SUMMARY / RELATED TOPICS

In statistics, isotonic regression or monotonic regression is the technique of fitting a free-form line to a sequence of observations under the following constraints: the fitted free-form line has to be non-decreasing everywhere, it has to lie as close to the observations as possible. Isotonic regression has applications in statistical inference. For example, one might use it to fit an isotonic curve to the means of some set of experimental results when an increase in those means according to some particular ordering is expected. A benefit of isotonic regression is that it is not constrained by any functional form, such as the linearity imposed by linear regression, as long as the function is monotonic increasing. Another application is nonmetric multidimensional scaling, where a low-dimensional embedding for data points is sought such that order of distances between points in the embedding matches order of dissimilarity between points. Isotonic regression is used iteratively to fit ideal distances to preserve relative dissimilarity order.

Software for computing isotone regression has been developed for the R statistical package, the Stata statistical package and the Python programming language. In terms of numerical analysis, isotonic regression involves finding a weighted least-squares fit x ∈ R n to a vector a ∈ R n with weights vector w ∈ R n subject to a set of non-contradictory constraints of the kind x i ≤ x j; the usual choice for the constraints is x i ≤ x i + 1, or in other words: every point must be at least as high as the previous point. Such constraints define a partial ordering or total ordering and can be represented as a directed graph G =, where N is the set of variables involved, E is the set of pairs for each constraint x i ≤ x j. Thus, the isotonic regression problem corresponds to the following quadratic program: min ∑ i = 1 n w i 2 subject to x i ≤ x j for all ∈ E. In the case when G = is a total ordering, a simple iterative algorithm for solving this quadratic program is called the pool adjacent violators algorithm.

Conversely and Chakravarti studied the problem as an active set identification problem, proposed a primal algorithm. These two algorithms can be seen as each other's dual, both have a computational complexity of O. To illustrate the above, let the x i ≤ x j constraints be x 1 ≤ x 2 ≤ … ≤ x n; the isotonic estimator, g ∗, minimizes the weighted least squares-like condition: min g ∈ A ∑ i = 1 n w i 2 where A is the set of all piecewise linear, non-decreasing, continuous functions and f is a known function. Robertson, T.. Order restricted statistical inference. New York: Wiley. ISBN 978-0-471-91787-8. Barlow, R. E.. Statistical inference under order restrictions. New York: Wiley. ISBN 978-0-471-04970-8. Shively, T. S. Sager, T. W. Walker, S. G.. "A Bayesian approach to non-parametric monotone function estimation". Journal of the Royal Statistical Society, Series B. 71: 159–175. CiteSeerX 10.1.1.338.3846. Doi:10.1111/j.1467-9868.2008.00677.x. CS1 maint: multiple names: authors list Wu, W. B.. "Isotonic regression: Another look at the changepoint problem".

Biometrika. 88: 793–804. Doi:10.1093/biomet/88.3.793

Vespers is an album by soprano saxophonist Steve Lacy recorded in 1993 and released on the Italian Soul Note label. The Allmusic review by Scott Yanow awarded the album 4 stars stating "lots of interesting tone colors and harmonies and stimulating solos... Well worth exploring". All compositions by Steve Lacy"Multidimensional" - 6:59 "If We Come Close" - 8:25 "Grass" - 9:24 "Wait for Tomorrow" - 4:35 "Across" - 5:58 "I Do Not Believe" - 9:26 "Vespers" - 6:15Recorded at Sear Sound in New York City on July 5, 6, 7 & 9, 1993 Steve Lacy - soprano saxophone Steve Potts - alto saxophone, soprano saxophone Tom Varner - French horn Ricky Ford - tenor saxophone Bobby Few - piano Jean-Jacques Avenel - bass John Betsch - drums Irene Aebi - voice

This article is the fifth sub-division of Lists of Marylebone Cricket Club players. It presents an alphabetical listing of cricketers who debuted for Marylebone Cricket Club in first-class matches during the inter-war period from 1919 until September 1939, after which first-class cricket was suspended until the 1945 season. Many of the players represented MCC after the Second World War but they are only listed here, as it was in this period that they made their MCC debuts. Players who debuted for MCC before the First World War can be found in List of Marylebone Cricket Club players; the club always played. The majority of MCC players in this period were contracted to county clubs or one of the two main university teams and appeared for MCC by invitation; some players were from other countries. For much of the 20th century, MCC organised international tours in which the England cricket team played Test matches; the players selected for these tours were contracted to MCC for the duration and appearances by them in non-Tests on the tour were for MCC, therefore all such players are included in this list.

MCC teams have always operated at all levels of the sport and players who represented the club in minor cricket only are out of scope here. The details are the player's usual name followed by the span of years in which he was active as an MCC player in first-class matches and his name is given as it appeared on match scorecards, followed by the club or team with which he was associated. Players who took part in Test cricket have their names highlighted in bold text. George Abell: G. E. B. Abell Ronnie Aird: R. Aird Ian Akers-Douglas: I. S. Akers-Douglas Antony Allen: A. W. Allen Basil Allen: B. O. Allen Gubby Allen: G. O. B. Allen. Tours: South America. Maurice Allom: M. J. C. Allom. Tours: Australia & New Zealand. Les Ames: L. E. G. Ames. Tours: Australia. Edward Armitage: E. L. Armitage Trevor Arnott: T. Arnott. Tours: West Indies. Hubert Ashton: H. Ashton Edgar Backhouse: E. N. Backhouse Hamer Bagnall: H. F. Bagnall Jim Bailey: J. Bailey Fred Bakewell: A. H. Bakewell. Tours: India & Ceylon. Wilf Barber: W. Barber.

Tours: Australia & New Zealand. Giles Baring: A. E. G. Baring John Barnes: J. R. Barnes Charlie Barnett: C. J. Barnett. Tours: India & Ceylon. Fred Barratt: F. Barratt. Tours: Australia & New Zealand. Hugh Bartlett: H. T. Bartlett. Tours: South Africa. Oliver Battcock: O. G. Battcock Arthur Baxter: A. D. Baxter. Tours: Australia & New Zealand. George Beet junior: G. H. C. Beet George Beet senior: G. Beet Brian Belle: B. H. Belle Herbert Benka: H. F. Benka Tris Bennett: C. T. Bennett. Tours: West Indies. Edward Benson: E. T. Benson. Tours: Australia & New Zealand. William Berridge: W. C. M. Berridge Reg Bettington: R. H. B. Bettington Edward Bleackley: E. O. Bleackley Spencer Block: S. A. Block Denis Blundell: E. D. Blundell Roger Blunt: R. C. Blunt Bill Bowes: W. E. Bowes. Tours: Australia & New Zealand. Ted Bowley: E. H. Bowley. Tours: Australia & New Zealand. Stuart Boyes: G. S. Boyes. Tours: India & Ceylon. David Brand, 5th Viscount Hampden: D. F. Brand. Tours: Australia & New Zealand. John Brocklebank: J. M. Brocklebank Geoffrey Brooke-Taylor: G. P.

Brooke-Taylor Ronald Brooks: R. C. Brooks Freddie Brown: F. R. Brown. Tours: Australia & New Zealand. Rainy Brown: G. R. R. Brown Stanley Brown: S. H. Brown Syd Brown: S. M. Brown Jack Bryan: J. L. Bryan. Tours: Australia. Robin Buckston: R. H. R. Buckston Brocas Burrows: M. B. Burrows Frederick Burton: F. A. Burton Richard Busk: R. D. Busk Reginald Butterworth: R. E. C. Butterworth Alexander Cadell: A. R. Cadell Freddie Calthorpe: F. S. G. Calthorpe. Tours: Australia & New Zealand. Ion Camp

Broxton Rocks is the single largest exposure of sandstone, about 4 miles in extent, found in the Altamaha Grit, a subterranean band of sandstone that lies under some 15,000 square miles of the Atlantic Coastal Plain. The Rocks, as it is referred to locally, consists of a series of cracks, damp cliff walls, a 10-foot waterfall, rugged outcrops up to 20 feet high, all carved into a shallow gorge over many centuries by Rocky Creek; the Broxton Rocks waterfall is Georgia's southernmost. A substantial part of the Broxton Rocks is a protected preserve of 3,799 acres, of which 1,528 acres are managed by The Nature Conservancy; the preserve lies on a direct line from Atlanta, Georgia, 185 miles by road to the north-west, to Jacksonville, Florida, 145 miles by road to the south-east. Broxton Rocks is located at 31°43'56.25"N, 82°51'11.75"W. The elevation is 243 feet. Broxton Rocks is located in Georgia. Part of the Atlantic coastal plain, Broxton Rocks' sandstone layers were created by the slow erosion of the Altamaha Formation, dating from the Middle Miocene era.

Fractures have opened up throughout the feature, some wide enough to allow a person to walk through, some narrow but deep. Where the waters of Rocky Creek, a first-order intermittent stream, drop to a lower level, a 10-foot waterfall has formed a pool in the sandstone before it flows out and through the lower reaches of the feature before draining into the Ocmulgee River. Broxton Rocks is the home to about 530 plant species, several of which are threatened or endangered species. Included among these are the green-fly orchid, grit portulaca, silky creeping morning glory, Georgia plume, filmy fern and shoestring fern; some species found. In spring, flower species like flame azaleas and fameflower bring a blaze of color to the ravine; the preserve lies in an area of longleaf pine ecosystem which once stretched from the Atlantic Ocean to the eastern reaches of Texas. The Nature Conservancy seeks to restore the longleaf pine to the lands it manages in the preserve through ecological restoration; the preserve is home to over 100 species of birds.

The near-threatened* Bachman's sparrow and the pileated woodpecker, whose drum-like peck can be heard over long distances, all nest here. Other animals include the armadillo, the woodrat, the flying squirrel, the vulnerable* gopher tortoise, the threatened* indigo snake. * Denotes species' conservation status Archaeological research shows that there was a Spanish-era dwelling believed to belong to aboriginal peoples. Broxton Rocks appears to have had several name changes in its history. Three decades ago it was more known locally as The Rocks. Ward's History of Coffee County, published in 1930, pp 271, says of Broxton Rocks, "'The Picnic Rocks' - Its ruggedness begins with the great grey boulders of the picnic rocks, known in former times as "falling waters," for there was quite a water fall at this spot, near the home of Major McNeill, one of the pioneer naval stores operators from Robeson County, North Carolina, who gave the place its name." He continues in the next paragraph, "From there on to the Ocmulgee River, there were two great cliffs lining each side of a wooded stretch through which this stream flowed, great grey boulders with crevasses in them, others poised perilously on top of each other just as though there had been a great upheaval there in the days gone by."

Ward appears to indicate that the local appellation for the feature was "The Picnic Rocks", but that a past name was "falling waters". Current research doesn't indicate if, or was not a translation from an indigenous tongue, e.g. Creek or Seminole. Off The Beaten Path Georgia: A Guide To Unique Places, 9th edition. ISBN 978-0-7627-4861-7 Wildflowers of Georgia. ISBN 0-8203-2179-6 Footprints Across the South: Bartram's Trail Revisited. ISBN 1-933483-07-5 Green-fly orchid image. Retrieved 2010-7-12. Flickr photo set for The Nature Conservancy. Cressler, Alan. Retrieved 2010-7-12. Broxton Rocks images, Dr Ready's home page, Middle Georgia College website. Retrieved 2010-7-12. Broxton Rocks Preserve by Brown's Guides. Retrieved 2010-7-12. Longleaf Pine Ecosystem, The New Georgia Encyclopedia. Retrieved 2010-7-12. Broxton Rocks, The New Georgia Encyclopedia. Retrieved 2010-7-13. Broxton Rocks wetlands Society for Georgia Archaeology. Retrieved 2010-07-12

Lady Octopus is a supervillainess in Marvel Comics. The character is depicted as a protégée to her predecessor of the name and an enemy to Spider-Man and Scarlet Spider. Lady Octopus' first appearance was in Amazing Spider-Man #406 and was created by J. M. DeMatteis and Angel Medina. Carolyn Trainer is the daughter of Seward Trainer, a student of Doctor Octopus. After Doctor Octopus was killed by Kaine during the "Clone Saga," Carolyn replaced the teacher she adored, she obtained a set of four tentacles identical to Octavius's and made use of a personal force-field that kept anything from hitting her. However, her tentacles could lash out from the shield at any time during its use, she took the "Doctor Octopus" name in honor of her beloved instructor and began a campaign to steal her father's research in merging reality and virtual reality. When she found her father was being protected by Scarlet Spider, she became jealous of the father-son relationship between him and her father, she tried but failed to blackmail her way into gaining Trainer's data by stealing a serum that could cure a ill Mary Jane Watson, resulting in her being beaten by Spider-Man and revealing she was working for the mysterious Master Programmer.

Carolyn continued her efforts to merge reality and virtual reality, ending up in a technological gang war against Mr. Tso and his boss Alistair Smythe with the Scarlet Spider in the middle of it, she hired the Looter and Aura, the Pro to assist her in this, as well as Stunner, succeeded in defeating Smythe and gaining the technology she needed before the Scarlet Spider thwarted her. The Master Programmer was revealed to be a digitized copy of Doctor Octopus' mind and Carolyn's overall plan had been to allow Master Programmer to exist in the real world resurrecting the original Doctor Octopus; this thwarted, she attempted to claim her father's then-comatose body and was captured by the police. She was involved in the resurrection of Doctor Octopus; the cult group known as The Hand, working for Rose, dug up Octavius' corpse and brought him back from the dead, albeit with large mental gaps. Carolyn returned the tentacles to him, she faded into the background. Carolyn Trainer made a small appearance in "Secret War".

She now calls herself Lady Octopus to distinguish her from her mentor. She was given a new suit of armor by Lucia von Bardas and Tinkerer, she and Hobgoblin V were defeated. They regrouped to a dock. Lady Octopus fought Captain America when the Fantastic Four join the battle. Just Lucia von Bardas activated the devices in the villains' suits linking them together to a giant bomb. After Daisy Johnson deactivated von Bardas, Lady Octopus and the other villains Lucia von Bardas manipulated were all hospitalized with severe injuries. Lady Octopus has been hired by Walter Declun to assist Absorbing Man, Hydro-Man, Killer Shrike, a Mandroid, Porcupine II, Rock to defend him from Black Panther and the Fantastic Four after they uncovered his plot to destabilize all of Wakanda on Doctor Doom's behalf. Walter Declun upgraded their technological equipment in order to perform the job. Lady Octopus was seen shortly before the Siege of Asgard when she went on a rampage in New York only to be defeated by Mockingbird and Ronin.