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dda3e93cb4fa7cd7cd63845090a65a6f3e7b5a73
the four-time defending champions, stanford, successfully defended their
the four-time defending champions, stanford, successfully defended their pac-12 title. the cardinal entered the ncaa tournament as the three-time defending champions, but were eliminated by akron in the quarterfinals. joining stanford in the tournament were oregon state, washington, and ucla.
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b6025e69d7321b93bb3c6d7cccac646ec6929ef2
the 2018 pac-12 conference men's soccer season was
the 2018 pac-12 conference men's soccer season was the 19th season of men's varsity soccer in the conference. the season began on august 24, 2018 and concluded on november 9, 2018.
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2f150c0cedf6af1e02afe9f81e48981adf133b8b
estes foster "easy" parham was an american professional
estes foster "easy" parham was an american professional basketball player. parham was selected in the 1948 baa draft by the st. louis bombers after a collegiate career at texas wesleyan. he played for the bombers for two seasons and then the philadelphia warriors for one season before ending his baa/nba career.
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0655d9836392bfafb5adf6cbfbf7593d8751bbf1
estes foster "easy" parham (december 27, 1921 –
estes foster "easy" parham (december 27, 1921 – october 4, 1982) was an american professional basketball player. parham was selected in the 1948 baa draft by the st. louis bombers after a collegiate career at texas wesleyan. he played for the bombers for two seasons and then the philadelphia warriors for one season bef...
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bf68bd6f41e9731ca3d91b9b9f2bf0ef2e9f1bc6
having worked his way through the shimizu s-pulse
having worked his way through the shimizu s-pulse youth system, he signed full professional terms at the start of the 2006 season. yamamoto has represented his country at several levels up to an including under 20, although has yet to break into the full national team.
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2f13d8069dbb67dd82db62fdd5b2013cefecb2e4
masaki yamamoto (山本 真希, yamamoto masaki, born 24
masaki yamamoto (山本 真希, yamamoto masaki, born 24 august 1987 in shizuoka prefecture) is a japanese football player currently playing for j1 league team matsumoto yamaga fc.
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ff3271a157a02bba175d6381fc8a1b8159434012
ariel john litang edu is a cypriot-born filipino
ariel john litang edu is a cypriot-born filipino professional basketball player who last played for toyama grouses of the japanese b.league. listed at 6 feet 10 inches (2.08 m) and 224 pounds (102 kg), he plays the power forward and center positions. he is a member of the philippine men's national basketball team.
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f2c7c5f319cec74b50ca4c7c148d976d9f926c87
edu was granted filipino citizenship from a young
edu was granted filipino citizenship from a young age after difficulties in receiving a cypriot passport, which made him eligible to play for the philippines in fiba competition. however, he still drew interest from the nigeria, cyprus, and great britain. in 2017, edu joined the philippines at the fiba 3x3 u18 world cu...
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4636af9b43a1a93b8fac931e8c35e9e70851b0e4
on april 12, 2018, edu signed a national
on april 12, 2018, edu signed a national letter of intent with the toledo rockets under head coach of tod kowalczyk. he played all 33 games, averaging 3.6 points, 3.9 rebounds and a team-high 1.7 blocks in 14.3 minutes per game. edu recorded 57 blocks in the season, the most by a freshman in program history. he was nam...
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12af23dc850cda674c6033efa87681fa4cff6642
edu began playing basketball at the age of
edu began playing basketball at the age of seven in the junior ranks of cypriot club ael limassol. he also played soccer in his childhood but began focusing on basketball due to his exceptional height. after his family moved to england a few years later, edu joined the bristol flyers cadet team and the swansea storm in...
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dbeb624b2e5e0e8e1f5bf0b3a524e773b0bf33e5
edu was born in cyprus to a nigerian
edu was born in cyprus to a nigerian father ayotunde edu and filipina mother josie litang-edu. his mother is a native of surigao city, philippines but moved to england for work after finishing her education. she met edu's father, a mathematics and physics professor. standing 6 ft 8 in (2.03 m), ayotunde played basketba...
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bf2470583b7b87a054a34cef1de41d101fc62093
ariel john litang edu (born january 1, 2000)
ariel john litang edu (born january 1, 2000) is a cypriot-born filipino professional basketball player who last played for toyama grouses of the japanese b.league. listed at 6 feet 10 inches (2.08 m) and 224 pounds (102 kg), he plays the power forward and center positions. he is a member of the philippine men's nationa...
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8b069e5b7da096a1837b8cc05345ef03ea8aac7d
the 2013–14 arizona wildcats men's basketball team represented
the 2013–14 arizona wildcats men's basketball team represented the university of arizona during the 2013–14 ncaa division i men's basketball season. the team was led by fifth-year head coach sean miller and played home games at mckale center in tucson, arizona as a member of the pac-12 conference. they finished the sea...
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f05ff15b01b31481bb0337c9dbe3966ae1983535
arizona's thirteen-game non-conference schedule had two road games,
arizona's thirteen-game non-conference schedule had two road games, two neutral-site games, and nine home games. the team spent thanksgiving in new york city for the 2013 nit season tip-off semifinal and championship rounds held at madison square garden. arizona was one of four regional hosts for the nit tip-off's firs...
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2e3ef574da6b2053d668dabd1ea2447bf4c32a23
arizona's 2012–13 team finished with a record of
arizona's 2012–13 team finished with a record of 27–8 after advancing to the ncaa tournament 's sweet sixteen. the team went 12–6 in the pac-12 regular season, putting them in a three-way tie for second place. in the pac-12 tournament, the team defeated colorado to advance to the semifinals, where they lost to ucla. ra...
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7b8cb4600ca8ab1b3474b069fbecfe511dbbc554
the 2013–14 arizona wildcats men's basketball team represented
the 2013–14 arizona wildcats men's basketball team represented the university of arizona during the 2013–14 ncaa division i men's basketball season. the team was led by fifth-year head coach sean miller and played home games at mckale center in tucson, arizona as a member of the pac-12 conference. they finished the sea...
wikipedia
0164cfc1d533ed69969350d2de43417b6a792160
florent hadergjonaj is a professional footballer who plays
florent hadergjonaj is a professional footballer who plays as a right-back for süper lig club alanyaspor. born in switzerland, he previously represented his birthplace at youth and senior levels before switching to play for the kosovo national team.
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ed906faa170150349183ed918a157bcfb179d855
on 9 may 2019, the football federation of
on 9 may 2019, the football federation of kosovo confirmed that hadergjonaj had obtained a kosovan passport and was ready to play for the kosovo national team in the next uefa euro 2020 qualifying matches. on 22 may 2019, hadergjonaj received a call-up from kosovo for the uefa euro 2020 qualifying matches against monte...
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bc3ff141460849460c4d1c609b6ea840f42433db
on 22 may 2017, hadergjonaj received a call-up
on 22 may 2017, hadergjonaj received a call-up from switzerland for the friendly match against belarus and the 2018 fifa world cup qualification match against faroe islands. on 1 october 2017, he made his debut with switzerland in a friendly match against belarus after coming on as a substitute at 46th minute in place ...
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ecae3ef3afa2127cc613259c13b33cb7accd9b69
on 25 september 2020, hadergjonaj signed a three-year
on 25 september 2020, hadergjonaj signed a three-year contract with süper lig club kasımpaşa. one day later, he made his debut in a 1–0 away defeat against hatayspor after being named in the starting line-up.
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2437eb63448cb50846a78cc07fe8a84ab9ff2275
on 31 january 2020, hadergjonaj joined süper lig
on 31 january 2020, hadergjonaj joined süper lig side kasımpaşa, on a six-month-long loan. two days later, he made his debut in a 1–1 away draw against ankaragücü after being named in the starting line-up.
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68fa9901960006768e57819e4a53182794820f42
on 8 march 2018, huddersfield town triggered a
on 8 march 2018, huddersfield town triggered a clause in hadergjonaj's loan agreement to make his transfer permanent. on 1 july 2018, he signed for huddersfield town on a three-year contract with a club option of a further season. on 11 august 2018, he made his debut in a 3–0 home defeat against chelsea after being nam...
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1fef8f3bf6516b25b48a624876dac4ebc02e3c35
on 24 august 2017, hadergjonaj joined premier league
on 24 august 2017, hadergjonaj joined premier league side huddersfield town, on a season-long loan. on 19 september 2017, he made his debut with huddersfield town in the 2017–18 efl cup third round against crystal palace after being named in the starting line-up.
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188e9c722d44189b28bb25dcbdab5da5a728458a
on 8 august 2016, hadergjonaj joined bundesliga side
on 8 august 2016, hadergjonaj joined bundesliga side ingolstadt 04, on a four-year contract. on 22 october 2016, he made his debut against borussia dortmund after being named in the starting line-up, and assist in the third goal during a 3–3 draw.
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f543a5aea107c989058b9943e6e59f40aa318c26
hadergjonaj is a youth exponent from young boys,
hadergjonaj is a youth exponent from young boys, he made his first swiss super league appearance on 29 september 2013 after being named in the starting line-up in a 1–0 home defeat against zürich. hadergjonaj made 11 league appearances during the 2013–14 season and he won the young boys' player of the year award after ...
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a5b6330fc7dbd3cfc2f3f9225a34f9c8e31df6a5
florent hadergjonaj (albanian pronunciation:; born 31 july 1994)
florent hadergjonaj (albanian pronunciation:; born 31 july 1994) is a professional footballer who plays as a right-back for süper lig club alanyaspor. born in switzerland, he previously represented his birthplace at youth and senior levels before switching to play for the kosovo national team.
wikipedia
e4dbb7cf590172162427347cc4adf20cde94573f
after college, lear was selected by the philadelphia
after college, lear was selected by the philadelphia warriors with the seventh pick of the 1956 nba draft. his nba career was brief, however: he appeared in just three games during the 1956–57 nba season and scored four points. he played for the easton madisons of the eastern professional basketball league (epbl) and w...
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c4d51c5e6ca625e2306d4bfbe82290f71773d063
a 6 ft 0 in (1.83 m) guard
a 6 ft 0 in (1.83 m) guard born in philadelphia, lear starred at temple university in his hometown during the 1950s. he earned the ncaa basketball tournament most outstanding player in 1956 after leading temple to the final four, where they lost to the university of iowa.
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d6d9c5d3796df386fc7b9894552273a12aec552e
in mathematics, the wasserstein distance or kantorovich–rubinstein metric
in mathematics, the wasserstein distance or kantorovich–rubinstein metric is a distance function defined between probability distributions on a given metric space m . it is named after leonid vaseršteĭn. intuitively, if each distribution is viewed as a unit amount of earth (soil) piled on m , the metric is the minimum ...
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5f771ab494131db5d43974819db6924dbb0184bd
it is also possible to consider the wasserstein
it is also possible to consider the wasserstein metric for p = ∞ {\displaystyle p=\infty }. in this case, the defining formula becomes: w ∞ (μ, ν) = lim p → + ∞ w p (μ, ν) = inf γ ∈ Γ (μ, ν) γ - e s s u p d (x, y), {\displaystyle w_{\infty }(\mu,\nu)=\lim _{p\rightarrow +\infty }w_{p}(\mu,\nu)=\inf _{\gamma \in \gamma ...
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ccc7f9b868ab7b806ca4193549b5941c7062735e
under suitable assumptions, the wasserstein distance w 2
under suitable assumptions, the wasserstein distance w 2 {\displaystyle w_{2}} of order two is lipschitz equivalent to a negative-order homogeneous sobolev norm. more precisely, if we take m {\displaystyle m} to be a connected riemannian manifold equipped with a positive measure π {\displaystyle \pi }, then we may defi...
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445122c5551573cbd997f3c33958797e46331f09
under suitable assumptions, the wasserstein distance w 2
style w_{2}(\mu,\nu)\leq 2\,\|\mu -\nu \|_{{\dot {h}}^{-1}(\pi)}.} in the other direction, if μ {\displaystyle \mu } and ν {\displaystyle \nu } each have densities with respect to the standard volume measure on m {\displaystyle m} that are both bounded above by some 0 < c < ∞ {\displaystyle 0<c<\infty }, and m {\displa...
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7d294238549e53e1d0063280fcf5303204f3bcb2
given two probability densities p, q {\displaystyle p,q}
given two probability densities p, q {\displaystyle p,q} on r n {\displaystyle \mathbb {r} ^{n}}, w 2 (p, q) = min v ∫ 0 1 ∫ r n ‖ v (x, t) ‖ 2 ρ (x, t) d x d t {\displaystyle w_{2}(p,q)=\min _{\mathbf {v}}\int _{0}^{1}\int _{\mathbb {r} ^{n}}\|{\mathbf {v}}({\mathbf {x}},t)\|^{2}\rho ({\mathbf {x}},t)\,d{\mathbf {x}}\...
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3af2a8e19dceb1fa0a8604d55e958834a0cd0ea5
1d example. when both μ, ν {\displaystyle \mu,\nu
1d example. when both μ, ν {\displaystyle \mu,\nu } are distributions on r {\displaystyle \mathbb {r} }, then integration by parts give e x ∼ μ − e y ∼ ν = ∫ f ′ (x) (f ν (x) − f μ (x)) d x, {\displaystyle \mathbb {e} _{x\sim \mu }-\mathbb {e} _{y\sim \nu }=\int f'(x)(f_{\nu }(x)-f_{\mu }(x))\,\mathrm {d} x,} thus f (x...
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10d27c4b05ff04db58825547f791c72099fa0699
for the second step, picture the infimal convolution
for the second step, picture the infimal convolution cone ◻ (− f) {\displaystyle {\text{cone}}\mathbin {\square } (-f)}, then if all secants of f {\displaystyle f} have slope at most 1, then the lower envelope of cone ◻ (− f) {\displaystyle {\text{cone}}\mathbin {\square } (-f)} are just the cone-apices themselves, thu...
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34458d5cea43a811dd85663e9a94610149f5b7fc
for the first step, where we used f
for the first step, where we used f = cone ◻ (− g) {\displaystyle f={\text{cone}}\mathbin {\square } (-g)}, plot out the curve of − g {\displaystyle -g}, then at each point, draw a cone of slope 1, and take the lower envelope of the cones as f {\displaystyle f}, as shown in the diagram, then f {\displaystyle f} cannot ...
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900635777860dae06a21bf89d662a6f9cf604ab7
thus, w 1 (μ, ν) = sup g
thus, w 1 (μ, ν) = sup g sup f (x) + g (y) ≤ d (x, y) e x ∼ μ + e y ∼ ν = sup g sup ‖ f ‖ l ≤ 1, f (x) + g (y) ≤ d (x, y) e x ∼ μ + e y ∼ ν = sup ‖ f ‖ l ≤ 1 sup g, f (x) + g (y) ≤ d (x, y) e x ∼ μ + e y ∼ ν. {\displaystyle {\begin{aligned}w_{1}(\mu,\nu)&=\sup _{g}\sup _{f(x)+g(y)\leq d(x,y)}\mathbb {e} _{x\sim \mu }+\...
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46d2884bf4cf4ee3bcc781c3b2b821f3959c554c
thus, w 1 (μ, ν) = sup g
\inf _{x}d(x,y)-f(x)}. since ‖ f ‖ l ≤ 1 {\displaystyle \|f\|_{l}\leq 1}, this implies g (y) = − f (y) {\displaystyle g(y)=-f(y)}.
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8a618e55f86df92589da815fd0934e5894fa98d1
it suffices to prove the case of k
it suffices to prove the case of k = 1 {\displaystyle k=1}. start with w 1 (μ, ν) = sup f (x) + g (y) ≤ d (x, y) e x ∼ μ + e y ∼ ν. {\displaystyle w_{1}(\mu,\nu)=\sup _{f(x)+g(y)\leq d(x,y)}\mathbb {e} _{x\sim \mu }+\mathbb {e} _{y\sim \nu }.} then, for any choice of g {\displaystyle g}, one can push the term higher by...
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7284a2673f23d47ab28f7365d6ee0c35c91e7a4c
theorem (kantorovich-rubenstein duality) — when the probability space
theorem (kantorovich-rubenstein duality) — when the probability space Ω {\displaystyle \omega } is a metric space, then for any fixed k > 0 {\displaystyle k>0}, w 1 (μ, ν) = 1 k sup ‖ f ‖ l ≤ k e x ∼ μ − e y ∼ ν {\displaystyle w_{1}(\mu,\nu)={\frac {1}{k}}\sup _{\|f\|_{l}\leq k}\mathbb {e} _{x\sim \mu }-\mathbb {e} _{y...
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aa2a46f1ef6215f4337a917414015f72b8367a65
for you to accept the deal, the price
for you to accept the deal, the price schedule must satisfy f (x) + g (y) ≤ c (x, y) {\displaystyle f(x)+g(y)\leq c(x,y)}. the kantorovich duality states that the shipper can make a price schedule that makes you pay almost as much as you would ship yourself.
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bae1af08d90f5ead33c2f34ed9d26e51bd8a3501
suppose you want to ship some coal from
suppose you want to ship some coal from mines, distributed as μ {\displaystyle \mu }, to factories, distributed as ν {\displaystyle \nu }. the cost function of transport is c {\displaystyle c}. now a shipper comes and offers to do the transport for you. you would pay him f (x) {\displaystyle f(x)} per coal for loading ...
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76a9e0a44ed9b2d63c1f021ef6f619e513b92c37
for the general case, the dual problem is
for the general case, the dual problem is found by converting sums to integrals: { sup f, g e x ∼ μ + e y ∼ ν f (x) + g (y) ≤ c (x, y) {\displaystyle {\begin{cases}\sup _{f,g}\mathbb {e} _{x\sim \mu }+\mathbb {e} _{y\sim \nu }\\f(x)+g(y)\leq c(x,y)\end{cases}}} and the strong duality still holds.this is the kantorovich...
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868e9b7ef0e07d1148f063903fa7ed5bfba1ffdf
by carefully writing the above equations as matrix
by carefully writing the above equations as matrix equations, we obtain its dual problem: { max f, g ∑ x μ (x) f (x) + ∑ y ν (y) g (y) f (x) + g (y) ≤ c (x, y) {\displaystyle {\begin{cases}\max _{f,g}\sum _{x}\mu (x)f(x)+\sum _{y}\nu (y)g(y)\\f(x)+g(y)\leq c(x,y)\end{cases}}} and by the duality theorem of linear progra...
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48c0c2e18eefaef52a166206808f0851c8d31023
discrete case: when m {\displaystyle m} is discrete,
discrete case: when m {\displaystyle m} is discrete, solving for the 1-wasserstein distance is a problem in linear programming: { min γ ∑ x, y c (x, y) γ (x, y) ∑ y γ (x, y) = μ (x) ∑ x γ (x, y) = ν (y) γ ≥ 0 {\displaystyle {\begin{cases}\min _{\gamma }\sum _{x,y}c(x,y)\gamma (x,y)\\\sum _{y}\gamma (x,y)=\mu (x)\\\sum ...
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be71f0bf1b0f2067b352cf2b475e43ed57de2432
ρ (μ, ν):= sup { ∫ m f
ρ (μ, ν):= sup { ∫ m f (x) d (μ − ν) (x) | continuous f: m → }. {\displaystyle \rho (\mu,\nu):=\sup \left\{\left.\int _{m}f(x)\,\mathrm {d} (\mu -\nu)(x)\,\right|{\text{ continuous }}f:m\to \right\}.}
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cf50d907f02ac41f5a078873d10a315759dd323e
w 1 (μ, ν) = sup { ∫
w 1 (μ, ν) = sup { ∫ m f (x) d (μ − ν) (x) | continuous f: m → r, lip (f) ≤ 1 }, {\displaystyle w_{1}(\mu,\nu)=\sup \left\{\left.\int _{m}f(x)\,\mathrm {d} (\mu -\nu)(x)\,\right|{\text{ continuous }}f:m\to \mathbb {r},\operatorname {lip} (f)\leq 1\right\},}
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c1ac9ef96b8129442b02adeac53724d8ee21de9d
it can be shown that w satisfies all
it can be shown that w satisfies all the axioms of a metric on the wasserstein space p (m) consisting of all borel probability measures on m having finite p th moment. furthermore, convergence with respect to w is equivalent to the usual weak convergence of measures plus convergence of the first p th moments.
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258d531055fd7d16ae92fd5c5479c63aa6ad8c05
in their paper ' wasserstein gan ', arjovsky
in their paper ' wasserstein gan ', arjovsky et al. use the wasserstein-1 metric as a way to improve the original framework of generative adversarial networks (gan), to alleviate the vanishing gradient and the mode collapse issues. the special case of normal distributions is used in a frechet inception distance.
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db3c486e434ff458f7a4b6f01706cef84cbadeca
let μ 1, μ 2 ∈ p p
let μ 1, μ 2 ∈ p p (r) {\displaystyle \mu _{1},\mu _{2}\in p_{p}(\mathbb {r})} be probability measures on r {\displaystyle \mathbb {r} }, and denote their cumulative distribution functions by f 1 (x) {\displaystyle f_{1}(x)} and f 2 (x) {\displaystyle f_{2}(x)}. then the transport problem has an analytic solution: opti...
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e0048c403f8620b229106f203222e007c8256ab9
let μ 1, μ 2 ∈ p p
to the formula w 1 (μ 1, μ 2) = ∫ r | f 1 (x) − f 2 (x) | d x. {\displaystyle w_{1}(\mu _{1},\mu _{2})=\int _{\mathbb {r} }\left|f_{1}(x)-f_{2}(x)\right|\,\mathrm {d} x.}
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e5c479a9d9f73b473a282ca0621cab28b26a3a3a
let μ 1 = n (m 1, c
let μ 1 = n (m 1, c 1) {\displaystyle \mu _{1}={\mathcal {n}}(m_{1},c_{1})} and μ 2 = n (m 2, c 2) {\displaystyle \mu _{2}={\mathcal {n}}(m_{2},c_{2})} be two non-degenerate gaussian measures (i.e. normal distributions) on r n {\displaystyle \mathbb {r} ^{n}}, with respective expected values m 1 {\displaystyle m_{1}} a...
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32bff16161fc46317b1951113c6c104e6acdd97f
let μ 1 = n (m 1, c
l (}c_{1}+c_{2}-2{\bigl (}c_{2}^{1/2}c_{1}c_{2}^{1/2}{\bigr)}^{1/2}{\bigr)}.} where c 1 / 2 {\displaystyle c^{1/2}} denotes the principal square root of c {\displaystyle c}. note that the second term (involving the trace) is precisely the (unnormalised) bures metric between c 1 {\displaystyle c_{1}} and c 2 {\displayst...
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2e7b87c52cd152f22224ad22b359c14f0a612aab
w p (p, q) = inf π (1
w p (p, q) = inf π (1 n ∑ i = 1 n ‖ x i − y π (i) ‖ p) 1 / p, {\displaystyle w_{p}(p,q)=\inf _{\pi }\left({\frac {1}{n}}\sum _{i=1}^{n}\|x_{i}-y_{\pi (i)}\|^{p}\right)^{1/p},}
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a709e3ddd7ac1589807524f5a3febe84d2cd90ed
if p {\displaystyle p} is an empirical measure
if p {\displaystyle p} is an empirical measure with samples x 1, …, x n {\displaystyle x_{1},\ldots,x_{n}} and q {\displaystyle q} is an empirical measure with samples y 1, …, y n {\displaystyle y_{1},\ldots,y_{n}}, the distance is a simple function of the order statistics: w p (p, q) = (1 n ∑ i = 1 n ‖ x (i) − y (i) ‖...
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79e1d07ecf14d6055acc2c3ab3577b32b8c19f0b
let μ 1 = δ a 1 {\displaystyle
let μ 1 = δ a 1 {\displaystyle \mu _{1}=\delta _{a_{1}}} and μ 2 = δ a 2 {\displaystyle \mu _{2}=\delta _{a_{2}}} be two degenerate distributions (i.e. dirac delta distributions) located at points a 1 {\displaystyle a_{1}} and a 2 {\displaystyle a_{2}} in r {\displaystyle \mathbb {r} }. there is only one possible coupl...
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a297d5182059aebab43f12ba9682bfe3d42ddd67
let μ 1 = δ a 1 {\displaystyle
_{1}} and a 2 {\displaystyle a_{2}} in r n {\displaystyle \mathbb {r} ^{n}}, and we use the usual euclidean norm on r n {\displaystyle \mathbb {r} ^{n}} as the distance function, then w p (μ 1, μ 2) = ‖ a 1 − a 2 ‖ 2. {\displaystyle w_{p}(\mu _{1},\mu _{2})=\|a_{1}-a_{2}\|_{2}.}
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5fa8dc8232d6d1e3ed91acd3d3553240eab4879e
the plan γ {\displaystyle \gamma } is not
the plan γ {\displaystyle \gamma } is not unique; the optimal transport plan is the plan with the minimal cost out of all possible transport plans. as mentioned, the requirement for a plan to be valid is that it is a joint distribution with marginals μ {\displaystyle \mu } and ν {\displaystyle \nu }; letting Γ {\displa...
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d115d24e1df878818299ef8d02d7ff4511a14385
that is, that the total mass moved out
that is, that the total mass moved out of an infinitesimal region around x {\displaystyle x} must be equal to μ (x) d x {\displaystyle \mu (x)\mathrm {d} x} and the total mass moved into a region around y {\displaystyle y} must be ν (y) d y {\displaystyle \nu (y)\mathrm {d} y}. this is equivalent to the requirement tha...
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06a0c234a39d19891a0abb541fb7ee242ea86526
that gives the cost of transporting a unit
that gives the cost of transporting a unit mass from the point x {\displaystyle x} to the point y {\displaystyle y}.a transport plan to move μ {\displaystyle \mu } into ν {\displaystyle \nu } can be described by a function γ (x, y) {\displaystyle \gamma (x,y)} which gives the amount of mass to move from x {\displaystyl...
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1d247a32983e34978119fee876ded71ea8ca6a7e
one way to understand the above definition is
one way to understand the above definition is to consider the optimal transport problem. that is, for a distribution of mass μ (x) {\displaystyle \mu (x)} on a space x {\displaystyle x}, we wish to transport the mass in such a way that it is transformed into the distribution ν (x) {\displaystyle \nu (x)} on the same sp...
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6ede71e286d93e70bfce5c2c4ecfe58c34c3a302
let (m, d) {\displaystyle (m,d)} be a metric
let (m, d) {\displaystyle (m,d)} be a metric space that is a polish space. for p ∈ {\displaystyle p\in }, the wasserstein p {\displaystyle p} -distance between two probability measures μ {\displaystyle \mu } and ν {\displaystyle \nu } on m {\displaystyle m} with finite p {\displaystyle p} - moments is w p (μ, ν) = inf ...
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838d602c198fda630537710405fb7b323c68ca0a
let (m, d) {\displaystyle (m,d)} be a metric
(a), {\displaystyle \int _{a}\int _{m}\gamma (x,y)\,\mathrm {d} y\,\mathrm {d} x=\mu (a),} ∫ a ∫ m γ (x, y) d x d y = ν (a). {\displaystyle \int _{a}\int _{m}\gamma (x,y)\,\mathrm {d} x\,\mathrm {d} y=\nu (a).}
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c13d2b8fb55112bef32be82309ac0d20f063e378
the name "wasserstein distance" was coined by r.
the name "wasserstein distance" was coined by r. l. dobrushin in 1970, after learning of it in the work of leonid vaseršteĭn on markov processes describing large systems of automata (russian, 1969). however the metric was first defined by leonid kantorovich in the mathematical method of production planning and organiza...
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f17438621ae357370ef74e53b7778136a7375be9
intuitively, if each distribution is viewed as a
intuitively, if each distribution is viewed as a unit amount of earth (soil) piled on m {\displaystyle m}, the metric is the minimum "cost" of turning one pile into the other, which is assumed to be the amount of earth that needs to be moved times the mean distance it has to be moved. this problem was first formalised ...
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a11d4c69d3540e2fa714ff058cb5c1dd808ff49d
in mathematics, the wasserstein distance or kantorovich –
in mathematics, the wasserstein distance or kantorovich – rubinstein metric is a distance function defined between probability distributions on a given metric space m {\displaystyle m}. it is named after leonid vaseršteĭn.
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7d26f360c9aff6931a274ee7bfab106fb8f1373e
harold francis uplinger was an american professional basketball
harold francis uplinger was an american professional basketball player and television producer. a 6'4" guard from long island university, uplinger spent the 1953–54 nba season with the baltimore bullets, scoring 86 points in 23 games. he was the northern league basketball player of the year at john marshall high school...
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e25f67b80a887029ef86bc92e9d55056ec7c3424
he worked for cbs in los angeles and
he worked for cbs in los angeles and new york as the production manager at kcbs, then as sports producer for the cbs television network.he produced the american side of live aid and was responsible for the international distribution of the 16-hour broadcast to 155 countries and raised $283.7 million for the band aid tr...
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092736148be1140c8d50da8da4640f08bb645706
he was the northern league basketball player of
he was the northern league basketball player of the year at john marshall high school, and an all-los angeles city player as well, going on to play for the national championship junior college team at los angeles city college before playing at l.i.u. for legendary coach clair bee. he is the only marshall high school (o...
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36539aee2ddd3d4fed04424b4a5d5f20b18277a4
everfest was an austin-based company that connects the
everfest was an austin-based company that connects the festival community online. festival-goers can find worldwide festivals, connect with friends, build a calendar and share content about festival experiences. festival organizers work with everfest to manage their online presence and market their event to attendees, ...
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1d87ce3166a1793f7aebaa4560246018a2b0f00e
everfest closed a $3.6 million series a round
everfest closed a $3.6 million series a round of venture capital funding in june 2017. the round was co-led by live nation entertainment and atx seed ventures. charlie walker of c3 presents and chris shonk of atx seed ventures joined everfest's board of directors as part of the deal.
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7f6a083d888fb69ad0efca8b14e2c288a5bb746c
everfest was named to the austin chamber of
everfest was named to the austin chamber of commerce's austin a-list of hottest startups on may 14, 2015, one of 12 winners from a pool of 275 nominees. they were one of four winners from 160 in the emerging category.
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38f0f36add10252d2cc63f42bc2f9733bc1471a4
in april 2015, everfest closed an angel round
in april 2015, everfest closed an angel round of funding totalling $1.5 million, which included notable individual investor bob kagle (founder of benchmark capital) and a group from atx seed ventures. everfest appeared on product hunt on april 5, posted by ryan hoover (founder of product hunt), and finished the day as ...
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a225dff6c2db53befa50434a2c938210eb8fdffe
everfest includes festivals of all types, grouping them
everfest includes festivals of all types, grouping them across 12 categories: art, book, civic, cultural, faith, food, film, historical, music, performance, seasonal, and unique. the platform uses an algorithm to recommend festivals to festival-goers based on their likes and locations, as well as festivals they prefer ...
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513a4aa6e0dc3d6605ba860fa58d89d75b92a45e
everfest was an austin-based company that connects the
everfest was an austin-based company that connects the festival community online. festival-goers can find worldwide festivals, connect with friends, build a calendar and share content about festival experiences. festival organizers work with everfest to manage their online presence and market their event to attendees, ...
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0866125938fdfce7758d585398ed4cfdbf75934b
hamady barro n'diaye is a senegalese professional basketball
hamady barro n'diaye is a senegalese professional basketball player for nanterre 92 of the lnb pro a. a 7-foot tall center, n'diaye played college basketball for rutgers university and was a second-round selection in the 2010 nba draft.
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fdb619f59ea184684d0209ba90a2d2953ba6f64d
on august 19, 2020, he signed with boulazac
on august 19, 2020, he signed with boulazac basket dordogne. without playing any competitive game with bbd, he has signed with Élan béarnais of the french lnb pro a on october 19, 2020.
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d209ec904426187fadcbac05a8a181a536291910
on august 18, 2017, n'diaye signed with the
on august 18, 2017, n'diaye signed with the italian team sidigas avellino for the 2017–18 season. after averaging 5.4 points and 3.7 rebounds per game, he re-signed with the team on august 9, 2018.
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4bb9594d2cda287d6d5a2eb365793c42c5119d88
on september 23, 2016, n'diaye signed a one-year
on september 23, 2016, n'diaye signed a one-year deal with the spanish club unicaja málaga. on january 31, 2017, he parted ways with unicaja. two days later, he returned to his former club bnei herzliya.
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cbea7029644b4642b2128a8feb8d8e8ff46aa6ca
in july 2016, n'diaye signed with the philippines-based
in july 2016, n'diaye signed with the philippines-based basketball club, mighty sports ph at the 38th william jones cup and later on winning the gold medal for the club with an unbeaten record of 8–0.
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310cd85e2137568a818dcdc20d54c235b0b567bf
on september 17, 2014, he signed with the
on september 17, 2014, he signed with the brooklyn nets. however, two days later, his contract was voided by the nets after he failed the required physical. in november 2014, he signed with byblos of the lebanese basketball league. on april 29, 2015, he signed with kia carnival of the philippine basketball association.
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a000e2eab739485800e8ca8412e1a257cd2adf55
on january 25, 2014, he was acquired by
on january 25, 2014, he was acquired by the delaware 87ers. on march 10, 2014, he was waived by the 87ers due to a season-ending injury. in may 2014, he joined guangxi rhinos of china.
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fdfd2ffd9d6a6e94ccbb8336c83b8c88ff3a99f4
he joined the dallas mavericks for the 2013
he joined the dallas mavericks for the 2013 nba summer league. on august 29, 2013, n'diaye's rights were acquired by the delaware 87ers in the 2013 nba development league expansion draft. in september 2013, he signed with the sacramento kings. on december 6, 2013, the kings assigned n'diaye to the reno bighorns of the ...
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3a4625792701ab27fe7aafa28b6d39515df69c41
in july 2012, he joined the indiana pacers
in july 2012, he joined the indiana pacers for the orlando summer league and the charlotte bobcats for the las vegas summer league. on september 25, 2012, he signed with the sacramento kings. however, he was waived on october 26. in november 2012, he joined tianjin ronggang of china for the 2012–13 season.
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6eca4a2965214e1bd60ee8e2d579f22e1ae4ea86
on june 24, 2010, n'diaye was drafted by
on june 24, 2010, n'diaye was drafted by the minnesota timberwolves with the 56th overall pick in the 2010 nba draft. his draft rights were then traded to the washington wizards. on january 6, 2011, n'diaye was assigned to the dakota wizards of the nba d-league. he was recalled on february 4, 2011. on december 10, 2011...
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2b092ee366f761be472fa7fd05697fe544d6908e
during his senior year at rutgers university, n'diaye
during his senior year at rutgers university, n'diaye had 145 blocks and averaged 4.5 blocks per game (the third highest in the nation). on march 9, 2010, during a 69–68 loss to cincinnati in the big east tournament, n'diaye ended the season with the 358 blocked shots in his career. he broke school records held by form...
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4b88b911cf1624a20e96cd5d45ed383f76eb0cb4
hamady barro n'diaye (pronounced hah-muh-dee en-jigh; born january
hamady barro n'diaye (pronounced hah-muh-dee en-jigh; born january 12, 1987) is a senegalese professional basketball player for nanterre 92 of the lnb pro a. a 7-foot tall center, n'diaye played college basketball for rutgers university and was a second-round selection in the 2010 nba draft.
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de6845759c99ba9edebfca03b3b2ac8d2c1dbcc0
the term "marcos mansions" refers to at least
the term "marcos mansions" refers to at least 50 upscale residences in the philippines of the family of 10th president ferdinand marcos. these are aside from the various overseas landholdings of the marcos family, which are spread around the world. the supreme court of the philippines considers these landholdings as pa...
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f1949a2b29c07c8059714aab357f8b064fbb3123
verification by the philippine government's commission on audit
verification by the philippine government's commission on audit after the ouster of the marcos family revealed that the construction, renovation, and maintenance of these various houses were paid for by the philippine government through the office of the president. maintenance and upkeep alone cost at least us$3.2 mill...
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0d506ec93efa665d708a34e7fd682d8fefee406b
there is also what is known as the
there is also what is known as the marcos twin mansion built by imelda marcos in casile, calamba, on the property donated by jose yulo, for their 25th wedding anniversary. ferdinand marcos in turn gifted imelda with 25 gold bullions.
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a11865b005f0d82211a10a707c1ad6d0b881f462
a different mansion, in tacloban, is noted for
a different mansion, in tacloban, is noted for having been the former site of the "impoverished quonset hut " which was imelda marcos's childhood home. when her husband became president of the philippines, imelda transformed the site into a 2000 square meter mansion with a shrine to the santo niño and a museum, which h...
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214f9c020f16113e0f4f0c374055d1454e04cea4
in tolosa, leyte, a muti-million dollar seaside resort
in tolosa, leyte, a muti-million dollar seaside resort was constructed in 1974, in time for the marcoses to entertain participants of the 1974 miss universe beauty contest, which was being held in the philippines that year. the property was severely damaged by typhoon haiyan in 2013.
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44ab04d591d697adf3caa235ff74ae6ab6627288
particularly notable is the malacañang of the north
particularly notable is the malacañang of the north mansion in paoay, ilocos norte, which was built by the philippine tourism authority (pta) in 1977, in time for ferdinand marcos's 60th birthday. the sandiganbayan anti-graft court stripped the marcoses of the property in 2014, voiding a 1978 agreement between marcos a...
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d764296165b3fb9a1b01e2c378df145dfd176959
closer to the main seat of power, marcos
closer to the main seat of power, marcos mansions were located in makati, parañaque, manila, and san juan. houses were once again designated for each of the three marcos children: a residence in seaside subdivision, parañaque was designated for bongbong marcos, one in wack-wack, mandaluyong was designated for imee marc...
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c925f3d16d4f7412bf4df0d620ab86c8d75df90b
located on the same road is a two-story
located on the same road is a two-story house called the "lualhati residence", whose title was held by marcos crony, jose y. campos, on behalf of the marcoses. another property, the banaue inn compound, is located just behind the campos house.
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305d9e40ce3a20806973c33562822f3f78cf5d83
among roughly 50 marcos mansions scattered throughout the
among roughly 50 marcos mansions scattered throughout the philippines, the nine properties located in baguio are among the most commonly covered by media reports, because of their reported opulence and because of their closeness to each other and to major tourist attractions: including mines view park, wright park, and...
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780c4d4d2f856ab7b04e2b2eead352a4e7f99ca3
locations of houses considered "marcos mansions" include properties
locations of houses considered "marcos mansions" include properties in baguio, in the ilocos region where the marcoses trace their ancestry, leyte where imelda marcos's family came from, and throughout the greater manila area and its outskirts.
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a1c3b75d54a24204c89ef1f726d0a965cd72bb55
in 2009, imelda marcos filed graft charges against
in 2009, imelda marcos filed graft charges against pcgg for "illegally confiscating" their family's assets. in question were more than 197 individual certificate of titles within the country, totaling 17,405,984 sq. meters.
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8138b6b8ad62f96bf2123cdb2af9346ad3ad4730
some of these properties are titled in the
some of these properties are titled in the name of marcos family members, but others are titled in the name of identified “ marcos cronies,” but reserved for the use of the marcos family. in some cases, several such mansions were located close together, with specific mansions meant for individual members of the family,...
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72e618b3be9f67246e91d218618597fdaba11bd6
along with the marcos jewels, their overseas landholdings,
along with the marcos jewels, their overseas landholdings, art collection, and imelda marcos's shoe hoard, the marcos mansions are frequently cited to illustrate the marcos family's wanton spending during the dictatorship. because the estimated cost of these mansions is much more than the income recorded in marcos’ swo...
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