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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. | wikipedia |
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. | wikipedia |
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. | wikipedia |
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... | wikipedia |
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. | wikipedia |
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. | wikipedia |
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. | wikipedia |
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... | wikipedia |
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... | wikipedia |
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... | wikipedia |
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... | wikipedia |
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... | wikipedia |
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... | wikipedia |
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... | wikipedia |
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... | wikipedia |
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. | wikipedia |
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... | wikipedia |
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 ... | wikipedia |
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. | wikipedia |
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. | wikipedia |
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... | wikipedia |
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. | wikipedia |
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. | wikipedia |
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 ... | wikipedia |
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... | wikipedia |
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. | wikipedia |
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 ... | wikipedia |
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 ... | wikipedia |
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... | wikipedia |
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... | wikipedia |
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}}\... | wikipedia |
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... | wikipedia |
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... | wikipedia |
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 ... | wikipedia |
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 }+\... | wikipedia |
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)}. | wikipedia |
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... | wikipedia |
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... | wikipedia |
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. | wikipedia |
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 ... | wikipedia |
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... | wikipedia |
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... | wikipedia |
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 ... | wikipedia |
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\}.} | wikipedia |
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\},} | wikipedia |
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. | wikipedia |
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. | wikipedia |
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... | wikipedia |
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.} | wikipedia |
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... | wikipedia |
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... | wikipedia |
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},} | wikipedia |
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) ‖... | wikipedia |
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... | wikipedia |
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}.} | wikipedia |
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... | wikipedia |
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... | wikipedia |
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... | wikipedia |
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... | wikipedia |
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 ... | wikipedia |
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).} | wikipedia |
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... | wikipedia |
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 ... | wikipedia |
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. | wikipedia |
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... | wikipedia |
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... | wikipedia |
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... | wikipedia |
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, ... | wikipedia |
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. | wikipedia |
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. | wikipedia |
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 ... | wikipedia |
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 ... | wikipedia |
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, ... | wikipedia |
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. | wikipedia |
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. | wikipedia |
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. | wikipedia |
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. | wikipedia |
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. | wikipedia |
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. | wikipedia |
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. | wikipedia |
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 ... | wikipedia |
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. | wikipedia |
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... | wikipedia |
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... | wikipedia |
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. | wikipedia |
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... | wikipedia |
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... | wikipedia |
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. | wikipedia |
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... | wikipedia |
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. | wikipedia |
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... | wikipedia |
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... | wikipedia |
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. | wikipedia |
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... | wikipedia |
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. | wikipedia |
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. | wikipedia |
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,... | wikipedia |
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... | wikipedia |
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