) _{(
ne w
\ ),
}) {\
n c
}| ,|
))\ |_{
BM O
m s
_{ >
S et
}) }\,
^{- |
over leftarrow
)} >
,\,\ ,\
R eg
Ġ\( [
, [\
Di am
k p
M at
^{* }}(\
})& =
}+ [
mul t
] }\|
de d
Ġ\ #
}| |_{\
(\ {\
b x
C T
}) ))\]
s d
ng th
box plus
lit y
p k
! }(
}}| |
c ri
Ġ )^{\
Ġ\ !\
-\ |
Ġ}\ |
v i
}-\ |\
}: (\
}) }+\|\
)} /
8 2
| -|
}} }\,
] .\
}] }\]
{) }}\
_{\ |\
1 000
}) )}\]
ĠC o
] )=
{ [\
}} }\,\
}) |_{\
ti t
}[ [
}^{- },
. +\
r b
al l
B r
}}( (\
0 10
j n
\[\ #\
}}{ {=}}
Ġw hen
\; .\]
e st
}_{* }^{
},\ |\
}] ,[
Ġc h
)= \]
Ġ- (
R F
ce s
S H
Ġ max
Ġ ^{-\
co v
Ġ )=\
: |
Di ag
cu r
Ġ )=
Ġ ho
su it
b u
k s
N S
226 378
t ex
ta l
er r
L M
X X
G D
Ġ )+
t ot
var Phi
}^{* }.\]
tex tit
ne arrow
] }=
Ġ& &\
se d
F ix
t z
}\| +\
inj lim
}),\ ,
var injlim
d b
a e
12 5
\| }\
C M
ap p
S q
Ġo ut
kl y
I rr
)! (
ro m
Ġ nu
ea kly
, }\\
{] }_{
Ġ )(
\[\{ (\
Ġd ist
Ġ set
}) /(
| {\
^{* })=\
0 75
il b
- (-
Sp in
i q
th e
)! }{
S M
) }|^{
+ [
\, :\,
pha n
}+ ...
) })(
}} >\
}\, :\,\
}: \,
B D
}^{+ }-
phan tom
}&\ \
Ġ2 4
{] }^{\
11 0
ar t
}},\ ,\
] :\
| }(
Ġn on
) }^{-
\ }\,.\]
})| =
B A
ĠH om
g x
)= {\
}\ ),
] }.\]
(\ ,\
er ror
{] }+
Ġ\ }\
}| -\
A X
ĠS p
Ġd u
\ }+
- }
im ize
}_{* }(\
)}( -
}^{\ {
)| <\
hom ot
_{- }^{\
h t
[ |\
Ġ )}{
_{* },\
)) |
y p
)} <
}}\ }_{
}}\ .\]
}_{ <
_{- },
: (\
\}\ }\]
tra ce
}^{- },\
Pro j
F S
Ġ1 7
}^{+ })\
}= \]
ale ph
\ ))
}} ]_{
)\, =\,\
homot opy
_{+ },\
b r
P er
L T
! }\]
de s
}_{+ }(\
Ġ}\ |\
! )^{
}] }{
1 12
n j
{[ }(\
Ġon ly
})\ !
)) }.\]
t d
s a
^{ [\
},\ |
Ġ\ !
Ex p
)| +\
ra ph
] ).\]
, :
k e
^{- }}\
)| |\
}_{ |\
] /(
\ },\\
me ter
Ġ3 2
co l
}}| _{\
_{( -
}) ]=\
}| -|
over brace
})\, ,\
)] ^{\
S C
Ġ\[ <
Ġi t
}) ]=
le ment
79 4
{[ }{
}_{+ }}
}},\ ,
=\ ;
}_{- }\
\,\ ,\
}}+ (\
{)} .\
}^{+ }_{\
]+ [
r ot
p l
{) },
av g
_{- }}\
} !\
Ġ2 1
5 12
^{* }.\]
a w
l t
),\ ;
;\ ,\
un ction
j m
sc ri
\[ {
}}^{ -\
var Gamma
con st
) }}=\
d c
ĠI I
})= (-
}\! +\!
L R
Ġ ;
= :
A R
B P
|= |
}})\ \
box ed
\ }-\
)}\ |_{\
}^{* }}(
L P
}\,\ |\
}| )^{
$ },\]
^{- }(\
}}}{ |
Ġco mp
Ġa b
Ġ\( -\
prec curlyeq
}) )^{-
Ġ}\ |_{
\ }=\{
a i
) }:\
}, |\
ad j
r g
{)}\, ,\]
n l
ĠT he
) }),\]
V ect
ch ar
M SE
â Ģ
\[= -\
{[}{ ]}{
l hd
} !}\
M F
f d
}) )}
}),\ ,\
o si
Ġ1 9
}_{- }(
}}^{* }(\
}^{+ }=\
Diam ond
}} }|\
B L
)| +
\[ =(
}) )}{
] })\
t f
i ce
}\; ,\]
: [
- [
o s
Ġ\[\ |\
C e
e e
Ġs a
}\| =
a su
n mid
})\ .\]
$, }\\
ens pace
Ġ sp
Lo g
D P
Ġ ))\
F r
| ,|
o sc
}}+ |
D E
] /
d L
n q
| )\]
ĠM e
ij kl
in e
] \,.\]
p d
Ġ lo
M P
| )^{\
C E
S I
d N
p oly
lr corner
Ġ\[\ |
Ġ= [
}}=\ {\
Ġt erm
i me
a se
Ġ=\ {\
ĠI m
})}{ |
}\! -\!
H ilb
}|\ ,\
i tion
5 00
)}\ )
\{\ |\
xx x
G W
}}^{ +}\
row n
+ {\
+ }(
t X
\ )}
^{\ {
})} <\
] }|\
}) ))\
^{* })=
Ġ3 0
}< +\
}&= &
)) )
\, |\
B u
t n
ro ng
ra meter
14 4
}\|\ |\
}}\ !\!\
}) }}
-\ ,\
$ }}
}), &
ab le
) })+\
r x
_{* }-
Ġ5 0
] }}\
c ho
d l
}: [
( {
Ġf rom
f rown
)}_{ (
C om
499 794
- {\
)|\ ,\
l j
o b
$ .}\]
] }\|\
)\; .\]
g o
}}, &
}) _{*}\
}\| ^{\
\! +\!
Ġ& -
* }^{
)}\ }\]
}_{+ },\
r op
)= |\
)}\ |^{
{| }.\]
T f
})\ ;\
f i
Ġ} }_{
co th
el se
v w
Ġ\ ;\
}= -(
)+ |
F F
\,\ ,
b ab
A T
D iv
P a
se c
c le
Ġâľ ĵ
Q u
m ix
\,\ |
_{* ,
}) )}{\
)=\ {(
R R
)] ,\]
Ġ times
ĠN o
T X
}\| }\
{] }-\
^{+ },\
}))\ \
}} }\\
re sp
,* }(
}}}{ {=
}\| +
. &
-\ ,
m d
\[ {}^{\
] )}\
( (-
da ta
^{- }_{\
sta nt
) }},\]
! }{(
F P
d Y
di sc
S ub
Ġ ),
Ġ )}
; -
B G
C t
a f
}} *\
Ġ exists
) _{-
arc cos
v v
}] }{\
^{- },
min imize
{| }+\
\ }_{\
S R
)}\, ,\]
i T
, }\
}\|\ |
}) }}{\
_{+ ,
ĠG L
] :=\
)| +|\
})& =\
] }^{\
}}( |\
Ġx y
\[( (\
t p
):=\ {\
)} ;
10 1
$ }}\
}} *
_{+ }+
}}, (
T u
... &
\[| (\
i lity
Ġh as
ĠC r
Ġp oint
}| >\
)) /
}}}\ |\
S w
Ġ2 3
up lus
o us
\[( {\
en ce
\;\ ;\
}) ;\]
s w
u m
}^{* }}{
Ġ= (-
a z
) }]\
D er
m r
| }}\
x leftarrow
Ġ2 5
}\, .\
}\,\ ,\,
Ġf unction
\| +
S W
math rel
M A
}) ].\]
}\, =\,
R E
th er
) })^{-
) }},\
}^{- }}\
})}{ }_{\
q t
)] (
le m
{$-$ }}\
V dash
}) ^{*}(
C V
p w
,* }\
_{* }^{-
ti sf
)! }{(
Ġ ex
A i
Ġ}\ {
)( (
)) >
):= (\
u w
cho ice
Q Coh
}| )\]
P U
ar y
)}= -\
^{ {\
)} ;\
Ġun i
\, ,\\
Ġ sub
^{* })^{\
b t
}\ }=\{
{[ }-\
e ri
_{* })
Ġd r
{[ }|
m l
mo st
)\, |\,
math choice
}= :
I P
}_{* ,\
{\ #
de n
}}) |\
ĠâĢ ĵ
se ch
}|= |\
{[ }\|\
/ |
= }
) }:=
li p
Ġ2 2
)| >
D a
a R
] \|_{
_{[ -
J ac
e u
e w
}] )
s y
c f
Ġ\ ;
! |\!
{\ }},\
}] ^{-
Ġm o
}_{* }
dash rightarrow
^{* })-
\ #\
ĠC N
ar ge
)\ |\]
N T
le x
ta tion
)| }{\
r f
B R
12 4
):= -\
Ġ ]\
Ġ +(
_{- ,
f ree
}}\ ,\]
Ġt ra
}([ -
Ġdi ag
{/ }\
}} }}{
D D
)= [\
L L
}] [
_{- },\
Ġ\[= :
=\ |
{] }(
^{+ }-
Sh v
e f
de c
co nt
}^{- }_{
se p
ig arrow
right squ
rightsqu igarrow
H P
Ġe t
ec tive
m j
Ġ )_{
)}\ }_{
_{* }}
}^{+ }+
}[\ ![
L E
:\ ;
w r
},\ ,-
dv ol
}):=\ {
:=\ ,\
* }(\
Ġr eg
k N
Ġ la
}^{+ }-\
& (\
}(\ ,\
T T
}} }[
em ma
[\ ,\
Ġ(\ (
co nd
}} ]=
})\ |\]
H C
a ff
}\, ,\\
q x
}\ {(
}{ -
}}| \]
< -
m c
xy z
) })}\
W F
arg max
Ġnu mber
Ġb e
)^{ +}\
}| )
j p
* (
Ġ& =-\
)} .\
}= &\
z I
rong ly
}| ^{-\
^{+ })\
Ġ supp
Ġ })}\
}) (-
}=\{ (\
Ġ6 4
ĠC t
L U
}}=\ |
\[|\ {
u x
Ġ ]
Ġ{ (\
ul ar
te st
{)}\ |
\ }}|
dash v
\}&\ {
line ar
low er
}-\ {
per f
D M
}}) }^{
,\ {\
] })\]
{| }(
\}\ )
Ġco nt
- }(
R m
d o
A S
A nn
s x
}$ }.\]
B l
Ġ )}{\
Ġor der
- }^{
Ġ4 0
\|\ |
Ġ\[ |
^{* }}\]
] <\
}& &\\
}})\ |_{
n or
}{* }{\
{ }^{(
Ġ /\
g y
o ri
16 0
] }_{\
\| ,\]
S NR
; ,\]
D L
P o
})^{* }\]
\|_{ (
Ġi k
S ing
c z
ĠC on
_{+ })\
Ġ(\ (\
A t
}}_{ +
in c
q p
I V
}\| +\|
}_{+ }
D A
Ġe qu
)) |^{
}^{+ }+\
C r
T P
\ }}(\
Ġ} }^{\
}}) |
19 2
Ġ\( (\
}| ^
})\ ,\]
Ġ\[ |\
}^{* *
}^{* })=\
C ap
)) <\
= (-
Ġco m
R M
) }}=
}\ ))
$ }\]
P f
g n
m t
N L
E rr
ta in
13 2
}} ;\]
{] },\
{\{ }-\
; }\\
) }}{(
n y
R P
q r
\, =\,
G F
}- [
)},\ \
I N
Ġ[ ]{
_{+ }}
E M
}} ]=\
co dim
Pro b
it H
}})\ ,\
:= (\
}- (-
}^{- })\
Ġ\(\ {
})= [
)|= |
}) )\,
\, .\
ĠI d
bab ility
_{ ,\
d M
\!\ !\!\
}( (-
_{* }+
E nt
) }),
t q
Ġ\[ [
})| =\
}] \|_{
p x
\, :\,\
)^{- (
k a
sp t
^{- |\
re v
d H
h k
o bs
}}\ }.\]
A rea
x e
:\ !
) })+
}) ))
tor s
}}| |\
_{- })\
})] (
cur ve
Ġ par
Ġ ))
_{\ ,
am ple
scri pt
P C
T S
^{* })-\
ii i
] \,,\]
(- (
}_{+ },
. .\]
Ġ }}}\
}^{- }\]
dx d
Ġe ff
{| }=\
}) }:=\
Ġa c
}}= [
v ir
Ġ error
4 00
}\ }}\]
}) .
})| }\
N C
}^{* },\]
un ded
)] +
\[[ (
N p
D om
u le
_{\ {|
Ġd o
{] }\,
})| .\]
\; ,\]
}) )(\
Ġ= |\
ol u
M T
Ġt ype
}}{ }^{
Ġ= &
R L
Ġ }|^{
al ue
^{ !
] }+\
th od
su ch
}, +
})= {\
)] -\
}:= -\
\ }.\
Ġ2 7
)\, (
}} })
)] +\
}^{* }}{\
k d
{] }\,\
C or
}] }(\
)] _{\
< (
Ġ{ *}\
}}^{+ }(
\ }|\
0 11
^{* })+\
~ {}
Ġ\[ <\
})| +|
or b
p f
,\,\ ,\,\
= \]
] ]\]
z w
ce nt
P I
big m
}_{+ }\]
{[ }\|
}+... +
T HH
co h
.. .\]
)| ,\]
x p
var Omega
13 4
M o
)) }(
_{+ }+\
)=\ |
}^{* })^{\
Ġ\[= (-
&* \\
Ġ var
)}= (\
con e
in u
^{* }).\]
}}_{ -
\,\ |\
s ti
{(}\ {
_{+ }-\
})}{ (\
C L
A e
}| /
}]= [\
}]+ [
s v
A b
g s
Ġra te
P Q
di s
Ġ }},\
\[ -(
j s
): (
) *\
Ġ exp
}}) =(
}^{+ })\]
n f
| )}\
r ig
)}}{ {=}}\
0 12
\ }}{
D T
Ġ )}(
long leftarrow
23 4
# }\
c at
{ *
Ġ$ (
n b
})\ },\]
{\{ }(\
) }+(
{| }=
\ })
}) }\|_{
Ġ\[ >
S el
th ere
{[ }|\
Sw ap
Ġs ym
Ġth en
)\ }
}^{* }\|^{
)| <
tr n
O T
}) }[
}):= (
d dagger
m x
)| (
}) }}\]
)_{ +}\
R an
B x
)} }^{\
n T
h g
G H
!\!\ !\!\
Ġsa tisf
)- |
is o
j h
}| ,
= [\
] )^{
Ġ\ {(
}+ [\
Ġ }}+\
24 0
P A
$ },\
}], [\
] &\
er s
\| ,\
st r
T N
\ }-
] ,\,
}) )_{\
{\ }}_{
re p
+ \]
Ġs ta
\!\ !\
Le b
H K
)| -
th m
Ġth ere
black square
G M
_{ !
Ġd is
}| }.\]
}\, _{
}\| +\|\
Ġ= |
form ly
}) })^{
P L
) }]\]
{( }{\
\ }}.\]
] |\
p en
}: \,\
) }}+\
-\ |\
_{- }-
^{- })\
}}{ [
}^{+ }=
e ver
circ le
] }-\
13 5
})] -\
c p
}^{+ })^{
}= :\
{) }|
] },\]
), -
Ġ deg
. -\
,+ }(
Ġ >\
}( {
}\! -\!\
! }{\
i ci
\, ,\,
}&= &\
script size
3 00
w e
ĠC R
)) <
}}, (\
G S
\[\ ,\
}^{* }\\
s b
}, ...
Ġf inite
cccc cccc
ĠP a
] /\
{\ }}=\
M S
)) :
c ard
r y
}{ [
Ġ2 6
Ġd v
12 34
) **
}\ }}(
}] )=\
B un
S N
\ }\,,\]
}_{* ,
Ġ=\ |
d G
}, *
L F
l cm
_{* }=\
De t
un i
$ }.\
I M
j a
}^{ {\
!\! /
Ġ=\ |\
! }.\]
N m
l s
}\ #\
_{* }}(
Ġ3 6
v u
Ġ )\,
),\ ;\
\, =\,\
}} ]^{
C Alg
cu t
}\! +\!\
i es
n on
};\ ,\
K K
}| {\
{|}\ ;
de x
ea k
Ġpro bability
B i
{(}\ ,\
tra in
C K
r p
Ġp er
}* _{
)^{* }\]
)\ },\
or phi
u re
}| }{|\
^{( {\
}}- (\
}} }}\]
C x
{| }\\
}}& -\
cy c
}_{- }^{
}| -|\
z x
}: |\
}\, ,\,
Ġ:=\ {
}: \|
}}+ |\
10 8
u mber
)+ (-
C u
o rm
}}^{- }\
Ġ prime
ga p
)( |
\! -\!\
)\, :\,
}}& =\
' {
t m
E P
x f
Ġs o
P erf
si de
[\ ![\
~ {}\
^{* })+
inu ous
s to
tri c
_{* }\]
}] =-
)+ \]
Ġ curl
R C
x u
w w
| },\]
co ker
12 1
n ce
L C
.. ,
}}=\ |\
Ġ }{(
}\,\ ,\,\
f r
v t
| )^{-
h a
Ġ ||
)= &\
Ġw eakly
. +
a si
}- \]
}) )}^{
lo ck
{)}\ |\
dx ds
tr ue
}} }^{(
{)}^{ -\
\ })=\
ect ed
U V
\% \)
}\, ,\,\
}\! =\!\
a cc
)\; ,\]
M e
m on
Ġ=\ {(
)^{ [
_{( -\
28 8
{) }&\
t b
|= |\
s at
)|= |\
h v
Ġ )^{-
)\, {\
le ngth
Ġ} [\
}^{\ ,\
ĠT ime
L D
}}| (
Ġ ext
= {\
M R
00 5
(-\ )
Con v
l p
, .
}}) }.\]
{ +}
u c
}^{* \
] }+
{) }|\
}}\| (
n v
}) )=(
)^{ (\
}}(\ {
}\ }+\
)] -
ĠV ar
; [
B y
C y
D w
\| }{
)) ).\]
Ġ5 6
^{* },\]
Ġcon stant
e i
homotopy limit
2 13
| },\
at e
^{* }}^{\
F T
b n
}} }}{\
^{- }}
}] )=
d Q
^{\ ,
tr op
}^{* })=
ĠL emma
R a
E S
t g
_{ {(
-\ {
}}_{ (\
}))\ ,\
\{\ ,
] ]\
a j
t N
\ (-\)
Ġd W
L u
Ġ rank
ma p
cri s
}}) /
}} ](
t k
or em
}}) )
n K
^{* }:
Ġdx dt
}] )^{
)) &\
}}[ (
}^{* }}(\
)) )=
})= \]
k T
}) *
}^{- }=\
sp ec
Ġint eg
P P
` `
:=\ {\
)& (
}}) }(
B T
}\ }^{
Ġ{ |
)( -\
)\, =\,
^{- },\
{) }>
})| |_{
[ {\
z y
[\ ,
Ġ over
))= (\
F l
\ }:
12 2
Con e
. \,
C n
O PT
\ }}{\
Ġ3 1
}+ {
}\| ,\]
10 5
^{* })}\
}] /
11 3
Y Z
d E
}) _
Ġ2 9
L in
)} /\
Ġ2 00
}:= [
M ax
N A
N E
big circ
o c
r ror
f ix
la tion
h f
)}{\ |
i w
e ar
Ġ inf
In v
}) )|\
)< +\
P V
Ġ( (
res tri
ĠS O
Ġ- (\
B F
] }-
v x
la ss
{| |
})] ^{\
L a
P SL
: |\
p ut
Ġ ^{*}\
)! }\]
Ġterm s
q z
\( {
R x
\| <\
})}{ }_{
) _
Ġ })+\
S ch
t ed
co m
\, ,\,\
}=( (
M D
Ġ_{ (
)/ (\
}}& =
J X
) }}}\
^{* }:\
}& =-\
U n
h y
M or
}}_{ [
}] ]\]
}& (\
\ })=
y n
}) }\,.\]
})( (
Ġ }),\
me n
^{* }}}\
\{ [
}^{+ }.\]
,\ !
la s
S ol
T op
] |
}_{\ #
fra me
ad d
Ġ )\,\
}$ -
Ġ ro
}_{+ }^{\
ve l
00 2
Ġ *}\
}= &
Ġme asu
G e
})| +
B in
= :\
I F
{ {(\
Ġ }).\]
^{+ })^{
on e
L O
}) })
}] \,\
}^{ <
Ġn t
})/ (\
. (
ĠC n
\ }\,
Ġ gen
|\ ;
}_{ /
A W
}}( [\
) }},
arrow right
G C
) }))\
d T
N t
{\ }}=
)) )=\
^{+ }\]
}}\, (
var Lambda
C O
Ġ vec
in i
^{* }),
** }
}}:=\ {
}}) :=\
] ]
tri v
)) }{|
re t
})| ^{\
he art
big triangledown
}| ,|\
, +}\
)\ }^{
ĠA x
)] }\
heart suit
p c
}}{ {=
ra ble
ĠP ro
)}}{ {=}}
K M
U U
}^{ >
}}{ }_{
_{* }+\
I s
ra c
)| ^{-
ici ent
|_{ [
}}{ }^{\
sin ce
}}| }\
{, }\]
b p
d Z
}^{* })^{-
&& &\\
) }}_{
=\ |\
:\ ;\
A E
| ).\]
_{+ }=\
. ,\]
p ol
^{* })^{-
_{{ }_{(
Ġ\(-\ )
T R
}) ],\]
}^{* }}\]
Ġi m
go od
Ġ })^{\
\| }{\
)| >\
{- (
v a
})] +\
) }}-
h u
}}^{* }\]
g p
)] ,\
f ib
Ġ })-\
^{+ }+
ro up
)= :
\ )-
};\ ,
&= &
|\ |
)) +(
11 11
V ec
l b
^{+ }}(
] ),\]
i le
}_{* }^{\
Ġ}\ ;
99 8
H T
Da sh
}$ ,
m h
{) },\\
B E
T w
})= |
restri ction
O rb
}\! =\!
Ġ edge
^{* }}{\
}[ -\
B U
L B
R G
\ };\]
f e
ab cd
)&= &
)= -(
] ),\
ĠR es
_{+ }}{
z t
F G
o ff
}))\ |_{
Ġ& (
18 0
Ġcon tain
big triangle
co re
})| }{
bigtriangle up
l ds
99 9
{ }{
Ġi x
{] }-
}}}{ (\
\! +\!\
ĠN umber
Ġ log
15 0
v Dash
Ġp osi
D C
D g
o f
}\ }\\
\|_{ *
23 1
Ġbo unded
D S
ri d
})| |
Ġ\[+ (\
n N
b l
}_{\ {|
12 6
Ġ inter
ii int
}}= [\
]{ }
P F
h h
Ġ\ %
), [
})}{ |\
ĠI n
r v
t H
k u
_{+ }^{-
w eakly
)}= -
+ }^{
Fro b
))\, .\]
P R
pa ct
K T
\{\ {
on ent
ĠA lg
Ġbo und
}} }^{-
}})\ |
Ġ3 3
A f
ĠD u
q s
{| }^{\
,\ ,\,
\ }(
\[ <
}) ^{*}(\
}^{* }|\
S V
}) )}.\]
}| }(
}\, +\,\
AB C
Ġ\[ -(
)) ,\\
& |
{ .}\]
}_{ (-
au g
A M
M in
b q
}: \\
re c
_{* }}{
ab s
ec tion
]- [
^{ {}^{
}] ).\]
}] ;
{| }(\
_{- (
era ge
14 5
olu tion
, ...
3 21
}} }[\
mo oth
i al
p tion
De f
Ġa v
})=\ {(
T L
}}) >
]= -\
A V
h r
r j
i H
: \|
Q P
\| ^
})\, |\,
a h
} ...\
ra m
}}\| (\
O D
g f
Ġ3 4
},\, -\
ĠD i
}}, ...,
38 4
ri t
\|\ ,\
_{+ }^{(
}) }&\
}\},\ {\
}} ].\]
S B
; {\
T v
si ble
le ave
A y
45 6
Ġ1 000
}^{* }}^{
Ġ_{ -
Ġ\[=\ |
2 16
p T
u q
Ġ ar
{( -\
[\ {
F in
^{ <
i A
i able
M on
T F
b al
er o
h x
{\ }}^{
)) },\]
Ġco nd
\ }}=\
}} .
^{* }|\
^{* }(-
}] \,
3 20
,\,\ ,\,
N a
] =(
f l
}\ )}
)\ }=\
_{- }+
) }}+
no rm
: }\
_{\ !
)| }
\ }).\]
S G
Ġ size
_{* }-\
x a
le n
arc sin
}]- [
] &
Ġ\ &\
)) )^{
)_{+ }^{
2 11
A U
B W
}) _{*}
de nt
|\ ;\
}\!\ !\!\
)) :=\
^{* }|
Ġ6 0
N M
t ch
| }=\
A s
{[ }-
Ġ3 5
Ġ })-
}}\ !\!
}\| }{
H e
ĠM o
}^{* (
}^{- }=
dy dx
\| +\|
O ut
{ }{}{
p u
_{+ }\]
}=- (\
\;\ ;
sq subseteq
]\ !\
R D
}})\ |\
})\ ;.\]
}\| <\
Ġcon v
= -(
> -
se n
Lo c
) {
P E
ds dt
_{* })\]
_{* }:\
C I
{[ }\,\
L A
{)} <\
Ġ8 0
Ġcon n
t c
Ġ3 7
}_{+ }.\]
ow er
)+ |\
]\! ]\
P M
it s
}):= (\
D N
\ }\,\
] ^{(
})| |\
W P
)) -(
}\| ^
Ġ da
up tau
mo de
\| |
:=\ {(
Ġs ign
P GL
}\ :
ĠA d
ĠY es
)) }=\
di ff
.. ..
34 5
c sc
| }(\
)} })\
T ot
Ġ 99
10 24
\( {}_{
ĠS L
Ġ4 8
I so
b z
n L
}} }}{{\
F M
a ce
{) }^
Ġ( -\
ĠC om
}}| |_{
ĠSp ec
P e
b w
}^{- }-
), (-
P oly
Ġcont inuous
}] |\
})| <\
}|_{ [
Ġ }}.\]
}^{* }:
Ġal most
r w
}+\ \
M a
o u
! }(\
^{+ }=\
2 000
Ġ case
Ġ )|^{
\| {\
}^{* }\|_{\
}: \|\
}_{+ })\
A ff
ĠA v
_{- }}
cccc cc
comp lement
> (
^{* }|^{
}& &
a ma
s j
\[\ ,
}_{+ })\]
) }})
C s
d U
ma in
}_{ ,
00 01
}$ },\\
}_{- }(\
I w
j t
in ed
) })}{
}{ }^{(
)| ,\
te p
H ol
q q
Ġ )\|_{
po st
S F
{( (
) })(\
)] ^{-
P u
a us
36 0
$ .}\
o rt
}} ...
}^{* })_{
)}( (
}^{- }+
und s
_{ !}\
}) }^{(
am p
}),\ ;
}( (-\
00 4
}):=\ {\
ro ss
Ġop en
Ġ qu
00 8
,- }(
)& -\
Ġ })(
}, +\
( .
Ġ })=\
)} |_{
ĠA ut
n R
}^{* }).\]
{| (
15 6
}$ .}\]
^{\# }
}) _{-
}} ]^{\
{\| }\]
:= -\
x v
d K
{(} [\
]\ }\
{] }_{\
})| -
}* (
$ }
}] \}\]
|- |\
âĢ Ļ
U E
,\ ;\;\
D h
var Delta
Ġ& =(
black triangleright
al ity
}^{* ,
}|\ !
st d
\ }}+\
10 4
frame box
,\ ;\;
}\, +\,
A z
}\ }+
}| }}\
}}, -
G A
N P
q n
Ġ\ ,\]
)}=\ {
Ġ )(\
{\| }(
_{- }}{
))^{ *
, (-
B er
m L
}^{* })+\
ĠS ym
,\, (
erf c
w x
})\ !\
\|\ ,
om ial
})] _{\
Ġ9 5
Ġre sp
})^{ +}\
Ġd B
) &-
), {\
F E
T ra
h ss
Ġe lement
L G
Ġ\[ :=
Ġd iff
}* |
) }))\]
),\ ,(
curve arrowright
+ }^{\
(\ ,
)) [
00 3
{\ '{
}} })^{
\ }>
{\ }}\\
em p
Ġf ix
Ġs h
ĠI II
sm ile
| )|
); \\
C Z
k o
t L
}{ =}\
ver ti
c T
c q
Ġ pri
}^{- }}
13 6
0 25
j r
)= :\
}}^{ +\
T erm
h yp
Ġ ge
B e
r dr
}} ]_{\
)}\ !
dx dv
Ġ4 2
dV ol
ama lg
}+ ||
}] /(
}^{( +
}^{* })-
}^{* })-\
), -\
})= [\
}; (
16 8
z q
| }+\
}{ {\
^{* }\\
m skip
ĠC M
_{+ }=
c v
}}_{ *
}_{+ }+
,* }(\
) }}-\
\[\ #\{
^{* }\|_{\
Ġ )|\
le ad
)) /\
k q
Ġ ref
Ġ{ }_{
\[= (\
R f
}}) ).\]
k b
}}\ ;.\]
}^{+ })
la x
}- {
ĠThe orem
E E
| }^{
^{* })(
au x
+ [\
s A
}[ {\
\[| {\
})) <\
T y
Ġ })_{
Ġ\[= [
}< (
}$ }\
u se
Ġc y
3 12
{| },\]
ca tion
L aw
M O
^{* }),\
}_{+ ,
)\,\ ,\
}< |
ĠO p
}\; =\;\
Pro x
\[( [
Ġ9 6
|\! |\!
g raph
m g
Ġ det
lo sed
22 2
Ġ| |\
m q
}^{- })\]
)) ]\
})| =|
}}[ (\
Ġ9 4
) }}^{(
P G
w s
{|}\ ;\
N O
}- [\
Ġ })+
o slash
Ġe l
})) >
}] ,\\
}}) )=
Ġs gn
),& (
\ }}^{
var Sigma
M U
] }^{(
Ġ} /
Ġc l
}$ },\]
Ġ\ }}\
sq cap
22 1
ty pe
mu m
Ġ= [\
Ġe n
me asu
R Hom
Ġ })=
^{* }\|\
ik x
Ġuni formly
\ }}=
\ }|\]
K S
var limsup
)}, &\
du al
M W
q k
po unds
\ }<\
}\, ^{
ĠL o
}})= (\
orphi sm
| }|\
me as
Ġu p
Ġp re
Ġ\[=\ |\
\ }},\
q c
})|\ ,
.& .&
k g
{) }}\]
_{* }^{(
}}, {\
j q
}} }&\
}}) /\
)) }=
v s
}^{* }&
Ġv ol
sin c
ir st
}\ }\}\]
)_{ |
i B
}^{* }\,\
Ġ} })\
}\| }{\
d I
Ġ |_{
}) }}.\]
}\| {\
}},\ |\
))= -\
ĠâĢ Ķ
H L
}}\ },\]
Ġi mp
]= [\
}\ {|
- [\
< |\
}^{+ ,
}{ $
}},\ |
Ġs pan
_{* ,\
po s
i ven
Ġp r
10 2
}+| |\
Q R
p j
{ <
})\ |+\
_{* }=
}) }[\
Ġon e
{ .
ĠL e
}}, -\
}}| =
# _{
$ }}}
9 05
{$-$ }}
i an
{ +
| }{|\
^{* }_{(
f u
t B
) })}{\
right rightarrow
}}) )=\
rightrightarrow s
E q
w f
t j
_{- }^{(
C G
Ġ= -(
Ġs in
ma rk
)\ }=
Ġ1 28
}^{* }:=\
R u
a il
}) *\
f ull
Ġ }}-\
)) ]
Ġl arge
24 3
}}^{- }(
Ġmo del
men sion
)= &
^{* }}=\
}}) |^{
)}{\ |\
)) .\
)+ {\
25 0
Ġho lds
|\ |\
^{* }[
}\, [
}=( -\
14 0
el d
se s
)\, |
A G
\, [
Ġ matrix
_{ !}
)+\ |
a X
nu m
\| -\
st rongly
Ġ9 0
+ }(\
}| )^{\
)\, |\
^{ {
}( .
N e
Ġ linear
ma ll
Ġâľ Ĺ
P ar
\,\ ,\,\
ct s
Ġ0 0
Ġi z
}}= (-
Ġposi tive
O P
{\ }}\,.\]
}^{* }[
Ġb c
rea sing
r q
x leftrightarrow
ci ty
G P
H R
ma xi
})| }{|
\[= -
cri t
]\ }.\]
)| |_{\
^{* };
Ġ\[= |
!\!\ !\
P W
)\ {
}^{* }:\
i L
{| }|
Q x
W e
are a
R B
)| |^{
}}| ^{\
)\| _
0 15
H M
O b
] })
] }^{[
)\, |\,\
# (
\ }|
] }}
u gh
bo w
ho rt
\{\ ,\
}^{+ },\]
ĠP rop
})| +\
}}\,\ |
S c
}}(\ |
\|\ |\
sta nce
}\; (
}{*}{\ (
| }|
si ty
}, {
< -\
O N
\ }}|\
{\ ,
Ġ{ [
!\!\ !
u d
}} }&
or k
^{+ }.\]
}) !
Av g
Y X
\ :
u f
w v
ti e
}}) &\
}_{* },\
Ġcom pact
la tive
Ġ& .
})] +
7 20
k G
Ġs ing
ĠK er
ne l
}}{ -
)} >\
Ġ\[= :\
osi tion
I R
Ġ )\\
Ġ& &&\
Ġ3 8
. -
\ }}+
\ }:\
}} }}(
de v
}^{* })(
}^{+ }}(
}$ }\\
S k
)) |_{
cr ys
13 3
N o
Z F
}\ })=\
ri c
)) ]\]
}\| ^{-
}}{( -
D B
K P
S f
Ġ lin
}}{ =}\
)}\ }\
}}}{ |\
}}\, |
[ [\
m f
Ġ }}+
^{* \
H t
N k
h p
}}) <\
l v
}_{ {}_{\
Ġcon st
K U
Ġ res
00 6
mi ze
}^{- (\
Ġd f
l f
}& =-
_{- }=\
\ })^{
^{* }/
}[ [\
Sub set
z u
Ġ +|
{] }\,.\]
, ...,\
}: {\
ol d
)^{* }(
F L
k L
| }-
Ġin v
(| |
T A
^{* }}_{
}\, =\
))\ }\]
\! =\!
Ġ )}^{
}| }=\
{\{ }|
24 6
Ġdx dy
ori thm
y t
Ġ\ &
^{\ ,\
}< -
^{* }&
})+ |
Con f
}) $
}) )/
sta b
so ft
}( *
,\, -\
Ġ5 00
Ġ }(-
)=\ \
A H
p b
|^{ (
T e
co f
00 7
})\, =\,\
jk l
bow tie
P B
\ }},\]
N D
] >
x q
}^{ {}^{
E u
Ġ top
ĠE nd
0 20
v mode
| &\
er ence
{) }=-\
}& &\
leave vmode
) _{*}\
; (\
g d
}) _{*}(
})^{ [
sma sh
! }=\
P H
g H
q a
Ġs pace
ĠE rror
F x
G ap
s ys
}} }\,.\]
\| )\
)) |\]
}(- ,
K t
at ch
^{* }),\]
Po i
x w
\[ <\
}: \{
O M
}}, ...,\
M x
n z
}) ],\
^{* }:=\
Ġpa rameter
âĢ ĵ
}} ]}\
)=\ |\
\| [
Ġ\[= |\
z f
Ġ ta
{\ }}+\
ĠC L
)}( {\
Ġw hi
U B
^{ >
et we
etwe en
0 13
}/ {\
ĠI nt
| )\,
}^{- }+\
)} ^
}\|=\ |
Ġst rongly
* }_{
_{- }^{-
_{+ }}(
on al
Ġ4 4
pen dent
}) }>
circle d
. },\]
}{ (-
}^{* })+
))\ |_{\
* _{\
F D
Ġ\[ {\
})= |\
Ġ\, ,\
! }+\
^{ !}\
text circled
}] =(
&& &&\\
I T
s ol
math ord
}) }&
}}) ^{*}\
,* }
bre ak
5 76
| }\,
|_{ (
. }&\
A n
F or
})\ }
})] -
}): (
R ad
i ck
Ġ\ ,(
}}) :
})}=\ |
Un if
Ġ sim
_{* }:
^{[ *
Ġ:= (
e pi
o tal
}) _{*}(\
ll ll
up beta
}\ }^{\
^{* }})\
); (
}] :
}] }=\
Ġ} &\
^{( +
Ġ4 5
Ġ }}=\
ma tion
}}\, {\
R i
s ph
ra tion
Ġ\( [(
{] }.\
T ype
{) }^{(
}] /\
n se
| )(
Ġs olution
)\, ,\\
K O
\[ {}_{\
{\ {\
A rg
C rit
I D
M K
)}\ ;
}^{- }-\
11 4
]= -
( {}^{
0 16
8 00
k in
Ġ data
)) }+\
)} })\]
}|\ !|\!
})] ^{-
Ġle ngth
}] =-\
)\; =\;\
}) }).\]
{\ ,\
g ph
}^{ {
^{- }|^{
ĠMe thod
u a
), ...,
}}}{\ |
@ @
}\| ,\
\[ +(
{) }+(
))^{ -\
99 98
$ }^{
_{- }=
}\; ,\
Ġ{* }
_{\# }\
R c
Ġv al
Ġsatisf ies
Q M
}}(\ |\
}}) [
Ġe v
T D
ci te
\ }},
] :=
)) }{(
on s
( (-\
Y Y
\, -
Ġ_{ +
\( {}^{
| }+
}| },\]
Ġt w
lead sto
}),\ ;\
eqq colon
})}{\ |
Ġu v
}/ \|\
12 7
22 5
ru e
n ing
Ġ} }_{\
})} <
})| +|\
K e
X Z
^{* ,
^{* }},
Ġ( {\
ĠT h
Ġp rop
) }]_{
Ġpa th
A ss
_{ <\
{)}\ .\]
ĠT M
\,\ }\]
}{| |
Ġif f
)! }.\]
ĠO r
V R
y ing
al most
}] }.\]
},\ ,\,
{) }=(
vert ex
Com p
s z
\, +\,
{| |\
)| ^
) }}{|
r z
}:=\ |
}) }\,,\]
lo ze
lin g
C W
Ġ3 9
}}| (\
loze nge
J Y
Ġv alue
\[(\ {
S x
u g
| [
)= +\
\{ {\
^{+ }=
24 5
Ge o
Ġ& =-
us ing
)+ [
ĠE xt
D V
x g
A p
Ġ )_{\
}\|_{ (
ĠS U
^{+ }}^{\
, <
| }\,\
ra int
{) }}.\]
)}{ =}\
{\| }(\
,+ }(\
\({ }^{-
+ -
V aR
Ġ }),\]
Ġ=\ ,\
t ing
ig en
\|_{ [
Ġp oly
{\{ }-
Ġ4 9
})\, |\,\
\[- (\
eff icient
2 12
> \]
J v
P ol
Ġ_{ *
}> (
G R
n H
w u
co st
u ct
igh t
)}_{ -
64 0
Ġpoint s
Ġvar iable
2 10
in al
{( }(-
Ġ+ (\
)}\, ,\
no ise
{) }}
sta ble
4 14
> -\
E L
Y T
} !}
ve s
) })_{\
ĠC ase
)| )\
})_{ +}\
^{+ }-\
})} .\
en tial
}}:=\ {\
E G
a ss
},\ ;\;
tri bu
Ġf orm
}}) <
ĠB V
)\, ,
{)} <
)< (
E H
g t
A F
}\ {(\
}\|_{ *
ĠE x
23 5
})) <
): \,
dr d
Co st
| )+
}= {
Ġ\[\ {
}^{* }\)
Ġ} ;\
}/ \|
})&= &
H o
)| }\]
ĠK L
,& (
Ġ:= -\
N n
big odot
}|\ \
}), ...,
}}[ -
up mu
}}\ ,\,\
}] ]\
)&= &\
when ever
p v
de al
Ġ\[ >\
re ct
}_{- }
76 8
o v
^{+ })\]
([ -
Ġ{* }(
H D
N K
ma ge
)}\ .\]
}] <\
/ |\
R ob
| (|
) })}
A r
S Q
Ġ }},
))\, ,\]
}} ],\
cal ly
}] [\
})| =|\
E X
\ }}^{\
ra nge
}| }+\
)- {\
E D
E F
Ġ hi
},\ ;\;\
R IS
] )^{\
c w
de pendent
00 9
Ġdeg ree
> _{
_{* }.\]
_{+ })
for e
}})\, .\]
Ġ }{|
}_{\ ,
}] }^{
q e
ll corner
Ġc d
Ġh ave
33 3
) }-(
] +(
_{\ _
})_{ |
11 5
\}\ }.\]
cent er
N I
w eak
var liminf
sq subset
\}\ .\]
k y
w z
}\ }\)
leq q
Ġ{ |\
}}=\ {(
st em
ĠD iff
(| |\
Ġconn ected
+ }_{
: -
L x
}\ })=
,- }\
MM D
( {}_{
Q C
}^{* }),\
{| }+
)| }{|\
O R
Ġd w
\[[ [
)}, &
Ġ9 8
S u
d C
Ġ ^{*
in ct
\, ;
}}:= (
Ġ multi
Ġ}\ |^{
Ġ^{ (\
Is om
! \,
ĠG r
Ġ4 1
})| }{\
0 14
f x
)\ ;\;\
)\, .\
f v
j u
me tric
ĠC C
)},\ ,
D t
U L
}^{* }|^{
{] }<\
23 6
leftarrow s
}) }^{-
}{ +}
)\ }}\
{(}\ {\
11 6
}_{+ },\]
Ġ\| (
]\! ]
]\! ]\]
, {
E C
b k
var Pi
^{* }}=
Ġi r
Ġp o
ĠPa rameter
}| },\
ĠC T
Ġ }))\
}} }\|_{
right leftarrows
Ġw e
\ )\
}}) &
un iv
Ġd m
ge bra
di c
R K
Ġ\( |\
)_{ [
{] }^{-
48 0
,* }_{
I G
| /\
}^{- })^{
}\| <
Ġgen era
L v
\| ^{-
}}) }(\
}}} <\
))= -
\; (
Ġ9 3
}]+ [\
) [-
Ġ )}(\
})^{ (\
\[\| {\
maxi mize
! (\
Ġ( |
... +
]{ }\
K l
f h
f w
+\ \
^{* }))\
{] }(\
11 7
, }\]
N F
u k
Ġ opt
}| ).\]
})}{\ |\
})\; ,\]
M V
| ),\]
}) )|
}^{* ,\
}& :=\
)}=\ |
&* &
o bj
}\ }|\
}}) },\]
,- (
Ġ7 2
R A
d D
Ġ }},\]
}{ -\
us p
Ġd V
- )\
}\ }-\
}=\ \
ge t
}^{* }\}\]
Ġt ran
triangleleft eq
E mb
N d
| }=
Ġ )|
}] \)
Ġt ot
{- -
}_{+ };
\|=\ |
t K
}] },\
}}) ]\
Re LU
Ġ7 0
}}^{+ }(\
C ol
j b
n il
}} ...\
))\ |\
dt dx
Ġfix ed
# \{\
. }}}{{\
Z Z
}^{* }|
\, +\,\
_{- })
10 3
^{+ })
}:\ ;
)\! =\!\
= ((
L f
R H
}\ })
lo op
^{- }}(
C d
t l
}^{- }_{\
Ġs qu
}}) ]\]
Ġconv ex
) })\|_{
D X
17 28
so c
) }}\,
Ġ cr
perf ect
)\, :\,\
]=\ {
0 21
m N
| }}{
Ġ\(\ |
}}:= (\
r h
re n
}}\,\ |\
)]\ ),
{| }>\
ĠA u
side set
d j
}} $
var triangle
ĠC d
Sp c
Ġcomp onent
Ġm n
iz ation
| :
\[\ {\{
_{* }}^{
$ }_{\
] }{(
b v
Ġ&= &\
! },\]
R W
Ġ= \]
_{* })^{
}}= {\
] }[
! ^{
N s
u es
le s
}:= [\
T U
)\ :
Ġn x
G G
N x
)) &
)) ),\]
Ġ+\ |\
6 18
A tt
R N
t es
Ġ eq
}} })=\
Ġ( [
}},\ ;
}}^{* }=\
s I
| }-\
^{* }=(
^{* };\
Ġ} &
M f
qu e
Ġ2 56
O L
Ġ ap
], [\
( .,
) })\\
A w
}} }).\]
li z
}} }(-
}] :=\
})+ \]
* (\
D ist
l c
l cl
Ġ })^{-
\ }<
\[\ {[
},\ ,\,\
^{* }\|
Ġd X
16 2
^{* }}+
K n
Ġ }}-
}\ }=\{\
ca use
ĠR ic
Ġg rad
Ġ:=\ {\
D W
K h
}})\ )
10 9
V u
| ^{-(
{| }_{(
Ġd p
ge s
,\, |
13 1
g u
{\| }|
Ġ4 3
du dv
Rob ba
ul corner
_{+ })\]
}_{* })\
}}< +\
6 00
i N
}} &-
}=\ {\{
ce n
dy ds
})\, (
g k
ho l
}\; =\;
: \{
}\ }\,.\]
}_{ [-
{\ }}\,\
fo ld
\[[ -
Ġma xi
P x
y e
rel y
) }}}{{\
N et
{( }\,
Ġ\[ [\
}] &
}] ;\
)+\ |\
an ti
$ ;}\\
\[( |
}. \\
ia nt
ale nt
$ }}}\
F R
M r
f il
| ,|\
}) _{*
}} ],\]
^{- })^{
}^{- ,
})| ,\]
):= -
| }{(
}{ }^{-
}^{* }}^{\
ĠA B
})) },\]
Ġ* }(
3 56
< _{
}^{* -
Sh t
$ }}_{
K R
}| }-
}}) )^{
}}= |
Ġin c
c N
var Psi
Ġm on
Ġ9 7
96 0
K N
M ul
Ġ\ .\]
\| <
}}) +(
Ġd im
ĠL i
\! :\!
4 32
K H
O C
}{ =}
la n
ll l
}| /\
co r
Ġ\[=\ {
+ }\]
h l
k c
11 8
Ġh y
\ },&\
m ot
}} /(
}}= \]
)] }{
measu re
E A
me s
{| }<\
Ġs c
})( -\
}|_{ (
Ġn p
sp in
}}\| \]
}_{- ,
}}^{* })\
si an
Ġ} ;
}}) }=\
)}| \]
Q T
c ed
}_{ =
\| }
}\, {
}})\ }\]
10 6
20 1
L HS
N B
l h
ra di
)= ((
_{- }+\
)| -\
Sp f
},\,\ ,\,
Ġwhen ever
] <
}\ },\\
hi ft
ĠH F
}* (\
a nt
ti v
}},\ ;\
}; {\
\}\ }\
Ġ rad
)\ |=
;\ ,\,
_{* })=\
\[[ (\
905 512
t C
^{* }}-
^{+ }}^{
o od
)}\ {
)) :\
{{ *
S m
Ġj k
Ġ5 4
ut e
Ġ left
Ġp t
}})^{ -\
Co ker
{)}\, ,\
] )+\
}{ -}
W h
c limit
)) }(\
_{* *
Ġinteg er
: \\
}^{* }=(
\, -\,
Ġk er
B H
R HS
g v
{ .}\
{\{ }\|
succ curlyeq
}}) |\]
)}{ }_{
ĠB o
\}\ !\
Re l
an n
^{** }(
M I
}\ }(
}= +\
_{[ -\
P re
h igh
Ġ sup
}) }}(
Ġc t
)| -|
ĠI nd
homotopy climit
SI NR
$ }^{\
0 24
J M
M t
de p
}_{\ ,\
}^{* }\|\
ĠD a
)] (\
)] \\
13 8
con n
Ġco st
3 24
Ġ }]\
}:=\ {(\
10 7
sk ew
Ġpa ir
X t
}^{* })}\
}\, ^{\
}; -
14 7
}^{[ -
Qu ot
x I
}\ )-
{( |
16 7
cy l
! /
! \]
+ (-\
\ };\
f p
| }}{\
text sf
})+ (-
17 5
}}\; ,\]
H z
}} }:\
)) ^
{)}\ ,\]
))\ )
22 4
01 9
Ġequ iv
F C
{) }&
Ġf i
\, ;\
Ġ4 7
A N
C k
ri s
ĠS h
01 8
}$ ,}\\
a in
i id
or y
))=\ {
Ġ7 5
,* }^{
3 11
b h
ti cal
}| &\
^{* }},\
_{- }\]
Ġ+\ |
- }^{\
O r
X A
\| >
ine ar
ĠAlg orithm
S cal
\ }),\]
}} })=
ĠMe an
Ġvec tor
v f
th ick
(\ !\
}}) :\
Ġ4 6
13 0
Ġ8 1
Ġsu rely
y l
}} }:=\
}}{ }_{\
00 000
}[\ {
}:= -
\; (\
or mal
Lo S
)}& =\
) }}\,\
Ġ}\ |_{\
_{+ })^{
})\, =\,
Ġ si
ho r
})=\ |\
Ġ }]
}|\ }\]
Ġwhi ch
. }}\
: {\
B a
] |^{
| _
}\, -\,
or der
))\ |^{
}\|\ ,
):=\ {(
diamond suit
Ġinf inite
Ġcond ition
% )
) })}\]
| )}
Ġ exist
Ġ\[+\ |\
}}}{\ |\
})& (
Ġ* }
C a
Ġ}\ {\
}& =(
_{+ ,\
{\{ }\,
\; ,\
)\| .\]
{\ #\
Ġf ac
}}\, (\
14 98
sti ma
ĠC l
ĠT ra
})| >
}}^{* },\
,* ,
s pace
{ >
}}) |_{
}^{+ }\\
|\, .\]
Ġel se
K G
i Y
Ġ ^{*}
la y
Ġ\( |
)& :=\
= &\
Q D
}+\ {
)) }+
)- (-
ĠL ip
Ġc n
em ph
Ġ\| (\
B N
c frac
}}^{ (-
/ [
A I
P X
{ ``
pri m
^{- }=\
}{\ (
\| -
}), -
14 6
)}+ (\
E I
b g
)} _
\[\| |
}> \]
+ +
J e
to n
{)}\ |_{
12 9
_{- }}(
}]\! ]\]
center dot
0 22
p li
Ġ |}\
Ġ proj
)\ ,\,
to tal
}] .\
}&\ |\
Ġb a
Ġb etween
}$ }\]
C ase
q b
Ġin d
})\, :\,
)^{* }=\
I K
R V
] })=\
] }\\
h D
:\ !\
ĠP r
Di sc
0 23
De s
}[\ ![\
})|\ ,\
&& &&
Reg ret
. }}}{{=}}\
G x
Ġ vertex
th en
ra nd
da ngle
Ġ{ }^{
)) },\
}\| }\]
Ġc losed
Ġs y
_{* }}(\
7 29
H N
a ng
f a
}\ }-
th o
ĠC E
\, _{
]\ .\]
H d
)^{* }=
}}^{+ }
}\|=\ |\
measure dangle
] [\
i rr
Ġ }),
^{* }}-\
ĠC F
Ġ6 6
( *
U C
Ġ\ ,\,\
)- |\
_{- }-\
ĠM od
Ġ )}.\]
in ing
^{* })}{
Ġd om
}}, [
}}+ \]
Ġre d
) }}|
N h
k z
p z
})\ |=\
er gy
})| <
prec sim
Ġ7 8
D ol
] ^
k A
}}\ #\
Ġg raph
{|}\ !\
}}^{* }}\
Tra ce
1 99
G rad
] )+
m is
}+ (-\
J K
m v
Ġ{ }^{\
pa th
}}+ [
6 25
t D
ga ther
ro ot
^{* }}+\
lu x
\ }=\{\
b it
wi st
un if
(- (\
)\, (\
Ġdist inct
9998 63
s cal
)}\ ;\
\|\ !\
ĠS et
Ġor d
! |
R o
V A
] )-
Ġ [-
ti o
Ġ\[ :=\
}: \]
}^{* }),\]
ble m
15 2
{/ }
3 22
Ġs ol
gather ed
h G
},\ ,(
Ġ}\ ;\
\|\ \
_{- })\]
}^{+ };
ĠR eg
}> -\
14 2
)\! .\]
ĠDa ta
=\ \
}}\, =\,\
}|< |
] )_{
m K
q m
u z
}) }}^{
}) )).\]
Ġ\( (-
}}: (
CV aR
D H
}| }+
om orphism
}^{+ }\|_{
)\, :=\,\
^{\# }(
. ,\
0 27
Ġ )},\
la nd
}|\ {
Ġm s
}\ }&\
)\| =\
64 8
C Y
| )+\
~ {
&= &\
Ġ&&& &
# (\
K x
a N
}{ {
ĠC PU
Ġs mooth
_{* }\|_{
{] }}{\
ab a
&* &*\\
}] \,.\]
}}) ^
,- }(\
ei ther
Ġsqu are
- ,
A Y
^{* }}.\]
te rm
u dx
}\ }}{
}}\ }_{\
}^{- })
11 9
}}\, |\
}< ...
L k
M H
P ri
la g
}([ -\
/ \|
n omial
Ġ }+(
Ġ ^{*}(
al se
}}) ,(
(( (
Ġ6 5
}+\| (
56 7
Ind Coh
ur corner
1498 15
j x
n M
_{ :,
op p
Ġn e
\[\| [
}< -\
Tr op
\[= \]
Ġ9 1
: &
\ }}}\
}] ),\]
)) >\
}\| >
ve d
/\ !\!/
10 10
] ),
}) )=(\
}} ]+\
^{* })_{
}] }=
Ġg iven
... \\
Ġ5 7
Ġ5 8
})) ]\]
A J
}^{ {}^{(
)}\ ,\]
\, {
Ġ5 5
xx xx
+ ,
V E
c L
Ġ\ }_{
}> -
Ġre al
tribu tion
) }^{*}\
S e
\ },\,
})_{\ #}\
19 6
L h
Ġ })}{
\| }\]
}&\ |
)] )\
}_{- },\
37 5
Ġme an
0 34
B O
}\ }}.\]
{) };\]
ci t
)|\ \
Ġ$ |
Ġ9 2
nor mal
) [(
Ġ sum
Ġ |^{\
^{* }))\]
}^{* }/
}_{* }}\
L d
| )^{-\
ĠC S
)( |\
In f
Ġle ast
] ;\]
}| }(\
Ġe i
ĠR F
}_{- }}\
99 99
here nt
Ġcontain s
] )}
s ig
ĠC A
}\, :=\,\
13 7
|}{\ (
Cu rl
E V
Ġ\ #\
me d
}^{+ })=\
{\{ }|\
}]\! ]\
}) }:
Ġf d
{\{ }\,\
): |
01 7
Ġmeasu rable
. }&
W A
| }}
Ġ }}=
}}| .\]
Co nt
N r
\ }}-\
h b
Ġ tri
le d
}] }|
})^{ |
ĠS ta
5 000
T W
c g
q d
v E
^{ +\
)| )
ĠP o
})) )=
Ġ7 6
\( {}^{\
] _{(
ra cle
)\ ),
}] :\
Ġe ss
ĠH S
)_{ |\
)] ,
2 64
k v
_{* })=
Ġin dependent
Ġcon ver
fin ition
Cor r
A lt
j d
}|\ |
ĠOr der
, >
D x
O bj
P Sh
m z
})\ {
Ġ1 13
^{+ }+\
]+ [\
F I
}\ }}{\
ma n
}^{+ })}\
15 5
' '
8 998
}\ }).\]
})\ }^{
}| )+
}\, {}^{\
}}_{ {\
ĠT V
})| |^{
Ġ5 2
Ġco efficient
| +(
Ġ ))^{
Ġ& (\
}\| }{\|
Ġh e
{\{ }\|\
* }_{\
y w
}) }^
Ġ= &-\
ĠV alue
check mark
18 4
t S
Ġ }}{(
}_{- }^{\
con j
Ġad j
; -\
S ta
S tr
W E
{) }:=\
}] &\
{] }\,,\]
11 00
}=( (\
17 6
sti ff
r N
Ġ li
}^{- }}{
Ġ\[= [\
SA T
B ar
G K
_{ .
^{- })
De n
}}) =-\
)( (\
16 9
}_{+ })}\
Ġdi am
Ġro ot
0 28
F A
s N
| ),\
Ġ ga
Ġ end
Ġ }}|
}) )\,.\]
era tion
Ġd d
ĠR ate
14 3
verti ces
. }}{{\
m y
}} })^{\
}{ }
}}_{ =
Th e
23 2
)\! =\!
T d
] }}(
Ġ can
era tions
15 9
ome o
]\! ]_{
D ir
S z
}} }}(\
}^{* }\,
}\| )\
:=\ !\
})) /\
en cy
O S
Q A
}) }}{{\
}}(\ {\
}\| }
ĠI V
)\, =\
)] )\]
,- }^{
{{ }_{
}}^{* },
tharpo ons
{: }\
V V
c j
^{+ },\]
22 3
100 00
Ġco r
0000 0000
8998 49
I nn
\ }^{-
Ġ ca
_{ +\
{) }=-
\| |\
})) :
T ri
W W
p y
t Y
Ġ quad
ra t
}{ **
})_{ [
:= [
)& =-\
Att n
, ..,
h n
m C
Ġ prod
}} }>
}}) }=
}& *
}& ...&
}:=\ |\
Ġno rm
$ }}}{\
8 64
G Sp
L t
j N
{ +}\
)) ,(
Ġd S
ĠM ax
23 3
Ġimp lies
n w
}}\ }
var iant
_{* }|^{
ĠV ol
}}= |\
bi as
) }}[
al t
}| +(
\| [\
0 30
E B
c lip
s hort
[\ !\
}}) .\
$ }(
d J
right lef
\| +\|\
un c
}}| =\
N c
i M
t P
}) })=
Ġs mall
}:\ ;\
Ġ\(\ |\
rightlef tharpoons
; |
}) )|^{
ĠC k
^{( -\
})=\ |
)( [
Ġs tep
}\|\ ,\
;\;\ ;\;\
ian ce
B v
C X
k B
)- [
}}) ,\\
)} ;\]
}^{+ }}\]
Ġ5 1
\% )
\ }|=
| }^{\
}) }:\
Ġ0 1
Ġc lass
Ġp eri
Ġequiv alent
G T
g ra
o ng
}^{ !
}}) }+\
uni formly
- }(\
Ġ ]_{
Big m
}\, +\
Ġ\[=\ ,\
_{+ }.\]
})) )=\
}{*}{\ (\
Ġdo es
ĠMo del
F it
] ,\,\
] \,,\
x h
Ġ ss
{) }/\
})+ |\
em b
33 6
cl ub
M B
u y
}) })=\
Ġ1 20
) }]=
S at
}) }=(
me an
{) }/
32 6
A g
] \|\
a ge
Ġ }^{*}\
}}= :
))^{ (
18 9
|\, |
Ġdef ined
Ġma ny
Ra nge
Ġtw o
d ig
Ġ right
^{ =
}| =(
ĠD f
,\, (\
val ue
& ...&
F B
^{- {\
)] }{\
vi al
! -\!
V I
n I
Ġt rue
{)}\ !\
club suit
S tar
W D
}\ {|\
qu ence
^{- }-
)}, ...,
|| (
Ġ7 7
r T
u al
Ġ app
^{* })}
\, =\
* }\]
A L
n et
w ork
su re
or el
{\{}\ {
T Q
U T
] ))\
c usp
o dic
}} ],
}\, {}_{
\, )\
{| }-\
ge om
)}( [
})+ {\
R ed
a xi
u i
}\ }]\]
&& &\
,+ }^{
4527 6
\ }}-
Ġ })}{\
}) }(-
}} }}.\]
si s
}& :=
ĠM SE
L IS
Q S
u h
}) }},\]
Ġ\[ -(\
^{* })\|_{
Ġ( (\
Ġb i
14 8
0 35
3 32
A c
M v
] }}{\
] \|_{\
Ġ )/
^{- })\]
}\, [\
),\ |\
ĠE q
Ġ(\ %)
,- )\
,+ }_{
. (\
T B
b ad
q j
}( {}^{
=\ {(\
Ġx x
}), {\
}; [
16 4
{{ }^{
)! }{\
Ġ7 9
Ġ&= &
8 45276
I f
] ))\]
i K
}| }=
ĠT otal
_{* }|\
}; (\
24 8
V al
v r
| )}{
in dex
ĠM L
)! !
S K
!\ ,\
) }]^{
= &
c lo
co herent
}& |
\! (
}}& (
28 0
})^{* }=
# }
n D
{( }-(
p g
ĠC s
}/ |
})- {\
Ġ+ |\
Ġ5 3
Ġto tal
P CA
Q Q
| [\
_{ ;
Ġ6 7
{, }\\
$, }\]
Ġdi mension
Ġsp e
: \|\
F X
f s
v y
v z
at ed
\| )^{
Ġd A
Ġe igen
Ġr s
&\ ,\
ĠU n
}\; (\
Ġ8 5
G O
}} }\,,\]
}\| -\
_{* })(
}_{+ }}(
})\, {\
Ġ5 9
})) ]\
lu e
no break
}\# _{
Ġpar t
$ })\
Ġk t
\[\| [\
Ġg r
\[[\ ![
Ġ\, {\
S i
a ut
| },
Ġ rel
}) )]
ga tive
ĠM at
^{+ }}{
16 5
$ };\\
F e
i th
y f
Ġ }^{(\
{\ }}\,,\]
big star
}}+ {\
Ġg roup
}}[ |
ne ss
88 6
) }]=\
H g
\ }\,,\
k ij
Ġ ve
Ġf ree
, {}^{
. }\\
w y
}} }<
}}\ ,\,
ĠC a
re du
ĠB C
})- |
}})\ |_{\
Ġ6 8
}})\, ,\]
ective ly
G en
M n
Q H
h j
p oint
t V
ph ys
^{- }\]
)) }+\|
})= :
)| }{(
cccc ccccc
pe ri
M u
Ġ low
}+ ((
er y
}^{- }.\]
\|_{ {\
}^{* }[\
), ...,\
it er
}]- [\
H y
n subseteq
Ġ subset
^{* })}{\
Ġt est
}}) ),\]
15 7
]= (\
Ġ6 3
+ _{
I O
\ })}\
q y
{\ }}\,
Ġ& +(
Ġb lock
Ġme thod
) }}}{\
H u
I A
] }}{
}}^{ [\
ĠC K
dt d
Ġ7 3
36 8
supset neq
)\; =\;
i on
k H
le v
ar m
ex act
ĠC H
}^{* }&\
})^{ |\
)},\ ,\
25 7
Ġ8 4
)=- (\
x b
Ġ cu
us t
{)}\ ;
ĠD F
}_{+ }=\
20 8
}}] -\
c M
Ġ )}+\
ĠT ype
_{* })-
): (\
en v
}},\ {
))\ ;
let e
21 5
Ġ8 9
})_{+ }^{
T Y
^{- }=
co ev
:=\ ,
)] }
)] =[
Ġ7 4
}<... <
T E
b X
Ġ ]}\
)}\ !\
ce ss
})< +\
)^{+ }
}|+|\ {
Ġmin i
\| }{\|
}\| |
<\ ,\
Ġin dex
Ġ6 2
0 48
J S
] )-\
i P
v c
Ġ subject
{\ }}.\
)+ [\
Ġk x
ĠS E
Ġlo ss
U f
] }:=\
)) :=
}\, _{\
}^{\# }\
scri ption
! }\,\
H od
\ }(\
^{ !}
ĠT x
}^{+ })=
}), [
tr y
)}}\ \
_{ =
}) )}(
}) )+(
^{- }+
Ġn ew
}[ ]
ĠE xp
}(- (
15 4
))- (\
|< |
Y M
Ġ operator
Ġ )}_{
Ġ }}\,\
|\ |_{
)= (-\
}] |
{= }\
FP dim
M G
y u
_{ !}(
)}_{ (\
Ġ8 8
G raph
J u
K u
] _{-
l x
m T
)\ {\
)| (\
dt ds
ĠCo v
asi coherent
{{* }}{{\
- },
E t
Ġ under
ma g
un t
}), -\
13 9
Ġ6 9
\! [
36 5
S oc
U R
] ^{-\
] ]_{
}, ..,
\|_{ *}^{
)) }+\|\
}& &&\\
19 8
Ġno de
] }\,\
}_{ (-\
}: &
})=\ \
}& {\
15 3
)\| <\
) }}}{
, }
C hi
H omeo
L K
}} }+\|
big times
}}{ =}
Ġi i
}}= :\
Ġw eight
Ad j
las si
F ree
t I
Ġ })(\
}} ]+
la st
))\ |
Ġw t
}})=\ {
Ġre pre
\ }})\
me r
})= -(
_{- }}^{
}^{+ })^{\
Ġr ot
})| (
})) &\
Ġ8 2
Lo ss
Ad m
Ġra nd
A Z
K B
g lo
i D
Ġ& =(\
^{* }}}{
}_{+ }}\]
}:= {\
! },\
T z
b cd
Ġ pi
}\ {-
Ġs ample
^{+ }|^{
ba se
)]\ !
/ {\
}{ [\
)\ (\
\{ [\
]\ ;
}}+ (-
}}| +
}* }\
be cause
Ġelement s
L Mod
P h
S pa
)}= [
19 5
Ġ:= (\
L n
Ġ row
ra tic
\|_{ (\
}\, ;
}\, -\,\
ing s
35 8
}}}{{= }}(
Ġpar ti
Ġmeasu re
! \{
H x
] )(
i ll
q v
+\ {
Ġp ower
32 8
Ran k
L N
L im
R X
] )}^{
n C
| )=\
)\ |}\
}{\ (\
}| }-\
^{* }}}
}] {\
};\ ,\,
}}\, |\,
15 8
)]\ ,\
tu re
}}^{+ }\]
3 23
E T
d ro
i X
}} }:
^{* }[\
16 6
})^{* }=\
0 40
z ero
}\, /
00 10
}^{+ }}{
cy cle
black triangle
h w
nd ard
li c
{{ }^{\
dig amma
] )}\]
l ct
w hi
Ġ )).\]
}) &-
}^{* }=(\
)| }.\]
}^{+ ,\
con stant
02 6
succ sim
)_{+ }
D U
i ed
k M
re al
_{+ }}{\
}\!\ !\!
Map s
Lin k
Ġbound ary
F N
] -(
}\ {\|
})\ },\
}] )+\
}^{* }/\
Ġa bs
}\| )\]
Ġ\( >
_{* }}{\
\,\ {
^{+ }}(\
dy dz
}< _{
) })|\
E is
Ġ nd
}] |^{
tri ct
ĠC I
Ġt n
Ġs tr
})| >\
Ġ6 1
tion al
Sp d
})\| _
Ġequ ation
E ff
)| ,|
})+\ |\
eigh bo
{: }
Ġ }))\]
}(\ ,
Ġ\[ +|
\,\ ,\,
Ġy es
&& &
F V
L emma
q T
{ }^{*}\
}^{+ }:=\
Ġma p
. }}
T ail
in st
da te
})\ |.\]
)) )-\
ci al
ĠS t
)}( -\
})| -|
)}| |\
ni form
orphi c
C U
D o
x d
}\ }}|
ti mal
tar get
Ġ} <\
Ġ= -(\
_{* };
{\| }|\
17 8
Ġ7 1
Ġbo th
C ard
f c
Ġ line
Ġ vertices
_{ |_{
}|\ }\
Ġd q
}}{( |
56 0
\ }|.\]
i J
n P
x r
Ġ })}
Ġ hom
sum ption
^{* }]\
{(}\ !\
=- (\
})] \\
33 1
Ġoth er
) }}\|
\ &
\ }]\
q N
lo cal
Ġ& \\
ver se
}^{( -\
)}{ }^{\
Ġc c
_{- ,\
\[\| |\
}_{* },
\% **
X P
] ]=
)\ }}
)}\ {\
}}^{ {}^{\
}: &\
)^{\ #
ĠA C
st ep
dy d
\# _{
}+... +\
ke w
D K
E v
R I
T m
\ }})\]
q i
Ġ ^{+
}| }{(
}}\, ,
)},\ ;
)}=\ {\
* ,
}\ }\,,\]
}^{* }}=\
}\,\ |\,\
19 4
19 7
c ell
c cu
i F
x s
}, (-
})\ }=\
), |
Ġ\[= -(
20 48
) }))
s T
se e
}}| +\
)> (
)\! ,\]
\,(\ ,
ML E
G B
\ }})
] }\,
}| )^{-
Ġb ut
}* |\
S y
X u
\ }]\]
j oint
k Q
}\ }}(\
}) ]}\
}) [-
op en
)}\ }.\]
^{* }]
}^{* })}{
{)}\ ;\
ĠS e
}^{+ }|^{
_{+ }\|_{
Ġh igh
}}^{* }-\
;\;\ ;
pa ra
}^{* };\
}}| +|
* )\
C ay
F f
\ }}_{
] \|
b er
}_{ {
}_{\ !
\) .
})^{- (
})\, ,
Ġ\[+ |\
}\; :\;
)* (
Ġsatisf ying
G E
Ġd R
Ġo bs
Ġsa me
0 45
se mi
_{* })+\
Ġb d
Ġal g
= (-\
K F
i cal
^{* }})
]\ ,\]
_{* })}\
Ġp q
})_{ |\
)^{- }\
}(- )\
)}, (
| )|\
}^{* }))\
\, -\,\
)}( |
}^{+ +
+| |
}}^{* })\]
25 5
den ti
\ };
co rr
}] ),\
{)}\ !
less approx
96 8
})= :\
)| &\
}[\ ,\
})\, :\,\
\[= (-
))}\ ,\
9 00
= +\
J N
}| ),\]
}})^{ (
Ġ8 7
30 4
})}=\ |\
Ġdiv i
}]\! ]_{
A k
I B
K f
\ }&
Ġ )}}\
{\ }}+
De c
_{- })^{
Ġ$ (\
)}= (-
34 6
Ġla y
3 15
4 20
E R
S ur
c tr
f y
r A
}( {}_{
}}\ },\
)}{ [
^{+ +
P O
ex c
|^{ |\
^{* }{\
}] )^{\
}^{* })(\
)} }_{\
]\ },\]
})) .\
)\| +\
}) ):=\
})\ }_{\
^{* }}|
)) )-
Ġ\( +
22 8
}_{* }\]
},\, |
Ġ8 3
}}] (\
XY Z
}! }\]
! }}\
: ,\
F ind
a T
| })\
}}{ ||
\| ,
)) ,&\
)| :
) })=(
: &\
E rror
f ind
h am
}} ])\
la w
}] )}\
Ġi h
}^{+ }}{\
}^{+ })_{
,\, |\
,+ }
78 4
N u
s L
in ition
)\ })\]
}| ||
nu ll
Ġ} >
ca y
}), ...,\
^{*}\ !
}> _{
}< (\
^{\# }\
Ġfunction s
Ġsta te
] }}\]
g m
q f
|\ }\]
Ġ} /\
ĠL ie
Ġc e
^{*}( (
con s
lef tharpoonup
}}: (\
! }=
w a
\, +
Ġt x
})}\ }\]
Ġ\, (\
/ /
ti es
\| )\]
ĠS H
18 5
Ġsin ce
$ }\}.\]
u rs
}} })_{
})\ }=
{) }},\]
}] }^{\
{\{ }{\
)}=\ |\
black lozenge
radi ent
C p
Ġ }}}
)^{ (|
ro l
)) ,&
ci ble
}}] )\]
tra ns
Ġsy stem
c R
h m
k f
{[ (
)}+ |
27 6
arc tanh
( {}^{\
R U
T G
c H
Ġ ]^{
Ġ curve
in n
}}) }{(
pro xi
):=\ |
16 1
25 2
\( {}_{\
m R
rc ll
)+\ \
ĠN A
}}- |
)] \,
14 9
20 11
|| |_{
)! \]
}): (\
)$ }.\]
- \]
f inite
| }\|
to l
}] >
}] },
{| }>
B s
] })=
t E
}) )|\]
}) ;\\
\|_{ -
Ġ} })\]
bul k
})( |
)}_{ [
|| }
18 8
_{\_ }
N q
s rc
}\ }:
}} }]\
am il
}] )_{
_{( (
) })|
t J
Ġ })_{\
Ġ }+\|\
}}) -(
00 11
}=( {\
)})\ |^{
99 5
)^{* }(\
& +
M p
f b
o in
ro n
ro ugh
ĠG en
flo w
Ġ4 00
22 0
}}^{- }
36 7
Ġse c
E d
F a
;\ {
Ġf irst
ĠS M
{[ }[
{|}\ {
)] }(
Ġ\[+\ |
Ġ\[+ (-
)< -
9 45
U p
g B
| =(
}) ),\\
)) }^{\
}\| [
Ġd g
lus ter
}^{+ };\
26 8
ĠProp osition
0 33
R y
U S
\ }),\
i rc
Ġ |_{\
}) )-(
}(\ !(
ĠC x
ss on
}))\ }\]
}\! (
Ġ }}|\
var triangleleft
}{\ #\
}| }^{
^{* }})\]
Ġ{ +}\
Ġn m
Ġn et
Ġn eighbo
})( {\
{\| (
}:= |
18 7
34 7
}$ }.\
Ġ8 6
I L
x A
}^{- })=\
}\, (-
Ġd vol
ĠN R
)}^{ (\
))}\ |\
)* _{
G N
] ].\]
u j
le ct
Ġ\ !\!\
(\ !
}= [(
}}{ -\
{) },&\
Ġi deal
}\|\ \
,- }_{
}. (
Ġ* &
Pa th
[ (-
)\ }_{\
}^{\ {\
Ġ1 42
)) +(\
}}) ^{*}
ĠA s
Ġz ero
Ġ3 00
}:= |\
17 7
PS H
) })\,
) }|_{\
F W
F y
a nge
Ġd n
40 5
B X
_{\ {(
),\ {
Ġn s
Ġ_{ [
Ġs te
_{* }\,\
,- },\
56 8
}}^{+ }}\
Ġinter val
: _{
W AW
t T
}) }),\]
^{* }\)
}] },\]
}}) _{(
ĠN N
}_{+ };\
24 7
}):= -\
ĠDe finition
\ }}\,
x D
y v
}) }}{(
}_{ ,\
)=\ {(\
pre d
}+\| (\
34 4
)}| |
!|\! |
N b
{) }^{*}\
)) )^{\
box dot
,- }/\
20 4
\! {\
64 5
Ġ** -
499 9
) )}\,
E CH
t F
}= ||
}\, ;\]
))\ .\]
):= |
17 0
Ġse quence
}|\, .\]
! |\
) _{*}
4 35
< (\
L H
a A
}_{ :,
\|_{ *}\
)& =-
02 9
Ġdi sc
Ġequivalent ly
Ġrand om
: \]
w ard
}\ }|\]
ma t
})\ ,\,\
}}) ]
un lhd
^{+ })^{\
):= [
Pr op
ic ro
75 0
})< (
' s
a da
}] \,,\]
}\,\ }\]
})+\ |
}}| >
Ġpoly nomial
< \,
{\ }}-\
ri z
Ġc s
Ġc ent
}^{+ }}^{
})) >\
is tic
IJ K
Cy c
Ri em
^{* ,\
}}+\ |(
{] },\\
ĠQ u
)! }=\
,& |
B z
K E
] .
] )^{-
i C
n V
v dx
}) ))^{
pi tch
li d
or e
re m
{] }}{
for k
}))\ |^{
17 4
})& -\
h A
m dim
}) )}=
bo und
}\|_{ [
)^{- (\
sta t
)] }\]
up alpha
26 7
}_{\# }(
. )\
B Z
D O
p N
Ġ split
Ġ }}\,
}=\ {[
}}) )_{
}_{+ }-\
000 5
M E
N V
e th
n sity
| )\,\
Ġ }}\|
}) })^{\
}) }_{(
&\ ,
}] }\|
}^{- }}(
ge ne
ij m
ĠB S
}}, |
})| }
)> -\
30 8
03 8
60 8
Ġ{* }(\
0 32
\ }|+|\{
Ġ err
\[ *
pri or
er v
ho colim
{) }:\
}] \|_{\
ĠB orel
16 3
23 7
19 0
Ġtra ns
g z
}\ },&\
(\ #\
{) }{\
}}) :=
Ġk l
Ġ:=\ {(
sy n
pitch fork
K d
Ġ }}}{
ti m
}{\ #
20 5
)\! +\!
? \]
O pt
h c
Ġ cap
{\ }}^{\
}}} .\
21 8
)! )^{
{= }
34 8
})] )\]
)^{* }.\]
40 96
J H
J W
\ }/\
] }(-
s eq
}( :,
}) )}+\
}\| ,\|
Ġ= {\
Ġk n
ĠS ing
21 7
Ġno ise
Ġla w
aus sian
- })\
T ime
X B
f erence
r K
v p
| )=
}\ }.\
}) *(
}| ^{(
): [
17 9
D z
}^{* }}}\
}^{* }>
Ġt f
}\|_{ -
}^{+ },\\
ĠR S
)! }(
\[[\ ![\
( +
D r
I u
] &=\
b ib
y b
le ction
{) }[
Ġ{ {\
)) )+
}\, ;\,
Ġa ss
)}{ -\
_{+ })}\
^{+ })=\
})\, ,\\
18 6
Ġex act
Q f
b lock
}= [-
}: -
{] }}\
21 9
)}- (\
tiv ity
. )
] )=[
z a
Ġ tor
\[\ {|
^{* }\,\
ĠS C
ĠT est
}}{( (
0 37
L r
] _
k C
v d
x F
=\ !\!\
})= ((
+( |
Ġin i
is H
) }}|\
- -
A o
P N
i ve
z g
| )-
Ġi a
}/ |\
))\ }.\]
ĠM in
_{+ }}^{
33 8
is k
78 9
ĠCon v
TN D
H am
w eight
z h
al f
\[\ {{\
)) }}\
Ġi e
Ġf ull
)| )\]
^{*}\ }\]
})\, |
})\, (\
23 8
], &\
})] }{\
* }^{\
)( {\
equ ality
)\,\ |
Ġo b
Ġ+ &\
24 4
15 1
})|\ \
Ġ| (
Ġconst raint
Fit t
bib ref
) }}}
> _{\
B PS
\ },&
x P
}) },\\
{) }:
co eff
}\, ;\
Ġ} <
_{* },\]
})| ^{-
))}\ \
)}}{\ |
Ġsu ff
)_{+ }\]
Ġdis tribution
$ }}{\
& [
8 110
] }}(\
Ġ lower
^{* }}\|
\| (-\
Ġp la
_{+ }[
\}\ {
\}\ ,\]
gen ce
}}\!\!\ !\
2 96
i S
n B
}{ ((
}, *}\
})\ ;\;\
li cit
^{* })(\
\{ +
)}( (\
)| ,|\
Ġm ix
{\| }_
^{+ })=
en c
Ġtra ce
V M
ig gs
in s
|\ }\
_{* }[
}\|\ !
}})\ |^{
25 8
J A
L arge
s hift
y g
}) }({\
}} }}^{
}_{\ {(
ds d
nu mber
pa ir
ĠC m
ĠT N
_{+ },\]
\},\ {\
35 7
Ġle vel
Ġsim ple
p L
t R
ra te
ho ld
)}{ -
re ad
],\ ;
}]= (\
}}[\ |\
8110 24
e k
i I
al y
}}) [\
re qu
ĠS T
_{* }}^{\
dy n
Ġre du
4 48
H erm
d ing
h s
k D
m M
| .\
}) })_{
}^{* }{\
}^{* })\|_{
ĠL inear
}},\ {\
ĠN on
}}}\ }\]
]= \]
pe rm
})^{+ }\]
})\ }}\
at t
^{* -
}& |\
ĠM ul
}^{+ }}(\
mod ule
Ġvariable s
H a
N f
c A
Ġ })}^{
ra cy
^{- }}^{
}| )+\
{) }}{(
}] ]
{| },\
\[( [\
_{* }).\]
Ġ\[=\ {\
}}| -
G u
i E
\, +\
Ġ- |
... &\
\!\ !\!
99 6
diag up
}): \,
ĠSp in
H W
w d
}{ =
\, ;\]
14 1
Ġde c
R r
\ })-
] }).\]
p A
t M
}) )}=\
}_{\ {|\
ĠK e
20 6
)! },\]
Ġth an
Ġ }}^{(
pri v
}| ]\
}}) ,(\
{| }|\
,\, {\
40 8
sa tisf
Ġlo cal
N orm
le vel
ap e
chi tz
ĠS ub
_{* }}\]
12 12
))}\ |
;\;\ ;\
redu cible
A q
[ -(
m A
s ample
}) }}=\
\| }.\]
:=\ ;\
st e
}}^{* }=
})) :\
): \,\
}}^{+ ,
$, }\
Ġsupp ort
Ġedge s
] }\|_{
}) ...
}}\ }}\
re nt
_{+ +
})| }\]
)\| (
04 9
K v
L W
| }\|\
}\ };\]
}) !}\
}} }),\]
hi t
}^{- })=
}\, {}^{
}}) }^{\
}}) _{*}\
{] },
}^{*}\ }_{
)(\ |
20 7
27 2
)}}{ (\
}! (
)^{+ }\]
Ġresp ect
i R
m D
^{* }}}(
{) },&
}}) =-
), |\
ps chitz
Ġis o
}_{- })\
)}}{ {=
]}{ [
mis sible
A Q
N g
f ar
i sh
ĠO ut
\; =\;\
an nel
05 0
29 4
In c
_{\# }
Ġquad ratic
c ross
{ }_{(
Ġ })\,\
le c
ri es
}^{* }\|
}:= (-
23 9
|| |
In j
\}+\ {
ĠAv erage
D Y
J E
\ }}\,\
^{ <\
)\ |^{\
\| :=\
}^{* }},\
Ġc over
Ġe m
{)}= \]
}^{\# }(
})&= &\
Ġreg ular
T K
X f
] })_{
s X
u lation
y a
| &
par se
Ġra di
+ {
, (-\
C z
F lag
}^{ <\
}) )}\\
}| |\]
}] +(
}}) },\
Ġ)\ |^{
99 7
K os
N H
V D
f k
s pa
Ġ )}-\
}} }=(
}| }\,\
}| (|
)) ;\
ĠG al
Ġal gebra
21 4
):= |\
25 9
che me
\; ,\\
]{ [\
eri or
asi s
{}{ {}^{\
rid ge
3 13
I X
Ġ }_{(
^{- }}^{\
}^{* }]
Ġ2 50
)) )+\
_{* }:=\
ĠN S
)\, +\,
Ġ&&& &\
]{[\ @@
> |
M h
T g
| )}{|
Ġ }+\|
}\ }/
(\ (\
}}\ }=\
lo ss
}, :
^{* })\|^{
}^{- },\]
)) )_{
Ġi y
Ġn b
_{* })+
Ġ\[= \]
Ġ- $
ĠP re
};\ {\
})| }{|\
)\| +\|
03 9
}) )\,,\]
^{* (
})= &\
};\ {
|\, ,\]
Ġno des
g b
}) !\
si c
co k
}\|_{ {\
_{- }.\]
)|^{ -\
vol u
})^{* }.\]
val u
&* &\
$ }}\,
) }]^{\
< _{\
P Z
}| )}\
ĠI rr
Ġr k
}; -\
per t
}_{+ }+\
})| ,\
\[[ {\
\! =\!\
Ex c
$ )}\]
0 56
J Z
K r
T a
h ull
o racle
Ġ arc
}} }((
)\ }+
}] {
}^{( {\
Ġn ear
)} .
]\ ;\
})( (\
Ġ* }(\
)\! -\!\
! )^{\
7 32
q w
v q
(\ {(
}| |(
)) ),\
Ġf in
}\| -
}}+ ||
^{+ }\|_{
)}= [\
01 00
04 4
ev al
T an
^{\ {\
par t
Ġf e
}\|_{ *}^{
)_{ (\
^{+ }}{\
^{*} |_{
|}{ **
there fore
) _{*
o o
x n
}) }},\
ti ce
lin k
}^{* }),
}^{* }(-
\, ^{
}}) )^{\
}|\ )
}|\ |\
Ġ\( {\
_{* }\|^{
Ġ}( (
|+\ |
}{*}{ **
thick sim
M z
g c
h z
}\ }>
)\ !\!\
Ġi id
}[\ ,
ĠD E
\) **
})| -\
Ġ+ }\
Ġ5 12
Ġdef inition
las ses
Ġhy per
Ġinfinite ly
D y
c I
t emp
,\ !\
}^{( *
ĠB i
_{* }}}\
})}\ .\]
Ġg ood
pt I
}{( |
}}{| |\
Ġre lative
\[\# \{\
fi ed
D b
M d
a Y
}^{ {(
}) }=-\
dy dt
Re m
)}_{ =
Ġ}^{ -\
...& ...&
O B
v ac
(\ |(
)\ })\
)= {}_{
ĠF M
:= -
conv ex
/ _{
G ra
c K
m H
p C
ri cal
su rd
}^{- }\|_{
Ġt yp
}|\ ,|
dx dz
{[ }{\
)\| +\|\
{< }
) }|}\
; }\]
] }^{-
h S
i Q
}: [\
Ġi c
ĠF ig
}}| }{
for mation
)\| +
19 3
}}] \\
po ch
Ġdi stance
Ġset s
! }\,
) }](
c D
}^{ !}\
in k
ta il
}} })(
}] }{(
Ġin j
})\, .\
)})\ ,\
27 5
35 4
26 378
A K
F rac
G V
J x
q l
}} }]\]
Ġ}\ }\
}}}\ {
}^{+ }}|
\[|\ {\
})^{- }\
22 7
& =-\
B t
Ġ sq
er n
}^{* }]\
)) [\
)) ]^{
}}) >\
Ġa x
)| /
}^{+ }}|\
liz ed
& (-
) })}(
C m
F H
] ,(
b A
t G
}) {
_{\ {|\
}, ...\
}| [
^{* *}\
{| }{\
_{+ }}\]
{- -}\
22 9
): \|
)}& =
0 36
F ib
S GD
W L
\ }/
\ '{
] })^{
r H
u D
Ġ },\\
^{- }}{
{| (\
}),\ |\
)\, +\,\
)}| =
)}\, |
)\; ,\
Ġei ther
! =\!\
] $
i tions
o de
Ġ }}}{\
Ġ ;\]
}) })(
}+ }\
}}{ [\
}| :
}| }|
)| -|\
ĠM C
}}- {\
)& =(
32 9
000 2
100 1
x H
}_{ **
{\ }},
na d
ve nt
45 0
28 9
05 5
ni tial
98 9
+ }}\
z G
Ġ /(
}^{ >\
Ġ1 50
}^{* }))\]
{(}\ |(\
)}{ }^{
di sk
Ġs m
}^{+ }[
if ied
,- }
45 7
28 6
37 6
]; \\
Ġprod uct
C Q
C v
})\ |+
}] }|\
), [\
Ġe nt
17 3
})] }{
cur v
H B
H V
L w
] }[\
t st
Ġ }}\|\
}\ }},\]
}) ],
)\ }=\{
se ction
}-\ {\
Ġ1 10
)}{ =}
ss ing
ĠF ro
\}\ },\]
20 2
Ġ\, |
}_{< }(
Ġdo main
Ġsym metric
. }}(\
R MSE
W g
}\ }}^{
}| _
\| >\
}^{* })}{\
Ġ2 000
Ġa cc
re ction
}^{+ }).\]
)! ^{
35 0
Pa rameter
Ġfac tor
H A
\ }$
g w
| )-\
}\ }}|\
}{ }{\
|\ )
}^{* *}\
or s
ij l
Ġ\( +\
))\ ;\
Ġp erm
})_{ (\
:\ :
24 9
32 5
xy x
}\{\ |\
}|| |_{
98 8
Ġparameter s
< [
A h
D eg
H G
J L
e ig
u tation
ad ic
^{- }+\
}\| )^{
{)}\ )
})+ [
Ġin equality
24 1
\; =\;
pr in
}! }{
Ġse nse
requ ency
D own
e b
| )}{\
Ġ using
Ġ= ((
di mension
}})\ }_{
)] |\
tt t
)& :=
Ġof f
[- ,-
26 9
04 7
)^{+ }}\
})}}{ {=}}
! _{
- },\
}} }},\
}, _{
}_{\ |\
}= {}^{
Ġ1 23
{) }>\
ĠB K
}^{+ }:
ĠD R
})( [
Ġ- {\
... ,(
17 1
icient ly
/ \|\
S yn
V e
c ro
Ġ\ ,\,
li s
^{* }}\,
}] _{(
})= &
Ġd P
}}, [\
Ġ| |_{
18 2
}}^{+ }=\
subsetneq q
!\!\!\!\ !\!\!\!\
sph eri
( +\
* },\
@ >
B n
E g
N G
U x
k w
s mooth
u sion
}- }\
})^{ +}
Ġc ell
ĠN L
}* }
99 43
17 2
28 5
}}&\ \
tra n
Ġse mi
bi lity
0 64
S Y
V W
W r
}| )(
ĠL R
}}+ [\
]^{ <\
ord in
)\! +\!\
po si
G U
S um
}) )=-
}}\ {(
}, ..
)=\ #\
}^{* }}=
Ġa a
{)}\ ;.\]
ĠM ap
ĠP er
sta rt
+| |\
sc l
up per
37 7
},& (
be st
010 1
Ġcy cle
! -\!\
K p
Z ar
{ '
Ġ })}\]
}_{ /\
ver s
}& [
ĠA T
ĠI t
ĠR o
})\, |\
Ġ}{ |\
2 99
H or
L g
a I
g on
s P
}( ^{
^{* }\,
}] }+\
Ġc ri
_{- }}{\
)| ,
}^{+ }|\
26 5
Ġ{- }\
!\! \{
499 886
Ġav g
ta tions
{) }-(
}] ^{(
}}_{ =:
ĠN a
ĠF ix
)] /
29 8
\[\# (\
Ġini tial
U A
f tarrow
s on
Ġ\ },\
{\ #\{
}} }}=\
})\ ),
^{* }>
Ġi p
\, ;\,
_{+ }}(\
Ġw eak
27 7
* [
H ull
x R
Ġ1 11
}\, -
it x
Ġv i
{- (\
}_{+ }-
76 5
Ġmaxi mal
B w
a B
b circ
f X
}) }/
)\ }\\
)= |\{
),\ ;\;
_{+ }\\
}< |\
20 3
20 10
18 1
{|}_{ (\
]\! ],
MM SE
) }}^{-
> ^{
V C
k F
Ġ }:
Ġ )}+
}\ }<\
}( +
}} }},\]
=\ {\{
}=\ ,\
}}\, :\,
V f
g K
p M
{\ }}_{\
}} };\
}} }/\
}{ +}\
|\ {\
co de
ĠA D
}}, {
ĠG ap
27 0
}]\! ]
^{! }_{
I E
N il
q A
| })\]
Ġ us
Ġ\ @@
)\ }+\
pha se
})\ {\
^{* }}^{(
}}) +(\
un it
ĠH H
\[|\ ,\
|| =
Gr p
39 5
) }:=(
P v
Q X
S ign
f alse
}\ }}=\
lo t
}] \}\
Ġ} .\
Ġd h
Ġg h
}}\, |\,\
Ġ+ }(
([ -\
Ġinc reasing
$ }\}\]
. },\
P y
R g
h M
Ġ )})\
}) }|^{
}} }}^{\
}= +
Ġ& &-
}| )=
{) }[\
}^{* }}+\
ij t
ĠA e
Ġs trict
ĠP S
}}_{\ {
deg ree
mp e
48 8
ne ar
ĠRe p
Ġse cond
Ġ{+ }(
! }+
5 04
H U
L s
M AX
| )}\]
big uplus
li ke
^{* })}\]
)) )}\
ĠS u
)\| =\|
Ġ[ (
,-\ ,
B I
J J
\ }}\|
y q
Ġ )},\]
}) !(
in ary
^{* }},\]
}] _{+
}] /(\
}\| (-\
ĠA n
_{( {\
}^{+ })-
)\, ,\,\
ĠP T
^{+ }}\]
}=(\ {
dv dx
37 49
38 5
Per v
GK dim
Ġrepre sen
z s
}| }}{
}^{+ }:\
Ġ^{ [
};\ ;
19 1
}}^{+ })\
SL E
* }=\
4 37
E r
R v
V S
a D
u la
y xy
Ġ )}=\
Ġ cut
}} }/
}}\ }=
var Theta
ĠC P
), +
Ġd Y
}}^{\ {
\[\{ [\
Co b
ĠMul ti
K A
] )}{\
b lk
c X
Ġ ln
_{ /
}\ }\,\
}) )),\]
}] ,\,
}^{- }:=\
)) ].\]
Ġa bo
Ġd k
.\ ,\
12 23
ĠF P
_{+ }|
dv du
Ġde nsity
\[{ }^{(
Ġmulti pli
Ġsuff iciently
& -(
- {
0 31
C c
] }&\
c lass
j T
Ġ }}\]
Ġi ter
\, [\
}\| |\
_{* }|
less dot
Co nd
lat ed
ull i
})\! =\!\
âĢ Ŀ
ĠDi ag
\ })-\
b ut
f rom
o id
lo m
)^{ (-
}| }}{\
}] :=
ĠC D
}}) }_{\
{| }<
)} *\
ĠL S
ĠS P
(- |
ĠD is
ĠP I
^{+ }\\
}))\ |\
}_{- }\]
}): \|
}}] -
74 9943
ule r
A a
K dV
M AP
S g
U LA
\ })}
a K
h C
p H
| -(
}\ }|
}( ]
Ġf ace
\, ,&\
}\) .
and om
32 7
ert y
}\; :\;\
)< -\
05 8
38 8
{, }\
)]= [\
Bi as
Ġfi eld
! .\]
& |\
}) )=-\
)\ },
|^{ |
}}_{ +}\
Ġk m
ĠS I
20 9
], |
)}}{ {
]+ (-
}}(- ,
29 5
Ġra tio
We yl
$ })\]
e h
f irst
s core
w h
}{ }^{*}
)\ !\!
bo unded
ds dx
}] })\
)) }-\
ĠS ection
Ġe stima
}^{+ }\}\]
Ġh ence
,- ,
14 40
})) }+
): \]
27 8
)}) ]\
|> |
Ġuni que
Ġcy c
Mul t
; =\;\
< \|
B matrix
Q N
V B
c B
m ld
}) }}(\
}) }+(
}} }^{(\
(\ !\!\
\,\ |_{
&- &-
TM F
Ġse p
)$ },\\
})\; =\;\
\[\# (
cur rent
do f
verti ble
) }}}\]
- }}\
6 75
\ &\
z v
Ġ })\]
Ġ )]
}} })}\
^{- }.\]
ĠC or
Ġin put
},\, |\
36 9
ess sup
Ġval ues
) }}\|\
H X
L V
b el
{ }>
Ġ Pic
_{ >\
le r
}}\ #
se nt
)}\ ;.\]
}^{* *}(
Ġ\(\ {\
}}|\ ,
}}^{- }\]
dr ds
33 7
30 5
26 0
Ġun it
tm f
) }].\]
) }}}{{=}}\
B d
N y
] /(\
h X
ro ll
{) }=(\
ĠC p
ĠC ar
ci sion
}\| }{\|\
Ġ=\ ,
Ġ- |\
\[| [
ol ute
|\, |\
res hold
so rt
so lid
iz ed
),\,\ ,\,
ment s
Ġsing ular
. &\
p la
Ġ\ {(\
\[\ {-
_{\ ,\
{| }_
_{* })-\
))\ }\
Ġy x
ĠK K
Ġ)\ |_{\
)}) &\
Ad d
|\! |\
\# \{
rcl rcl
\|=\ |\
: .\]
H O
T Z
n A
Ġ )}-
}) }}+\
^{- }}(\
\, -\
Ġ- ,
ĠU p
}=- {\
}\! :\!
cd h
no ulli
98 4
08 8
46 5
> +\
L an
k R
x B
}} }^
)= {
}] })\]
Ġs n
}^{+ })-\
Ġ}( -\
98 5
}|> |
$}} }}{\
lv l
$ },
6 78
= _{
H f
v b
v k
Ġ limit
}\ }|=
}, {}^{
}= &-\
pi c
}| )=\
ro und
}^{- }\\
\|_{ -\
}^{* }}.\]
)- \]
ĠN C
34 9
}]=\ {
Ġlo op
Me an
M GL
X U
\ }),
o sed
s B
Ġ mu
su rf
)) }}{
_{* }/
}^{+ }/\
Ġb asis
up omega
\% \
}}/ (\
Ġdiff er
0 78
J T
S v
W H
b D
Ġ rt
}) })-\
Ġ\ }\]
ft er
}] )+
Ġx z
}\,\ |_{
Ġ( |\
_{+ }^{*}}\
\[\|\ ,\
})| |_{\
))^{ *}\
99 2
33 5
05 9
res sion
]- [\
nn z
St k
glo b
b B
b ic
g roup
x mapsto
z d
Ġ na
}) }>\
}) ;(
ar o
^{* }<
^{* })}(
}] }_{
\| },\
)) }-
Ġ} |_{
}}) }+
{| {\
}\| >\
Ġn or
(- ,
/\ !
{\| }\,\
\[| |(
}_{+ +
]}\ {
}}^{* })^{
35 2
04 1
F Y
G X
m P
| )^{(
Ġ\ }}
(\ !(
})\ |=
}] }\|\
\{ +\
\, ^{\
}/ [
_{* }}\|\
}}}\ )
ĠM axi
Ġm m
Ġ- }\
)\,\ ,\,\
_{| |
05 7
Ġ{* }\]
66 7
Ġmo st
Mo del
> =\
E f
L at
M m
Q F
T s
\ }}_{\
] )}{
s Set
}\ }),\]
si ve
ri er
^{* })\\
}] }}\
)) {\
Ġt e
Ġ_{ -\
ĠS D
_{* }|^{\
Ġr ig
\}\ ;.\]
}}\, .\
ay er
\ })+
] |_{
r L
le xi
at er
\| )
Ġf low
Ġc lo
^{+ }|
}_{+ },\\
20 22
}_{* }\|_{
64 9
,* }\]
Ġco lumn
SV D
D n
Q e
a E
_{ |_{\
}) ]}
}_{ +\
}} }+\|\
bm o
)) )(
Ġi jk
re te
ĠB x
)\, ,\,
)] [
Ġin du
}}\| _
arrow left
28 4
35 5
Ġtra in
T HR
\ })^{\
a L
a S
s low
}( ||
\[ >
_{\ !\!
)\ )}
lo bal
eq sim
ĠS R
ĠX Y
ĠR an
ĠP ar
24 2
27 9
,+ }^{\
Mod ule
79 2
39 7
Ġcon e
ĠRe LU
$ }(\
& {\
C art
] ]=\
p ot
Ġ }\,.\]
^{* _{
Ġ\[\ {\
Ġa ff
Ġco v
\!\!\!\ !\
U M
\ }}(-
d log
e A
g i
p K
Ġ *\
over leftrightarrow
Ġi ts
\|\ !
}& &&&\\
})_{ !}(
28 7
46 7
|}{\ (\
Ġdiag onal
Ġen ergy
ĠLo g
Ġcomponent s
- }+
/ \,
L ag
Z X
[ \]
\ }^{(
\ }))\]
o log
u H
Ġ }:\
}( .,
at u
}=\ |(
Ġ_{ (\
{[ }\,
\[(\ {\
Ġo bj
{(}( -\
amil y
) ...
* },
c st
| }_{
Ġ }}^{-
^{- }}\]
Ġ\[ (-
^{* }))
chi ld
)-\ {
ĠS upp
)| }{\|
Ġin it
Ġ}( {\
\!\ !\!/
18 3
34 56
}$ },\
30 6
}}[\ |
fi cation
E N
,\ #
}} }^{*}\
rho od
}^{* }}-
}\, )\
Ġd F
\[( |\
Ġy z
}_{+ +}^{
{{ ?
}}^{* }_{
no ugh
/ \,\
H k
M w
] }:
o h
q h
| }}\]
| :\
}^{ {}_{
}| )|
}}( {
Ġ1 60
}^{* }}-\
ĠB R
^{-\ |
Ġe nough
ĠH e
ĠD M
)& (\
25 4
})] )\
)\|\ |
26 6
98 6
);\ ,
Ġker nel
L p
n F
}) }((
}+\ {\
}^{* }=\{
}}_{ *}(
Pi v
ĠF e
11 52
}_{+ })
{|\ {
Ġ}{ (\
ju ga
3749 03
9 75
G p
L Q
N eu
R ow
S ec
l w
Ġ })\|_{
}\| }.\]
bigg m
ĠB B
ĠS hv
34 3
Ġ\, |\
})\| ^
46 8
Ġir reducible
O rd
s D
s amp
v ia
}} }}{{=}}\
am ic
tor d
}^{* };
_{- }}\]
}^{+ }),\
ĠG M
Ġ$ [
ch y
)}=\ {(
Ġ5 000
}}[ |\
)}) _{(
)[ [
04 6
mi tive
fix ed
) }}&\
5 88
H iggs
T n
a M
Ġ }-(
}) }]\
}(\ {(
}| }}
))\ }_{
}}}\ !\
ĠD G
}}| }
}}| +|\
}> |
):= (-
}* _{\
)\| ,\]
)\| =\|\
\{( -
29 7
)_{+ }^{\
iz x
)$ }\\
Ġcom mu
6 56
U niform
e B
Ġ\ !\!
}{ }_{(
bol ic
^{- })=
Ġt A
ĠS ize
Ġ\( {}^{
Ġv s
_{- })=
Ġm k
Ġal ong
\[= :
33 33
(\| (\
|+\ |\
\# }\
: }
B ad
M X
O A
V T
}} ;\\
+\ ;
^{- })^{\
}}) ;\
}|\ |_{
]\ |^{
ĠT R
Ġ\( [-
ĠF or
33 9
}}& &\\
39 2
}}\! =\!\
black triangleleft
ens or
ĠDe scription
ĠLe b
D p
] }=(
a H
s C
| :=\
Ġ cos
Ġ ^{*}(\
}\ }(\
}\ }]\
}) )=\{
}} },\\
de m
}{ -}\
}^{* }<
)- [\
\, )\]
}}\, ,\\
Ġ6 00
30 9
},- ,
Ġan ti
pq r
)$ -
MF C
}|\! |_{
Ġup per
ris tic
lom orphic
# \,
+ )\
8 96
> =
I Z
J f
K C
O U
Z C
ti ble
^{\ |
{( |\
)=\ #\{
ĠC ond
)) )^{-
)| }=\
ĠR T
_{+ })=\
}\) **
+| (
}}^{* }-
})] /
},- )\
blk diag
A cc
G l
V er
ma j
}) )}(\
}-\ \
}}^{ |\
}] )-\
Ġa u
)}{ {\
_{- })}\
/\ !\
}_{+ })^{
40 9
})\| <\
Ch ar
})\! -\!\
J I
N W
\ }}}{
e o
r X
t ree
w or
Ġ )]\
}\ }<
}( {}^{\
in x
(\ (
Ġ\[= ((
box minus
}_{+ ,\
}}\, =\,
not e
],\ ;\
lat tice
06 8
Ġre c
Ġmini mal
6 55
K a
P l
f it
n E
ma nd
al gebra
^{- })=\
)}\ |\]
\| ,\|
ĠC B
}^{* }=-\
}\, -\
}}) ),\
Ġc m
12 13
10 11
}}-\ |
})> (
LS I
FF T
! }-\
, ...\]
F u
O O
}} ]}
hi s
)) ;\]
Ġ= :\
ĠL P
}}- |\
})) ^
)}) /
Sym p
|\! |
ĠRe lative
gene ous
E s
F ac
P g
R ay
T I
}} }}}\
ar ning
+\ ;\
si st
}| },
hi cle
ĠC u
)) ))\]
}\, :
]\ ;.\]
Ġc op
_{- },\]
(- )\
Ġw ell
}_{* })\]
35 9
fin al
Ġho r
) }:=\{
3 34
B f
}} })-
}} }\|_{\
qu ery
^{* }=(\
Ġt ree
}}) )(
Ġe mb
ĠP ri
\[| ||
)] =(
})) [
\},\ ;
\},\ ,\
,+ ,
Tor s
Ġlin k
Ġlay er
- })
. }}(
I sing
] ^{*}\
_ \
b H
Ġ )^{-\
}= ||\
{| }[
}^{+ })+\
^{+ })-
25 3
))=\ {\
\; :\;
)^{* }}\
|}{ }
}}\! +\!\
Ġresp ectively
C ar
E SS
I H
V P
k E
y d
Ġ\ ;\;\
_{\ {-
}}\ })\]
at ure
}^{* }+(
)) |_{\
Ġ=\ {(\
ĠS ec
})_{ ,
ĠE n
}}| =|
... +\
}}^{- }(\
}_{- },
64 4
45 5
gen era
|}{\ |
reg ular
)\! -\!
}))- (\
Set s
0 95
K k
O G
P in
S tep
x T
)}^{ [
}_{* }-\
06 5
49 5
dxdy dt
denti ty
- ((
6 79
: -\
= {
C as
D PD
s er
s depth
w c
\[ +(\
ar io
}- (-\
}+\ ,\
^{* }}\|_{
ĠS tab
12 00
Ġp erf
Ġr v
}), [\
}_{* }=\
&& &&\
})^{* })\]
Ġsu rf
4999 31
$ })=\
* })\
3 99
3 000
T H
] )=(
Ġ gap
ma rg
}(\ {|
^{* }=\{
}^{* }:=
}\, +
{| }\,(
Ġc p
}^{+ })}^{
}})\ }\
}}{( -\
44 4
Ġit erations
Ġcomp lex
poly log
va tive
cen ario
+ ((
L y
f m
}_{ <\
Ġf g
),\ ,\,
_{- }\\
ĠD o
ĠD iv
on ential
)}, {\
}_{- }=\
Ġ10 1
)! }\,\
04 3
Ġlo cally
fi eld
ei ch
}}{{= }}(
- ,\
4 75
E ll
o i
r opy
w n
x Rightarrow
ma tch
}) [(
me try
)^{ [\
}}(\ ,\
{| }-
Ġb ad
{\| }+\
}}\, +\,\
], &
36 6
}}:=\ |
04 2
96 9
38 6
98 7
RE S
& ,
H Q
] )_{\
] _{+}\
m E
x c
}) )}+\|
-\ (
var triangleright
Ġ1 0000
}] |_{
}^{- }}^{
)) /(
re es
}^{+ }}^{\
Ġh yp
}}^{* })
)}) >
37 9
})]\ !
})^{* },\
Ġmod u
Ġequ al
$ }}}}
& *\
, ...\
- }-
: }&\
M Q
O F
r B
u rce
}( ((
)\ #
^{* }}|\
^{* ,*}(
Ġc ross
}}| ^{-
22 22
}}^{* }.\]
uv w
}^{\# }
\)\ (
ĠBo und
Ġparti tion
Ġste ps
$ })
B Q
F v
h L
i V
Ġ }}}(
}( +\
lo pe
^{* }:=
^{* }}}\]
ge o
}& =(\
ĠA dd
Ġs cal
vec h
)_{ -\
_{+ })-
}}}{ [
};\ ;\
Ġ(\ {
ab q
rr rr
38 7
Cy l
) })}^{
C ut
C au
I Q
M k
T p
T ree
] }}^{
Ġ am
Ġ cal
Ġ er
(\ #
)\ }-
)\ |\,\
+\ |(
par ity
\| -\|
}\, ,&\
Ġi v
Ġ\[= -(\
ĠD om
:= |
}}| ,\]
il ar
15 00
28 1
aus s
Ġprop er
bit ra
& ,\
3 16
4 96
W Z
u ps
_{\ !\
si dual
ad v
tor y
Ġf o
}\| [\
}^{+ }=\{
Ġ{\ |
25 00
Ġ\, |\,
,* }_{\
N l
R Z
g A
Ġ }=-\
}} }),\
}| -(
ap x
[\ {\
}] ),
}\, :\
\, ;\,\
}}) |_{\
}}) -(\
Ġn k
Ġc lasses
ĠS ch
Ġp n
_{- }},\
)| )^{
ĠN T
ĠR un
_{+ })=
{\{ }[
))= \]
}+| (
)}| |_{
]+ \]
}}\! +\!
ĠCo nt
Ġsing le
Ġdivi des
- ,-\
. }(
C lo
P K
R Mod
)}\ ,(
^{* }}\|\
}^{* }_{+
^{( *
)-\ (
Ġs ti
_{- })=\
ĠE qu
ik t
}$ .}\
Ġde ri
38 1
78 8
0 76
K D
O bs
a C
a F
c losed
j ac
j oin
z p
{ *}
at es
tar y
}] )-
}}_{ /
Ġn c
Ġs tab
})- |\
})( |\
Ġin vertible
30 3
})/ {\
Min imize
Ġ\(|\ )
ĠData set
}&* \\
B ord
N ull
S X
h q
Ġ }^{*
)\ (
}| )-
}] )(
Ġa ct
ĠN eu
ĠM A
Ġ{\ {
16 00
\[[ -\
34 1
98 0
06 7
46 6
Op en
Tri v
- }_{
J P
J V
L m
\ })+\
c C
f n
t Z
v g
}) )&
}} }}+\
}} })^{-
}, -(
}}{ =
Ġ1 12
&\ |
ĠA N
ĠM N
)/ {\
)! \,
)! !(
)}+ |\
99 4
27 3
ea sible
cop y
Pri m
Ġnet work
) }}\,.\]
\ :\
h H
s F
s H
z c
{ `
Ġ }+(\
}) )}{(
}) }}{{=}}\
}] <
)) _{(
Ġi q
ĠT HH
\[\| (-\
\[\{ |\
})\, =\
Ġ\[+\ ,\
multi map
~{} ~{}
measu rable
. }}}{{=}}
; }\
L I
Ġ )),\]
Ġ argmin
)\ }|\
qu asicoherent
{( (\
Ġ& \|\
}\, :=\
})= -(\
\,\ {\
})- (-
}^{+ (
}_{+ })}^{
^{*} _
}_{* }^{(
25 1
33 0
44 1
Ġ{* })\
ty p
tra p
iz er
). (
{< }\
+ },
3 64
L c
P os
R O
u N
z A
Ġ ],\
}) }]\]
ar se
&\ |\
Ġal go
}}^{* }+
56 5
}=\{\ ,
79 5
07 2
{: }}=\
Ġabo ve
4 12
W S
[ ]{
] })^{\
] _{+
{ }^{*}
{ /\!\!/
Ġ }.\]
Ġ }^{*}
al k
}} })-\
},\ !
na t
tri p
),\ |
Ġc b
})}\ )
}^{+ }|
))= (-
): \\
\[\{\ ,
27 4
48 6
}): |
_{{}_{ [
def ined
Ġ{* }}\
po rt
IN V
Ġcond itions
conn ected
B Y
R Q
o ci
Ġ }}[
}\ :\
}) }}=
{\ }}-
wi rt
}\| ,
re en
ĠT ran
)}( |\
)| },\]
}]\ }_{
\! (\
)}}{\ |\
np ut
Con j
}\,(\ ,
In dex
&* &*
ĠCo st
Ġcomp lete
cond ition
,\,\,\,\ ,\,\,\,\
Ġso ft
4 000
c E
Ġ )\,.\]
}(\ #
eg ory
}] ]=
}^{* }}|
)) ,\,
Ġf r
}& &&
Ġc at
ĠS ol
}),\ ,(
}^{+ }&\
Ġj i
Ġco l
78 7
07 7
Eu cl
Ġstrict ly
C q
N at
P art
R p
a city
j v
Ġ0 00
{) }}_{\
}^{- }|^{
}^{*}\ }\
)}) ]\]
05 1
Ġse e
Ġbe long
_{! }(\
\({ }^{*}\)
$ }}^{
K Q
N or
O E
s M
y h
Ġ ver
)\ }-\
},\ !\
{( {\
}| )}{
ro ups
{) }}{|
}^{- {\
Ġt N
Ġt u
Ġd l
ĠT rue
\,\ }\
ĠW e
)}(\ {
}\}\ {
45 8
26 2
{)}+ \]
06 9
08 5
Con st
Ġad missible
Ġcor resp
{\{}{\ }}{
ĠMaxi mum
0 96
D is
D im
I t
] ]^{\
x L
z er
al low
co der
}}_{ =\
ci p
ĠA p
ĠT X
\}\ !\!\
}]\ |^{
)=( (\
)! !}{(
)})\ }_{
mix ed
ew ton
Ber n
T OL
f act
w ind
Ġ ll
Ġ }}{{\
}) },&\
Ġ\ }^{
})= +\
})=\ {(\
_{* }),
^{+ ,
ĠG F
}))\ }_{
)}= {\
): |\
ik l
99 0
\; .\
Ġ:= -
06 6
]\! ]_{\
dxdy dz
IP W
cont inuous
ĠInt er
K X
n er
t Q
z P
Ġ )&\
Ġ })}.\]
se u
)}\ },\]
)=\ ,\
^{* }))^{
}] )=[
ĠC O
ĠC X
)) )\\
}}) )-
{| }}{\
pro b
Ġc N
di sp
}^{+ })+
\[\|\ ,
)(\ |\
{{ }_{\
ref l
30 7
05 4
,* },
:, :,
})\! =\!
;\,\ ,\,
\}-\ {
^{(+ )}_{
. }\,\
9 55
H I
M ed
] >\
j e
m w
p ub
Ġ cases
ti ent
)) )}{
)) |=
ĠB P
:= |\
Ġin di
34 0
}$ )}\]
37 4
76 7
|\! |_{
term s
Ġalgo ri
) })}.\]
3 14
C b
] ]^{
] <+\
f pp
q B
| ,\\
ma nn
{\ }}}\
lo city
}| |=
ĠC q
Ġ= (-\
<\ !
Ġw ork
dr y
)> -
28 2
000 3
Le ftarrow
ome nt
})},\ |
Ġ{* }_{
{, }
dimension al
, {}_{
> \,
X v
] ],\]
g onal
q Q
r D
t W
}_{ -(
}} ]=[
}^{- })_{
Ġn r
ĠB A
\,\ |\,\
}}| |_{\
et s
\! [\
]+ (\
44 7
78 5
]\! ]}\
Ġpro blem
Qu ad
) })]
+ }=\
, {}^{\
- }=
h et
p I
v G
y c
Ġ })|\
}) }\,,\
^{\ |\
}(\ #\
nu s
Ġ{ -(
tri vial
}\| ).\]
Ġk g
<\ !\
Ġc KP
ĠI nitial
)\, :=\
}}, |\
Ġh eigh
{\| }.\]
}}| }{|
Ġ$ \{
)\|_{ (
>\ !
23 0
)\| (\
48 5
}): [
75 8
38 9
mo geneous
) _{*}(
E uc
P erm
\ }))\
}\ #\{
}) )^{*
}} }=-\
}}\ },
geq q
^{* }+(
Ġ\[\ ,\
Ġa e
Ġ= :
Ġd H
ĠA cc
Ġp os
ĠD v
ĠG aussian
{{ !
36 2
)$ .}\]
,\,\,\ ,\,
K SD
R SS
S YT
V alue
f ac
r R
w b
Ġ }||
Ġ ]{
}\ }_{(
}) )},\
Ġ\ ,-
}} }|^{
}}) )-\
)}{ (-
ĠN F
{)} |_{
Ġo ccu
34 2
45 9
}): \,\
_{[\ ![
{|}\,\ ,
mi ssing
fi ll
)\},\ {(
= +
D I
I mp
I mage
W V
\ })>
a co
Ġ )}=
Ġ mult
in put
}}) ^{*}\]
}\,\ |\,
}}| |^{
,- }^{\
|| |\
Ġan aly
}}: |
})},\ |\
Ġdi rect
cs ch
Ġgenera ted
Ġeigen value
Ġstr uct
! +\!
D s
M g
V X
W X
\ }=(
x Q
Ġ }^{*}(
}\ }^{-
}) }/\
}{ }_{*}
Ġ1 25
}}) }\\
ĠA A
Ġc luster
ĠH y
tt er
Im m
xx t
}(| |\
)}) ).\]
leftrightarrow s
56 9
ne gative
Da ta
ĠParameter s
! =\!
. }}{{=}}\
6 88
C g
a P
f dx
Ġ phase
}_{ :
ph g
)\ }^{\
da p
}- ((
}^{- })(
}^{* })_{\
Ġ} })
ci l
}\| ,\|\
}\|_{ (\
}\|_{ *}\
}& +
ĠB u
})}\ {
^{+ }|\
}+( |
}< _{\
)! }+\
as c
64 7
}}:=\ {(
,+ }+\
}}^{+ },\
})\|\ |
,\; (
}! }.\]
Fil t
ob lv
lay er
peri odic
* ,\
D Q
H dg
K g
N z
q X
u P
^{* }}}{{\
Ġ_{ |
ĠR E
}}- [
sta ll
,- },
20 21
}}^{- ,
dz dt
up downarrow
26 3
))\, ,\
Ġch a
Do F
; =\;
= _{\
X T
\ }}\|\
] )}.\]
c F
c S
f ast
j c
k S
l arge
n leq
}^{- })^{\
}}) }}\
}}) )+\
Ġn ormal
id ual
})- [
ĠI T
_{+ })-\
)}, (\
{}_{ [
)! !}{
35 1
sk w
05 2
29 3
60 7
iH t
) $,
* }}\
> }\
A pp
D c
K J
N X
N umber
] })(
h K
Ġ arg
}^{ =
Ġ\ ;\;
{\ }}(
ft p
}_{\ |
^{* }&\
)) }|
}}_{ +}(
)} &-
})= (-\
ĠT or
_{- }\|_{
_{- })+
^{+ }).\]
)] \|_{
... =
{{ +
en sion
60 9
95 8
)|\, .\]
Ġda y
ĠTh m
4 31
; |\
B h
L X
S o
W x
s top
x k
| }[
Ġ prox
Ġ ))}\
}\ }}+\
}) )}+\|\
^{\ #\
var iance
la ce
^{* }/\
}] \|\
}: -\
}^{* })}\]
}^{* }]\]
ĠA i
Ġc ho
_{* }[\
_{* })}{
}_{+ }).\]
Re f
)}= \]
}}^{- }}\
},\, (\
})] |\
75 2
50 8
Ġma tch
Ġad ja
ĠLi pschitz
tho gonal
, ||
A rt
T otal
g iven
Ġ )},
}} },&\
^{* +
Ġ1 44
}^{* }})\]
}\, =
Ġe vent
ĠD T
}\}\ }\
}([ (
ik s
}):=\ {(
kl t
te l
05 3
08 7
76 9
SD E
Ġinteg ral
})\|+\ |\
Ġconver ges
! +\!\
. }{\
E n
Q v
\ }=-\
Ġ })\,
Ġ tan
Ġ ^{-(
}) }),\
}_{ !
{\ }}<\
=\ !(
su sp
^{* },\\
}] ].\]
\, :\
di r
ĠE stima
{\| (\
ĠK O
ch ain
)/ |
):= [\
}_{* }^{-
Ġdx d
tu rn
77 4
,: }\
{* }{
0 110
G m
P Y
W B
f ace
i G
Ġ )}{(
}} }+(
}}\ ;\;\
ri ch
matri ces
)) ]=\
}}) ,&\
un r
{| }\|
}[ ||\
Ġb all
Ġ10 24
})) |_{
Ġ| }{
}\! :=\
Ġ\, =\,\
}}^{+ },
);\ ,\
)_{+ }}\
Ġsp ec
! ,\
, ((
Ġ )}^{\
}\ }}}\
{\ }},\\
ad m
}| ),\
^{* }}^{-
^{* }}}{\
}] }+
Ġi b
ĠN ot
}}}\ .\]
)_{ |_{
})| )\
}}[ [
})\| ,\]
76 6
Ġevery where
RS B
|/ |
Ġperi odic
riz on
. **
; ,\
Z T
d ddot
}\ {{\
}} }>\
}_{\ !\
Ġ_{ *}\
ĠS W
00 25
}}\, ,\,\
)}, -
Ġ\[+ [
75 7
29 2
}=[ (\
38 0
08 0
}=|\ {
Ġsta rt
roll ary
Ġsti ff
P RM
S ig
b N
b R
h ard
m F
s R
Ġ ell
Ġ }}\\
Ġ ^{+}\
}) ^{*}}\
}_{ |_{
}} }}{{
}{ }^
)\ ;\;
^{- }-\
{) }:=
co fib
}^{* }},
}^{* }})\
Ġf lat
}}) ^{*}(
Ġv is
Ġv ir
{[ }[\
}}+\ |(\
}))\ |_{\
}\}\ !\
}}^{* }\|_{
)! !\
pre Module
ik j
64 6
40 7
\[(- )^{\
Gra ss
E nv
J y
Q L
S im
\ }>\
b atch
Ġ ))=
Ġ )+(
su s
^{* }}\,\
\{\ {\
Ġs k
ĠT e
12 96
Ġp s
ĠN one
}}=\ {(\
})^{\ #
}_{+ }:\
}_{- }}
)\| }{
}$ }}\
95 2
SD P
})\! +\!\
Ġav erage
whi le
! \|
) $,}\\
/ ((
3 10
C w
E i
J g
\ ((
k ji
}) ^{*},
}) };\]
}) ]=[
{\ !
}| }|\
[\ ;\
}] }-
}] &=\
)) ;
}\,\ {
ĠL ear
11 10
^{*}( {\
_{[ (
up pi
30 2
96 7
Ġcontain ing
Ġsign al
))^{* }\]
rdr dx
The orem
seu do
- )=
. }\;
P OD
\ }|=\
] |\]
p op
u ble
z T
la tions
})\ ,\,
Ġ1 26
}] }-\
\{ -(
sim ple
)-\ |
Ġs cale
_{* }),\]
})}\ ,\]
\[| [\
}}| <\
}_{+ }=
_{[ [
ba s
}}^{* }+\
40 6
AB A
Ġ{- }(
ran ch
Ġcont rol
hy po
Ber noulli
+ },\
. }.\]
C i
C ho
E Z
W f
] )\\
a o
b all
q S
u A
{ *}\
| }}.\]
}\ }},\
}) })+
}} }=(\
Ġ1 80
ĠS i
ĠS pe
Ġ\( <
}]\ }.\]
23 45
20 23
})] [
)}| }{
,* }^{\
},& |
08 9
09 7
0000 00
Ġcontain ed
& :
, _{
M ST
Z B
g P
n ext
z L
| ]\
}) }=(\
)\ }}\]
na ive
^{- },\]
}] ))\]
)} *
ĠA t
)\, -\,
ĠR MSE
ĠD P
};\ ,\,-
}:= &\
}}:=\ |\
40 4
}{}{ -
{\}} ;\]
) }}[\
G I
H yp
L CB
N is
T o
W R
] :=\{
c Q
v ing
y r
Ġ })}(
Ġ )>
}} }^{*}
ot ential
^{* })=(
}: \,\,
Ġt d
ĠB e
}}= +\
_{+ }:=\
^{+ })-\
ere nt
36 3
}}}{{=}}\ {
Ġse lf
Ġdiv is
}\,:\, |
BD P
mon ic
Ġar bitra
F J
K V
R Y
] ):=\
q P
Ġ circ
}) }:=
)\ }(
op f
)}\ ,\,\
\| ).\]
}^{- |
}^{* })\\
),\ {\
Ġn T
Ġu sed
ĠT C
}^{+ })(
Ġr n
ĠR x
})+\ \
}}| <
}}\, :\,\
^{*} })^{
Ġ}( [
\[= |\
}_{- })\]
},\, {\
en ti
}\! :
}\! (\
an ce
28 3
}}^{+ }}
val ues
Ġsub space
Me thod
ĠPro blem
Ġge ne
normal size
) }^{*}
* |\
7 07
U P
\ }}^{(
^{ !}(
}) })^{-
})\ |}\
}| :\
^{* }}_{\
}^{- }<\
})^{ (-
ij ab
}}^{\ ,
Ġs table
Ġ\( [\
ĠR a
)}| =\
ac tion
inter leave
AB CD
26 1
Ġinteg ers
+ }+\
- }\]
\ }}}
| })^{
| )_{
^{ ?
)\ |\,
}= {}_{
{( }((
}=\ {-
co unt
}\, ;\,\
{(}\ |(
Ġ} })^{
48 4
Ġde nse
96 6
46 9
eigh ts
58 4
Ġdis k
Ġap proxi
9 47
D m
H it
P sh
X W
l mn
z m
| })
| }(-
)\ }&\
}= _{
{) }}=\
co d
}^{( (
}^{- }}\]
ĠC at
}}) ;
),\ ,\,\
ij r
Ġs at
{\| }\|
Ġ(\ |
}}\, ^{
}_{* })
})& (\
}}: \,
})]\ ,\
}}^{+ }_{
88 8
95 7
Pro f
Ġad d
\[\# _{
Poi sson
Ġ\(> \)
semi stable
Ġdec reasing
Ġalgori thm
4 64
b M
y i
Ġ ))=\
}} })+\
)\ #\
}=\ #
{) }_{(
Ġ{ }_{\
)) ),
}}) {\
sp oly
Ġs d
ĠT S
_{* }\|\
)\, -\,\
ĠR IS
_{+ }|^{
^{+ }},\
)|\ ,|
(( |
(( {\
ab y
Ġ_{\ {
Ġ)\ |\
Ġ}}\ |_{
,+ },\
HS IC
Qu asicoherent
eu c
Ġinj ective
stall ine
C ent
g G
v L
} .}\]
to ch
la b
bo ol
\| }(
Ġf il
}}) }_{
ge nt
_{* }\|
_{( +
ĠR andom
}}+ ||\
_{+ -
)|\ |
{- }{\
Ġ-\ ,\
}}^{( +
})) }^{\
Ġ| =
99 3
})] \,
is sion
44 3
}}] ^{-
Ġtra ining
}}&= &\
Ġposi tion
amp ling
tho ds
$ }=\
4 16
F O
\ };\\
f D
u F
x rightleftharpoons
^{ [(
}) })-
}} }}{{=}}
}, {}_{
ex it
}=\ ,
eg ori
Ġd L
Ġ( +
_{* }),\
_{* })^{\
))\ |\]
Ġv dx
\,\ }.\]
Ġ- (-
}))\ )
,\,\ |
}\}\ }.\]
dz ds
}_{* }}(\
,+ }\|_{
)$ }\
MC G
}\,|\ ,(
ĠLe ngth
Ġperi od
) }:=(\
C BC
G lo
s W
t wist
v h
| |\]
Ġ ),(
}\ },\,\
}, +}(
)) ,(\
Ġa ction
ĠA l
Ġs l
_{* }})\
ĠN e
Ġm t
)}, ...,\
{{ <
}}}( -\
48 1
,* }=\
Ġco un
78 6
SO R
sn r
ation s
tain ed
Ġpri m
! \,(
0 79
R ot
X g
| {}_{
ra ct
|_{ (\
}=\ #\
Ġ& [
ap er
}\, ,&
ĠL M
{)}\ ,(
Ġk in
Ġ\( {}^{\
_{* })^{-
Ġr un
^{+ })+\
):=\ |\
}_{* }}
)! }\,
ĠO bj
([ (
ni an
,+ }^{(
}}] }{\
66 6
_{\# }^{
abc de
den ce
Ġtran sm
Ġfac tors
Ha ar
volu tion
Ġcorresp ond
) .}\]
T ran
m I
p lan
r st
| {
Ġ }\,,\]
Ġ ](
Ġ matrices
la p
}| )}{\
ver gence
}}^{ -(
^{* })|
}}{\ ,\
dx dr
ĠS y
ĠV al
ĠD h
_{+ }\,\
_{+ }}+\
_{+ })(
tr s
}}\| +
(| (
))= |
Ġth rough
pre s
Ġ\, |\,\
)}| +\
000 4
Ġde s
el ds
ess inf
09 4
)* _{\
CF D
Ġdis joint
}$, }\]
})\|+\ |
emb ed
> .\]
H w
V F
\ }}}{\
\ }|+
f ig
| }&\
Ġ ri
Ġ ],
}\ {[
}} }}=
}| )\,\
)= &-\
^{* }}[
{) }+(\
}^{* }<\
}^{* }=-
)) )\,
^{( (
sp e
ĠB D
_{- }|\
_{- }<
Ġg radient
ĠG S
tt ing
}$ }
56 6
Ġco ordin
}}: [
ome tric
}. (\
^{\# }(\
vi ded
}}\!\!\ !
$ })=
3 19
= [-
= [(
K s
S eq
U CB
W G
] })+\
q ftp
Ġ ph
Ġ& \|
}| )|\
\| :
}^{- ,\
ĠC c
\, ]
}}_{ *}\
{| }&\
{| }\,.\]
}}^{\ {\
ĠS A
_{* }}=\
_{- })(
ĠN t
Ġy ear
}[\ {\
Tr ue
em i
)&\ \
Ġ8 00
}})=\ {\
48 7
48 9
50 9
}&= &-
{|}\,\ ,\
}}\! -\!
vi ce
resp ectively
\{+ ,-\
( ^{
) }}(-
4 29
C AC
F U
] )}(
c P
c over
q g
r U
ma te
}) ))_{
Ġ& -(
Ġ& +(\
}| )-\
)= +
Ġd b
Ġk i
ĠS pan
fo l
):= {\
}}^{* }}
27 1
\{( (
sym metric
)$ },\]
pp ing
CF L
Ġpro cess
Ġit eration
PI NN
$ }-\
3 96
N LoS
j L
q C
w q
Ġ )/\
}) })}\
}) *_{
}] }_{\
\|_{ {}_{\
)) },
\{ ||
}}) /(
Ġu u
Ġ= &-
:=\ |
}& [\
ĠS G
))\ ,\]
Ġ- }(
ĠP oly
Ġb ase
Ġg ra
,\, [
}|_{ (\
ba sed
):\ ;
{)}\, .\
})< -
}^{\# }(\
^{! }_{\
Cor e
lassi cal
spheri cal
aco bi
) })+(
N j
N v
T est
T eich
[ {
] }]\
b F
i mage
o se
p ow
)\ }\,.\]
at ter
^{* })|\
}] ^
}^{- }}(\
ĠS S
ĠI nf
}^{+ }/
ĠP D
ĠG P
)}^{ +\
}}|\ ,\
Sp r
}$ ;}\\
Le ngth
05 51
\% ,
44 9
Ġma ss
Ġ&& +\
})_{+ }\]
Ġst d
Ġprop erty
Ġsup er
Ġtri vial
Ġadja cent
) _{-}\
; &
T EP
k X
|\ }.\]
int eg
par ti
{( }{
}^{* })}
}}_{ *}(\
}\| -\|
Ġn y
ĠA P
ĠS GD
_{* }}+\
_{* }}[
\,\ |\,
Ġb ot
}; |
sh ea
}_{+ }}|
13 24
)! !}\
)}) <\
up psi
up delta
47 7
}\}+\ {
ĠEx ample
ĠNa me
) }]_{\
4 40
F h
N on
R t
U X
V x
] }:\
n G
x S
}\ }/\
}) }||
}) )}\|
}, .
Ġ& |
Ġ1 30
ĠC v
)) }}{\
}}) }-\
}|\ ,|\
ĠA c
Ġm p
ĠF ull
11 12
pt R
}}| }{\
Ġo ri
}^{*}( -\
}\! :=\!\
49 7
Ker r
09 1
St d
dn er
_{\# }(
Com m
{\# }
& =-
R n
U D
U lt
b T
Ġ ))+\
th at
ar dner
tri es
}^{- }).\]
}^{- })+\
}|\ }.\]
Ġs ph
}}=\ \
}}= &\
|_{\ {
)}+ \]
})] }\]
}|_{\ {
28 80
}]^{ <\
,+ }\]
,+ },
})\; =\;
olu tions
Ġmaxi mum
Ġabs olute
& [\
C f
E nc
Q B
S ph
i Z
Ġ })\\
}\ }}^{\
}\ })-
}) })+\
=\ )
}}\ ),
ho ck
}| }\,
rc h
}}_{ [\
}\,\ ,(
ĠA E
.\ ;
Ġp res
}^{+ }<\
\[(\ |
}})\ }.\]
_{+ }|\
}}^{- },
Ġth us
\[\{\ {\
}\! :\
an ish
|( |\
)}| +
dash arrow
44 2
06 3
Ġ* }}\
95 1
95 4
)}:=\ |
^{** },
Ġbe fore
* |
5 77
7 00
h J
u T
Ġ })|^{
}\ }}=
)\ },\\
}| (|\
}| /|
)= [(
{) }}_{
}^{- }|\
Ġu l
Ġd U
ĠD C
})-\ {
Ġh t
}_{+ }\\
)\,\ |\
Ġ}( |
)_{\ #}\
\! \{
)^{* },\
ect ral
39 4
Ġ* })\
mm se
{* }{\
circle arrowright
Ġne gative
* }=
> }
B q
D Alg
E uler
J F
R h
S in
S hi
i deal
| ))\
Ġ ]_{\
}\ })^{
in variant
al ly
ar ed
^{- }},\
}+\ ,
[\ !
\, ,&
}\| }=\
ĠB U
ĠD L
)] +[
il d
})| }.\]
** (
** \(\
Ġ+ (-
20 20
Ġ}^{ [
\[= [
)}}{ |\
)\|\ |\
}|| (\
75 5
55 8
}! \,
\# (
}|< |\
CR B
const raint
{}{ {
\: .\]
\ )=
i U
n Q
x N
Ġ }|}\
}= {}^{\
)) }{|\
Ġt p
{| }}\
\|\ ,\|
\{\ !\!\
_{- };
_{- }\|_{\
00 20
ĠM AX
ĠR ad
ĠK dV
Ġw ave
per fd
(( (\
})| ^
}}\| {\
\[[ [\
Ġ| +
45 4
37 3
79 7
})^{* },\]
]\! ],\
})[ [
Ġle arning
])= [\
Ġho ld
Mul ti
Down arrow
fpp f
rich let
# \{(
0 60
B eta
K z
M c
T J
V G
X e
w k
y R
Ġ }}}\]
de R
}| }\\
\| }(\
pa rameter
ĠC G
}^{* }|_{
}}) }-
}}) )}\
)+ (-\
Ġd N
Ġs cheme
_{* }{\
^{+ }|_{
}> =
}_{+ }}(\
23 04
}^{*}( {\
}$ }_{
)}| (
96 5
06 1
08 6
66 8
ĠAv g
ĠPo i
Ġcent er
poch s
. }\,
A bs
F o
q L
v ity
}) })_{\
}, *}(
})\ |^{\
}- )\
eg el
end s
ĠC Z
}}_{ |
}^{+ })}
Ġy y
Ġr x
Ġ10 8
}_{* }+\
Ġ| (\
}): \]
50 7
88 0
SS YT
ĠDe ep
Ġsta ndard
IF AR
ĠLo ss
$ {\
$ }}(
* )\]
- ||
3 01
D J
F K
L z
M IN
W M
h gh
m icro
Ġ frac
math acc
}} };
ar ch
}| )\,
li ce
^{* })]\
}^{* }}[
un fold
}|\ {\
ĠB G
di an
st s
\[|\ !|\!|
(-\ |
}_{+ }}|\
}+( (\
})| )\]
Ġ\[+\ ,
))^{ +
back sim
ĠO D
\},\ ;\
{\}}\ .\]
08 4
{|}\, |
ran ce
tim ization
mathacc ent
) }}}(
) *}\
) }],\]
. +(
5 25
< \|\
] }&
] };
k P
p ure
w R
Ġ succ
Ġ ))-\
^{ [-
}( _{
}) $}.\]
Ġ\ }=\
}_{\ {\|
}| +\|
Ġi u
Ġa xi
Ġ}\ }.\]
{(} [-
Ġk j
Ġs r
Ġs kew
vec tor
ĠI ter
{] }}\]
{] }&\
Ġ{\ |\
}})\ .\]
_{+ }}}\
^{+ }}}\
ĠG u
Re c
^{*}( -\
oth er
)\| ^
Ġ\,\ |
56 1
)}} <\
Ġse ch
Ġme tric
]: |
comp lex
Ġuni form
^{! }(\
com pact
hy dro
+ ...+
8 40
A lb
O DE
] {(
] $}.\]
w dx
| )}(
Ġ triangle
Ġ ^{*}_{
Ġ }]_{
ra ted
}} }:=
_{\ !\!\
lo ad
)) }{(\
}}) )+
)} /(
)} <+\
ĠL C
ĠA b
}}= -(
_{+ })+
^{+ }:=\
]}\ {\
-( |
Ġin variant
})(\ |
}=-\ ,\
Ġis omorphism
Ġ}{ {\
en ces
as k
}\; .\
)^{* })\]
56 3
000 6
,* },\
Du al
Ġ* },\
!\! /\
58 9
fin e
})\! -\!
Ġfinite ly
_{\! {}_{
}^{{ }_{(
GO E
Fe yn
) [\![
A MP
H v
J B
L eg
R am
] *
b etween
n is
w ar
^{ {}^{(
}) }=-
}| }^{\
}^{- }),\
)) ))\
Ġf a
Ġ=\ |(
}& (-
Ġc x
vec t
ĠE B
}), |
}_{+ })}
14 23
dz d
}_{* }}(
che s
Ġ| {\
})] (\
36 00
}}[\ ![
)}\, =\,\
29 1
06 2
Ġ{* },\
Ġ{* },
^{** }
Ġare a
}|\, ,\]
ime n
ĠAd am
! \|\
) })=(\
- ),
5 40
E CT
I Br
K m
V U
j y
z B
Ġ }\,(
}) .}\]
}) )+(\
}} !
}}\ })\
}, (-\
}, [-
^{- [
)}\ ;,\]
}/ [\
ĠL ea
Ġk r
ĠT op
}}}\ ;\
^{+ }}-\
}_{+ }:
^{*}( [
div idual
\[=\ |
|| }{
)! (\
)! }(\
96 1
79 3
59 2
69 0551
]\, :\,
^{(- )}_{
comp osition
})_{+ }^{\
})\! +\!
mon o
`` \
Hod ge
shea ves
imen sion
) }})=\
5 24
: \{\
S mall
f ic
l q
}\ })}\
me rical
}} })+
cal l
su r
er g
^{* })_{\
^{* }\|\]
Ġ1 40
)) ]_{
{| }}{
Ġn h
}|\ ;
}[ :,
}\,\ \
{)}\ ;,\]
}}^{\ #
_{* })}
ĠH L
12 21
_{- }|^{
00 12
(- {\
}_{* }\|^{
as tic
)}) )=\
37 2
55 9
95 3
}\,| |\,
db l
Ġdu al
Ġcop ies
" \
" \]
- (-\
4 45
D NN
J C
] }),\]
a ck
b S
h ar
j w
k I
w o
x E
x K
x m
}\ }=-
}_{\ _
se m
li cy
)) |=\
\, _{\
)} [-
re st
ĠL ayer
)^{\ #\
ĠA ccu
ĠB MO
Ġc R
ĠH C
ĠH ess
}^{+ }[\
})_{ +}
_{+ }\,
}}| }\]
bra n
})^{- (\
^{*} <\
}|_{ {\
\; {\
Ġ[ [
98 3
po i
ĠRe ference
SW AP
Ġexp onent
,. )\
Ġspe ed
! }{(\
, [-
4 226
A LG
I W
\ }\|
h as
w ave
Ġ ]^{\
}_{ =:
},\ ,\,\,\
era ture
^{* }_{-
Ġ1 32
}^{* }((
)) )}{\
Ġt v
}\| )
Ġk e
ĠB atch
it z
))\ },\]
_{- -
)| }=
:\ :\
_{+ }).\]
})| (\
}{| |\
Ġpair s
) }):=\
* }^{-
E w
S d
b L
b its
h R
i dx
r M
z ation
Ġ }))
Ġ )}|
Ġ ))^{\
}\ }),\
}} }}_{
ti s
}}\ ;\;
}+ _{
}=\ {{\
}| })\
co vol
co mb
}}) *\
it e
ĠT f
Ġp ol
Ġ\[=\ ,
ĠF il
}> _{\
13 13
Ġth is
}_{[ -\
88 5
tra t
{{( *
Ġra n
allow break
Ġgene ric
deR ham
, ..
; &\
S pace
] }\,.\]
b E
o g
Ġ },\]
-\ {\
su lt
}- ||
}| })\]
Ġ}\ !\
]\ }_{
}[ (-
Ġe s
ĠH K
Ġg lobal
^{+ }}-
)] )^{
))= [
)})\ |\
)^{* },
}|| |\
ct ed
}&= &-\
39 3
07 3
else where
Ġemb ed
4 23
4 25
8 75
I g
O FF
a th
h I
p X
Ġ }+|
Ġ {(-
}) ),(
}} }}{(
}^{\ ;
na ch
})\ })\]
^{- }}{\
Ġa bj
), (-\
Ġk k
Ġc ard
})- [\
_{( [
ĠM I
}(- ,\
et ti
Ġ10 5
},\,\ |
78 3
58 7
^{\# },
\# (\
Ġop timal
Ġsurf ace
E e
N Q
S a
c pl
r C
r V
w g
Ġ )})
}) !}{
}}) )_{\
Ġn n
ĠB y
Ġs er
_{- }),\
}^{+ }:=
ĠD S
ĠF S
,- )\]
})=( (\
}\; |
)^{* },\]
,* }}\
39 0
Ġra m
dec reasing
ou rce
) .\\
4 21
B k
S eg
X L
d den
k K
m G
| |}\
} ..
^{ {(
}\ };
\[ :=
de ns
}= &-
se l
ro rs
}}^{ |
De l
\| }=\
ĠC W
}^{* })\|^{
Ġ= &(
ĠB L
ĠM ini
(- |\
/\ !/
Ġm x
ĠR m
pt l
\[|\ !|\!
Ġ(\ |\
})| &\
Ġin dividual
}}[ {\
_{| (
)^{* })\
})< _{
!\! \{\
Ġre n
IJ KL
}]}{ [
MP C
.... ....
{}{{ }^{*}}{\
ĠAccu racy
* }}
4 13
Q y
j ec
q D
Ġ ]+\
}}\ }^{
^{- }),\
}}^{ [-
^{* })\,
Ġ\[\ ,
}] \,,\
}^{* })=(
)) ]=
}}) }\|
)| =(
{] }|
)_{ ,
\[(\ |\
}}| )\
38 2
78 0
]\! .\]
SS I
Ġ&& &-
Ġla bel
We il
}|\!|\! |_{
ĠBi as
ode sic
ĠLear ning
! -
. }{
B ind
B AD
I RS
M y
X w
] }\)
] ],\
e le
m Q
o cc
q depth
s J
x U
Ġ },\,
ta tive
}, ||
})\ },
}| )}{|
}] ))\
}^{* }},\]
^{( |\
Ġc ar
Ġs b
12 56
ĠM V
ĠM ed
})+ [\
ĠD imension
}_{+ }},\
)}_{ -\
]^{ [
}}^{- },\
)}) ^{*}\
36 1
000 8
)}} >
50 6
76 3
]\! ].\]
09 2
77 7
) _{*}(\
5 27
8 01
< {\
A O
H ur
S ep
] )/
g q
l ar
p D
q F
w I
| }\\
Ġ let
Ġ )=(
}_{ !}\
)^{ **
}| }}\]
^{* }}}^{
}^{* ,*}(
}}_{ -\
Ġk s
}& -(
_{* }([
}^{+ }=(
ĠR L
11 01
}), |\
\) :
}}| >\
ch ed
)},\ |
})(\ |\
)}= |
}}^{* \
ĠO b
}^{[ *
}\! :\!\
)}) :
}}] }\]
he ight
|}{\ |\
^{** }(\
}}}{{= }}(\
\)\ (\
ĠGen era
Ġradi us
{{< }}{{\
) {}^{
. }(\
\ }^
h U
w ay
| ),
Ġ maps
Ġ }}{|
}} }))\]
+\ {\
}}^{ {\
Ġx n
Ġ2 40
Ġi dentity
}}) ]=\
{| }[\
}\| },\
), -(
cu racy
}/ \{\
_{- }\,\
}), ...,(
_{+ }),\
^{+ }:
{- -}
{)} .
Ġ** (
)}) )=
48 3
Ġco de
}! )^{
Alg orithm
SA M
Ġch annel
valu ed
$ }}}_{
+ }=
, <\
: [\
E qu
] }),\
b Y
s Y
s ome
Ġ ]=\
}\ }:\
ma ry
}) }}{\|
Ġ\ {-
}+\ #\
}| &
}| .\
}] ;\]
}^{* }\|\]
)} [(
}^{+ }),\]
st ru
_{+ }},\
_{+ }^{*}\
:= [\
sta n
ab d
Ġin to
Ġ| -
)})\ }\]
)|_{ (
44 6
08 3
49 4
07 4
}}\; =\;\
ie w
Ġdiff erent
tiv ation
Ġoccu rs
! }\\
H Z
K I
c pt
s V
v is
Ġ )}}{
Ġ }+|\
de an
}=\ |(\
)}\ !\!\
li an
}^{* }}+
}\, )\]
Ġi kx
Ġf ail
}}) })\]
Ġa fter
}/ \{
ĠL u
ĠS ymbol
Ġp d
)| +(
ĠN M
}; &
Ġ\,\ |\
{)}\, =\,\
,+ }+
49 1
ke y
ram ified
Ġtran si
5 36
X S
[ }\
\ }:=\
] }_{(
] },(
] ]+[
h ed
o k
Ġ }:=\
Ġ target
}^{ !}
}) }\|_{\
}) ):=
}) )].\]
,\ {(
de suit
su c
Ġ1 24
}] -(
Ġt L
}}) })\
}}) ].\]
Ġa bc
ĠL E
di tive
_{* }}-
ĠH ilb
bf d
Ġv ia
Ġr d
ĠE M
}}- \]
}\) :
}_{+ }^{-
})| -|\
}\}\ .\]
|| (\
}$ }\}.\]
Co ng
\[- {\
96 3
}&= &(
ne igh
ir th
46 1
46 3
Bi mod
spa desuit
ĠCond ition
! }(-
* })\]
B m
G f
G et
M HM
N LS
S gn
X V
\ }}&\
] })-\
] }{}^{
r Q
| )(\
}\ }\,
}\ }}+
}} })_{\
=\ !\!
=\ ;(
ri x
}^{\ #\
}| ]\]
Ġf requency
un k
}}^{\ ,\
}),\ |
^{+ }}=\
Ġ10 9
_{| |\
Co eff
35 3
ac l
^{*}, -
98 1
06 25
55 4
\[+ (-
95 9
)^{+ }(
CF K
BMO L
Ġho rizon
GH Z
ĠCom p
Ġpri mitive
- }_{\
< }\
M s
P s
Q b
b K
e con
g xy
r I
z b
}\ }_
)\ }}{\
}^{\ |\
ho lds
^{* }=-\
^{* })]
{) };\
}^{- }}{\
)) ,\,\
\, )\,\
Ġt y
ĠS o
ĠS w
ĠT P
ĠN et
ĠP V
_{+ }}-\
{\| }\|\
^{+ }_{(
}}- (-
}}| -\
\[|\ {(
}_{+ })}\]
}}\| .\]
}}[ -\
du e
}\; ,\\
19 20
}\;\ ;\;
Ġ* },
Di rac
}! }{\
Ġun if
Ġ\! -\!
}}]= [\
}}&= &
Ġga in
Ġderi vative
4226 38
= {}^{
S Z
v j
x dx
Ġ }_{-
ra ng
}) }+|
}) )^{*}\
Ġ\ {|
}} })(\
^{- ,
}^{* }{
}}) }\,\
{| }\|\
pro g
ĠB ase
\,\ \
ĠR M
}}| =|\
)|\ }\]
}\{ [\
)]\ }\]
60 6
)\; :\;
49 2
57 60
Ġra nge
ĠDe f
}}_{+ }^{
olu me
short mid
) }],\
* \]
H MR
o sp
x j
_{ {}^{
}) ^{*})\
}) ),&\
Ġ\ })\
)\ }}{
op ulation
Ġ& |\
li ft
{) }^{+}\
{) }&=\
}: \,|
\|_{ {}_{
)) .
)) })\]
Ġf amily
or th
{| }^{-
Ġu b
sup er
re ed
ĠB M
ĠT u
_{* }}+
Ġe pi
Ġ\[= {\
})}\ }_{
Ġ- [
_{+ })+\
rel int
ĠW eight
=( (\
15 36
{]}\ .\]
\[[\ ,\
te ri
)}| +|
Ġde p
}): \\
}}^{+ })\]
78 2
08 2
46 2
^{*}) ^{*}\
Ġse g
})}+\| (
Ġpa ra
}^{(+ )}(
ĠFig ure
via tion
Ġarbitra ry
/ _{\
F DR
M RT
R z
S kew
T OP
\ }|,\]
e H
h T
s G
Ġ })|
}\ }}-\
\[ :
}, ((
{) }^{*}
)) })\
\{ *
Ġt z
}}) ,&
Ġs w
ĠS emi
_{* }}^{-
)\, [
)_{ {}_{
Ġh alf
ĠG raph
}:= \]
\[= |
Ġ|\ ,
}_{* }-
pre v
\[\{\ ,\
kl m
)[ (\
,\; |
Ġvec tors
Sta nd
Ġconstraint s
satisf ies
! \{\
F m
n exists
| }<\
Ġ current
}} }}-
})\ }\\
ad dle
^{- }\|_{
se g
^{* })>
co e
}] _
}] )_{\
\| },\]
}^{- }&\
}\, )
Ġ}\ }\]
}\| /
re at
ĠL ower
ck ing
ĠB r
ĠN aN
ĠF unction
ĠP R
ĠP SL
_{+ }}=\
_{+ }^{*}\\
Ġb k
Ġg rid
^{+ })}\
\}\ ;\
)] }.\]
)] =-\
}_{+ }}{
}}\, _{
20 19
)}, [
})) ;\]
)}) <
55 2
]\! ]=
Ġre qu
97 4
Ġdy n
Ġch ain
Ġba sed
whi ch
ctr l
+ }}
\ })}{
k J
}) };\
}{ {}_{
}}\ }}
Ġ1 29
}] ]=\
}^{* }]=
)) ],\]
}}) }|
Ġd M
Ġp otential
)| {\
}\|\ ,\|
)\, ;\,
ĠD D
ĠP L
{\| }\,
^{+ ,\
Ġ3 20
ce pt
)] \,.\]
,- }\]
Ġl k
)}= :
\[= :\
}}\|\ |
})) [\
})] \|_{
con c
)}| .\]
ac p
,* }=
lu id
]-\ {
55 5
\}=\ {(
ĠRe f
Ġ\! -\!\
Ġreg ion
Ġgen erator
.&.& .&.&
liz ation
Ġcri tical
atu res
9 64
9 28
9 72
> +
A rc
H aus
\ })=\{
] :(
n om
z M
| )/
| |^{\
| }}{|
Ġ box
Ġ }=(
Ġ ]=
}) )}_{
}} }\,,\
}, +}\
se lf
Ġ0 10
^{* }):=\
^{* })\,\
^{* }|}\
}^{- }),\]
Ġi l
cu m
re lax
Ġc T
})}\ ;\
}}}\ {\
{] }>
{] }=-\
ĠM ar
Ġb u
)|\ ,|\
(( |\
)}}\ |_{
)}\, |\,\
Ad S
ĠDe t
_{> ,
cri tical
112 2
,: }\|_{
}}{{= }}(\
ĠTra ining
Ġve hicle
ĠSing le
$ }\,.\]
, &-
3 18
A ST
F EM
G AP
G auss
[ ]{\
\ }\|\
] }/
] )|\
f R
t binom
x xy
Ġ })\|^{
Ġ ^{*})\
}) };
Ġ\ #\{
Ġ1 27
Ġa bi
Ġd rd
Ġk h
ĠA nn
_{* }((
Ġp w
)| }}\
}\|\ ,\|\
Ġ^{ |
for ma
})} <+\
}_{* }.\]
}* &
}\; |\;
Ġ&= :
Ġ* &*&
57 1
ĠâĢ ľ
ĠCo rollary
Ġnon zero
rop ic
}^{** },
rac te
|\!|\! |
}(* )\
Si egel
spherical angle
) }^{*}(
) }),\\
* \\
- }}
> |\
D q
\ )-\(
] }}.\]
q K
q R
w acc
y I
z K
Ġ )[
}} }}-\
ot one
})\ :
})\ }+
^{* }||_{
pa tible
}^{- }\}\]
ij s
ĠA f
Ġs f
_{- }).\]
Ġm oment
ĠF un
_{+ }^{*
\}\ !
rel u
}))\ .\]
})| ,|
oth e
\; :\;\
Ġ[ (\
38 3
)\! )\]
}! \]
68 6
ea ch
Ġla st
Ġdivis or
5 28
5 44
8 192
P SS
R d
Y D
Z W
] })+
e z
g ch
j H
q H
u B
\[ *\
^{- }),
Ġ0 2
De p
Ġ1 16
Ġ1 36
\| {
row th
)) }}\]
Ġf f
Ġn kQ
cu bic
Ġd c
ĠS ample
_{* }},
Ġp ert
ĠN u
}}}\ ;
ĠI nput
}^{+ }\,
_{+ })_{
{\| }\!\
ĠG e
}_{+ }^{(
)/ [
}\;\ ;\;\
)}\, |\,
+\| (\
)_{+ }.\]
SA N
}_{\# }(\
}\: .\]
Ġdiffer enti
- }=\
M b
P w
S imp
] &=
e pt
g U
s parse
| }(|
Ġ ))-
}}\ {(\
la te
}+ {}^{
li j
Ġc f
Ġs ymbol
ĠS el
ĠS tep
Ġ\( =
_{* }},\
_{- (\
_{- }}}\
ĠF ed
}}+ {
_{+ }^
}}| -|
}=( [
13 23
}< \|
)}_{ >
Ġal so
}}\| |
)! }+
)! \,(
)\| <
45 3
pr ot
37 1
}))^{ (
75 9
,-\ ,\
no des
78 1
pe ak
^{** })\
^{** }-
Tw Sp
\|\, .\]
Ġpo st
Ġrepresen tation
, ^{
0 99
G v
R k
e K
f lip
m se
q E
t U
z R
Ġ ^{+}(
}\ })+
^{- *
^{- }},
)) }<\
}}) ))\]
}}) ^{*}(\
}}) ;\]
re ss
\{\ !\
ĠA X
ĠA z
}}+\ \
)| ]\
ĠM U
st rong
ĠF E
_{+ })^{\
ĠK M
ĠU niform
}_{+ }),\
}_{+ }^{*}\
})_{\ #
ĠO PT
}}}( (\
}\;\ ,
an y
Le v
37 0
|=\ |
|< |\
^{\# }_{
}{}{ }]
AD M
Ġcap acity
ĠLea ve
, ^{\
4 24
8 47
A m
K Z
N IP
Q Y
T t
i des
x C
Ġ ])\
}\ }|.\]
ma sk
}} }([
Ġ{ +}
Ġx t
}^{* }]_{
)) )}\]
Ġi P
}\| -\|\
ĠL L
}& :
^{-\ |\
_{* }}_{
_{* }>
Ġm d
})| /
\[=\ |\
}\! /_{
40 2
40 3
cccc ccc
,* )\
}=[ -\
\}= \]
58 6
)^{+ },
_{! }^{\
Ġqu asi
Ed ges
! )\
. }}{\
6 59
L b
O sc
S l
S te
g trap
Ġ )-(
Ġ })).\]
}\ }\|
ma ss
da y
mu lation
}| [\
^{* }]\]
Ġ1 22
Ġi mage
\, (-
Ġt s
Ġu r
ĠS q
ĠT F
Ġp aper
ĠP e
)},\ ;\
et c
)}\, ,
Ġde cay
Ġ}{\ |
Ġcon juga
)})^{ (
Ġsu rj
}! }{(
68 9
})\; ,\
ori ze
ĠPro b
(. );\
toch astic
ĠPoi sson
gtrap prox
$ }^{(
. },
4 10
4 22
5 13
I AA
V ir
\ }}[
\ }}\\
] }_{[
m rk
p J
u R
Ġ lim
Ġ )),\
}) }}-\
}= <
{( }||
}}^{ {}^{
Ġ{ [\
}^{* ^{\
}}_{ {}_{
),\ ;\;\
Ġd ue
ĠL B
{)}\ ,\,\
ĠA F
ĠS NR
_{* }))\
_{* })\,
12 22
12 80
Ġv anish
)| },\
})_{ /
ĠE G
}}| {\
})| ,|\
}}\| }\
)=( [
^{*}(\ {
64 1
an ced
Ġdx ds
})\|\ |\
)}\,\ |
07 0
)\! ,\
},\; (
Ġ{+ }}\
vi rt
}}}{{= }}-\
}}_{+ }(\
ĠCom ple
inn er
Ġcyc lic
+ ,\
0 123
D d
E U
E st
M Y
Q K
j ik
m Y
v A
Ġ name
Ġ }_{\{
Ġ }}}.\]
Ġ ``
\[ :\
}} }]
}, ||\
la ble
text minus
}}( [-
^{* }}[\
Ġ1 17
Ġ1 92
co arse
}}) }+\|\
Ġ}\ ,\,\
)+ _{
})= {
Ġd Z
Ġg d
ĠG D
ln ot
per s
}/\ !\!/
}}\| +\
))^{ *}
}}^{* },\]
Ġ10 4
^{*}_{ [
Ġ\| {\
)}) |^{
56 2
}|| .\]
,+ }=\
)})^{ -\
)_{+ }}{
SE P
})}_{ =
RS T
Ġexact ly
Ġus er
! +
) }})_{
0 98
F g
J d
N w
Q U
Z A
\ }]
\ })_{
] })-
b C
k V
v n
{ +\
| )}{|\
Ġ )}_{\
}) ...\
ri ft
^{- }).\]
set s
\, :=\,\
Ġa ngle
]\ ;,\]
ul t
_{+ }&
Ġh f
Ġg l
^{+ })+
{\{ }[\
})}{ -
}))\ |
}_{+ })}.\]
}{| (
^{*}( (\
}}\| =\
\[=\ {
dz dw
)! .\]
Ġ| +|
+|\ {
45 1
08 1
SO C
)\! )\
}))}\ |\
_{< }(
Ġ{+ }^{
Ġnu ll
SW F
den se
AS SO
Ġso urce
ĠVar iable
Ġmini mum
Ġneighbo rhood
Ġass oci
) }),(
+ }-
+ }-\
B SO
C J
R OM
\ })}\]
h N
j f
Ġ ),\\
Ġ triv
}^{ /
ra ction
}{ }^{*}\
qu o
^{- })+
Ġ& \{
{) },\,
co mm
ĠC lass
Ġ} }).\]
)+ ((
)} &-\
}\,\ {\
ĠV e
ĠE d
}}+ ...+
... \,
}}\, =\
}{( |\
})| }{(
Ġin cl
Ġ| +\
)})\ |
}})= {\
}})= (-
Ġ&= (-
58 5
68 7
Ġdi rection
^{** }_{
PS U
}}\; ,\
., }\
CM on
sw arrow
emp erature
+- +-
* }.\]
4 01
B GL
E l
F Z
Q z
\ }=-
] ))=
c de
u ge
x aby
| }_{\
| ))^{
Ġ )\]
Ġ )<\
Ġ )})\]
Ġ ]-\
Ġ ^{*}\]
}\ };\
Ġ& &-\
wi t
{) },\,\
}}) }+\|
),\ ;(
_{* }]\
_{- }:=\
)| ).\]
00 13
ĠM a
ĠP C
Ġh h
}}- [\
}}| (-\
ĠU E
ĠW P
,- ,+
Ġ+ }
Ġ10 6
en na
})\,\ |
}}& (\
an c
cd f
|\,\ |
}}^{+ }=
55 7
yy y
09 3
68 5
97 3
fe as
Ġinter se
Ġconver gence
dap tive
B g
N J
Q s
] ^{+}\
a ij
k fl
o x
s Q
z D
à ©
Ġ }|^{\
}) )^{*}\]
}_{ >\
ta ge
}_{\ #}\
}=\ #\{
sq supset
Ġ1 21
Ġ{ {}^{\
}^{- })+
}^{- ,+}\
)) |.\]
Ġt wist
)^{\ {
fo ot
_{- })-
ĠI RS
ĠM R
Th ere
}&\ {
ĠE ff
ĠR f
ĠK S
):=\ #\{
}\) ]
)|\ ;\
^{*}\ {
)})\ |_{\
}\; |\
)* }
CA T
}); (\
Ġmod ule
tg t
ZF C
Get S
( =\
) }}}{{=}}
/ **
N i
P et
U N
b P
_{ ]
\[ :=\
})\ }}
})\ }=\{
^{* }}\\
}\, :=\,
\, =
ca b
sp l
ĠL d
ĠA ll
<\ ;\
ĠH W
12 35
ĠM P
}^{+ }\,\
}^{+ })^{-
)\, ;\]
})_{ <
Ġm icro
ĠR n
ĠD B
ĠF r
_{+ }^{*}
Ġw or
}=( |
}_{- })
ik jl
ip tic
)\| ,\
45 2
up date
ir d
Ġ* &\
80 9
Ġ{+ }(\
cyc lic
Ġtop olog
bran ch
* }-\
. }\;\
L inear
N um
W res
] }},
] };\
i W
m S
r F
r S
u de
Ġ }|_{\
Ġ ):\
le g
ta ck
si te
)}\ |(
}| )}\]
)=\ {\{
}: \{\
ĠC ap
Ġf ol
}}) ](
}}) _{*}
Ġa q