Darren Aronofsky is an American filmmaker and screenwriter. His films are noted for their surreal and disturbing elements based in psychological horror and drama. Aronofsky attended Harvard University, where he studied film and social anthropology, the American Film Institute where he studied directing, he won several film awards after completing his senior thesis film, Supermarket Sweep, which went on to become a National Student Academy Award finalist. Aronofsky's feature debut, the surrealist psychological thriller Pi, was shot in November 1997; the low-budget, $60,000 production, starring Sean Gullette, was sold to Artisan Entertainment for $1 million, grossed over $3 million. Aronofsky's followup, the psychological drama Requiem for a Dream, was based on the novel of the same name by Hubert Selby, Jr; the film garnered strong reviews and received an Academy Award nomination for Ellen Burstyn's performance. The film generated considerable controversy due to the graphic nature of several scenes, was released unrated.

After writing the World War II horror film Below, Aronofsky began production on his third film, the romantic fantasy sci-fi drama The Fountain. The film received mixed reviews and performed poorly at the box-office, but has since garnered a cult following, his fourth film, the sports drama The Wrestler, was released to critical acclaim and both of the film's stars, Mickey Rourke and Marisa Tomei, received Academy Award nominations. In 2010, Aronofsky was an executive producer on The Fighter and his fifth feature film, the psychological horror film Black Swan, received further critical acclaim and many accolades, being nominated for five Academy Awards, including Best Picture and Best Director. Aronofsky received nominations for Best Director at the Golden Globes, a Directors Guild of America Award nomination for his work on Black Swan. Aronofsky's sixth film, the biblically inspired epic Noah, was released in 2014 becoming Aronofsky's first film to open at No.1 at box office. His seventh film, the psychological horror mother!, sparked controversy upon release due to its biblical allegories and depiction of violence, polarized audiences.

Aronofsky was born in the Brooklyn borough of New York City, New York, the son of teachers Charlotte and Abraham Aronofsky, grew up in the borough's Manhattan Beach neighborhood. He said he was "raised culturally Jewish, but there was little spiritual attendance in temple, it was a cultural thing—celebrating the holidays, knowing where you came from, knowing your history, having respect for what your people have been through." He graduated from Edward R. Murrow High School, he has one sister, who attended a professional ballet school through high school. His parents would take him to Broadway theatre performances, which sparked his keen interest in show business. During his youth, he trained as a field biologist with The School for Field Studies in Kenya in 1985 and Alaska in 1986, he attended school in Kenya to pursue an interest in learning about ungulates. He said, "he School for Field Studies changed the way I perceived the world". Aronofsky's interest in the outdoors led him to backpack his way through the Middle East.

In 1987, he entered Harvard University, where he majored in social anthropology and studied filmmaking. He became interested in film while attending Harvard after befriending Dan Schrecker, an aspiring animator, Sean Gullette, who would go on to star in Aronofsky's first film, Pi, his cinematic influences included Akira Kurosawa, Roman Polanski, Terry Gilliam, Shinya Tsukamoto, Hubert Selby, Jr. Spike Lee, Satoshi Kon, Jim Jarmusch. Aronofsky's senior thesis film, Supermarket Sweep, was a finalist in the 1991 Student Academy Awards. In 1992, Aronofsky received his MFA degree in directing from the AFI Conservatory, where his classmates included Todd Field, Doug Ellin, Scott Silver and Mark Waters, he won the institute's Franklin J. Schaffner Alumni Medal. Aronofsky's debut feature, titled Pi—sometimes stylized as π—was shot in November 1997; the film was financed in part from numerous $100 donations from friends and family. In return, he promised to pay each back $150 if the film made money, they would at least get screen credit if the film lost money.

Producing the film with an initial budget of $60,000, Aronofsky premiered Pi at the 1998 Sundance Film Festival, where he won the Best Director award. The film itself was nominated for a special Jury Award. Artisan Entertainment bought distribution rights for $1 million; the film was released to the public that year to critical acclaim and it grossed a total of $3,221,152 at the box-office. Pi was the first film to be made available for download on the Internet. Aronofsky followed his debut with Requiem for a Dream, a film based on Hubert Selby, Jr.'s novel of the same name. He was paid $50,000, worked for three years with nearly the same production team as his previous film. Following the financial breakout of Pi, he was capable of hiring established actors, including Ellen Burstyn and Jared Leto, received a budget of $3,500,000 to produce the film. Production of the film occurred over the period of one year, with the film being released in October 2000; the film went on to gross $7,390,108 worldwide.

Aronofsky received acclaim for his stylish direction, was nominated for another Independent Spirit Award, this time for Best Director. The film itself was nominated for five awards in total, winning two, for Best Actress and Cinematography. Clint Mansell's soundtrack for the film was

Degree Preserving Randomization is a technique used in Network Science that aims to assess whether or not variations observed in a given graph could be an artifact of the graph's inherent structural properties rather than properties unique to the nodes, in an observed network. Cataloged as early as 1996, the simplest implementation of degree preserving randomization relies on a Monte Carlo algorithm that rearranges, or "rewires" the network at random such that, with a sufficient number of rewires, the network's degree distribution is identical to the initial degree distribution of the network, though the topological structure of the network has become distinct from the original network. Degree preserving randomization, while it has many different forms takes on the form of a simple approach: for any network consisting of N nodes with E edges, select two dyadically tied nodes. For each of these dyadic pairs, switch the edges such that the new dyadic pairs are mismatched. After a sufficient number of these mismatches, the network loses its original observed topography.

As is common with algorithms based on Markov chains, the number of iterations, or individual rewires, that must occur on a given graph such that the graph is sufficiently random and distinct from the original graph is unknown, though Espinoza asserts that a safe minimum threshold is Q ∗ E, where Q "is at least 100". Others have provided input for this issue, including one author who states that a safe minimum may instead be at least E 2 ∗ l n, where epsilon lies in a range between 10 − 6 and 10 − 7, though the correct number is not presently known. There are several cases in which published research have explicitly employed degree preserving randomization in order to analyze network properties. Dekker used rewiring in order to more model observed social networks by adding a secondary variable, π, which introduces a high-degree attachment bias. Liu et al. have additionally employed degree preserving randomization to assert that the Control Centrality, a metric they identify, alters little when compared to the Control Centrality of an Erdős–Rényi model containing the same number of N nodes in their simulations - Liu et al. have used degree preserving randomization models in subsequent work exploring network controllability.

Additionally, some work has been done in investigating how Degree Preserving Randomization may be used in addressing considerations of anonymity in networked data research, shown to be a cause for concern in Social Network Analysis, as in the case of a study by Lewis et al. The work conducted by Ying and Wu, starting from a foundation of Degree Preserving Randomization, forwarding several modifications, has showed moderate advances in protecting anonymity without compromising the integrity of the underlying utility of the observed network. Additionally, the method is similar in nature to the broadly used Exponential random graph models popularized in social science, indeed the various forms of modeling networks against observed networks in order to identify and theorize about the differences expressed in real networks. Degree Preserving Randomization provides a simple algorithmic design for those familiar with programming to apply a model to an available observed network. What follows is a small example showing how one may apply Degree Preserving Randomization to an observed network in an effort to understand the network against otherwise random variation while maintaining the degree distributional aspect of the network.

The Association of Internet Researchers has a Listserv that constitutes the majority of discussion threads surrounding their work. On it, members post updates about their own research, upcoming conferences, calls for papers and engage one another in substantive discussions in their field; these emails can in turn constitute a directed and temporal network graph, where nodes are individual e-mail accounts belonging to the Listserv and edges are cases in which one e-mail address responds to another e-mail address on the Listserv. In this observed network, the properties of the Listserv are simple to calculate - for the network of 3,235 individual e-mail accounts and 9,824 exchanges in total, the observed reciprocity of the network is about 0.074, the is about 4.46. Could these values be arrived at through the nature of the network's inherent structure? Applying the E 2 ∗ l n rule, this network would require around 67,861 individual edge rewires to construct a sufficiently random degree-preserved graph.

If we construct many random, degree preserving graphs from the real graph, we can create a probability space for characteristics, such as reciprocity and average path length, assess the degree to which the network could have expressed these characteristics at random. 534 networks were generated using Degree Preserving Randomization. As both reciprocity and average path length in this graph are distributed, as the standard deviation for both reciprocity and average path length are far too narrow to include

Sir Murray Louis Tyrrell was an Australian public servant, noted as the Official Secretary to the Governor-General of Australia for a record term of 26 years, 1947–73, in which time he served six governors-general. Born in Kilmore, Tyrrell was educated at Orbost and Mordialloc and Melbourne Boys' High Schools, he married Ellen St Clair Greig on 6 May 1939. They had three children, two daughters born first, Leonie Ellen and Margot Evelyn, a son, Michael St Clair, he served for over 45 years in the Australian Public Service. For most of this time he was assistant secretary or personal secretary to a succession of Ministers including the Prime Minister, Ben Chifley. Tyrrell succeeded Rear Admiral Sir Leighton Bracegirdle as Official Secretary to the Governor-General, William McKell, in March 1947. Tyrrell served Sir William McKell's successors Sir William Slim, Lord Dunrossil, Lord De L'Isle, Lord Casey and Sir Paul Hasluck; the Queen named him a Commander of the Royal Victorian Order, for his service rendered during the Royal Visit in 1954.

He was appointed a Commander of the Order of the British Empire in 1959. Both of these honours occurred during Sir William Slim's term. Tyrrell had a small but pivotal role to play in the establishment of the Australian Conservation Foundation; the ACF began in the second half of 1964, after a suggestion was made to Tyrrell by Prince Philip, Duke of Edinburgh while visiting Australia in 1963. He voiced an idea that Australia could become involved in conservation by establishing a branch of the World Wildlife Fund. Tyrrell convened a meeting that came to the conclusion that, if a conservation body was to exist, its efforts should be directed at conserving Australia's own heritage. From this the ACF emerged. Murray Tyrrell was appointed a Knight Commander of the Royal Victorian Order in 1968, during Lord Casey's term; this was awarded for personal service to the Queen, was not on recommendation from the Prime Minister. He had been attached to the Royal Household at Buckingham Palace from May to August 1962.

After his retirement in 1973, which occurred during Sir Paul Hasluck's term, he was succeeded by David Smith. In 1977, he was named the Australian of the Year, jointly with Dame Raigh Roe. Sir Murray lived at 11 Blundell Street, New South Wales, in an old heritage cottage still called "Sir Murray Tyrrell's Cottage", he was an Alderman of the Queanbeyan City Council 1976–1980. Tyrrell died on 13 July 1994 in Canberra, at the age of 80. 1954 – Commander of the Royal Victorian Order, in connection with the Royal Visit 1959 – Commander of the Order of the British Empire 1968 – Knight Commander of the Royal Victorian Order Australian of the Year biography