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id stringlengths 40 40	title stringlengths 15 120	text stringlengths 41 3.14k	source stringclasses 2 values
d5393cf9269ce12a5b9333c83612f4ac9855940f	if z has a binomial distribution with parameters	if z has a binomial distribution with parameters n and p, then the expected value of z is given by e = np and the variance of z is given by var = np (1 – p). letting n = m + m and substituting e for np gives	wikipedia
1211974b3abed592b33da0fc616d8fe6406a1323	consider the sum, z, of two independent binomial	consider the sum, z, of two independent binomial random variables, x ~ b(m, p) and y ~ b(m, p), where z = x + y. then, the variance of z is less than or equal to its variance under the assumption that p = p, that is, if z had a binomial distribution. symbolically, v a r (z) ⩽ e (1 − e m 0 + m 1) {\displaystyle var(z)\l...	wikipedia
9a2d7cd3bafb1ac9eaa8d4e56019eb36b41e5560	the binomial sum variance inequality states that the	the binomial sum variance inequality states that the variance of the sum of binomially distributed random variables will always be less than or equal to the variance of a binomial variable with the same n and p parameters. in probability theory and statistics, the sum of independent binomial random variables is itself ...	wikipedia
b988012d2969f31e1172f15f4c0620154133e734	in graph theory, the blossom algorithm is an	in graph theory, the blossom algorithm is an algorithm for constructing maximum matchings on graphs. the algorithm was developed by jack edmonds in 1961, and published in 1965. given a general graph g =, the algorithm finds a matching m such that each vertex in v is incident with at most one edge in m and \|m\| is maximi...	wikipedia
bf37a328c9e57de5163ef67c2bac0565f479510a	the matching problem can be generalized by assigning	the matching problem can be generalized by assigning weights to edges in g and asking for a set m that produces a matching of maximum (minimum) total weight: this is the maximum weight matching problem. this problem can be solved by a combinatorial algorithm that uses the unweighted edmonds's algorithm as a subroutine....	wikipedia
96bcce2b7dc9ca0702b6a0af5eab553bdffbb3a7	when g is bipartite, there are no odd	when g is bipartite, there are no odd cycles in g. in that case, blossoms will never be found and one can simply remove lines b20 – b24 of the algorithm. the algorithm thus reduces to the standard algorithm to construct maximum cardinality matchings in bipartite graphs where we repeatedly search for an augmenting path ...	wikipedia
85032de1405ce6c313b1aaca63ac4d75db2d78ac	each iteration of the loop starting at line	each iteration of the loop starting at line b09 either adds to a tree t in f (line b10) or finds an augmenting path (line b17) or finds a blossom (line b20). it is easy to see that the running time is o (\| e \| \| v \| 2) {\displaystyle o(\|e\|\|v\|^{2})}.	wikipedia
6c27dc4c8da2029c3f049879a95b6307f1493c04	finally, it locates an augmenting path p′ in	finally, it locates an augmenting path p′ in the contracted graph (line b22) and lifts it to the original graph (line b23). note that the ability of the algorithm to contract blossoms is crucial here; the algorithm cannot find p in the original graph directly because only out-of-forest edges between vertices at even di...	wikipedia
a8b10ad6b3abdd6add85087f9210f4286e65684d	the following four figures illustrate the execution of	the following four figures illustrate the execution of the algorithm. dashed lines indicate edges that are currently not present in the forest. first, the algorithm processes an out-of-forest edge that causes the expansion of the current forest (lines b10 – b12).	wikipedia
2bd28e4a35bfb3c108fcdce3c4b4fe26459f09ab	the construction procedure considers vertices v and edges	the construction procedure considers vertices v and edges e in g and incrementally updates f as appropriate. if v is in a tree t of the forest, we let root(v) denote the root of t. if both u and v are in the same tree t in f, we let distance(u,v) denote the length of the unique path from u to v in t.	wikipedia
6b2719d4353d1a0f2f4b216066c0916eed5e48c9	the search for an augmenting path uses an	the search for an augmenting path uses an auxiliary data structure consisting of a forest f whose individual trees correspond to specific portions of the graph g. in fact, the forest f is the same that would be used to find maximum matchings in bipartite graphs (without need for shrinking blossoms).in each iteration th...	wikipedia
96d334f467544800bc775a3d6ea971c45e52743c	g' has an m' -augmenting path if and	g' has an m' -augmenting path if and only if g has an m -augmenting path, and that any m' -augmenting path p' in g' can be lifted to an m -augmenting path in g by undoing the contraction by b so that the segment of p' (if any) traversing through v is replaced by an appropriate segment traversing through b. in more deta...	wikipedia
c1782454cab2848610a84a17bb7cf72c497782e4	given g = (v, e) and a matching	given g = (v, e) and a matching m of g, a blossom b is a cycle in g consisting of 2 k + 1 edges of which exactly k belong to m, and where one of the vertices v of the cycle (the base) is such that there exists an alternating path of even length (the stem) from v to an exposed vertex w.	wikipedia
ebeec65075cc65c8ef7aed3b7bbbb8a81dade75d	by berge's lemma, matching m is maximum if	by berge's lemma, matching m is maximum if and only if there is no m -augmenting path in g. hence, either a matching is maximum, or it can be augmented. thus, starting from an initial matching, we can compute a maximum matching by augmenting the current matching with augmenting paths as long as we can find them, and re...	wikipedia
c5d2946fa4af4d066a7e10b08aaf03b9d6946a2b	given g = (v, e) and a matching	given g = (v, e) and a matching m of g, a vertex v is exposed if no edge of m is incident with v. a path in g is an alternating path, if its edges are alternately not in m and in m (or in m and not in m). an augmenting path p is an alternating path that starts and ends at two distinct exposed vertices. note that the nu...	wikipedia
aa616044ef7ecec61f38ff2fa97963b5f13ccc23	a major reason that the blossom algorithm is	a major reason that the blossom algorithm is important is that it gave the first proof that a maximum-size matching could be found using a polynomial amount of computation time. another reason is that it led to a linear programming polyhedral description of the matching polytope, yielding an algorithm for min- weight m...	wikipedia
a761abf9d15f76dd4931a5e70a4d65d19039b5e2	the algorithm runs in time o (\| e	the algorithm runs in time o (\| e \| \| v \|), where \| e \| is the number of edges of the graph and \| v \| is its number of vertices. a better running time of o (\| e \| \| v \|) {\displaystyle o(\|e\|{\sqrt {\|v\|}})} for the same task can be achieved with the much more complex algorithm of micali and vazirani.	wikipedia
48ff043e59937a50792fbba32d97223fae35ef98	in graph theory, the blossom algorithm is an	in graph theory, the blossom algorithm is an algorithm for constructing maximum matchings on graphs. the algorithm was developed by jack edmonds in 1961, and published in 1965. given a general graph g = (v, e), the algorithm finds a matching m such that each vertex in v is incident with at most one edge in m and \| m \| ...	wikipedia
9b811446239e5c5d7ca8a9f625aa4071dedfc1b7	florent krzakala is a french physicist and applied	florent krzakala is a french physicist and applied mathematician, currently a professor at epfl. his research focuses on the resolution of theoretical problems in physics, computer science, machine learning, statistics and signal processing using mathematical tools inspired by the field of statistical physics.	wikipedia
b6d07273dc13008e593f0be1bf67378769350b19	florent krzakala was named a junior fellow of	florent krzakala was named a junior fellow of the institut universitaire de france in 2015. he received a grant from the european research council for his work on compressed sensing in 2012. he received the atos-fourier price in 2018. he was the holder of the cfm chair in data-science in ecole normale supérieure from 2...	wikipedia
1bd7b17966679bb49de817cf89108ecacf9f36ef	trained as a theoretical statistical physicist, florent krzakala	trained as a theoretical statistical physicist, florent krzakala studied problems involving complex assemblies of simple elementary components, especially in the context of spin glasses and disordered systems. his attention has then switched to computer sciences, statistics and applied mathematics, where conceptually s...	wikipedia
87feef346997714846288f4080095a56a2d314d7	he then moved to the sapienza university of	he then moved to the sapienza university of rome as a postdoctoral researcher, where he studied various statistical physics topics such as glassy systems, monte-carlo simulation techniques, and out-of-equilibrium dynamics in the laboratory of prof. giorgio parisi. in 2004, he was named associate professor at espci pari...	wikipedia
9d752606cfe3fcf5195ce62528e7d8261f970798	florent krzakala grew up in marseille, france, where	florent krzakala grew up in marseille, france, where he studied at the lycée saint-exupéry and aix-marseille university, and then moved to paris for his graduate studies. after a master's degree in particle physics, he switched field to statistical physics for his phd, which he obtained in 2002 jointly from the pierre ...	wikipedia
9fcb76010a52a3f80aa8153ec2536f366b79d4db	florent krzakala (born march 22, 1976 in nancy,	florent krzakala (born march 22, 1976 in nancy, france) is a french physicist and applied mathematician, currently a professor at epfl (École polytechnique fédérale de lausanne). his research focuses on the resolution of theoretical problems in physics, computer science, machine learning, statistics and signal processi...	wikipedia
2f86404c7ff94521fa227e37be50f08773156db4	though the thermostat does not generate a correct	though the thermostat does not generate a correct canonical ensemble (especially for small systems), for large systems on the order of hundreds or thousands of atoms/molecules, the approximation yields roughly correct results for most calculated properties. the scheme is widely used due to the efficiency with which it ...	wikipedia
c13450c50485ae9c932c6141e3c2188ecb69263e	in this scheme, the system is weakly coupled	in this scheme, the system is weakly coupled to a heat bath with some temperature. the thermostat suppresses fluctuations of the kinetic energy of the system and therefore cannot produce trajectories consistent with the canonical ensemble. the temperature of the system is corrected such that the deviation exponentially...	wikipedia
dab1aca56e1f112d92477f730698c3913c874e9b	giacomo rizzolatti is an italian neurophysiologist who works	giacomo rizzolatti is an italian neurophysiologist who works at the university of parma. born in kyiv, ukssr, he is the senior scientist of the research team that discovered mirror neurons in the frontal and parietal cortex of the macaque monkey, and has written many scientific articles on the topic. he also proposed t...	wikipedia
1c6931431f0f7d76cd0cc47ab7627b24f43f0d7f	giacomo rizzolatti (born 28 april 1937) is an	giacomo rizzolatti (born 28 april 1937) is an italian neurophysiologist who works at the university of parma. born in kyiv, ukssr, he is the senior scientist of the research team that discovered mirror neurons in the frontal and parietal cortex of the macaque monkey, and has written many scientific articles on the topi...	wikipedia
a033ffed3d9d99382ee4bbd3342c9fcc500d3038	a high-frequency approximation for scattering or other wave	a high-frequency approximation for scattering or other wave propagation problems, in physics or engineering, is an approximation whose accuracy increases with the size of features on the scatterer or medium relative to the wavelength of the scattered particles. classical mechanics and geometric optics are the most comm...	wikipedia
e7ddcde821b68adb82b0cb84e5146901a763703f	less extreme approximations include, the wkb approximation, physical	less extreme approximations include, the wkb approximation, physical optics, the geometric theory of diffraction, the uniform theory of diffraction, and the physical theory of diffraction. when these are used to approximate quantum mechanics, they are called semiclassical approximations.	wikipedia
1e38b6941ca9ad3191ff847bb3104fbb6802a139	a high-frequency approximation (or "high energy approximation") for	a high-frequency approximation (or "high energy approximation") for scattering or other wave propagation problems, in physics or engineering, is an approximation whose accuracy increases with the size of features on the scatterer or medium relative to the wavelength of the scattered particles.	wikipedia
caec81f02bcb551b972d16ebe764ffeda51d7633	higashi-abiko station was opened on october 12, 1950	higashi-abiko station was opened on october 12, 1950 as a station on the japan national railways (jnr). the station was absorbed into the jr east network upon the privatization of the jnr on april 1, 1987.	wikipedia
204f253edf6d6a8067933b47a95380eed80b5320	higashi-abiko station (東我孫子駅, higashi-abiko-eki) is a passenger railway	higashi-abiko station (東我孫子駅, higashi-abiko-eki) is a passenger railway station in the city of abiko, chiba prefecture japan, operated by the east japan railway company (jr east).	wikipedia
72c1794db8ce196d7c9facaf383d1b1efbdab47e	pluton was a téméraire class 74-gun french ship	pluton was a téméraire class 74-gun french ship of the line built at toulon. she was one of two prototypes for a derivative sub-class of the original design; this sub-class was specially intended for construction in some of the shipyards in states occupied by the french, where there was less depth of water than in the ...	wikipedia
cf5d68e09e75a6f7d55b5314e097b2789a74f8cd	she was captured by spain in cadiz on	she was captured by spain in cadiz on 14 june 1808 and commissioned in the spanish navy as pluton. she was renamed montañes on 20 april 1810, and was eventually broken up in 1816.	wikipedia
0d1ae9cd6f464613c629af5a6d413b05f2b11fda	the pluton took part in the battle of	the pluton took part in the battle of trafalgar under captain julien cosmao -kerjulien, and escaped to cádiz with other ships. two days later, on 23 october 1805, she was the flagship of the counter-attack from cádiz, together with indomptable, neptune, rayo and san francisco de asis. they managed to recapture the sant...	wikipedia
81a65bf32fc778475383ceb32031f5b3276ed33b	pluton was a téméraire class 74-gun french ship	pluton was a téméraire class 74-gun french ship of the line built at toulon. she was one of two prototypes for a derivative sub-class of the original design; this sub-class (slightly smaller than the primary design) was specially intended for construction in some of the shipyards in states occupied by the french, where...	wikipedia
e82e705388d7abc175381413c32e828dce469a5a	girard "gerry" mcdonald is an american former professional	girard "gerry" mcdonald is an american former professional ice hockey player who played eight games in the national hockey league (nhl) for the hartford whalers between 1981 and 1984. he grew up on elmlawn road in braintree, massachusetts. gerry graduated from braintree high school in 1976 and north adams state college...	wikipedia
f4ef53797f1becdaed3049ddd117d6f8908dd1cd	girard "gerry" mcdonald (born march 18, 1958) is	girard "gerry" mcdonald (born march 18, 1958) is an american former professional ice hockey player who played eight games in the national hockey league (nhl) for the hartford whalers between 1981 and 1984. he grew up on elmlawn road in braintree, massachusetts. gerry graduated from braintree high school in 1976 and nor...	wikipedia
09801126e8e7b2a6eea8e199a03a4938dd30e5cb	femicide in turkey is murders in which women	femicide in turkey is murders in which women are killed for reasons related to their social roles, such as being killed on the grounds of "honor cleansing". it is one of the acts of violence against women in turkey. the number of femicides has increased significantly in turkey in the 2000s, compared to previous years. ...	wikipedia