title: Alexandra Kollontai

text: Kollontai admonished men and women to discard their nostalgia for traditional family life. "The worker-mother must learn not to differentiate between yours and mine; she must remember that there are only our children, the children of Russia's communist workers." Under Communism, both men and women would work for, and be supported by, society, not their families. Similarly, their children would be wards of society, raised in common. However, she also praised parental attachment: "Communist society will take upon itself all the duties involved in the education of the child, but the joys of parenthood will not be taken away from those who are capable of appreciating them."


title: Sadhana Sargam

text: Sadhana Sargam (née Ghanekar, born 7 March 1969) is an Indian singer known for her playback career in Indian cinema predominantly in Hindi, Bengali, Telugu and Tamil language films. She is a recipient of the National Film Award and Filmfare Awards South. She has also won five Maharashtra State Film Awards, four Gujarat State Film Awards, and one Orissa State Film.


title: Sadhana Sargam

text: Sargam was born to a family of musicians at Dabhol, the seaport town in Ratnagiri District of Maharashtra. Her mother Neela Ghanekar was a classical singer and music teacher and knew arranger–composer Anil Mohile, who then arranged music for Kalyanji-Anandji. He introduced Sargam to them, and she was in the children's chorus in "Pam Pararampam, Bole Jeevan Ki Sargam" sung by Kishore Kumar in G. P. Sippy's "Trishna" (1978). Sargam performed at music festival Sawai Gandharva at the age of 4.


title: Sadhana Sargam

text: She sang the popular song Ek Anek Aur Ekta for Doordarshan at the age 6. The song was composed by Vasant Desai. Speaking about her memory of singing the song, Sargam said, "My parents took me for that recording. I don't remember much of it. It feels quite surreal when I hear it now." Sargam studied at the A. B. Goregaonkar English School in Goregaon, Mumbai.


title: Sadhana Sargam

text: She won a Central Government scholarship at the age 10 and this led to a 7-year learning stint under Pandit Jasraj. From childhood she was also learning and performing with Vasant Desai for his documentaries, children's films and stage shows. Desai advised her mother that Sargam was competent enough to handle both classical and light music and should remain in touch with both, as her mother wanted her to take up light singing. In fact, it was Desai who recommended that she learn under Pandit Jasraj.


title: Sadhana Sargam

text: Sargam made her playback debut in "Kanku Pagli", a Gujarati film. Her first Hindi song was the solo "Door Nahin Rehna" from the film "Rustom". However, Rustom was delayed and was released only in 1985, and Sargam ’s first released film was Subhash Ghai's "Vidhaata" (1982) in which she sang the song "Saat Saheliyan" for actress Padmini Kolhapure. The song, composed by Kalyanji-Anandji, also had the voices of Kishore Kumar and Alka Yagnik.


title: Sadhana Sargam

text: Sargam continued to sing in films like "Taqdeer, Pighalta Aasmaan, Raj Tilak, Karishma Kudrat Ka" (in which she was the only female singer), but it was only with "Har Kisiko Nahin Milta" ("Janbaaz" 1986) that she was noticed.


title: Sadhana Sargam

text: "Khudgarz" was followed by "Khoon Bhari Maang" (1988) and Sargam also began to sing for other composers like Anu Malik, R. D. Burman, Anand Milind and sparingly under Laxmikant–Pyarelal. Her main hits continued to be with Rajesh Roshan, which included 'Jab Koi Baat Bigad Jaaye' / Jurm, 'Radha Bina Hai' / Kishan Kanhaiya, and songs in "Dariya Dil, Aasmaan Se Ooncha and Jaisi Karni Waisi Bharni". She also sung several songs in B.R. Chopra's popular television series Mahabharat (1988).


title: Sadhana Sargam

text: She got a boost from "Tridev" (Kalyanji – Anandji – Viju Shah) in 1989 in which she worked on "Main Teri Mohabbat Mein" and "Gajar Ne Kiya Hai Ishara".


title: Sadhana Sargam

text: In the early 1990s, Sargam emerged as one of the most sought-after female singers, along with Kavita Krishnamurthy, Alka Yagnik, Anuradha Paudwal and Poornima. She sang for composers like Nadeem–Shravan, Anand–Milind, Anu Malik, Jatin – Lalit, Bappi Lahiri, Viju Shah and Dilip Sen – Sameer Sen.


title: Sadhana Sargam

text: For the 1992 film "Vishwatma", she sang "Saat Samundar Paar" for debutant Divya Bharti which became a chartbuster. The same year she sang "Teri Umeed Tera Intezar", "Teri Isi Ada Pe Sanam" in "Deewana" and "Aashiqui Mein Har Aashiq" in "Dil Ka Kya Kasoor". The songs were superhits. Sargam would have become the voice of Divya Bharti were it not for the latter's untimely demise. Also in 1992, she sang the enduring duet “Pehla Nasha” by Jatin-Lalit with Udit Narayan in the film Jo Jeeta Wohi Sikander.


title: Sadhana Sargam

text: Her most critically acclaimed Hindi songs from the 2000s are in the film "Water", composed by A. R. Rahman, in which she sang three songs: "Aayo Re Sakhi", "Piya Ho" and "Naina Neer". Her other notable songs in Hindi with the same composer include "Aahista Aahista" from "Swades", "Chupke Se" and "Naina Milaike" from "Saathiya", "Chanda Re" from "Sapney", "O Palanhare" from "Lagaan", "Jhulaa Bahon Ka" from "Doli Saja Ke Rakhna", and "Banno Rani" from "1947: Earth". Her other notable rhapsodic Hindi hits are "Neele Neele Ambar Par" from "Kalakaar", "Jab Koi Baat Bigad Jaye" from "Jurm", "Pehla Nasha" from "Jo Jeeta Wohi Sikandar", "Na Kajre Ki Dhar" from "Mohra", "Tere Dar Pe Sanam" from "Phir Teri Kahani Yaad Aayee", "Jhinimini" from "Maqbool" and "Aao Na" from "Kyun! Ho Gaya Na...".


title: Sadhana Sargam

text: Sargam has sung more than 200 songs in Tamil, almost all of them having been well received. Her hits include, but not limited to, "Vennilave" from "Minsara Kanavu", "Nenje Nenje" from "Ratchagan", "Snehithane" from "Alaipayuthey", "Swasame" from "Thenali", "Konjum Mainakkale" from "Kandukondain Kandukondain", "Anbae Sugama" from "Paarthale Paravasam", "Deewana Deewana" from "Gemini", "Vaanaville Vaanaville" from "Ramanaa", "Chanakya Chanakya" from "Dum", "Manmadhane Nee" from "Manmadhan", "Thaiyyatha Thaiyyatha" from "Thiruttu Payale", "Akkam Pakkam" from "Kireedam", "Enadhuyirae" from "Bheemaa", "Mukundha Mukundha" from "Dasavathaaram", "Om Zaarare" from "Kuselan", and "Kaiya Pudi" from "Mynaa".


title: Sadhana Sargam

text: With nearly 100 tracks to her credit in Telugu, her hits include "Vennelave" from "Merupu Kalalu", "Snehithuda" from "Sakhi", "Palike Gorinkaa Chudave" from "Priyuralu Pilichindi", "Sathamaanaa Mannadile" from "Mrugaraju", "Baba Neeku Mokkutha" from "Baba", "Jaajimalli Thota" and "Kommallo Koyila" from 'Ninu Chusaka Nenundalenu', "Pedave Palikina Matallone" from "Naani", "Ela Vacchenamma" from "Sankranti", "Manasa" from "Munna", "Mooga Manase" from "Nava Vasantham", "Ninnena" from ""Salute"", "Panchirey" from "Konchem Ishtam Konchem Kashtam", "Kanu Paapalloo Prema" from "Shambo Shiva Shambo", "Anthapuramloo" and "Avuna Neevena" from "Rudhramadevi".


title: Sadhana Sargam

text: Sargam won her first Star Screen award for "Chupke Se Lag Ja Gale" from "Saathiya". She also won Filmfare, IIFA, Star Screen, GIFA, Apsara awards, Zee Cine Award, Star Screen Award and Stardust Best Playback Singer Female award nomination for "Aao Na" from " Kyon Ho Gaya Na..!" She received prestigious Zee Cine Award at Dubai for "Halki Halki Mulaqate Thi" from "Kuch Na Kaho" in 2003. She is the only playback singer from India who currently sings in 27 Indian languages. She won the National Film Award for Best Female Playback Singer for the song "Pattu Solli" from Thankar Bachan's cult classic movie "Azhagi"; the music was by maestro Ilaiyaraaja, whom she has praised, time and again, for "giving her such a wonderful song, and making her eligible for the National Award".


title: Sadhana Sargam

text: Sargam sang several songs in Hindi and Odia for music director Kajol-Saroj. She has also sung the Tamil version of "Mann Mohana" from the Hindi film "Jodhaa Akbar". Another foot-tapping recent solo Tamil song is "Sutri Varum Bhoomi" from the Vidhyasagar-composed "Jeyamkondaan" and "En Nenjil" from "Baana Kaathadi". She also sang the track "Rara Are Tu Aaja.. " for the Hindi-dubbed version of "Chandramukhi" in 2008. Sargam's Kannada song "Marali Mareyagi" from the movie Savaari in 2009 was well-received and won several accolades. The recent Ilaiyaraaja-composed Tamil film "Naan Kadavul" has a song titled "Amma Un Pillai" featuring her voice. In 2014, Sargam sang for A. R. Rahman in India's first-ever photorealisitc motion capture film, "Kochadaiiyaan", which was lip-synced by "Deepika Padukone" on screen. The same year, Sargam recorded two other hit tracks, "Kannukkul Pothivaippen" in "Thirumanam Enum Nikkah" and "Sonnathu Sonnathu" in "Aranmanai". In 2015, she sang two songs for Ilaiyaraaja in the historical drama, "Rudhramadevi (soundtrack)".


title: Sadhana Sargam

text: In 2011, Sargam made a contribution to the spiritual music world by singing an album: Mahalaxmi Mukti Samvad, MMS i.e. Mahalaxmi's Dialogues of Salvation. The lyrics are written by Dr. Pradeep Wagh. This album was released at the hands of spiritual Guru Vidyavachaspati Dr. Shankar Abhyankar.


title: Sadhana Sargam

text: In 2013, Sadhana Sargam sang a romantic duet with Udit Narayan ,"Ek Dil Hai Toota Idhar Bhi" penned by Raghvendra Singh in the music direction of Navin Manish for Rajshri Production's TV show Jhilmil Sitaaron Ka Aangan Hoga on Sahara One channel.


title: Sadhana Sargam

text: In 2014, Sargam recorded a bhajan, "O Kaanha Kaa Tohe Arpan Karun " penned by Raghvendra Singh in the music direction of Navin Manish for Rajshri productions TV show Mere rang mein rangne waali on Life Ok channel.


title: Sadhana Sargam

text: In 2015, Sargam, along with Kumar Sanu, recorded the runaway hit track, "Dard Karaara", from "Dum Laga Ke Haisha" in Anu Malik music. In 2017, the duo joined once again, but to record the title track for a TV serial, "Yeh Un Dinon Ki Baat Hai"; the song became an instant hit.


title: Sadhana Sargam

text: In 2018, Sargam sang an energetic and inspiring song "Houn Jau Dya" in Madhuri Dixit's Marathi film debut, Bucket List. The song also has the voices of Shreya Ghosal and Shaan.


title: Sadhana Sargam

text: In 2019, Sargam, along with Jonita Gandhi recorded a song, "Nee Sirichalum" from the Vishal-starrer, Action. The same year to commemorate the 500th episode of the hit serial Sembaruthi, Sargam and Vijay Prakash dueted a song in the music direction of Sekar Sai Barath.


title: Sadhana Sargam

text: In June 2021, Sargam collaborated with A R Rahman and Gulzar to record the song "Meri Pukaar Suno." The emotionally gravid track has an ensemble of six other singers: Alka Yagnik, K.S. Chithra, Shreya Ghoshal, Shashaa Tirupati, Armaan Malik and Asees Kaur. Described as a "heartfelt song of healing" by Rolling Stone India, the video for the song, featuring all the singers, was directed by Nazeef Mohammed.


title: Sadhana Sargam

text: Sargam sang her first song in the year 1992 film called Daan Pratidan, music composed by Ajoy Das. The following year Bappi Lahiri approached her to sing in the film Tomar Rakte Amar Sohag. She sang in films like Sagar Kinare, Kotha Chilo, Phiriye Dao and Dhushar Godhuli. She has sung the song "Holo Dhonno Jibon" along with Sonu Nigam in the film Bandhan (2004) which has been remade in Hindi as superhit "Hum Mar Jaayenge", sung by Arijit Singh and Tulsi Kumar. Further, she also sang "Akashe Batase Chal Sathi Ure Jai" with Kavita Krishnamurthy in Moner Majhe Tumi (2003), but the film's title track, her duet with Udit Narayan, "Premi O Premi" became an enormous hit.


title: Sadhana Sargam

text: Beginning her career in the early 1980s, Sargam has sung over 15,000 film and non-film songs in 36 Indian languages including Hindi, Marathi, Tamil, Telugu, Assamese, Bengali, Gujarati, Nepali, Meitei, Odia, Kannada, Malayalam and many others. In 2002, she became the first non-South Indian singer to win the National Award for a South Indian song. She is also the first non-South Indian singer to receive two Filmfare South Awards in the same year.


title: Sadhana Sargam

text: She is the only playback singer who actively participates and sings devotional and meditation songs for spiritual foundations like Prajapita Brahmkumari Vishwavidyalaya and Satya Saibaba. Her 2015 bhajan "Sai Ram Sai Shyam Sai Bhagwan" has crossed more than 100 million views on YouTube, and is immensely popular throughout India. Sargam has recorded hundreds of devotional albums in various languages, especially in Hindi, Gujarati, and Bengali.


title: Sadhana Sargam

text: Having achieved all prestigious awards in India, she is surprisingly yet to receive a Filmfare Award. In fact, she has neither won a Filmfare nor National Award for a Hindi song. Though she has numerous tracks to her credit (more than 2000 songs in Hindi alone), she had only been nominated twice for Filmfare Awards; once in 1989, for "Main Teri Hoon Janam" and sixteen years later, in 2005, for "Aao Na". Coincidentally, her contemporary, Alka Yagnik bagged the coveted trophies, both times.


title: Sadhana Sargam

text: Sargam's work in the international films Earth (1998 film) and Water are not happenstance, explains Deepa Mehta, the films' director. Mehta says, "I'm not fond of high pitched Indian women's voices. So there's this wonderful singer Sadhana Sargam, whose voice is low and we used her voice." On her frequent collaborations with Sargam, Rahman says, "I am surprised every time I work with her." Her other notable international collaboration was with Bally Sagoo, with whom she recorded Sometimes, Sometimes, a remixed version of the well known Kabhie Kabhie Mere Dil.


title: Sadhana Sargam

text: Sargam's voice is the favorite of artists like Lata Mangeshkar, Asha Bhosle, K.S.Chithra, Sunidhi Chauhan A R Rahman, Ilaiyaraaja, Amitabh Bachchan, Shashaa Tirupati and others.


title: Brenda Fassie

text: Brenda Nokuzola Fassie (3 November 1964 – 9 May 2004) was a South African singer, songwriter, dancer and activist. Affectionately called MaBrrr by her fans, she is also known as the "Queen of African Pop", the "Madonna of The Townships" or simply as The Black Madonna. Her bold stage antics earned a reputation for "outrageousness"; ironically, her Xhosa name, Nokuzola, means "quiet", "calm", or "peace".


title: Brenda Fassie

text: Brenda Nokuzola Fassie was born in Langa, Cape Town on 3 November 1964, the youngest of nine children. She was named after the American singer Brenda Lee. Her father died when she was only two years old; with the help of her mother, a pianist, she soon started earning money by singing for tourists.


title: Brenda Fassie

text: When she was 16 years old in 1981, she received a visit by Hendrick "Koloi" Lebona. As a result, she left Cape Town for Soweto, Johannesburg, to seek her fortune as a singer. Fassie first joined the vocal group Joy (filling in for one of the members who was on maternity leave) and later became the lead singer for a township music group called Brenda and the Big Dudes. She had a son, Bongani, in 1985 by a fellow Big Dudes musician. She married Nhlanhla Mbambo in 1989, but the pair divorced in 1991. Around this time she became addicted to cocaine and her career suffered as a result.


title: Brenda Fassie

text: With very outspoken views and frequent visits to the poorer townships of Johannesburg, as well as songs about life in the townships, Fassie enjoyed tremendous popularity. She also used her music to oppose the apartheid regime in South Africa. In 1989, she released the song "Black President" as a tribute to Nelson Mandela, a political prisoner and later the first Black president of South Africa. Known best for her songs "Weekend Special" and "Too Late for Mama", Fassie was dubbed "The Madonna of the Townships" by "Time" magazine in 2001.


title: Brenda Fassie

text: In 1995, she was discovered in a hotel with the body of her female lover, Poppie Sihlahla, who had died of an apparent overdose. Fassie underwent rehabilitation and got her career back on track. However, she still had drug problems, and returned to drug rehabilitation clinics about 30 times in her life. From 1996 on she released several solo albums, including "Now Is the Time", "Memeza" (1997), and "Nomakanjani?". Most of her albums became multi-platinum sellers in South Africa; "Memeza" was the best-selling album in South Africa in 1998.


title: Brenda Fassie

text: On the morning of 26 April 2004, Fassie collapsed at her home in Buccleuch, Gauteng, and was admitted into a hospital in Sunninghill. The press were initially told that she had suffered cardiac arrest, but later reported that she had slipped into a coma brought on by an asthma attack. The post-mortem report revealed that Fassie had taken an overdose of cocaine on the night of her collapse, and this was the cause of her coma. She stopped breathing and suffered brain damage from lack of oxygen. Fassie was visited in the hospital by Nelson Mandela, Winnie Mandela, and Thabo Mbeki, and her condition was front-page news in South African papers. She died aged 39 on 9 May 2004 in hospital, without regaining consciousness, after her life support machines were turned off. According to the South African "Sunday Times" and the managers of her music company, the post-mortem report also showed that she was HIV-positive. Her manager, Peter Snyman, denied this aspect of the report. Her family, including her long-term partner, were at her side when she died.


title: Brenda Fassie

text: Fassie won five South African Music Awards: Best Female Artist and Song of the Year in 1999, Best-Selling Release of the Decade and Best Song of the Decade in 2004, and Lifetime Achievement Award in 2005. She also won three Kora Awards: Most Promising Female Artist of Africa and Best Female Artist of Africa in 1996, and the Jury Special Award in 2001. She was voted 17th in the Top 100 Great South Africans.


title: Brenda Fassie

text: Her son Bongani "Bongz" Fassie performed "I'm So Sorry", a song dedicated to his mother, on the soundtrack to the 2005 Academy Award-winning movie "Tsotsi". In March 2006 a life-size bronze sculpture of Fassie by artist Angus Taylor was installed outside Bassline, a music venue in Johannesburg.


title: Brenda Fassie

text: Fassie also contributed to Mandoza's album "Tornado" (2002), Miriam Makeba's album "Sangoma" (1988), and Harry Belafonte's anti-apartheid album "Paradise in Gazankulu" (1988). She sang on two of the soundtrack albums for "Yizo Yizo" (both released in 2004).


title: Alex Cross (novel series)

text: Alex Cross is a crime, mystery, and thriller novel series written by James Patterson. The series focuses on Metropolitan Police Department detective and father Alex Cross as he faces threats to his family and the city of Washington, D.C. Supporting characters include two of Cross's children, Damon, and Janelle, as well as his grandmother Nana Mama. The series is usually narrated in first-person perspective by Alex Cross, and occasionally from the villains' point of view in third-person.


title: Alex Cross (novel series)

text: The series has been running since the 1990s and is ongoing. Nearly all have made bestsellers lists and garnered favorable reviews, especially "Double Cross;" "Cross Fire;" "I, Alex Cross;" and "Alex Cross, Run".


title: Alex Cross (novel series)

text: The series is published worldwide, with Little, Brown currently holding publication rights in the United States, in paperback, hardcover, and audiobook editions. The first book in the series, "Along Came a Spider", was released in 1993 to positive reviews, spawning a series of over twenty subsequent novels. The series has led to three films, "Kiss the Girls" (1997), "Along Came a Spider" (2001), and "Alex Cross" (2012).


title: Alex Cross (novel series)

text: Alex Cross is a widower-detective-father who often fights against threatening villains—and criminals who wish to kill Cross and others. It mainly focuses on Cross trying to solve very difficult cases while attempting to maintain a relationship with his family. For example, in "Merry Christmas, Alex Cross", Cross misses out on Christmas Eve and Christmas itself to focus on finding and defeating a terrorist group. One of his regular foes in the earlier books is Gary Soneji, the "Mastermind" who wants to kill Cross, out of revenge for Alex putting him in prison. In some books, Cross sometimes works with—or against—the President/Secret Service in a few books such as "Along Came a Spider", "Jack & Jill, I, Alex Cross", and "Kill Alex Cross". An ongoing theme in the earlier novels is the unsolved murder of his first wife, Maria. Cross later reveals another reason for trying to solve the cases: so he can protect his family from danger. Cross currently lives on Fifth Street in Southeast Washington, D.C., along with grandmother Nana Mama, children Damon, Janelle ("Jannie"), and Alex Jr. ("Ali"), and his current and new wife, Brianna "Bree" Stone-Cross.


title: Alex Cross (novel series)

text: When Alex was 9, his father died of alcoholism, a year after his mother died. He went to Washington, D.C., to live with his grandmother—Nana Mama. During his childhood, he met his later best friend John Sampson. He also later met his wife, Maria, in Washington, and married her. After giving birth to two children, a few months or years later, she is murdered. Alex later meets a woman named Christine, who becomes pregnant, giving birth to an additional third child for the Cross family—Ali. She later leaves Ali with Alex dealing with traumatization over her kidnapping in "Pop Goes the Weasel". Afterwards, she tried claiming custody over Ali and succeeded. However, she later gave Ali back to Alex, who had joined the FBI at the time. His deadliest foes are Geoffrey Shafer and Gary Soneji; both have been killed through the course and events of the book series.


title: Alex Cross (novel series)

text: In "Cross", Alex discovers who really killed his wife, and will do anything to take down her murderer. He learns he was chasing a false killer, and the real killer is Jimmy Hats, whom Sampson killed long ago. At the end of the novel, Alex comes to terms with Maria's death and moves on with his life. "Double Cross" sees Alex as he falls in love again—with detective Bree Stone; he must also assist her in the case of DCAK, a murderer, known as DC Audience Killer, as he retired from the FBI before the events of "Cross". In "I, Alex Cross", he decides to find and solve the murder case in which his late niece, Caroline Cross, was the victim. He later learns who the murderer is—the president's husband—but the murderer is later killed by an agent from the Secret Service. Also in the book, Alex proposes to Bree and she accepts, becoming his fiancée. By "Cross Fire", Alex and Bree get married and face off once more against Kyle Craig, who dies at the end. With Kyle dead, Alex, Bree, and his family experience a sense of peace, something they haven't felt for a long time.


title: Alex Cross (novel series)

text: In "Kill Alex Cross", after Nana Mama finds a girl trying to steal from their house, she and Bree agree to adopt the girl towards the end of the book; he also goes on the case to rescue the new president's children. In "Merry Christmas, Alex Cross", Alex risks everything to solve a case, stop possible murders, help a church, and must use every skill he knows of to help him solve the case and may not make it to Christmas dinner alive. Alex misses Christmas which upsets him and his wife, Bree. In "Alex Cross, Run" renowned plastic surgeon, Elijah Creem, is arrested and wants revenge on Alex. Alex eventually defeats Creem. However, one of Alex's stalkers, who is bent on murdering Alex, kills Ava after having the foster care services take her away from the Cross family for alleged drug use. Alex, in retaliation and along with Sampson and Bree, finds the killer and arrests him. At the end of the novel, several issues are left unresolved, such as Alex's lifetime problem: endangering his family's life as well as his own. He ponders whether he should stay with the Metro Police. His therapist assures him he will eventually outgrow the issue, or solve it somehow. There are also some unresolved issues between Alex and Bree as well, but their love for each other continues to remain strong, helping them recover.


title: Alex Cross (novel series)

text: "Cross My Heart" is the twenty-first novel in the series. For most of the novel, Alex is trying to solve a double killer case in which the murderers kill prostitutes. Soon Alex and Bree learn that there is only one murderer, who has multiple personalities, and arrest him. Additionally, Bree is searching for Ava, when Alex realizes that the teen may have killed a girl and faked her own death. Halfway through the novel, Damon is offered a ride home by a strange woman - throughout the novel it's revealed that the Cross family were being watched - and the woman drugs Damon afterwards. Meanwhile, her accomplice kidnaps the rest of the family including Bree, Ali, Nana Mama, and Alex's daughter. They alert Cross he can do nothing to try to save his family. Meanwhile, Ava reappears along with Sampson, assuring him to continue life normally while they handle the kidnappings. The novel was released in November 2013. A subsequent novel titled "Hope to Die" was released in November 2014 and continued the events in "Cross My Heart". It was followed by a 23rd novel named "Cross Justice", released in November 2015, in which the Cross family travels down south to help one of Alex's cousins who is wrongly accused of murder. At the end of "Cross Justice", Alex finds his long lost father Jason, who was presumed dead for over three decades but in reality had been a police sergeant in Florida. A 24th novel, "Cross the Line", was released in 2016, in which Alex and Bree look for a killer who is murdering criminals and another killer who has murdered one of their former police chiefs. In "Cross Kill", Alex and his partner, Detective John Sampson, are ambushed by an Gary Soneji imposter and Alex goes on a desperate mission to uncover the truth about the mysterious attacker while having no idea that it would have terrible consequences. In "Detective Cross", Alex is awaiting trial for the killing of two of the Sonjei followers and has to help his wife, Chief of Detectives Bree Stone, in stopping a mysterious bomber from setting off deadly explosives before it is too late. In "The People vs. Alex Cross", Alex is on trial for murder, and he also has to assist his former partner, Detective John Sampson, in finding missing blonde women and prevent them from being brutally murdered on the internet while trying to prove his innocence with a determined prosecution hoping to put him behind bars. In "" A leader has fallen, and Alex Cross joins the procession of mourners from Capitol Hill to the White House. Then a sniper's bullet strikes a target in the heart of DC. Alex Cross's wife, Bree Stone, newly elevated chief of DC detectives, must solve the case or lose her position. The Secret Service and the FBI deploy as well in the race to find the shooter. Alex is tasked by the new President to lead an investigation unprecedented in scale and scope. But is the sniper's strike only the beginning of a larger attack on the nation?


title: Alex Cross (novel series)

text: The earlier novels were initially named after children's rhymes, but from 2006 the lead character's name started appearing in the titles.


title: Alex Cross (novel series)

text: Overall there have been three theatrical films of the Alex Cross series - "Kiss the Girls", " Along Came a Spider", and "Alex Cross". All met with negative reviews and poor box-office results.


title: Alex Cross (novel series)

text: Two films, based on the first Cross novels, have been made starring Morgan Freeman ("Kiss the Girls" and "Along Came a Spider"), both released to negative reaction. Both of them are very loose adaptations of the books, with "Along Came a Spider" changing many of the plot's elements, while "Kiss the Girls" changes nearly the entire story's plot, except for the fact that Alex's niece is kidnapped and its primary antagonist is Casanova. A significant, and well-noted, change upon the books in the movies is that John Sampson is not white but African-American, like Alex himself. Kyle Craig is briefly seen in "Kiss the Girls". "Along Came a Spider"'s adaptation was also changed with the film taking out major plot elements or changing them. For instance, Jezzie Flannagan and Alex Cross are dating in the book, but are described as only friends in the film. Also, the most important changed elements is Gary Soneji dies, which would therefore erase him from any future adaptation of "Cat and Mouse", nor does Soneji escape from prison, nor is the trial in court seen or mentioned in the film. A proposed third film based on "Pop Goes the Weasel!", but after "Along Came a Spider" was panned at the box office, the plans were canceled.


title: Alex Cross (novel series)

text: Many years after "Along Came a Spider"s release, a reboot was revealed to be in the works, set for a 2011 release date. Idris Elba was attached to the film as the role of Alex Cross. It was rumored to be based on "I, Alex Cross", but director Rob Cohen denied this, revealing he only titled the film like such so as to tell fans: "their hero was back"; to avoid confusion the film's name was changed to "Alex Cross" with Tyler Perry replacing Elba. Edward Burns and Matthew Fox were later confirmed to star as Cross's partner, Tommy Kane, and the main antagonist, Picasso. The film was later confirmed to be based on the 12th book in the series, "Cross". The film was released on October 19, 2012, to mixed to negative reviews. The film was a minor box office bomb, grossing $34 million against its $35 million budget. Matthew Fox and Tyler Perry were praised for their roles in the film.


title: Alex Cross (novel series)

text: Despite negative reception, a sequel based on "Double Cross" is being created, with Perry and Patterson in early talks for a deal for a sequel. Perry was confirmed to reprise his role as Cross for the sequel. The film still needs casting and a script however. A deal is being finalized between Patterson and Perry.


title: Alex Cross (novel series)

text: However, as of 2021, no official word has been said on the sequel, with only news of Patterson and Perry signed on for the film in 2013 Prior to the film's release, it was announced that Double Cross would be adapted into a film, with Perry reprising his role. However, the film was cancelled after Alex Cross did not perform well at the box office.


title: Alex Cross (novel series)

text: Amazon Studios ordered a television series adaptation titled "Cross" with Aldis Hodge will star and Ben Watkins will serve as showrunner from Paramount Television Studios and Skydance Television.


title: Alex Cross (novel series)

text: The book series have been released in paperback and hardcover, while it can be listened to on audio book or excerpts from the series can be read online at the official JamesPatterson.com website or others. "Merry Christmas, Alex Cross", the latest book in the Cross series, was reported to, unlike its predecessors, be barely over 300 pages. Most of the recent novels have usually grossed between 300 and 400, with a rarity of over 400 pages. The films have also subsequently been released in 1997, 2001, and 2012 with both and Morgan Freeman and Tyler Perry getting the chance of portraying Cross in the films, most recently Perry in the third film.


title: Alex Cross (novel series)

text: The series has been given mixed to positive reviews, with the exception of the 18th book "Kill Alex Cross", which has been given mixed to negative reviews, and "Cross Country", which received mixed reviews. Many have criticized "Kill Alex Cross" while few have given it positive reviews. So far, the most positively-received book is either "Double Cross" or "I, Alex Cross". The series has at numerous times been on the "New York Times Bestseller" list for several weeks. Goodreads.com said ""I, Alex Cross" is without a doubt the best, revealing new surprises and scares at every turn. It is even scarier than "Along Came a Spider"—and by far, better! This is Patterson at his best." "Double Cross" was on the "New York Times Bestseller" list (at number 1) for numerous weeks before being eventually surpassed.


title: Alex Cross (novel series)

text: The film series, however, did not fare well, with all three films garnering a negative reception. The most recent film, "Alex Cross", received poor reviews and had an underwhelming performance at the box office. "Kiss the Girls" was the best-received film in the series.


title: Government shutdowns in the United States

text: In the United States, government shutdowns occur when there is a failure to enact funding legislation to finance the government for its next fiscal year or a temporary funding measure. Ever since a 1980 interpretation of the 1884 Antideficiency Act, a "lapse of appropriation" due to a political impasse on proposed appropriation bills requires that the US federal government curtail agency activities and services, close down non-essential operations, furlough non-essential workers, and only retain essential employees in departments covering the safety of human life or protection of property. Voluntary services may only be accepted when required for the safety of life or property. Shutdowns can also occur within and disrupt state, territorial, and local levels of government.


text: Since the enactment of the US government's current budget and appropriations process in 1976, there have been a total of 22 funding gaps in the federal budget, ten of which have led to federal employees being furloughed. Prior to 1980, funding gaps did not lead to government shutdowns, until Attorney General Benjamin Civiletti issued a legal opinion requiring the government to be shut down when a funding gap occurs. This opinion was not consistently adhered to through the 1980s, but since 1990 all funding gaps lasting longer than a few hours have led to a shutdown.


text: Some of the most significant shutdowns in U.S. history have included the 21-day shutdown of 1995–1996 during the Bill Clinton administration over opposition to major spending cuts; the 16-day shutdown in 2013 during the Barack Obama administration caused by a dispute over implementation of the Affordable Care Act (ACA); and the 35-day shutdown of 2018–2019 during the Donald Trump administration, the longest shutdown in US history, caused by a dispute over the funding amount for an expansion of the U.S.–Mexico border barrier.


text: Shutdowns cause the disruption of government services and programs, including the closure of national parks and institutions (in particular, due to shortages of federal employees). A major loss of government revenue comes from lost labor from furloughed employees who are still paid, as well as loss of fees that would have been paid during the shutdown. Shutdowns also cause a significant reduction in economic growth (depending on the length of the shutdown). During the 2013 shutdown, Standard & Poor's, the financial ratings agency, stated on October 16 that the shutdown had "to date taken $24 billion out of the economy", and "shaved at least 0.6 percent off annualized fourth-quarter 2013 GDP growth".


text: Under the separation of powers created by the United States Constitution, the appropriation and control of government funds for the United States is the sole responsibility of the United States Congress. Congress begins this process through proposing an appropriation bill aimed at determining the levels of spending for each federal department and government program. The finalized version of the bill is then voted upon by both the House of Representatives and the Senate. After it passes both chambers, it proceeds to the President of the United States to sign the bill into law.


text: Government shutdowns tend to occur when there is a disagreement over budget allocations before the existing cycle ends. Such disagreements can come from the president – through vetoing any finalized appropriation bills they receive – or from one or both chambers of Congress, often from the political party that has control over that chamber. A shutdown can be temporarily avoided through the enactment of a continuing resolution (CR), which can extend funding for the government for a set period, during which time negotiations can be made to supply an appropriation bill that all involved parties of the political deadlock on spending can agree upon. However, a CR can be blocked by the same parties if there are issues with the content of the resolution bill that either party has a disagreement upon, in which case a shutdown will inevitably occur if a CR cannot be passed by the House, Senate or president. Congress may, in rare cases attempt to override a presidential veto of an appropriation bill or CR, but such an act requires there to be majority support of two-thirds of both chambers.


text: Initially, many federal agencies continued to operate during shutdowns, while minimizing all nonessential operations and obligations, believing that Congress did not intend that agencies close down while waiting for the enactment of annual appropriations acts or temporary appropriations. However, Attorney General Benjamin Civiletti issued two opinions in 1980 and 1981, that more strictly interpreted the Antideficiency Act in the context of a funding gap, along with its exceptions. The opinions stated that, with some exceptions, the head of an agency could avoid violating the Act only by suspending the agency's operations until the enactment of an appropriation. In the absence of appropriations, exceptions would be allowed only when there is some reasonable and articulable connection between the function to be performed and the safety of human life or the protection of property. However, even after the Civiletti opinions, not all funding gaps led to shutdowns. Of the nine funding gaps between 1980 and 1990, only four led to furloughs.


text: Shutdowns of the type experienced by the United States are nearly impossible in other forms of government:


text: While government shutdowns prior to the 1995–1996 shutdowns had very mild effects, a full federal government shutdown causes a large number of civilian federal employees to be furloughed. During a government shutdown, furloughed government employees are prohibited from even checking their e-mail from home. To enforce this prohibition, many agencies require employees to return their government-issued electronic devices for the duration of the shutdown.


text: Because of the size of the government workforce, the effects of a shutdown can be seen in macroeconomic data. For example, with payment delayed to 1.3 million workers, and 800,000 employees locked out, confidence in the job market decreased but recovered within a month of the 2013 shutdown, and GDP growth slowed 0.1–0.2%. Still, the loss of GDP from a shutdown is a bigger sum than it would cost to keep the government open.


text: However, the complete effects of a shutdown are often clouded by missing data that cannot be collected while specific government offices are closed.


text: Additionally, some effects of the shutdown are difficult to directly measure, and are thought to cause residual impacts in the months following a shutdown. Some examples include destroyed scientific studies, lack of investment, and deferred maintenance costs. The length of the 2018–2019 shutdown curtailed safety and law enforcement investigations, caused air travel delays as essential workers stopped showing up, shut down some facilities for Native Americans and tourists, and delayed regulatory approvals and immigration hearings for non-detainees.


text: The exact details of which government functions stop during a shutdown is determined by the Office of Management and Budget.


text: During the 2013 shutdown, the moral philosopher Peter Singer argued in "Slate", that shutdowns were evidence that the U.S. Constitution's separation of powers constituted "a fundamental flaw."


text: In 2019, following the end of the 2018–19 shutdown, Michael Shindler argued in "The American Conservative" that shutdowns protect popular sovereignty. He writes, "No other political phenomena so forcefully and dramatically obliges the whole people to recognize that their ideological divisions have become so great that the exercise of their sovereignty has become virtually impossible," and "During a shutdown, the government, which is bound by elaborate mechanisms to the national will, becomes confused. For a moment, it seems as if the march of American history is at a standstill. There are only two means of moving forward: either government officials follow the will of something other than the nation or the nation engages in a momentous reconciliation of its will."


text: This list includes only major funding gaps which led to actual employee furloughs within federal departments of the US government. It does not include funding gaps that did not involve shutdowns of government departments, in which examples include: a brief funding gap in 1982, in which nonessential workers were told to report to work but to cancel meetings and not perform their ordinary duties; a three-day funding gap in November 1983 that did not disrupt government services; and a 9-hour funding gap in February 2018 that did not disrupt government services.


text: On 1 May 1980, during the presidential term of Jimmy Carter, the Federal Trade Commission (FTC) was shut down for one day after Congress failed to pass an appropriations bill for the agency, due to differing opinions towards its oversight of the US economy. Prior to the shutdown, a review had been made of the 1884 Antideficiency Act regarding Congressional approval of agency funding, in which initial opinion on the subject had been that this did not require a government agency to be closed down in the wake of the expiration of their funding, before Attorney General Benjamin Civiletti overruled this opinion with his own on 25 April 1980, stating that a provision of this act stipulated to the contrary. Five days later, the FTC was shutdown after Congress delayed funding for the agency in order to seek approval for an authorization bill to limit the agency's investigative and rule-making abilities following criticism of the FTC's aggressive monitoring of the economy.


text: The 1980 shutdown was the first time a federal agency shut down due to a budget dispute, with around 1,600 federal workers for the FTC being furloughed as a result, and Federal Marshals deployed to some FTC facilities to enforce their closure. The shutdown ended after one day when Carter threatened to close down the entire US government if Congress did not pass spending bills by 1 October later that year, with economists of the time estimating that the 1-day shutdown of the FTC cost the government around $700,000, the majority of which was towards back pay for the furloughed workers. In the aftermath of the shutdown, Civiletti issued a revised edition of his original opinion on 18 January 1981, detailing that shutdowns would still require agencies that protect human safety or property to continue operating if funding for them expired.


text: In 1981, 1984, and 1986, thousands of federal employees were furloughed for a period of between 12 and 24 hours during both presidential terms of Ronald Reagan. The deadlocks focused on disagreements by Reagan towards Congressional bills that went against his political beliefs and goals. The first shutdown took place on 23 November 1981, lasting for a day and placing 241,000 federal employees into furlough, after Reagan vetoed a proposed appropriation bill that contained a reduced set of spending cuts than he had proposed for select government departments. While the shutdown affected only a number of government departments, economists of the time believed that it cost taxpayers an estimated $80–90 million in back pay and other expenses over the entire day.


text: The second shutdown occurred on the afternoon of 4 October 1984, with 500,000 federal employees placed on furlough during this period, after Reagan mounted opposition towards the inclusion of a water projects package and a civil rights measure within the proposed appropriations bill that day. While the shutdown covered around nine of the 13 appropriations bills that had not been passed at that point, Congress was forced to remove both of the opposed elements of the bill and include funding of the Nicaraguan Contras as a compromise to end the shutdown, with economists believing that the short period cost taxpayers an estimated $65 million in backpay.


text: The third shutdown took place over a similar period and furloughed the same number of federal employees on 17 October 1986. Economists estimated that this period cost the US government $62 million in lost work. All government agencies were affected by this shutdown.


text: The shutdown of 1990 occurred during the presidential term of George H. W. Bush and focused on a disagreement over several measures he proposed for the 1991 appropriations bill - the inclusion of major tax increases, despite Bush's campaign promise against , and major cuts in spending towards benefit programs, including Medicare, to combat deficit reduction. On 5 October 1990, liberal Democrats and conservative Republicans, led by then House Minority Whip Newt Gingrich, opposed the initial appropriations package, with Bush vetoing the second resolution to the spending bill the following day on 6 October.


text: The shutdown lasted until 9 October, when Bush agreed to remove his proposed tax increases and reduce the amount of spending cuts, in return for Congress providing a concession on the amended bill to allow for increasing income tax on the wealthy. The effects of the deadlock were lessened due to the fact that the shutdown occurred across the Columbus Day weekend - 6 October to 8 October. Only 2,800 workers were furloughed over this period, with national parks and museums, such as the Smithsonian, being closed, and a handful of departments unable to function, with the cost to the government for lost revenue and back wages being estimated to around $2.57 million.


text: Between 1995 and 1996, the US government faced two shutdowns during the presidential term of Bill Clinton, who opposed proposed appropriation bills for 1996 by congressional Republicans (who had a majority in both chambers) and House Speaker Newt Gingrich. Both Gingrich and the majority of Congress sought to pass bills that would reduce government spending, much against Clinton's political objectives for 1996. Clinton objected to funding cuts affecting education, the environment, and public health. One proposed bill threatened to block a scheduled reduction he had planned towards premiums within Medicare. Both sides had differing opinions over the impact the proposed House bills would have over economic growth, medical inflation, and anticipated revenues, with Clinton vetoing the bills over amendments added to them by congressional Republicans, despite Gingrich threatening to refuse to raise the country's debt ceiling.


text: The first shutdown took place on 14 November 1995, after a CR issued on 1 October had expired, and meetings between Democrat and Republican leaders failed to end the deadlock. The effect of the deadlock led to the majority of government departments being closed down and 800,000 federal workers being furloughed as a result. Although the shutdown ended five days later on 19 November, the political friction between Clinton and Gingrich over the US budget remained unresolved, and on 16 December 1995, after further spending bills failed to secure approval, a second shutdown took place. Although lasting 21 days, fewer departments were closed down, and around 284,000 federal workers were furloughed during this period. The shutdown was eventually ended on 6 January 1996, when White House and Congressional negotiators worked out a balanced budget agreement, which included approval towards modest spending cuts and tax increases.


text: Both shutdowns had a contrasting impact on the major political players in the deadlock. Gingrich's political career was negatively impacted by the shutdowns, in part due to a comment he made during the deadlock that made it sound like his reasons for it were petty. Clinton's presidential term was positively improved by the shutdown and cited as part of the reason behind his successful re-election to the White House in 1996.


text: Some effects of the shutdowns included the government, tourism, and airline industry losing millions of dollars in revenue during this period, with disruptions made towards the processing of passports and visas, and work on medical research and toxic waste cleanup being halted.


text: The shutdown of 2013 occurred during the second Obama term, focusing on a disagreement between Republican-led House of Representatives and the Democratic-led Senate towards the contents of the 2014 Continuing Appropriations Resolution bill, alongside other political issues. Congressional Republicans, encouraged by conservative senators such as Ted Cruz, and conservative groups such as Heritage Action, sought to include several measures to the bill in late 2013 that could delay funding for the 2013 Affordable Care Act (ACA) and thus allow time for changes to be made to the act. However, both Obama and Democratic senators refused to agree to these measures, seeking instead for the bill to maintain government funding at then-current sequestration levels with no additional conditions.


text: The shutdown took place on 1 October 2013, as a result of an impasse over the contents of the bill, with the House unable to approve any CRs before this date. Democrats opposed further efforts by congressional Republicans, led by House Speaker John Boehner, to delay funding of the ACA, and rejected piecemeal Resolution bills proposed by them to resolve the shutdown. As Congress was at an impasse amidst rising concerns that the US would default on public debt, US senators - particularly then Senate Minority Leader Mitch McConnell and then Senate Majority Leader Harry Reid - negotiated a deal to end the deadlock. Their proposal, which won a Senate vote, approved an amended Resolution bill that would keep funding at sequestration levels, temporarily suspend the debt limit until 7 February 2014, and include a concession to congressional Republicans on the ACA by applying stricter income verification rules in regards to health insurance. Boehner eventually withdrew further objections and delaying attempts against the ACA upon the country being within hours of breaking its debt limit on 16 October 2013, with Congress approving the bill for Obama's signature the following day.


text: The 16-day shutdown had considerable impact upon the United States: approximately 800,000 federal employees were put on furlough, while an additional 1.3 million had to report to work without any known payment dates during this period, costing the government millions in back pay; major government programmes concerning Native Americans, children, and domestic violence victims, alongside the legal processing of asylum and immigration cases, and sexual assault cases handled by the Office of Civil Rights, were badly disrupted by the shutdown; tourism was greatly impacted due to the closure of national parks and institutions during the shutdown and cost the government millions in lost revenue; and US economic growth was reduced during this period. In political circles, the shutdown had a negative impact on Republicans, as over half of Americans held Republicans accountable for the deadlock, in comparison to public opinion on the accountability of both the Democrats and Obama during this period.


text: The shutdown of January 2018 was the first to occur during the presidential term of Donald Trump and was centered around a disagreement on the issue of immigration. By the start of October 2017, Congress had failed to approve an appropriation bill to fund the US government in 2018, and instead passed three CRs to keep federal agencies open until 19 January 2018. The failure to establish a permanent spending bill was due to Democratic senators insisting that any proposed House bill needed to include funding for the Deferred Action for Childhood Arrivals (DACA) immigration policy and assurances against deportation for immigrants that fell under the DREAM Act. Republicans refused to pass such bills, citing that discussions on immigration and those individuals under DACA would not be held until mid-March of the following year. A senate vote to extend the 2018 Continuing Appropriations Resolution on 19 January 2018, which had passed a congressional vote the previous day, failed to achieve a majority, after Democratic senators led a filibuster aimed at forcing Republicans to invoke a shorter duration of CR and thus invoke negotiations that could lead to extensions of the DACA policy. but failed to achieve a majority, as Democrats sought a shorter duration of CAR to force negotiations.


text: The shutdown took place on 20 January 2018, and led to approximately 692,000 federal workers being furloughed. An attempt by Democrats to protect the payment of military personnel during the deadlock was rejected by Republicans, after Senate Majority Leader Mitch McConnell stated that funding had to be restored for the entire US government rather than for individual government branches. Despite the bill's failure, both sides engaged in negotiations that eventually culminated with a deal on a proposed stopgap measure to fund the government for four weeks - as part of the proposal, Democrats agreed to end their filibuster and approve the Republican's measure, in exchange for fresh talks on the DACA policy and DREAM Act within newly proposed Resolution bill. The measure was approved in the House and passed a Senate vote, effectively ending the shutdown on 23 January.


text: The impact of the shutdown was not as severe as in previous deadlocks - most government departments, such as the Department of Energy and the Environmental Protection Agency, were able to continue their functions during the 3-day deadlock despite their workers needing back-pay in the aftermath, and only a third of National Parks in the United States were closed down. In the aftermath of the shutdown, the Senate debated on a bill for the 2018 Bipartisan Budget Act to provide 2-year funding for the military, and provide an extension to the Resolution to keep the government funded for another six weeks. However, the negotiations suffered delays that triggered the brief 9 February spending gap, though this merely lasted for nine hours, causing little disruption.


text: The shutdown of December 2018–January 2019 was the second to occur during the presidential term of Donald Trump, and was due to a disagreement over negotiations for Trump's wall along the Mexico–United States border. Trump sought to have the appropriation bill for 2019 include a funding measure on border security, providing $5.7 billion toward construction of the wall. Democrats refused to support the bill, citing that the funding would be a waste of taxpayer money and questioned the effectiveness the new wall would have, opting to propose bills that would include funding for border security, but towards improving pre-existing security measures. Trump initially backed down on demands for border wall funding, but reversed this decision on 20 December 2018 over pressure from supporters, refusing to sign any CRs that did not include it.


text: The shutdown began on 22 December 2018, after Democrats refused to support a new CR in the Senate that included approximately $5 billion for the new border wall, and continued to block further attempts upon taking control of Congress on 3 January 2019 following the 2018 mid-term elections. Although he had support from several Republicans, including Senate Majority Leader Mitch McConnell, Trump faced stiff opposition to border wall funding from House Speaker Nancy Pelosi and Senate Minority Leader Chuck Schumer, with neither party able to break the political impasse through negotiations, rallying public support through televised addresses, offering proposals on alternative border security funding measures, or making concessions for a proposed appropriation bill with regards to the DACA policy. The deadlock eventually ended on 25 January 2019, when both chambers of Congress approved a plan to reopen the US government for 3 weeks, in order to facilitate a period of negotiations to determine a suitable appropriation bill that both parties could agree upon, with Trump endorsing the deal amidst rising security and safety concerns.


text: The 35-day shutdown, the longest in US history after surpassing the 21-day shutdown of 1995–1996, led to 380,000 federal workers being furloughed, and an additional 420,000 workers were required to work without any known payment dates during this period, forcing many to find other paid work or protest against the extended period of the deadlock. The extent of the funding gap had further major impacts - sharp reductions had to be made on SNAP payments, and the Internal Revenue Service faced extensive delays on processing tax refunds worth around $140 billion; a lack of resources due to the funding gap impacted the work of several agencies, with the FBI facing major disruptions that risked compromising a number of investigations being conducted at the time; staff shortages in the Transportation Security Administration caused a number of airports to be closed down as a result; and economic growth was severely reduced by billions of dollars.


text: According to the Congressional Budget Office, the shutdown cost the government $3 billion in back pay for furloughed workers, plus $2 billion in lost tax revenues due to reduced tax evasion compliance activities by the Internal Revenue Service, and a smaller amount of lost fees such as for visits to national parks, for a total of about $5 billion.


title: Classical Chinese

text: Classical Chinese, also known as Literary Chinese (古文 "gǔwén" "ancient text", or 文言 "wényán" "text speak", meaning


title: Classical Chinese

text: "literary language writing"), is the language of the classic literature from the end of the Spring and Autumn period through to the either the start of the Qin dynasty or the end of the Han dynasty, a written form of Old Chinese (上古漢語, "Shànɡɡǔ Hànyǔ"). Classical Chinese is a traditional style of written Chinese that evolved from the classical language, making it different from any modern spoken form of Chinese. Literary Chinese was used for almost all formal writing in China until the early 20th century, and also, during various periods, in Japan, Ryukyu, Korea and Vietnam. Among Chinese speakers, Literary Chinese has been largely replaced by written vernacular Chinese, a style of writing that is similar to modern spoken Mandarin Chinese, while speakers of non-Chinese languages have largely abandoned Literary Chinese in favor of their respective local vernaculars. Although languages have evolved in unique, different directions from the base of Literary Chinese, many cognates can be still found between these languages that have historically written in Classical Chinese.


title: Classical Chinese

text: Literary Chinese is known as ' (, "Han writing") in Japanese, ' in Korean (but see also ') and ' () or "Hán văn" () in Vietnamese.


title: Classical Chinese

text: Classical Chinese refers to the written language of the classical period of Chinese literature, from the end of the Spring and Autumn period (early 5th century BC) to the end of the Han dynasty (AD 220), while Literary Chinese is the form of written Chinese used from the end of the Han dynasty to the early 20th century, when it was replaced by vernacular written Chinese. There is also a stricter definition for the Classical period, ranging from Confucius (551–479 BCE) to the foundation of the Qin dynasty.


title: Classical Chinese

text: Literary Chinese is often also referred to as "Classical Chinese", but sinologists generally distinguish it from the language of the early period. During this period, the dialects of China became more and more disparate and thus the Classical written language became less and less representative of the varieties of Chinese (cf. Classical Latin, which was contemporary to the Han Dynasty, and the Romance languages of Europe). Although authors sought to write in the style of the Classics, the similarity decreased over the centuries due to their imperfect understanding of the older language, the influence of their own speech, and the addition of new words.


title: Classical Chinese

text: This situation, the use of Literary Chinese throughout the Chinese cultural sphere despite the existence of disparate regional vernaculars, is called diglossia. It can be compared to the position of Classical Arabic relative to the various regional vernaculars in Arab lands, or of Latin in medieval Europe. The Romance languages continued to evolve, influencing Latin texts of the same period, so that by the Middle Ages, Medieval Latin included many usages that would have been foreign to the Romans. The coexistence of Classical Chinese and the native languages of Japan, Korea and Vietnam can be compared to the use of Classical Latin in nations that natively speak non-Latin-derived Germanic languages or Slavic languages, to the position of Arabic in Persia, or the position of the Indic language Sanskrit in South India and Southeast Asia. However, the non-phonetic Chinese writing system causes a unique situation where the modern pronunciation of the classical language is far more divergent (and heterogeneous, depending on the native – not necessarily Chinese – tongue of the reader) than in analogous cases, complicating understanding and study of Classical Chinese further compared to other classical languages.


title: Classical Chinese

text: Christian missionaries coined the term Wen-li () ("the principles of literature", "the book language as opposed to the colloquial") for Literary Chinese. Though composed from Chinese roots, this term was never used in that sense in Chinese, and was rejected by non-missionary sinologues.


title: Classical Chinese

text: Chinese characters are not alphabetic and only rarely reflect sound changes. The tentative reconstruction of Old Chinese is an endeavor only a few centuries old. As a result, Classical Chinese is not read with a reconstruction of Old Chinese pronunciation; instead, it is always read with the pronunciations of characters categorized and listed in the Phonology Dictionary (韻書; pinyin: "yùnshū", "rhyme book") officially published by the Governments, originally based upon the Middle Chinese pronunciation of Luoyang in the 2nd to 4th centuries. With the progress of time, every dynasty has updated and modified the official Phonology Dictionary. By the time of the Yuan Dynasty and Ming Dynasty, the Phonology Dictionary was based on early Mandarin. But since the Imperial Examination required the composition of Shi genre, in non-Mandarin speaking parts of China such as Zhejiang, Guangdong and Fujian, pronunciation is either based on everyday speech as in Cantonese; or, in some varieties of Chinese (e.g. Southern Min), with a special set of pronunciations used for Classical Chinese or "formal" vocabulary and usage borrowed from Classical Chinese usage. In practice, all varieties of Chinese combine these two extremes. Mandarin and Cantonese, for example, also have words that are pronounced one way in colloquial usage and another way when used in Classical Chinese or in specialized terms coming from Classical Chinese, though the system is not as extensive as that of Southern Min or Wu. (See Literary and colloquial readings of Chinese characters)


title: Classical Chinese

text: Japanese, Korean or Vietnamese readers of Classical Chinese use systems of pronunciation specific to their own languages. For example, Japanese speakers use "On'yomi" pronunciation when reading the kanji of words of Chinese origin such as 銀行 ("ginkō") or the name for the city of "Tōkyō" (東京), but use "Kun'yomi" when the kanji represents a native word such as the reading of 行 in 行く ("iku") or the reading of both characters in the name for the city of "Ōsaka" (大阪), and a system that aids Japanese speakers with Classical Chinese word order.


title: Classical Chinese

text: Since the pronunciation of all modern varieties of Chinese is different from Old Chinese or other forms of historical Chinese (such as Middle Chinese), characters that once rhymed in poetry may not rhyme any longer, or vice versa. Poetry and other rhyme-based writing thus becomes less coherent than the original reading must have been. However, some modern Chinese varieties have certain phonological characteristics that are closer to the older pronunciations than others, as shown by the preservation of certain rhyme structures.


title: Classical Chinese

text: Another phenomenon that is common in reading Classical Chinese is homophony (words that sound the same). More than 2,500 years of sound change separates Classical Chinese from any modern variety, so when reading Classical Chinese in any modern variety of Chinese (especially Mandarin) or in Japanese, Korean, or Vietnamese, many characters which originally had different pronunciations have become homonyms. There is a famous Classical Chinese poem written in the early 20th century by the linguist Chao Yuen Ren called the "Lion-Eating Poet in the Stone Den", which contains only words that are now pronounced with various tones in Mandarin. It was written to show how Classical Chinese has become an impractical language for speakers of modern Chinese because Classical Chinese when spoken aloud is largely incomprehensible. However the poem is perfectly comprehensible when read silently because Literary Chinese, by its very nature as a "written" language using a logographic writing system, can often get away with using homophones that even in spoken Old Chinese would not have been distinguishable in any way.


title: Classical Chinese

text: The situation is analogous to that of some English words that are spelled differently but sound the same, such as "meet" and "meat", which were pronounced and respectively during the time of Chaucer, as shown by their spelling. However, such homophones are far more common in Literary Chinese than in English. For example, the following distinct Old Chinese words are now all pronounced "yì" in Mandarin: "*ŋjajs" 議 "discuss", "*ŋjət" 仡 "powerful", "*ʔjup" 邑 "city", "*ʔjək" 億 "100,000,000", "*ʔjəks" 意 "thought", "*ʔjek" 益 "increase", "*ʔjik" 抑 "press down", "*jak" 弈 "Chinese chess", 逸 "flee", 翼 "wing", 易 "change", 易 "easy", and 蜴 "lizard".


title: Classical Chinese

text: Romanizations have been devised giving distinct spellings for the words of Classical Chinese, together with rules for pronunciation in various modern varieties.


title: Classical Chinese

text: The earliest was the Romanisation Interdialectique (1931–2) of French missionaries Henri Lamasse, of the Paris Foreign Missions Society, and Ernest Jasmin, based on Middle Chinese, followed by linguist Wang Li's "wényán luómǎzì" (1940) based on Old Chinese, and Chao's General Chinese Romanization (1975).


title: Classical Chinese

text: Classical Chinese is distinguished from written vernacular Chinese in its style, which appears extremely concise and compact to modern Chinese speakers, and to some extent in the use of different lexical items (vocabulary). An essay in Classical Chinese, for example, might use half as many Chinese characters as in vernacular Chinese to relate the same content.


title: Classical Chinese

text: In terms of conciseness and compactness, Classical Chinese rarely uses words composed of two Chinese characters; nearly all words are of one syllable only. This stands directly in contrast with modern Northern Chinese varieties including Mandarin, in which two-syllable, three-syllable, and four-syllable words are extremely common, whilst although two-syllable words are also quite common within modern Southern Chinese varieties, they are still more archaic in that they use more one-syllable words than Northern Chinese varieties. This phenomenon exists, in part, because polysyllabic words evolved in Chinese to disambiguate homophones that result from sound changes. This is similar to such phenomena in English as the "pen–pin" merger of many dialects in the American south and the "caught-cot" merger of most dialects of American English: because the words "pin" and "pen", as well as "caught" and "cot", sound alike in such dialects of English, a certain degree of confusion can occur unless one adds qualifiers like "ink pen" and "stick pin." Similarly, Chinese has acquired many polysyllabic words in order to disambiguate monosyllabic words that sounded different in earlier forms of Chinese but identical in one region or another during later periods. Because Classical Chinese is based on the literary examples of ancient Chinese literature, it has almost none of the two-syllable words present in modern Chinese varieties.


title: Classical Chinese

text: Classical Chinese has more pronouns compared to the modern vernacular. In particular, whereas Mandarin has one general character to refer to the first-person pronoun ("I"/"me"), Literary Chinese has several, many of which are used as part of honorific language (see Chinese honorifics).


title: Classical Chinese

text: In syntax, Classical Chinese is always ready to drop subjects and objects when a reference to them is understood (pragmatically inferable). Also, words are not restrictively categorized into parts of speech: nouns are commonly used as verbs, adjectives as nouns, and so on. There is no copula in Classical Chinese, "是" (pinyin: "shì") is a copula in modern Chinese but in old Chinese it was originally a near demonstrative ("this"); the modern Chinese for "this" is "這" (pinyin: "zhè").


title: Classical Chinese

text: Beyond grammar and vocabulary differences, Classical Chinese can be distinguished by literary and cultural differences: an effort to maintain parallelism and rhythm, even in prose works, and extensive use of literary and cultural allusions, thereby also contributing to brevity.


title: Classical Chinese

text: Literary Chinese was adopted in Korea, Japan, and Vietnam. The "Oxford Handbook of Classical Chinese Literature" argues that this adoption came mainly from diplomatic and cultural ties with China, while conquest, colonisation, and migration played smaller roles.


title: Classical Chinese

text: Classical Chinese was the main form used in Chinese literary works until the May Fourth Movement (1919), and was also used extensively in Japan, Korea, and Vietnam. Classical Chinese was used to write the Hunmin Jeongeum proclamation in which the modern Korean alphabet (hangul) was promulgated and the essay by Hu Shih in which he argued against using Classical Chinese and in favor of written vernacular Chinese. (The latter parallels the essay written by Dante in "Latin" in which he expounded the virtues of the vernacular "Italian".) Exceptions to the use of Classical Chinese were vernacular novels such as "Dream of the Red Chamber".


title: Classical Chinese

text: Most government documents in the Republic of China (Taiwan) were written in Classical Chinese until reforms in the 1970s, in a reform movement spearheaded by President Yen Chia-kan to shift the written style to vernacular Chinese. However, most of the laws of Taiwan are still written in a subset of Literary Chinese. As a result, it's necessary for today's Taiwanese lawyers to learn this language.


title: Classical Chinese

text: Today, pure Classical Chinese is occasionally used in formal or ceremonial occasions. The "National Anthem of the Republic of China" (), for example, is in Classical Chinese. Buddhist texts, or sutras, are still preserved in Classical Chinese from the time they were composed or translated from Sanskrit sources. In practice there is a socially accepted continuum between vernacular Chinese and Classical Chinese. For example, most official notices and formal letters are written with a number of stock Classical Chinese expressions (e.g. salutation, closing). Personal letters, on the other hand, are mostly written in vernacular, but with some Classical phrases, depending on the subject matter, the writer's level of education, etc. With the exception of professional scholars and enthusiasts, most people today cannot write in full Classical Chinese with ease.


title: Classical Chinese

text: Most Chinese people with at least a middle school education are able to read basic Classical Chinese, because the ability to read (but not write) Classical Chinese is part of the Chinese middle school and high school curricula and is part of the college entrance examination. Classical Chinese is taught primarily by presenting a classical Chinese work and including a vernacular gloss that explains the meaning of phrases. Tests on classical Chinese usually ask the student to express the meaning of a paragraph in vernacular Chinese. They often take the form of comprehension questions.


title: Classical Chinese

text: The contemporary use of Classical Chinese in Japan is mainly in the field of education and the study of literature. Learning the Japanese way (kanbun) of decoding Classical Chinese is part of the high school curriculum in Japan. Japan is the only country that maintains the tradition of creating Classical Chinese poetry based on Tang dynasty's tone patterns.


title: Classical Chinese

text: The use of Classical Chinese in these regions is limited and is mainly in the field of Classical studies.


title: Classical Chinese

text: In addition, many works of literature in Classical Chinese (such as Tang poetry) have been major cultural influences. However, even with knowledge of grammar and vocabulary, Classical Chinese can be difficult to understand by native speakers of modern Chinese, because of its heavy use of literary references and allusions as well as its extremely abbreviated style.


title: Linear congruential generator

text: A linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear equation. The method represents one of the oldest and best-known pseudorandom number generator algorithms. The theory behind them is relatively easy to understand, and they are easily implemented and fast, especially on computer hardware which can provide modular arithmetic by storage-bit truncation.


title: Linear congruential generator

text: are integer constants that specify the generator. If "c" = 0, the generator is often called a multiplicative congruential generator (MCG), or Lehmer RNG. If "c" ≠ 0, the method is called a mixed congruential generator.


title: Linear congruential generator

text: When "c" ≠ 0, a mathematician would call the recurrence an affine transformation, not a linear one, but the misnomer is well-established in computer science.


title: Linear congruential generator

text: The Lehmer generator was published in 1951 and the Linear congruential generator was published in 1958 by W. E. Thomson and A. Rotenberg.


title: Linear congruential generator

text: A benefit of LCGs is that an appropriate choice of parameters results in a period which is both known and long. Although not the only criterion, too short a period is a fatal flaw in a pseudorandom number generator.


title: Linear congruential generator

text: While LCGs are capable of producing pseudorandom numbers which can pass formal tests for randomness, the quality of the output is extremely sensitive to the choice of the parameters "m" and "a". For example, "a" = 1 and "c" = 1 produces a simple modulo-"m" counter, which has a long period, but is obviously non-random.


title: Linear congruential generator

text: Historically, poor choices for "a" have led to ineffective implementations of LCGs. A particularly illustrative example of this is RANDU, which was widely used in the early 1970s and led to many results which are currently being questioned because of the use of this poor LCG.


title: Linear congruential generator

text: This is the original Lehmer RNG construction. The period is "m"−1 if the multiplier "a" is chosen to be a primitive element of the integers modulo "m". The initial state must be chosen between 1 and "m"−1.


title: Linear congruential generator

text: One disadvantage of a prime modulus is that the modular reduction requires a double-width product and an explicit reduction step. Often a prime just less than a power of 2 is used (the Mersenne primes 2−1 and 2−1 are popular), so that the reduction modulo "m" = 2 − "d" can be computed as ("ax" mod 2) + "d" . This must be followed by a conditional subtraction of "m" if the result is too large, but the number of subtractions is limited to "ad"/"m", which can be easily limited to one if "d" is small.


title: Linear congruential generator

text: If a double-width product is unavailable, and the multiplier is chosen carefully, Schrage's method may be used. To do this, factor "m" = "qa"+"r", i.e. and . Then compute "ax" mod "m" = . Since "x" mod "q" < "q" ≤ "m"/"a", the first term is strictly less than "am"/"a" = "m". If "a" is chosen so that "r" ≤ "q" (and thus "r"/"q" ≤ 1), then the second term is also less than "m": "r" ≤ "rx"/"q" = "x"("r"/"q") ≤ "x" < "m". Thus, both products can be computed with a single-width product, and the difference between them lies in the range [1−"m", "m"−1], so can be reduced to [0, "m"−1] with a single conditional add.


title: Linear congruential generator

text: A second disadvantage is that it is awkward to convert the value 1 ≤ "x" < "m" to uniform random bits. If a prime just less than a power of 2 is used, sometimes the missing values are simply ignored.


title: Linear congruential generator

text: Choosing "m" to be a power of 2, most often "m" = 2 or "m" = 2, produces a particularly efficient LCG, because this allows the modulus operation to be computed by simply truncating the binary representation. In fact, the most significant bits are usually not computed at all. There are, however, disadvantages.


title: Linear congruential generator

text: This form has maximal period "m"/4, achieved if "a" ≡ 3 or "a" ≡ 5 (mod 8). The initial state "X" must be odd, and the low three bits of "X" alternate between two states and are not useful. It can be shown that this form is equivalent to a generator with a modulus a quarter the size and "c" ≠ 0.


title: Linear congruential generator

text: A more serious issue with the use of a power-of-two modulus is that the low bits have a shorter period than the high bits. The lowest-order bit of "X" never changes ("X" is always odd), and the next two bits alternate between two states. (If "a" ≡ 5 (mod 8), then bit 1 never changes and bit 2 alternates. If "a" ≡ 3 (mod 8), then bit 2 never changes and bit 1 alternates.) Bit 3 repeats with a period of 4, bit 4 has a period of 8, and so on. Only the most significant bit of "X" achieves the full period.


title: Linear congruential generator

text: When "c" ≠ 0, correctly chosen parameters allow a period equal to "m", for all seed values. This will occur if and only if:


title: Linear congruential generator

text: This form may be used with any "m", but only works well for "m" with many repeated prime factors, such as a power of 2; using a computer's word size is the most common choice. If "m" were a square-free integer, this would only allow "a" ≡ 1 (mod "m"), which makes a very poor PRNG; a selection of possible full-period multipliers is only available when "m" has repeated prime factors.


title: Linear congruential generator

text: Although the Hull–Dobell theorem provides maximum period, it is not sufficient to guarantee a "good" generator. For example, it is desirable for "a" − 1 to not be any more divisible by prime factors of "m" than necessary. Thus, if "m" is a power of 2, then "a" − 1 should be divisible by 4 but not divisible by 8, i.e. "a" ≡ 5 (mod 8).


title: Linear congruential generator

text: Indeed, most multipliers produce a sequence which fails one test for non-randomness or another, and finding a multiplier which is satisfactory to all applicable criteria is quite challenging. The spectral test is one of the most important tests.


title: Linear congruential generator

text: Note that a power-of-2 modulus shares the problem as described above for "c" = 0: the low "k" bits form a generator with modulus 2 and thus repeat with a period of 2; only the most significant bit achieves the full period. If a pseudorandom number less than "r" is desired, is a much higher-quality result than "X" mod "r". Unfortunately, most programming languages make the latter much easier to write (codice_1), so it is the more commonly used form.


title: Linear congruential generator

text: The generator is "not" sensitive to the choice of "c", as long as it is relatively prime to the modulus (e.g. if "m" is a power of 2, then "c" must be odd), so the value "c"=1 is commonly chosen.


title: Linear congruential generator

text: The series produced by other choices of "c" can be written as a simple function of the series when "c"=1. Specifically, if "Y" is the prototypical series defined by "Y" = 0 and "Y" = "aY"+1 mod m, then a general series "X" = "aX"+"c" mod "m" can be written as an affine function of "Y":


title: Linear congruential generator

text: The following table lists the parameters of LCGs in common use, including built-in "rand()" functions in runtime libraries of various compilers. This table is to show popularity, not examples to emulate; "many of these parameters are poor." Tables of good parameters are available.


title: Linear congruential generator

text: As shown above, LCGs do not always use all of the bits in the values they produce. For example, the Java implementation operates with 48-bit values at each iteration but returns only their 32 most significant bits. This is because the higher-order bits have longer periods than the lower-order bits (see below). LCGs that use this truncation technique produce statistically better values than those that do not. This is especially noticeable in scripts that use the mod operation to reduce range; modifying the random number mod 2 will lead to alternating 0 and 1 without truncation.


title: Linear congruential generator

text: LCGs are fast and require minimal memory (one modulo-"m" number, often 32 or 64 bits) to retain state. This makes them valuable for simulating multiple independent streams. LCGs are not intended, and must not be used, for cryptographic applications; use a cryptographically secure pseudorandom number generator for such applications.


title: Linear congruential generator

text: Although LCGs have a few specific weaknesses, many of their flaws come from having too small a state. The fact that people have been lulled for so many years into using them with such small moduli can be seen as a testament to the strength of the technique. A LCG with large enough state can pass even stringent statistical tests; a modulo-2 LCG which returns the high 32 bits passes TestU01's SmallCrush suite, and a 96-bit LCG passes the most stringent BigCrush suite.


title: Linear congruential generator

text: For a specific example, an ideal random number generator with 32 bits of output is expected (by the Birthday theorem) to begin duplicating earlier outputs after results. "Any" PRNG whose output is its full, untruncated state will not produce duplicates until its full period elapses, an easily detectable statistical flaw. For related reasons, any PRNG should have a period longer than the square of the number of outputs required. Given modern computer speeds, this means a period of 2 for all but the least demanding applications, and longer for demanding simulations.


title: Linear congruential generator

text: One flaw specific to LCGs is that, if used to choose points in an n-dimensional space, the points will lie on, at most, hyperplanes (Marsaglia's theorem, developed by George Marsaglia). This is due to serial correlation between successive values of the sequence "X". Carelessly chosen multipliers will usually have far fewer, widely spaced planes, which can lead to problems. The spectral test, which is a simple test of an LCG's quality, measures this spacing and allows a good multiplier to be chosen.


title: Linear congruential generator

text: The plane spacing depends both on the modulus and the multiplier. A large enough modulus can reduce this distance below the resolution of double precision numbers. The choice of the multiplier becomes less important when the modulus is large. It is still necessary to calculate the spectral index and make sure that the multiplier is not a bad one, but purely probabilistically it becomes extremely unlikely to encounter a bad multiplier when the modulus is larger than about 2.


title: Linear congruential generator

text: Another flaw specific to LCGs is the short period of the low-order bits when "m" is chosen to be a power of 2. This can be mitigated by using a modulus larger than the required output, and using the most significant bits of the state.


title: Linear congruential generator

text: Nevertheless, for some applications LCGs may be a good option. For instance, in an embedded system, the amount of memory available is often severely limited. Similarly, in an environment such as a video game console taking a small number of high-order bits of an LCG may well suffice. (The low-order bits of LCGs when m is a power of 2 should never be relied on for any degree of randomness whatsoever.) The low order bits go through very short cycles. In particular, any full-cycle LCG, when m is a power of 2, will produce alternately odd and even results.


title: Linear congruential generator

text: LCGs should be evaluated very carefully for suitability in non-cryptographic applications where high-quality randomness is critical. For Monte Carlo simulations, an LCG must use a modulus greater and preferably much greater than the cube of the number of random samples which are required. This means, for example, that a (good) 32-bit LCG can be used to obtain about a thousand random numbers; a 64-bit LCG is good for about 2 random samples (a little over two million), etc. For this reason, in practice LCGs are not suitable for large-scale Monte Carlo simulations.


title: Linear congruential generator

text: Free Pascal uses a Mersenne Twister as its default pseudo random number generator whereas Delphi uses a LCG. Here is a Delphi compatible example in Free Pascal based on the information in the table above. Given the same RandSeed value it generates the same sequence of random numbers as Delphi.


title: Linear congruential generator

text: Like all pseudorandom number generators, a LCG needs to store state and alter it each time it generates a new number. Multiple threads may access this state simultaneously causing a race condition. Implementations should use different state each with unique initialization for different threads to avoid equal sequences of random numbers on simultaneously executing threads.


title: Linear congruential generator

text: There are several generators which are linear congruential generators in a different form, and thus the techniques used to analyze LCGs can be applied to them.


title: Linear congruential generator

text: One method of producing a longer period is to sum the outputs of several LCGs of different periods having a large least common multiple; the Wichmann–Hill generator is an example of this form. (We would prefer them to be completely coprime, but a prime modulus implies an even period, so there must be a common factor of 2, at least.) This can be shown to be equivalent to a single LCG with a modulus equal to the product of the component LCG moduli.


title: Linear congruential generator

text: Marsaglia's add-with-carry and subtract-with-borrow PRNGs with a word size of "b"=2 and lags "r" and "s" ("r" > "s") are equivalent to LCGs with a modulus of "b" ± "b" ± 1.


title: Linear congruential generator

text: Multiply-with-carry PRNGs with a multiplier of "a" are equivalent to LCGs with a large prime modulus of "ab"−1 and a power-of-2 multiplier "b".


title: Linear congruential generator

text: A permuted congruential generator begins with a power-of-2-modulus LCG and applies an output transformation to eliminate the short period problem in the low-order bits.


title: Linear congruential generator

text: The other widely used primitive for obtaining long-period pseudorandom sequences is the linear-feedback shift register construction, which is based on arithmetic in GF(2)["x"], the polynomial ring over GF(2). Rather than integer addition and multiplication, the basic operations are exclusive-or and carry-less multiplication, which is usually implemented as a sequence of logical shifts. These have the advantage that all of their bits are full-period; they do not suffer from the weakness in the low-order bits that plagues arithmetic modulo 2.


title: Linear congruential generator

text: Examples of this family include xorshift generators and the Mersenne twister. The latter provides a very long period (2−1) and variate uniformity, but it fails some statistical tests. Lagged Fibonacci generators also fall into this category; although they use arithmetic addition, their period is ensured by an LFSR among the least-significant bits.


title: Linear congruential generator

text: It is easy to detect the structure of a linear-feedback shift register with appropriate tests such as the linear complexity test implemented in the TestU01 suite; a boolean circulant matrix initialized from consecutive bits of an LFSR will never have rank greater than the degree of the polynomial. Adding a non-linear output mixing function (as in the xoshiro256** and permuted congruential generator constructions) can greatly improve the performance on statistical tests.


title: Linear congruential generator

text: Another structure for a PRNG is a very simple recurrence function combined with a powerful output mixing function. This includes counter mode block ciphers and non-cryptographic generators such as SplitMix64.


title: Linear congruential generator

text: A structure similar to LCGs, but "not" equivalent, is the multiple-recursive generator: "X" = ("a""X" + "a""X" + ··· + "aX") mod "m" for "k" ≥ 2. With a prime modulus, this can generate periods up to "m"−1, so is a useful extension of the LCG structure to larger periods.


title: Linear congruential generator

text: A powerful technique for generating high-quality pseudorandom numbers is to combine two or more PRNGs of different structure; the sum of an LFSR and an LCG (as in the KISS or xorwow constructions) can do very well at some cost in speed.


title: Liturgical colours

text: Liturgical colours are specific colours used for vestments and hangings within the context of Christian liturgy. The symbolism of violet, blue, white, green, red, gold, black, rose and other colours may serve to underline moods appropriate to a season of the liturgical year or may highlight a special occasion.


title: Liturgical colours

text: There is a distinction between the colour of the vestments worn by the clergy and their choir dress, which with a few exceptions does not change with the seasons of the liturgical year.


title: Liturgical colours

text: In the Roman Rite, as reformed by Pope Paul VI, the following colours are used, in accordance with the rubrics of the General Instruction of the Roman Missal, Section 346.


title: Liturgical colours

text: On more solemn days, i.e. festive, more precious, sacred vestments may be used, even if not of the colour of the day. Such vestments may, for instance, be made from cloth of gold or cloth of silver. Moreover, the Conference of Bishops may determine and propose to the Apostolic See adaptations suited to the needs and culture of peoples.


title: Liturgical colours

text: Ritual Masses are celebrated in their proper colour or in white or in a festive colour. Masses for Various Needs, on the other hand, are celebrated in the colour proper to the day or the season or in violet if they bear a penitential character. Votive Masses are celebrated in the colour suited to the Mass itself or even in the colour proper to the day or the season.


title: Liturgical colours

text: The rules on liturgical colours in the 1960 Code of Rubrics, whose observance is still permitted in the circumstances indicated in the 2007 document "Summorum Pontificum" on use of the 1962 Roman Missal, which incorporates them, differ from the current rubrics in the following respects:


title: Liturgical colours

text: Pope Pius X raised the rank of the Sundays after Epiphany and Pentecost, so that on those that fell within common octaves, green was used instead of the colour of the octave, as had previously been the rule; on Sundays after Pentecost that fell within privileged octaves (i.e., the octaves of Corpus Christi and of the Sacred Heart), the liturgical color of the feast was retained.


title: Liturgical colours

text: The rules on liturgical colours before the time of Pope Pius X were essentially those indicated in the edition of the Roman Missal that Pope Pius V promulgated in 1570, except for the addition of feasts not included in his Missal. The scheme of colours in his Missal reflected usage that had become fixed in Rome by the twelfth century.


title: Liturgical colours

text: The Byzantine Rite, which is used by all the member churches of the Eastern Orthodox Church, the Byzantine Lutheran Churches and the Eastern Catholic Churches of Byzantine Rite, does not have a universal system of colours, with the service-books of the Byzantine tradition only specifying "light" or "dark" vestments in the service books. In the Greek tradition, maroon or burgundy are common for solemn feast days, and a wide variety of colours are used at other times, the most common of which are gold and white.


title: Liturgical colours

text: Slavic-use churches and others influenced by Western traditions have adopted a cycle of liturgical colours. The particulars may change from place to place, but generally:


title: Liturgical colours

text: The colours would be changed before Vespers on the eve of the day being commemorated. During Great Feasts, the colour is changed before the vespers service that begins the first day of a forefeast, and remains until the apodosis (final day of the afterfeast).


title: Liturgical colours

text: Under Western influence, black is often used in the Slavic churches for funerals, weekdays of Great Lent, and Holy Week as a sign of penance and mourning, but in the second half of the 20th century, the ancient white became more common, as a sign of the hope of the Resurrection.


title: Liturgical colours

text: In the tradition of the Russian Orthodox Church, up to nine different liturgical colours may be used throughout the year.


title: Liturgical colours

text: The Coptic tradition, followed by the Coptic Orthodox Church and the Coptic Catholic Church, only uses white vestments, with gold and silver being considered variations of white. The only exception is during Passion Week when black is used. Nonetheless, trimmings of red, gold or blue may be found on some vestments.


title: Liturgical colours

text: The liturgical tradition of Ethiopia, followed by the Ethiopian Orthodox Church and the Ethiopian Catholic Church, embraces a wide variety of liturgical colours. In Eritrea, similar traditions are followed.


title: Liturgical colours

text: The Evangelical Lutheran Church in America (ELCA), uses a similar colour scheme as that of the Anglicans and their Scandinavian Lutheran counterparts, with the use of gold only for the Easter Vigil and Easter Sunday services and Holy Week using scarlet rather than crimson. Blue is used for Advent. White is used for Christmas, Epiphany, Sundays of Easter, Holy Trinity, and Christ the King. For Lent, purple is used. During the time after Pentecost and the Epiphany, green is used.


title: Liturgical colours

text: Both the Lutheran Church–Missouri Synod (LCMS) and the Wisconsin Evangelical Lutheran Synod (WELS) use a similar system, but with purple being the primary colour for both Advent and Lent (with blue being the alternate colour for Advent only), and the use of gold in place of white for both Christmas and Easter (in similar practice to the Catholic Church). In the WELS, the use of red is also done during the "Period of End Times", a period of the Church regarding the teachings of the Book of Revelation, culminating in the creation of the New Jerusalem (corresponding to Christ the King in the ELCA). In all three churches, including the ELCA, red is also worn on the last Sunday of October, in celebration of the Reformation on October 31, when Martin Luther nailed the 95 Theses onto the door of Wittenberg Castle Church.


title: Liturgical colours

text: Most Anglican churches use the colours appointed in the Roman Rite, usually in its post-1969 form, with the exception of Sarum Blue replacing violet for Advent, but some use the earlier form, with, for instance, black in place of red on Good Friday. Some churches use black at Masses for the dead, but more commonly white or purple is used. For historical reasons much of the worldwide Anglican Communion takes a noticeable lead from the practice of the Church of England. Since the 1980 Alternative Service Book, liturgical colours have been recommended for seasons, with more detailed advice offered as part of the Common Worship series of liturgies, including colours for all Sundays and festivals printed in the 'core volume' next to collects.


title: Liturgical colours

text: The Church's published Lectionary now makes detailed suggestions for liturgical colour throughout the year, which corresponds almost exactly with the above table of Roman Rite (post-1969 usage) usage with five minor exceptions, and one more significant one:


title: Liturgical colours

text: The colour scheme suggested by the Church of England also indicates where gold vestments should be used in those churches that possess gold and white as distinct colours. The use of rose-pink vestments, as in the Roman Rite table above, was mentioned as an option in early editions of Common Worship, and is a listed option in the annual published lectionary; however, later Common Worship publications have begun to refer to this practice as "traditional" reflecting its resurgence.